Handbook of group decision and negotiation [Second ed.] 9783030496289, 3030496287

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D. Marc Kilgour Colin Eden Editors

Handbook of Group Decision and Negotiation Second Edition

Handbook of Group Decision and Negotiation

D. Marc Kilgour • Colin Eden Editors

Handbook of Group Decision and Negotiation Second Edition

With 177 Figures and 99 Tables

Editors D. Marc Kilgour Department of Mathematics Wilfrid Laurier University Waterloo, ON, Canada

Colin Eden Strathclyde Business School University of Strathclyde Glasgow, UK

ISBN 978-3-030-49628-9 ISBN 978-3-030-49629-6 (eBook) ISBN 978-3-030-49630-2 (print and electronic bundle) https://doi.org/10.1007/978-3-030-49629-6 1st edition: © Springer Science+Business Media B.V. 2010 2nd edition: © Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Foreword

A decade ago, the publication of the first edition of the Handbook of Group Decision and Negotiation was an important step for the INFORMS GDN section and our scientific community. The handbook complements the GDN journal and the annual GDN conferences as a further way of communicating our research to a wider audience. I therefore gladly accepted the invitation of the handbook editors Colin Eden and Marc Kilgour to contribute a foreword to this volume as the current president of the INFORMS section on Group Decision and Negotiation. After 10 years, this new edition of the handbook provides an excellent overview of the stock of knowledge that our community has accumulated, and also of the important developments that have taken place during the past decade both in our field of research and in our community. The scientific innovations will be elaborated in detail in the following chapters of this volume; I therefore will follow the tradition of the preface for the first edition, written by the then president of the GDN section Melvin Shakun, and focus on the developments of our community during that time frame. First of all, I would like to express my gratitude, both personally and on behalf of the section, to my three predecessors in the function of a section president, Melvin Shakun, Marc Kilgour, and Gregory Kersten. Our group would not exist, and would never have reached the status it has today, without the continuous effort and support from Mel Shakun. He founded the section as a part of INFORMS in 1989 and started the journal in 1992. He continued to lead the section as president until 2014, and served as editor-in-chief of the journal until 2016. He also initiated the first GDN conference in Glasgow in the year 2000, initially as a one-time event at the start of the new millennium. The huge success of that conference led to a sequence of annual conferences, which continues almost uninterruptedly until today. In 2003, he created the textbook series Advances in Group Decision and Negotiation, in which the first edition of this handbook was published. The GDN community is deeply indebted to Mel for his scientific contributions to the foundations of our field, for his inspiring leadership, and for his personal example as a colleague for whom connectedness is not just a scientific concept, but a way of life that enriches everyone with whom he is in touch. Perhaps no one has contributed more and shaped the development of our community more in the past decade than Gregory Kersten, who served as section v

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Foreword

president from 2017 to 2019 and as editor-in-chief of the GDN journal from 2016 until he unexpectedly passed away in May 2020. Gregory was born in Warsaw, Poland, and graduated from the Warsaw School of Economics. His strong research interest in group decisions and negotiations led to the development of the first algorithms and computer programs to support negotiations in the early 1980s. He migrated to Canada in 1984, where he held professorships at several universities. By developing the first web-based negotiation support system Inspire in the early 1990s, he helped to establish the field of electronic negotiations, to which he was one of the main contributors until his death. Our community will always remember Gregory for his scientific contributions, his dedication to the growth and development of the section and the journal, and also for his personal warmth and friendliness. The main instruments of the section are the GDN journal, the GDN conferences, and the Springer book series. The last decade has seen a strong and healthy development of the GDN journal form from just over 620 pages published in 2010 to twice that size, over 1200 pages in 2020. The excellent standing of the journal, which now has completed its 29th volume, is exemplified by its impact factor of 1.7. I am confident that this positive development will continue under the leadership of the two new editors-in-chief, Gert-Jan de Vreede and Mareike Schoop, who were appointed in 2020. The GDN conference series started in the year 2000. A list of the first ten conferences is presented in the preface of the first edition of this handbook, which was formally presented at the GDN conference in Delft 2010. For the sake of completeness, a list of all conferences follows: 2000 Glasgow, Scotland, UK 2001 La Rochelle, France 2002 Perth, Australia 2003 Istanbul, Turkey 2004 Banff, Alberta, Canada 2005 Vienna, Austria 2006 Karlsruhe, Germany 2007 Mont Tremblant, Quebec, Canada 2008 Coimbra, Portugal 2009 Toronto, Ontario, Canada

2010 Delft, Netherlands 2012 Recife, Brazil 2013 Stockholm, Sweden 2014 Toulouse, France 2015 Warsaw, Poland 2016 Bellingham, USA 2017 Stuttgart, Germany 2018 Nanjing, China 2019 Loughborough, United Kingdom

The turbulent developments of the past decade have left traces in the list of GDN conferences. In 2011, a conference that was planned in the Middle East had to be canceled because of the political situation there. In 2020, a planned conference in Toronto could not take place because of the COVID pandemic, although the submitted papers were published in two proceedings volumes. Since the 2014 conference, selected papers presented at GDN conferences are published in proceedings volumes in the Springer Lecture Notes in Business Information Processing in addition to local proceedings of all papers. At the GDN conferences, the annual GDN Section Award is presented. Recipients so far were: 2004, Melvin F. Shakun; 2005, Gregory E. Kersten; 2007, D. Marc Kilgour; 2008,

Foreword

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Colin Eden; 2010, Gert-Jan de Vreede; 2012, Floyd Lewis and Rudolf Vetschera; 2013, Keith W. Hipel; 2014, Hannu Nurmi; 2015, Katia Sycara; 2016, Fran Ackermann; 2017, Adiel Teixeira de Almeida; 2018, Pascale Zaraté; and 2019, Tung Bui. The 2020 section award was awarded to Liping Fang, but the official ceremony had to be postponed until 2021 because of the cancellation of the conference. In 2014, a special GDN lifetime achievements award was presented to Melvin Shakun. It is notable that most of these recipients feature in this handbook. Best Paper Awards have been presented at GDN meetings beginning in 2014. Young Researcher Awards have been presented at GDN meetings beginning in 2016. For lists of winners, consult the GDN webpage at https://connect.informs.org/groupdecision-and-negotiation. Since the publication of the first edition of this handbook, four volumes have been published in the Advances in Group Decision and Negotiation book series: e-Democracy: A Group Decision and Negotiation Perspective, edited by David Rios Insua and Simon French (2010) Models for Intercultural Collaboration and Negotiation, edited by Katia Sycara and Michele Gelfand (2013) Emotion in Group Decision and Negotiation, edited by Bilyana Martinovsky (2015) Systems, Procedures and Voting Rules in Context, by Adiel Teixeira de Almeida, Danielle Costa Morais, and Hannu Nurmi (2019) The conferences, the GDN journal, the book series, and also this second edition of the handbook all provide clear evidence of the rapid evolution and the progress in the field of group decision and negotiation. As witnessed by the necessary cancellations of two of our conferences, the past decade has been characterized by many turbulences and a high level of uncertainty and unforeseen developments. It has also shown us the importance of collaboration, joint effort, and peaceful methods to resolve conflict. Our scientific contributions to achieve this have never been more important. I would like to thank all researchers involved in our community, in particular the authors and the editors of this handbook, for their efforts and their important contributions. May the handbook contribute to the development and growth of the field of group decision and negotiation, and to the solution of the most important problems of our time. Institute for Business Decisions and Analytics University of Vienna Vienna, Austria December 2020

Rudolf Vetschera

Contents

Volume 1 Part I

.......................................

1

Introduction to the Handbook of Group Decision and Negotiation . . . . D. Marc Kilgour and Colin Eden

3

Part II

Introduction

Justice and Fairness in Negotiation . . . . . . . . . . . . . . . . . . . .

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Just Negotiations, Stable Peace Agreements, and Durable Peace . . . . . Daniel Druckman and Lynn Wagner

21

Methods to Analyze Negotiation Processes . . . . . . . . . . . . . . . . . . . . . . Rudolf Vetschera, Sabine T. Koeszegi, and Michael Filzmoser

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Negotiation Processes: Empirical Insights . . . . . . . . . . . . . . . . . . . . . . . Michael Filzmoser, Rudolf Vetschera, and Sabine T. Koeszegi

61

The Notion of Fair Division in Negotiations . . . . . . . . . . . . . . . . . . . . . . Christian Klamler

81

Sharing Profit and Risk in a Partnership . . . . . . . . . . . . . . . . . . . . . . . . Yigal Gerchak and Eugene Khmelnitsky

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Part III

135

The Context for Group Decision and Negotiation . . . . . . .

Advances in Defining a Right Problem in Group Decision and Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Melvin F. Shakun and Bilyana Martinovski Role of Emotion in Group Decision and Negotiation . . . . . . . . . . . . . . . Bilyana Martinovski

137 157

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Contents

Impact of Cognitive Style on Group Decision and Negotiation . . . . . . . Sébastien Damart and Sonia Adam-Ledunois

193

Communication Media and Negotiation: A Review . . . . . . . . . . . . . . . . Ingmar Geiger

211

Negotiation Process Modelling: From Soft and Tacit to Deliberate . . . . Tomasz Szapiro

231

Holistic Preferences and Prenegotiation Preparation . . . . . . . . . . . . . . . Tomasz Wachowicz and Ewa Roszkowska

255

Context and Environment in Negotiation . . . . . . . . . . . . . . . . . . . . . . . . P. J. van der Wijst, A. P. C. I. Hong, and D. J. Damen

291

Neuroscience Tools for Group Decision and Negotiation . . . . . . . . . . . . Adiel Teixeira de Almeida, Lucia Reis Peixoto Roselli, Danielle Costa Morais, and Ana Paula Cabral Seixas Costa

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Part IV

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Crowd-Scale Group Decisions . . . . . . . . . . . . . . . . . . . . . . .

Supporting Community Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Masahide Horita and Yu Maemura

341

Crowd-Scale Deliberation for Group Decision-Making . . . . . . . . . . . . . Mark Klein

355

Discussion and Negotiation Support for Crowd-Scale Consensus . . . . . Takayuki Ito

371

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395

Group Decisions: Choosing a Winner by Voting . . . . . . . . . . . . . . . . . . Hannu Nurmi

413

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439

Participatory Modeling for Group Decision Support Alexey Voinov

Group Decisions: Choosing Multiple Winners by Voting D. Marc Kilgour

Part V Game Theory Developments for Group Decision and Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Looking Back on Decision-Making Under Conditions of Conflict . . . . . Liping Fang and Keith W. Hipel

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From Game Theory to Drama Theory . . . . . . . . . . . . . . . . . . . . . . . . . . Jim Bryant

485

Using Drama Theory to Model Negotiation . . . . . . . . . . . . . . . . . . . . . . Jim Bryant and Peter Bennett

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Contents

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531

Negotiation as a Cooperative Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . Özgür Kıbrıs

545

Non-cooperative Bargaining Theory Kalyan Chatterjee

Conflict Resolution Using the Graph Model: Individuals and Coalitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Marc Kilgour, Keith W. Hipel, and Liping Fang

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Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Keith W. Hipel, D. Marc Kilgour, Haiyan Xu, and Yi Xiao

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Volume 2 Part VI

Group Support Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . .

625

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627

Time, Technology, and Teams: From GSS to Collective Action . . . . . . . Laku Chidambaram, Jama D. Summers, Shaila M. Miranda, Amber G. Young, and Robert P. Bostrom

655

Group Support Systems: Past, Present, and Future Fran Ackermann

Group Support Systems: Experiments with an Online System and Implications for Same-Time/Different-Places Working . . . . . . . . . Mike Yearworth and Leroy White

681

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707

Systems Thinking, Mapping, and Group Model Building . . . . . . . . . . . George P. Richardson and David F. Andersen

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Collaboration Engineering for Group Decision and Negotiation . . . . . . Gert-Jan de Vreede, Robert O. Briggs, and Gwendolyn L. Kolfschoten

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Behavioral Considerations in Group Support . . . . . . . . . . . . . . . . . . . . Colin Eden

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Group Decision Support Practice “as it happens” . . . . . . . . . . . . . . . . . L. Alberto Franco and Christian Greiffenhagen

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Procedural Justice in Group Decision Support . . . . . . . . . . . . . . . . . . . Parmjit Kaur and Ashley L. Carreras

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Group Support Systems: Concepts to Practice Fran Ackermann and Colin Eden

Looking Back on a Framework for Thinking About Group Support Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Viktor Dörfler

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Part VII

Contents

Multiple Criteria Analysis for Group Decisions . . . . . . . . .

861

Multicriteria Methods for Group Decision Processes: An Overview . . . Ahti Salo, Raimo P. Hämäläinen, and Tuomas J. Lahtinen

863

Multiple Criteria Decision Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . Salvatore Corrente, José Rui Figueira, Salvatore Greco, and Roman Słowiński

893

Multiple Criteria Group Decisions with Partial Information About Preference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adiel Teixeira de Almeida, Eduarda Asfora Frej, Danielle Costa Morais, and Ana Paula Cabral Seixas Costa

921

Group Decision Support Using the Analytic Hierarchy Process . . . . . . José María Moreno-Jiménez, Juan Aguarón, María Teresa Escobar, and Manuel Salvador

947

Group Decisions with Intuitionistic Fuzzy Sets . . . . . . . . . . . . . . . . . . . Peijia Ren, Zeshui Xu, and Janusz Kacprzyk

977

Group Decisions with Linguistic Information: A Survey . . . . . . . . . . . . Yue He and Zeshui Xu

997

A Group Multicriteria Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1023 Guy Camilleri and Pascale Zaraté Part VIII

Electronic Negotiations . . . . . . . . . . . . . . . . . . . . . . . . . . .

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E-Negotiations: Foundations, Systems, and Processes . . . . . . . . . . . . . . 1051 Gregory Kersten and Hsiangchu Lai Electronic Negotiation and Behavioral Elements . . . . . . . . . . . . . . . . . . 1099 R. P. Sundarraj Negotiation, Online Dispute Resolution, and Artificial Intelligence . . . . 1125 John Zeleznikow Negoisst: Complex Digital Negotiation Support . . . . . . . . . . . . . . . . . . . 1149 Mareike Schoop Online Dispute Resolution Services: Justice, Concepts, and Challenges Ofir Turel and Yufei Yuan

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Agent Reasoning in AI-Powered Negotiation . . . . . . . . . . . . . . . . . . . . . 1187 Tinglong Dai, Katia Sycara, and Ronghuo Zheng Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1213

About the Editors

D. Marc Kilgour is professor of mathematics at Wilfrid Laurier University and adjunct professor of systems design engineering at the University of Waterloo. His expertise in the application of mathematical principles to models of decision-making made him one of the earliest contributors to the emerging field of group decision and negotiation, which he sees as lying at the intersection of mathematics, engineering, and social science. In addition to his work as an originator of the Graph Model for Conflict Resolution, he has also contributed innovative applications of game theory and related methodologies to international relations, arms control, environmental management, negotiation, arbitration, voting, and fair division. Professor Kilgour has been active in the organization of GDN meetings for over two decades, was president of the INFORMS Section on Group Decision and Negotiation in 2014–17, and received the INFORMS GDN Appreciation for Outstanding Service Award in 2017.

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About the Editors

Colin Eden is emeritus professor of management science and strategic management at Strathclyde Business School. He has been involved in the Group Decision and Negotiation community from its outset. His research interests have been focused on the provision of group support as a part of strategy making in top management teams and problem structuring during operational research projects. Alongside these interests, he has been involved in the analysis of project failure as a part of litigation, and in this work he has used a group support system to help unravel what happened in the projects. Recent research has explored the ways in which group decision support can aid teams in developing effective strategies to mitigate in complex risk situation where risk systemicity is rife (particularly with multiple vicious cycles).

Contributors

Fran Ackermann School of Management, Faculty of Business and Law, Curtin Business School, Curtin University, Perth, WA, Australia Sonia Adam-Ledunois CNRS, DRM, [MLab], Université Paris-Dauphine, Université PSL, Paris, France Juan Aguarón Grupo Decisión Multicriterio Zaragoza, Facultad de Economía y Empresa, Universidad de Zaragoza, Zaragoza, Spain David F. Andersen Rockefeller College of Public Affairs and Policy, University at Albany, State University of New York, Albany, NY, USA Peter Bennett Department of Health, Health Protection Analytical Team, London, UK Robert P. Bostrom University of Georgia, Athens, GA, USA Robert O. Briggs San Diego State University, San Diego, CA, USA Jim Bryant Sheffield Business School, Sheffield Hallam University, Sheffield, UK Guy Camilleri IRIT, Toulouse Université, Toulouse, France Ashley L. Carreras School of Business and Economics, Loughborough University, Leicestershire, UK Kalyan Chatterjee Department of Economics, The Pennsylvania State University, University Park, PA, USA Laku Chidambaram Michael F. Price College of Business, University of Oklahoma, Norman, OK, USA Salvatore Corrente Department of Economics and Business, University of Catania, Catania, Italy Ana Paula Cabral Seixas Costa CDSID – Center for Decision Systems and Information Development, Universidade Federal de Pernambuco, Recife, PE, Brazil Departamento de Engenharia de Produção, Federal University of Pernambuco, Recife, Brazil xv

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Contributors

Tinglong Dai Carey Business School, Johns Hopkins University, Baltimore, MD, USA Sébastien Damart CNRS, DRM, [MLab], Université Paris-Dauphine, Université PSL, Paris, France D. J. Damen Tilburg University, Tilburg, The Netherlands Adiel Teixeira de Almeida CDSID – Center for Decision Systems and Information Development, Universidade Federal de Pernambuco, Recife, PE, Brazil Gert-Jan de Vreede University of South Florida, Tampa, FL, USA Viktor Dörfler Management Science Department, University of Strathclyde Business School, Glasgow, UK Daniel Druckman Schar School of Policy and Government, George Mason University, Arlington, VA, USA Macquarie University, Sydney, NSW, Australia University of Queensland, Brisbane, QLD, Australia Colin Eden Strathclyde Business School, University of Strathclyde, Glasgow, UK María Teresa Escobar Grupo Decisión Multicriterio Zaragoza, Facultad de Economía y Empresa, Universidad de Zaragoza, Zaragoza, Spain Liping Fang Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, Canada José Rui Figueira CEG-IST, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal Michael Filzmoser Institute for Management Science, TU Wien, Vienna, Austria L. Alberto Franco School of Business and Economics, Loughborough University, Leicestershire, UK Universidad del Pacifico, Lima, Peru Eduarda Asfora Frej CDSID – Center for Decision Systems and Information Development, Universidade Federal de Pernambuco, Recife, PE, Brazil Ingmar Geiger School of Management, Aalen University, Aalen, Germany Yigal Gerchak Department of Industrial Engineering, Tel Aviv University, TelAviv, Israel Salvatore Greco Department of Economics and Business, University of Catania, Catania, Italy Portsmouth Business School, Centre of Operations Research and Logistics (CORL), University of Portsmouth, Portsmouth, UK

Contributors

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Christian Greiffenhagen Department of Sociology, The Chinese University of Hong Kong, Shatin, Hong Kong Raimo P. Hämäläinen Systems Analysis Laboratory, Department of Mathematics and Systems Analysis, Aalto University School of Science, Aalto, Finland Yue He Business School, Sichuan University, Chengdu, Sichuan, China Keith W. Hipel Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada A. P. C. I. Hong Tilburg University, Tilburg, The Netherlands Masahide Horita The University of Tokyo, Tokyo, Japan Takayuki Ito Department of Social Informatics, Kyoto University, Kyoto, Japan Özgür Kıbrıs Faculty of Arts and Social Sciences, Sabanci University, Istanbul, Turkey Janusz Kacprzyk Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Parmjit Kaur Department of Economics and Marketing, Faculty of Business and Law, De Montfort University, Leicester, UK Gregory Kersten InterNeg Research Centre and J. Molson School of Business, Concordia University, Montreal, QC, Canada Eugene Khmelnitsky Department of Industrial Engineering, Tel Aviv University, Tel-Aviv, Israel D. Marc Kilgour Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada Christian Klamler Institute of Public Economics, University of Graz, Graz, Austria Mark Klein Center for Collective Intelligence, Massachusetts Institute of Technology, Boston, MA, USA Sabine T. Koeszegi Institute for Management Science, TU Wien, Vienna, Austria Gwendolyn L. Kolfschoten Better Samenwerken, Delft, The Netherlands Tuomas J. Lahtinen Systems Analysis Laboratory, Department of Mathematics and Systems Analysis, Aalto University School of Science, Aalto, Finland Hsiangchu Lai Department of Business Administration, School of Management, National Taiwan Normal University, Taipei, Taiwan Yu Maemura The University of Tokyo, Tokyo, Japan Bilyana Martinovski Center for Cognitive Semiotics, Lund University, Lund, Sweden

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Contributors

Shaila M. Miranda University of Oklahoma, Norman, OK, USA Danielle Costa Morais CDSID – Center for Decision Systems and Information Development, Universidade Federal de Pernambuco, Recife, PE, Brazil José María Moreno-Jiménez Grupo Decisión Multicriterio Zaragoza, Facultad de Economía y Empresa, Universidad de Zaragoza, Zaragoza, Spain Hannu Nurmi Department of Philosophy, Contemporary History and Political Science, University of Turku, Turku, Finland Peijia Ren School of Business Administration, South China University of Technology, Guangzhou, China George P. Richardson Rockefeller College of Public Affairs and Policy, University at Albany, State University of New York, Albany, NY, USA Lucia Reis Peixoto Roselli CDSID – Center for Decision Systems and Information Development, Universidade Federal de Pernambuco, Recife, PE, Brazil Ewa Roszkowska Faculty of Economics and Finance, University of Białystok, Bialystok, Poland Ahti Salo Systems Analysis Laboratory, Department of Mathematics and Systems Analysis, Aalto University School of Science, Aalto, Finland Manuel Salvador Grupo Decisión Multicriterio Zaragoza, Facultad de Economía y Empresa, Universidad de Zaragoza, Zaragoza, Spain Mareike Schoop Information Systems Group, University of Hohenheim, Stuttgart, Germany Melvin F. Shakun Leonard N. Stern School of Business, New York University, New York, NY, USA Roman Słowiński Institute of Computing Science, Poznań University of Technology, Poznań, Poland Systems Research Institute, Polish Academy of Science, Warsaw, Poland Jama D. Summers University of Tennessee, Knoxville, TN, USA R. P. Sundarraj Department of Management Studies, Indian Institute of Technology Madras, Chennai, India Katia Sycara Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA Tomasz Szapiro Institute of Econometrics, Decision Analysis and Support Unit, SGH Warsaw School of Economics, Warsaw, Poland Ofir Turel California State University, Fullerton, CA, USA P. J. van der Wijst Department Communication and Cognition, Tilburg University, Tilburg, The Netherlands

Contributors

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Rudolf Vetschera Institute for Business Decisions and Analytics, University of Vienna, Vienna, Austria Alexey Voinov Center on Persuasive Systems for Wise Adaptive Living (PERSWADE), University of Technology Sydney, Sydney, NSW, Australia University of Twente, Enschede, The Netherlands Tomasz Wachowicz Department of Operations Research, University of Economics in Katowice, Katowice, Poland Lynn Wagner International Institute for Sustainable Development, Winnipeg, MB, Canada Leroy White Warwick Business School, University of Warwick, Coventry, UK Yi Xiao Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada Haiyan Xu College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China Zeshui Xu Business School, Sichuan University, Chengdu, Sichuan, China Mike Yearworth Business School, University of Exeter, Exeter, UK Amber G. Young University of Arkansas, Fayetteville, AR, USA Yufei Yuan McMaster University, Hamilton, ON, Canada Pascale Zaraté IRIT, Toulouse Université, Toulouse, France John Zeleznikow La Trobe University Law School, Bundoora, VIC, Australia Ronghuo Zheng McCombs School of Business, The University of Texas at Austin, Austin, TX, USA

Part I Introduction

Introduction to the Handbook of Group Decision and Negotiation D. Marc Kilgour and Colin Eden

Contents What Is Group Decision and Negotiation? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Organization of this Handbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 1: Justice and Fairness in Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 2: The Context for Group Decision and Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 3: Crowd-Scale Group Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 4: Game Theory Developments for Group Decision and Negotiation . . . . . . . . . . . . . . . . . . . . . Part 5: Group Support Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 6: Multiple Criteria Analysis for Group Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part 7: Electronic Negotiations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Groups of individuals, whether formally organized or not, benefit from the ability to make good collective decisions. Individuals who have interests in common are better off if, as a group, they can search for, identify, and agree on courses of action with a net benefit to all. Organizations must often craft plans and policies that integrate information from their members, and reflect members’ individual understandings of the organization’s abilities, preferences, and aims. Formal procedures are often applied to make, and study, collective decisions. The mission of Group Decision and Negotiation as an academic and professional field is to study approaches to group decision-making, especially systematic approaches, and to identify when they produce better, more informed decisions. The aim of Group Decision and Negotiation is to evaluate, understand, develop, and D. M. Kilgour (*) Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada e-mail: [email protected] C. Eden Strathclyde Business School, University of Strathclyde, Glasgow, UK e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_1

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implement ways to improve collective decision processes. The aim of this Handbook is simple: Make the methods, conclusions, and products of Group Decision and Negotiation research and practice widely available in a form suitable for practitioners, students, and researchers. Keywords

Group Decision and Negotiation · Collective decision-making · Formal model · Negotiation model · Group Decision Support

What Is Group Decision and Negotiation? The ability to reach informed and appropriate collective decisions is probably a prerequisite for civilization, and is certainly a valuable asset for individuals as they interact, and for all types of organizations as they function. The use of formal procedures for reaching a collective decision is often recommended, and it is now widely understood that collective decision-making is more successful if approached systematically, or with the right kind of group support. Group Decision and Negotiation (GDN) is the academic and professional field that aims to understand, develop, and implement these ideas in order to improve collective decision processes. The aim of this Handbook is simple: Make the methods, conclusions, and products of Group Decision and Negotiation research and practice widely available in a form suitable for practitioners, students, and researchers. Group Decision and Negotiation includes the development and study of methods for assisting groups, or individuals within groups, as they interact and collaborate to reach a collective decision. The broad aims of the field are to provide a range of procedures – including both analytical support and process support – that will improve, and possibly even optimize, collective decisions. The range of GDN is enormous, reflecting the breadth of the structural, strategic, tactical, social, psychological, and even computational issues faced by individuals and groups as they narrow in on a collective choice. The field of GDN encompasses procedures, techniques, and support systems designed to help negotiating or cooperating decision-makers deal with complex issues more efficiently or more effectively. The development of GDN is an excellent illustration of interdisciplinary synergy, as its approaches are drawn from operations research, computer science, psychology, social psychology, political economy, systems engineering, information systems, social choice theory, game theory, system dynamics, and other fields. Moreover, this research is being carried out around the globe, as demonstrated by our count of 21 different countries around the world where authors of chapters of this Handbook are working. Negotiations involve governments, regional and nongovernmental organizations, as well as individuals and other groups. Corporate and governmental organizations must regularly craft group decisions as they develop policy and make strategy. At the individual level, interpersonal relations, for example, within families, organizations,

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or neighborhoods, are characterized by negotiations. The availability of electronic communication has given rise to e-negotiation of individuals and agents, as well as sophisticated group support systems (GSS). Connected to the ubiquity and importance of group decision and negotiation are several age-old problems as well as many new ones. All of these aspects of GDN are considered in this Handbook. In some areas of GDN, scholars find it useful to distinguish between group decisions and negotiations. They understand a group decision as a shared decision problem in which two or more concerned parties must make a choice, which all parties must accept, while seeing negotiation as a process in which two or more independent, concerned parties may make a collective choice, or may “walk away” and make no choice at all. An alternative view is that group decision is a generic process whereas negotiation is specific. An important difference, though not a characterization, is that negotiation often includes a distributive dimension which group decision almost always lacks. These distinct viewpoints reflect not only the possible outcomes but also the process, the numbers of participants, the existence of common ground, and the types and modes of participation. In yet another part of the field, the terms group decision and negotiation cannot be disentangled – they are joint decisions that arise through subtle or “soft” social and psychological interaction. The field of Group Decision and Negotiation exhibits both unity and diversity. It always concerns decisions that reflect the input, and the interests, or two or more individuals or groups. Information is crucial, and there is a role for emotion. The same ideas apply in simple person-to-person interaction and in sophisticated computer systems with thousands of participants. In the Handbook of Group Decision and Negotiation, we accept all of these perspectives, and more. Our aim is to introduce them to the reader and to convey an idea of their implications. With these diverse perspectives, we will cover the field of Group Decision and Negotiation as it is now, and as it seems likely to develop in the future.

Organization of this Handbook Each chapter of this Handbook is an essay on an important or emerging topic in Group Decision and Negotiation, written by an acknowledged expert or experts. Keywords, some of which are standardized but many of which were selected by the authors, will help the reader to pinpoint particular topics. The Index can also serve this purpose. Note that each chapter contains a list of other chapters recommended by the authors as relevant to the chapter topic. This Handbook has seven parts. 1. Justice and Fairness in Negotiation. What should be the objective of a group decision or a negotiation? In this part, we explore the implications of ideas of justice and principles of fairness for the outcome of a group decision or negotiation.

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2. The Context for Group Decision and Negotiation. In what circumstances should Group Decision and Negotiation principles and practices be invoked? In this part, the main issue is how and when GDN processes apply to real problems. 3. Crowd-Scale Group Decisions. Many group decisions involve so many parties that communication is the major issue. In this part, the focus is on support systems aimed at communities, along with approaches to the use of voting to make group decisions. 4. Game Theory Developments for Group Decision and Negotiation. Game Theory has had a major influence on negotiation and group decision modeling, as demonstrated by several chapters in this part on game-based approaches to negotiation and group decision. 5. Group Support Systems. This part contains a review of approaches to supporting groups, including not only how the support systems work but also how they can be used improve decision-making and improve the group’s understanding of itself. 6. Multiple Criteria Analysis for Group Decisions. Multiple criteria methods, which are well developed for single decision-maker problems, can be applied to group decision problems, often with provision for uncertainty or partial information. 7. Electronic Negotiations. Online dispute resolution helps individuals or organizations to negotiate. Electronic agents may assist human negotiators, or negotiate with humans or with each other. This part contains a review of techniques, successes, and outcomes.

Part 1: Justice and Fairness in Negotiation The first part of the Handbook addresses the role of justice and fairness in negotiations, asking how they should affect outcomes and processes, and illustrating how they apply to specific problems. In an important sense, the ideas of justice and fairness provide ways of assessing the outcome of any group decision or negotiation, and thus constitute standards for evaluating procedures, theories, and support systems for any group decision process. It should therefore not be surprising when they reappear later in this Handbook. Daniel Druckman and Lynn Wagner discuss the role of justice when rival groups negotiate to end civil wars, with success measured by the durability of resulting peace agreements. They weigh the relative importance of distributive justice as compared to procedural justice, concluding that procedural approaches that aim to implement equality, a distributive concept, generally produce better outcomes. They go on to discuss third-party roles and the importance of trust and problem-solving processes. Rudolf Vetschera, Sabine T. Koeszegi, and Michael Filzmoser present a model that describes negotiation processes as evolving simultaneously along a substantive dimension (the issues to be resolved), a communication dimension (the tactics

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adopted), and an emotion dimension, on which negotiators try to influence each other. Recent technical advances now make it possible to follow real-world negotiations in all three dimensions simultaneously. One ongoing development is a new understanding of the consequences in the substantive dimension of appeals to fairness in the emotional dimension. Michael Filzmoser, Rudolf Vetschera, and Sabine T. Koeszegi follow up on the previous chapter by collecting empirical evidence of how the emotional content of a negotiation can be found, at least in part, “between the lines” of the tactical content. They assess data from actual negotiations to relate efficiency of outcome (any other outcome is worse for at least one party) to fairness and balance. The contribution of Christian Klamler is a detailed study of whether, and how, fairness can actually be implemented in the outcome of a group decision or negotiation. The greatest difficulty arises in a common problem, the allocation of indivisible items – where fairness is sometimes impossible. A discussion of properties related to fairness facilitates the introduction, illustration, and analysis of ten procedures for allocating indivisible items to two parties, and to offer some suggestions about which procedure is best in various contexts. Yigal Gerchak and Eugene Khmelnitsky close Part 1 with their answer to a question: How should a partnership be structured when the major issue is the division of uncertain future profits (or losses) between the partners. Clearly, a solution should reflect the partners’ beliefs about future profits as well as their attitudes to risk, and can also depend on each individual’s alternatives. Some standard bargaining solutions are applied to find alternatives that the partners can agree upon.

Part 2: The Context for Group Decision and Negotiation The second part of our Handbook opens up discussion about the context for group decisions and negotiations. Much of the work reported in the Handbook focuses on analysis and process, but those aids to addressing conflict, negotiation, and decision are set within the context of human nature: cognitive style ranging from rational to emotional. And, of course, the environmental context and the nature of the communication media through and within which the negotiation and decision takes place can impact what can be achieved. The context of all group decision and negotiation is the problem definition –but there is always a danger of an error of the “third kind” – solving the wrong problem. As much as the group itself, GDN analysts and facilitators may be instrumental to constructing and defining the wrong problem. We start this part by exploring the views of Melvin F. Shakun and Bilyana Martinovski on dynamic problem structuring as an attempt to ensure this error does not occur. The role of emotion is a fundamental aspect of human behavior and many authors make reference to its significance. It is a powerful context to all work in group decision and negotiation. Bilyana Martinovski addresses emotion as a key aspect in group-based problem structuring and solution finding. She presents a survey of the

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state-of-the-art of the field as well as providing a framework for the analysis of emotion in group decision and negotiation. The chapter also provides an example of such analysis. Alongside the role of emotion sits the role of the cognitive style of the different members of a group decision and negotiation episode. Sébastien Damart and Sonia Adam-Ledunois discuss the significance of cognitive diversity. They consider the various ways in which cognitive style might be understood and introduce a cognitive mapping-based method as a way of facilitating an improvement in group decision performance, exploiting several cognitive styles. Perhaps the most significant contextual changes over the last two decades have been developments in electronic media such as email, video conferencing, and instant messaging. Ingmar Geiger reviews these developments and their significance for group decision and negotiation. He focuses specifically on the role of media richness theory, the task/media fit hypothesis and media synchronicity theory as communication theoretical foundations. He uses these theoretical frameworks and a general review of the field to discuss communication media choice in negotiation. Although inevitably much of the research on group decision and negotiation utilizes the explicitly stated knowledge and views of the participants in the process, this knowledge exists within the context of tacit knowledge. Tacit knowledge plays an important part in any group process, and particularly in mediation. Tomasz Szapiro explores the impact of tacit knowledge on the results of negotiation. He merges different perspectives in negotiation analysis to justify a general framework for identification of tacit knowledge interventions. So far, in considering context, authors have focused on cognitive and behavioral aspects. We now move on to consider the pre-negotiation process and outcomes as an important context, and consider the environment for negotiation. The chapter by Tomasz Wachowicz and Ewa Roszkowska specifically focuses on pre-negotiation preparation. They consider how to manage the different preferences of participants in negotiation, and analyze various options that may be used for designing a holistic pre-negotiation preference elicitation protocol, presenting the results of one hybrid holistic protocol in a bilateral negotiation support system. Our next chapter focuses on a particular context of group decision and negotiation that may be the most obvious contextual consideration, and one that can sometimes be a significant negotiation in its own right – the location of the negotiation. Per van der Wijst, Alain Hong, and Debby Damen examine how location impacts the mindset of the participants. They report on an experimental study, using a virtual reality laboratory, where the effects of environment on psychological variables can be measured. The final chapter of this part takes us to a new and interdisciplinary field – the use of neuroscience tools in group decision and negotiation. Neuroscience may be especially helpful in our field as neural data can be used to improve predictions about human choices and the outcomes they produce. Adiel Almeida, Danielle Morais, Ana Paula Costa, and Lucia Roselli demonstrate the Neuroscience approach to GDN, showing how its tools can give a better understanding of human preferences and improve support systems.

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Part 3: Crowd-Scale Group Decisions Some group decisions are remarkable because they are made by groups, typically large ones, in which individuals may not be acquainted with each other; they communicate, deliberate, and come to a shared understanding without physical proximity. The internet has made an enormous difference in such contexts, enabling some groups to develop good ideas and feasible policies. Promising software to moderate such groups is now under development. Also in this part is a discussion of one of the most common procedures for integrating opinions in order to make a decision: voting. Voting is always an option, especially for a large, diffuse group, and may be particularly à propos in certain contexts. To begin the discussion of crowd-scale group decisions, Masahide Horita and Yu Maemura describe community conflicts, which address problems that affect all members of a community. They show how GDN techniques have assisted with the resolution of some specific public conflicts. They also identify important theoretical and practical issues that have yet to be addressed, such as group support that captures the linguistic and spatial dimensions of many public issues, and make some suggestions about new GDN approaches that may be able to assist with future community decisions. Mark Klein continues this theme by stressing that crowd-scale deliberation is the most appropriate way to address many important and complex social problems. He argues that such deliberation should be supported by many types of disciplinary expertise, and suggests that standard group-decision approaches are unable to deliver that support at the required scale, resulting in Pareto-suboptimal outcomes. He then discusses some recent advances in social computing technology that promise to address these failings. Takayuki Ito’s interest is in facilitation for large-scale online discussion groups, specifically crowd-scale discussion support. It has been convincingly demonstrated that, in large online groups, the presence of a facilitator is critical to establishing and maintaining productive and coherent discussions. But it is difficult for human facilitators to serve large online groups, which operate 24/7. Facilitator support software has now been deployed and is promising. Early experience with an automated facilitation agent is also discussed. Alexey Voinov takes a different approach, proposing Participatory Modeling, a technique for involving as many stakeholders as possible in a group decision process. He argues that, for a good group decision, what is needed is an openended process in which a common model of the system at stake is developed, a process that involves shared learning and interaction. Levels of participation can differ, but stakeholder knowledge of the system must be synchronized in order to move toward consensus. Next come two contributions on voting procedures. First, Hannu Nurmi describes many voting systems that have been developed to identify one candidate, or alternative, that is the “collective will.” He points out that, given a set of voter opinions, it is sometimes possible to identify a single reasonable (or democratic) choice, but that often there are several plausible alternatives. In fact, single-winner

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voting systems are often evaluated in the context of several classical paradoxes of social choice. The analysis of opinion distributions can lead to identification of profile restrictions that are relevant to the choice of voting system. D. Marc Kilgour concludes the part with a study of the use of voting to select not one alternative, but several. Among the issues that plague multi-winner voting is “tyranny of the majority,” wherein a subset of the voters controls more than its share of the set of winners. This phenomenon can occur whenever single-winner procedures are applied, simultaneously or sequentially, to select multiple winners. There are some ways to avoid this problem, including some voting systems specifically designed for multi-winner voting.

Part 4: Game Theory Developments for Group Decision and Negotiation Game Theory (and Decision Theory) have been the source of many approaches to Group Decision and Negotiation. The developments include Non-cooperative and Cooperative Game Theory models of negotiation. But many other systems have branched off from Game Theory, resulting in structures that are designed for analysis of negotiations or group decisions. These structures, although not strictly games, bear many similarities to them. First off, Liping Fang and Keith W. Hipel contribute a retrospective analysis of two papers they wrote, with K. Jim Radford, in the 1990s. They look back on “Decision Making under Conditions of Conflict,” classifying conflicts according to the number of participants and the number of objectives, illustrating their classification, and discussing how these distinctive problems can be analyzed. They update a list of flexible decision support systems that can assist in the analysis of genuine conflicts in aims and objectives, and suggest several possible priorities for future research. Next, Jim Bryant describes how some issues with the use of games to model conflict situations led to the evolution of Drama Theory. One concern was the importance of perceptions and the fact that, when perceptions change, behavior can change as well. There is an important gap between Nigel Howard’s theory of inducement, a Drama Theory approach which is not fully rational, and Game Theory. Drama Theory is now a complement to Game Theory, including components of anticipated reaction, counter-reaction, and credibility, but always focusing on specific confrontations. Jim Bryant and Peter Bennett follow up with a specific study of Drama Theory models of negotiations. They outline the main features of Drama Theory, including its emphasis on the dilemmas inherent in a confrontation. They see it as a practical means to analyze strategic conflicts, utilizing several schemas characterizing dilemmas. They go on to describe other modes of application of Drama Theory, including immersive role play, and continue with a review of software tools that can facilitate such applications.

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Within Game Theory, the most influential treatment of bargaining was the Nash Bargaining Solution. Kalyan Chatterjee describes two major lines of research into negotiation within Non-cooperative Game Theory, both of which can be traced to the Nash Bargaining Solution and its non-cooperative offshoot, the Nash Demand Game. The first was the introduction, by Chatterjee and Samuelson, of incomplete information in the context of a buyer and a seller; it gave a new perspective on efficiency in bargaining. The second was the Rubinstein model of alternating proposals and costly delay. Subsequent studies include strategies for making demands and the role of time and coalitions in bargaining. Özgür Kıbrıs presents an overview of the Cooperative Game Theory models of GDN processes, including the analysis of these models. Again, the original ideas can be found in the Nash Bargaining Solution and the development of the axiomatic method to analyze it. This approach has given rise to many formal bargaining rules, which can be studied using many axioms of fairness and efficiency. The discussion also includes ordinal bargaining, the Nash program, and implementation issues. One of the most successful systems for the analysis of strategic conflicts, which include both group decisions and negotiations, is the Graph Model for Conflict Resolution, the subject of the next two chapters. First, D. Marc Kilgour, Keith W. Hipel, and Liping Fang describe the basics of a graph model – the decision-makers, states, state transitions (graphs), and (ordinal) preferences – which can be used to model a strategic conflict. They then discuss and illustrate individual stability definitions, the foundation for most graph model analyses, and continue with the Decision Support Systems that automate the modeling and analysis processes. Finally, they set out the definitions and principles underlying the extension of the graph model to coalitions of decision-makers. To conclude this part, Keith W. Hipel, D. Marc Kilgour, Haiyan Xu, and Yi Xiao outline the major extensions to the Graph Model. The matrix method not only makes stability calculations much more efficient, it also provides a solid foundation for preference representation, allowing simple (crisp) preferences to be replaced by uncertain preferences, which may be fuzzy, gray, or probabilistic. Another new development is the inverse perspective, in which desired states and stability types are inputs and preferences to achieve them are outputs. A model of a real-world water export conflict is used to illustrate these developments.

Part 5: Group Support Systems The development and use of computer-based group decision support systems goes back three decades. Over this period, older systems have been strengthened and new systems have been developed; indeed, the significant new system “strategyfinder” was introduced as this Handbook came into being (see chapter ▶ “Group Support Systems: Past, Present, and Future”). This part of the Handbook focuses on Group Support Systems (GSSs). Fran Ackermann introduces these developments in GSSs and provides not only a sense of the history of their development but also a view of their future. She also

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gives the reader a feel for their achievements, and the variety of underlying modeling approaches by considering five of the best established support systems from inception to recent work. This exploration looks at original aims, system development over time, and the problems and industries supported. The exploration also considers underlying modelling approaches. Laku Chidambaram, Jama Summers, Shaila Miranda, Amber Young, and Robert Bostrom continue this story by providing a synthesis of research on group development in the context of group support systems (GSS). They show that, as digital technology became ubiquitous, accessible through mobile devices, and more powerful in its capabilities, teams using these affordances gained the ability to transcend organizational boundaries, and membership became fluid, with members entering and exiting at will. They argue that new group support systems have made collective action broader, more flexible, and more inclusive, and that new approaches are needed to study these impacts. In our next chapter, Mike Yearworth and Leroy White introduce experiments into widening the effectiveness of a GSS in a way that utilizes technological opportunities – using cloud-based GSS. Their development seeks to have a direct impact on the way in which problems can be structured by the group, making it more likely that the “right” problem is addressed (see the chapter ▶ “Advances in Defining a Right Problem in Group Decision and Negotiation”). The development of online GSS is discussed with a particular focus on two emerging research questions: the future role of the facilitator and the commonalities of online GSS and social media platforms as different-times/different-places group working. The first three chapters of the part on GSS provide a broad introduction to the field. The next subsection displays three approaches to Group Support in practice: (i) the use of a causal mapping GSS – illustrating concepts and practice, (ii) the use of interactive group model building as group support, and (iii) the use of collaboration engineering. Fran Ackermann and Colin Eden focus on one particular GSS and how it seeks to attend to soft negotiation in the context of complex problems. They explore, through a real case example, a number of soft negotiation implications. The analysis of the real GSS case is undertaken from the perspective of key assertions derived from (i) GSS literature – such as the way a GSS offers anonymity, procedural justice, a boundary object, and increased creativity, (ii) established recommendations for effective soft negotiation, and (iii) where appropriate, research into failed decisions. Their exploration leads them to make practical recommendations on the use of a GSS. Group model building, where a group is supported through the process of constructing a simulation (System Dynamics) model of a complex problem, is a powerful GSS process. George Richardson and David Andersen are experts in taking an endogenous dynamic perspective to group negotiations. They explore scripts for introducing model concepts, initiating systems mapping, eliciting system feedback structure, formulating formal models with client groups, and using them to help build a negotiated consensual view of their shared mental models. In a similar way to Ackermann and Eden, they use the model as a boundary object. In the previous two chapters, the authors utilize sophisticated GSS modelling software to represent the boundary object, and then they analyze it. However, GSS

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technology and methods may be challenging for an organization without experienced facilitators. Gert-Jan de Vreede, Robert Briggs, and Gwendolyn Kolfschoten introduce a Collaboration Engineering approach to address this issue. They explain how the approach improves group work and group decision and negotiation. Collaboration engineers design collaborative work practices using a facilitation pattern language consisting of “thinkLets” – facilitation techniques that create predictable patterns of collaboration. The third subsection on Group Support Systems considers some of the issues faced in understanding how and why they work. To begin, Colin Eden writes about his experiences of using GSS over many years and with a wide range of organizations. The chapter highlights a series of interrelated issues that significantly affect the success and failure of group support for decision and negotiation. He emphasizes the role of a GSS as a Transitional Object and Boundary Object, but also considers the behavioral aspects of group support – for example, political feasibility and the development of emotional commitment. In seeking to understand what happens when GSS is used, there has been a growing interest in the micro-analysis of group support sessions. Alberto Franco and Christian Greiffenhagen explore group support “as it happens.” They argue that, in order to develop better GSS practice, it is crucial to understand how it is actually used by those involved in situ. In order to gain a more nuanced understanding of GDS practice, their research focuses on what GSS practitioners actually do with their craft. They demonstrate this approach through a real example of the moment-to-moment activities of a group using a GSS. Parmjit Kaur and Ashley Carreras follow a similar approach to researching GSS by exploring the role of Procedural Justice in a real GSS intervention. Their case illustrates the use of GSS in the development of an agreed identity and vision for an organization and the identification of its strategic priorities. They focus on the dimensions of procedural justice and how using a “dual facilitation process” helps to support positive extra-role behaviors that facilitate successful renegotiation. Finally, Viktor Dorfler updates the framework for thinking about Group Decision Support that was introduced in the early stages of development of the GDN field. There have been major developments in the broad context surrounding GDSS, including the improved understanding of decisions on the conceptual side, and many aspects of computer development, such as artificial intelligence and big data on the technical side. Yet, he suggests, many of the observations, arguments, and conclusions offered nearly 40 years ago are still valid today. But now artificial intelligence could become important to the future of GDN.

Part 6: Multiple Criteria Analysis for Group Decisions Important decisions are often taken by groups of decision-makers who have multiple criteria in mind as they choose among alternatives. An important component of GDN is the understanding and support of Multiple Criteria Decision-Making (MCDM). The acronyms MCDM and MCDA (MCD Analysis) are essentially

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synonymous, with each being favored by different authors. In this part, we present the principles of multi-criteria methods, the mathematical formulation, and the methods available, including many analytical methods that support groups. Ahti Salo, Raimo Hämäläinen, and Tuomas Lahtinen start the part with a fulsome overview of MCDM. They consider the way in which an MCDM formulation can foster collaboration, lend structure to the decision process, and help in managing problem complexity. They offer guidelines for the design of MCDAassisted group decision processes, outline widely used MCDA methods, examine behavioral factors related to the MCDA process. They finish with their views about the future of MCDM. The subsequent chapter provides an introduction to the detailed mathematics of MCDA: Notation, Problematics, and Main Approaches. Salvatore Corrente, Jose Figueira, Salvatore Greco, and Roman Slowinski introduce in detail the main principles of MCDM and present the basic approaches and methodologies. These first two chapters of this part provide all of the necessary background to MCDM for group decision and negotiation. The next five chapters address different methods and issues in the use of MCDM. We start with an overview of preference modelling approaches for aiding Multicriteria Group Decision-Making using only partial, imprecise, or incomplete information about preferences. Adiel de Almeida, Eduarda Frej, Danielle Morais, and Ana Paula Costa consider how to reduce the amount of information required from group members in order to conduct analysis that will lead to a good decision. They present a flexible elicitation procedure using an interactive decision support system. José María Moreno-Jiménez, Juan Aguarón, María Teresa Escobar, and Manuel Salvador introduce the Analytical Hierarchy Process (AHP). They offer three important contributions to the field by considering consistency in group decisions, aggregation of individual preference structures, and the Bayesian approach. They also discuss cognitive orientation in group decision processes. Peijia Ren, Zeshui Xu, and Janusz Kacprzyk address the use of intuitionistic fuzzy preferences in decision-making. They provide an overview of the use of intuitionistic fuzzy sets from the perspectives of information fusion, intuitionistic preference relations, and multi-attribute group decisions. They present a series of practical uses of intuitionistic fuzzy sets in supply chain management, healthcare, and hydropower station risk assessments. Yue He and Zeshui Xu show how linguistic terms and their extensions can be used to express the preferences of decision-makers directly. They discuss hesitant fuzzy linguistic term sets, probabilistic linguistic term sets, and double hierarchy hesitant fuzzy linguistic term sets. They introduce and compare methodologies for information fusion, preference expression, and group decisions. While they acknowledge that group decision-making based on linguistic information brings many challenges, they argue that the approach provides theoretical and practical value to decision-makers. This part on multiple criteria analysis is completed by a chapter on software that adopts the multicriteria paradigm. Guy Camilleri and Pascale Zaraté describe their GRoUp Support system (GRUS), a web-based system that can be used

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synchronously or asynchronously, in distributed or non-distributed settings. A human facilitator assists the participants as they develop both private and public criteria and preferences, and apply tools for evaluation and collaboration. GRUS has been tested and used in a variety of contexts.

Part 7: Electronic Negotiations The internet has the capacity to link individuals – and individuals who can communicate can also negotiate. This capacity is now being exploited more fully by GSS developments (see the chapters ▶ “Group Support Systems: Past, Present, and Future,” and ▶ “Group Support Systems: Experiments with an Online System and Implications for Same-Time/Different-Places Working”). Historically, electronic negotiation, which began with the use of internet as a communication device, soon developed into a research tool, as monitored communication with restricted terms could be easily analyzed. Subsequently, electronic agents in various forms were developed and positioned on the internet, and are now used to mediate human negotiation, to negotiate with humans, and to negotiate with each other. The themes of this final part of the Handbook are the rapid development of electronic negotiation and its implications. Gregory Kersten* and Hsiangchu Lai provide a sweeping overview of foundations, systems, and processes of e-negotiation, or negotiation conducted over the internet. Their classification of e-negotiation systems reflects both structure and usage. Many factors combined to make e-negotiation common today, including the development of artificial intelligence, multimedia availability, software services, new business models, and increased access to data, especially cloud data. The rapid growth in e-negotiation systems is a consequence of the interaction of social and technical phenomena. Next, R.P. Sundarraj addresses the linkage of e-negotiation and behavior, arguing that behavioral elements can and should be integrated into e-negotiation systems. He outlines a framework that can address this problem, incorporating a characterization of preferences and the resulting modification in negotiation strategy. He discusses and illustrates the trade-off of fidelity against tractability that determines the level of automation exhibited by an e-negotiation system with behavioral features. John Zeleznikow traces the development of Online Dispute Resolution and online Negotiation Support Systems. They evolved from settlement-oriented and rule-based to case-based systems incorporating ideas from Artificial Intelligence and Game Theory. He reviews the application of various systems for intelligent negotiation support in domains including family law and international disputes, commenting on the importance of user needs versus technology, and ending with a discussion of ideal features for an online dispute resolution system. Mareike Schoop’s chapter concerns process support for humans negotiating electronically. Negotiation Support Systems differ substantially in their levels of support for complex digital negotiations. The system Negoisst integrates

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communication support, decision support, and contract management, and has been used around the world for two decades to teach digital negotiations, to support negotiation experiments and competitions, to train future negotiators, and to enhance digital negotiation skills. In their chapter, Ofir Turel and Yufei Yuan show that Online Dispute Resolution services are essential to resolve disputes arising in e-commerce, or in other contexts in which the disputants are physically distant. Online Dispute Resolution is, explicitly or implicitly, an electronic negotiation system that dispenses justice on the internet. Classification of these services clarifies distinctions in level of support, objectives, and costs. A principle-based dispute resolution system, if available, is recommended for its combination of affordability, timeliness, balance, and follow-up. The concluding chapter in this part is a study by Tinglong Dai, Katia Sycara, and Ronghuo Zheng of autonomous negotiating agents, which are of interest from the points of view of both social sciences and mathematics. They focus on mathematical models of reasoning in a negotiation, which may be analytical, offering structural predictions and managerial insights, or computational, featuring optimization algorithms and heuristics governed by artificial intelligence. Together, these models can be implemented in autonomous processes, producing a set of negotiating agents that can engage in realistic decentralized negotiations.

Conclusions As we prepared this Handbook, our objective was to balance recognition of the past with a view to the future. We gave special emphasis to the integrative approaches that have characterized GDN throughout its development – studying problems using broad social science principles, analyzing them mathematically, or developing algorithms and software to address them – all the while incorporating managerial measures, strategies, and principles. Because the core problems of GDN are usually ill-structured, dynamic, and suited to many different perspectives, these integrative approaches have led to most of the successes that GDN has achieved. As much as the commonalities of the problems it addresses, it is the interplay of different forms of reasoning and analysis that characterizes this unique field. Nonetheless, we believe that the contents of this Handbook show how much more the field can benefit from integration within and across the seven parts. Thus, the second edition of the Handbook of Group Decision and Negotiation recognizes both the diversity and the integrity of the field. The process of reaching a collective decision can be studied both in theory and in practice; problems can be understood in terms of underlying principles or computational issues; ideas from a wide range of disciplines can be adapted to build systems that address real problems, but only after appropriate, and usually substantial, modification. Group Decision and Negotiation has made an impact on both the theory and the practice of individuals and groups making choices in their common interest. We believe that it will continue to succeed, even as we recognize that it faces great

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challenges. In the future, there will be technological developments relevant to the field, developments that will drive its evolution in new directions. There is no question that GDN as we know it today was facilitated, and even shaped, by the technologies of the past. We have no special qualifications for prediction, so we will not attempt to predict which issues will turn out to be crucial in the future, or which current problems will shrink and become tractable. We predict only that the focus and implications of GDN will change, but that the fundamental problems will remain the same. We are confident that Group Decision and Negotiation will be important far into the future, and that it will continue its interdisciplinary and multidisciplinary traditions. Up to now, it has advanced on a broad front, a strategy that has served theorists and practitioners very well. Collective decision-making will be no less important in the future, and GDN will make major contributions. Equally, we are confident that there is a firm basis for future developments in our discipline. We have done our best to set out that foundation in this second edition of the Handbook of Group Decision and Negotiation.

Part II Justice and Fairness in Negotiation

Just Negotiations, Stable Peace Agreements, and Durable Peace Daniel Druckman and Lynn Wagner

Contents Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How Justice Influences Negotiation Processes, Outcomes, Stability, and Durability . . . . . . . . . . . Justice and Negotiation: A Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Research on the Role of Justice in Peace Agreements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distributive Justice and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Procedural Justice and the Stability of Agreements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Equality Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Third Party Roles in Equality Provisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Justice and Durable Peace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Search for Mechanisms: Trust and Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion and Policy Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

The role of justice in negotiations between rival groups and the durability of resulting peace agreements is presented. The presentation draws on information about group negotiation processes and agreements concluded to end civil wars in countries around the world. Relationships between the presence and importance of distributive justice (DJ) in the agreements, and their stability, are first explored. D. Druckman (*) Schar School of Policy and Government, George Mason University, Arlington, VA, USA Macquarie University, Sydney, NSW, Australia University of Queensland, Brisbane, QLD, Australia e-mail: [email protected] L. Wagner International Institute for Sustainable Development, Winnipeg, MB, Canada e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_7

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The difficulty of the conflict environment is shown to have the strongest impact upon stability. However, the DJ principle of equality is found to reduce the negative impact of difficult conflict environments on their stability. Next, the presence and importance of procedural justice (PJ) are examined in the negotiation processes that led to the signing of the peace agreements. Significantly more stable agreements occurred when a process based on PJ led to agreements emphasizing equality. Third, research on the impacts of DJ and PJ on long-term peace is reviewed. Peace is shown to emerge from a path that unfolds from microlevel negotiation to macro-level reconciliation and institutional change. The chapter continues with discussions of third party roles in the peace process and the importance of trust and problem-solving processes. The chapter concludes with a consideration of policy implications derived from the findings. Keywords

Negotiation · Justice and fairness · Procedural justice · Distributive justice · Negotiation process · Negotiation outcome · Peace agreements · Trust

Overview This chapter discusses the role of justice in negotiations between rival groups and the durability of resulting peace agreements. It draws on information about group negotiation processes and agreements concluded to end civil wars in countries around the world, mostly during the early 1990s. Possible relationships between the presence and importance of distributive justice (DJ) in the agreements, and their stability, were first explored. The difficulty of the conflict environment was shown to have the strongest impact upon stability. However, the DJ principle of equality was found to reduce the negative impact of difficult conflict environments on their stability. An emphasis on equality was also associated with more forward-looking agreements, which were found to be more stable than backward-looking ones. Next, the presence and importance of procedural justice (PJ) were examined in the negotiation processes that led to the signing of the peace agreements. Significantly more stable agreements occurred when a process based on PJ led to agreements emphasizing equality. A close examination of how the equality principle was expressed in the agreements revealed three main types of provisions: equal measures, equal treatment, and equal shares. Agreements with equal treatment and/or equal shares were associated with forward-looking outcomes and high stability, and equal measures with a more backward-looking outcome and poorer stability. Third party roles were then assessed in four select cases. In both cases of high stability (Mozambique, Zimbabwe), third party intervention was central to the formulation of high equality agreements and to implementation. In the cases of low/no stability (Angola, Rwanda), third parties did not work actively to promote agreement based on forward-looking or any equality provisions. The findings suggest that negotiators and third parties should strive for

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agreements based on equal treatment and/or equal shares, since they are more stable during the implementation period and beyond, and that a variety of tactics and approaches (both facilitating and forceful) can serve that objective. The research continued with an examination of the impacts of justice on macrolevel societal peace. Sixteen durable peace variables were included in an expanded data set of 50 cases of peace agreements. Among the key findings were relationships between procedural justice and societal peace over the course of 8 years following the negotiated agreement. Specifically, we discovered a path going from PJ during the negotiation process to DJ in the outcome to stable implementation of the agreements and to societal peace. Of particular interest were the importance of two PJ principles, fair treatment and transparency, and the role of community activities during the post-agreement period. A discussion of possible explanations for these findings and implications for a culture of peace conclude the chapter. Issues concerning the role of justice in negotiation have been addressed by scholars and practitioners in a number of areas in social science. These areas include the study of civil wars, international trade negotiations, historical negotiations on security issues, law, organizational management (see the chapters ▶ “Group Support Systems: Concepts to Practice” by Eden and Ackermann and ▶ “Behavioral Considerations in Group Support” by Eden, ▶ “Procedural Justice in Group Decision Support” by Kaur and Carreras for examples of the impact of PJ in the design and use of Group Support Systems), and social psychology. They focus attention on group decision processes that occur in this domain. We have learned from these studies about how justice influences negotiation processes, outcomes, implementation, and the durability of societal peace. A review of the justice literature precedes a discussion of our projects on stable and durable peace. We then develop implications of the findings for practice and policy.

How Justice Influences Negotiation Processes, Outcomes, Stability, and Durability The influence of justice on negotiation processes and dynamics has been explored in interpersonal (e.g., Deutsch 1985), organizational (e.g., Konovsky 2000), and international (e.g., Zartman et al. 1996) contexts. A study of international negotiations across four issue areas (trade, the environment, ethnic-sectarian conflict, and arms control) found that negotiators regularly act upon justice considerations and that these can affect the process in numerous ways (Albin 2001). At the most basic level, they may guide the framing of the issues – proposals put forward, the exchange and evaluation of concessions, and the formulation of agreements – and thereby facilitate the trade-offs, particularly when parties share the same or compatible notions of justice. An associated concept is the norm of reciprocity; that is, mutual responsiveness to each other’s concessions. Research has distinguished several different patterns of how concessions are made while negotiating. These include “comparative responsiveness” – that is, acting based on a comparison of one’s own and the other’s

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tendencies to concede (Druckman and Bonoma 1976; Druckman and Harris 1990) – and “diffuse reciprocity” – that is, acting to ensure that roughly adequate or sufficient, rather than specifically equal or comparable, concessions are made to establish a balanced agreement overall (Albin 2001). Distributive justice considerations may complicate the bargaining process, cause deadlocks and stalemates, and become subject to negotiation themselves. This pertains to the situation in which parties endorse competing justice principles or interpretations (applications) of them. In the end, however, reaching agreement usually requires formulating terms that can earn the respect and voluntary approval of all parties and their constituencies partly by appealing to their sense of justice. Negotiators are thus motivated to act on terms that can be generally accepted as reasonable and balanced. The search for such terms frequently leads them to balance and combine several justice principles in the terms of agreements. This very act of balancing is also associated with justice, in a situation in which no distributive justice principle emerges as morally superior on its own and several are needed to take account of relevant factors and different circumstances (Zartman et al. 1996). Similarly, a study of how public resources and burdens are allocated demonstrates that decision makers must balance different justice principles and that major theories of justice fall short of capturing these real-world nuances (Young 1994). The presence of procedural or process justice is also widely regarded as adding legitimacy to the results (Albin 2008). Beyond this, however, general systematic conclusions about how justice in the negotiation process influences the terms of agreements and the outcome are few. In an analysis of international trade talks, adherence to procedural justice while negotiating was found to increase the chances for mutually beneficial agreements (Kapstein 2008). In her study of the Liberian peace process, Hayner (2007) found that stable agreements depended on both procedural justice (fair representation of stakeholder groups) and confronting complex issues during the negotiation process. Along similar lines, Hollander-Blumhoff and Tyler’s (2008) field experiments showed that when procedural justice principles are evident in the process, the negotiators are: (a) more willing to disclose information, (b) more trustworthy, (c) more likely to attain an integrative agreement, and (d) be more durable. These findings were supported by Wagner (2008) in her study of a dozen historical cases of security talks and by Konovsky (2000) in her review of the management literature. Whether procedural justice promotes agreements based specifically on distributive justice is disputed in both research and policy debates. In the context of business organizations, Konovsky (2000) did find a relationship between procedural (process) justice and distributive justice in the outcome.

Justice and Negotiation: A Framework A framework that organizes the justice and negotiation literature was developed by Druckman and Wagner (2016). Realizing that justice studies concentrated on particular stages of negotiation, they placed the research in one of four stages: prenegotiation, negotiation processes, negotiation outcomes, and implementation of agreements or postnegotiation.

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With regard to decisions made during the prenegotiation stage, the research focused on the framing of group or community boundaries, which is important for expanding or limiting inclusion of various stakeholders in the negotiation process (Mikula and Wenzel 2000). It also provided insights into the way that negotiating norms are developed, the difference between self and collective interests (Lind and Tyler 1988), and preferences for alternative distributive principles (Deutsch 1985). With regard to the negotiating process, we have learned about relationships between PJ and motivational orientations as self-interest or group values (Pruitt and Carnevale 1993), the importance of shared identities in building the trust needed to implement PJ principles (Tyler and Blader 2003), the interesting concept of false justice (Lind and Tyler 1988), and the way that PJ can balance the playing field between parties that are asymmetrical in power (Kapstein 2008). A particularly compelling finding is the co-varying relationships (as additive or interactive) among PJ, trust, and problem-solving behavior. The justice research on negotiation outcomes has focused attention on distributional benefits in terms of the distributions accorded under different DJ principles (equality, proportionality, compensation, need). The research has probed the decision processes used to reach each of these types of outcomes and the impacts of these outcomes on the stability of agreements. Another popular research topic has been the relationship between PJ and DJ (Wagner and Druckman 2017). Questions explored have included the strength of the relationship between these types of justice, the relative contribution of PJ and DJ to perceptions of fairness, and the compensating effects of these principles in the sense of whether adherence to PJ principles during the process offsets disappointing distributional outcomes (Brockner and Wisenfeld 1996). On implementing agreements, the research has concentrated on the role of PJ in restoring relationships between the parties during the postnegotiation period including long-term reconciliation (Tyler and Blader 2003), the role played by spoilers in preserving agreements (Stedman 2000), and implications for other negotiations being conducted in parallel or in sequence (Spector and Zartman 2003). A set of hypotheses were generated for each stage culminating in a path that depicts the way justice in the process leads to outcomes with consequences for compliance and reconciliation. Another contribution made by Druckman and Wagner’s review is alternative perspectives on justice and negotiation. One perspective emphasizes systemic or nonlinear processes, another focuses on linear sequences. The former considers justice as part of a system of interacting variables that have bidirectional and circular effects. The latter construes justice as part of a chronological sequence as depicted by the stages idea discussed above. An advantage of systemic thinking is that it places a negotiation in a larger context of interacting influences. It reveals the dynamics of justice perceptions: for example, the circular relationship among PJ, trust, problem solving, and integrative outcomes. A question raised by this perspective is what sets the cycle in motion; does trust precede or follow adherence to PJ principles? This is a question of order, which is addressed by the sequential perspective. Thus, the perspectives can be regarded as being complementary. For example, trust reinforces PJ and problem solving which, working together, move the talks toward a durable agreement. Similarly adherence to PJ principles, encouraged by third parties, reinforces trust and problem solving leading to positive outcomes.

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Research on the Role of Justice in Peace Agreements The extensive literature on negotiations to end civil wars includes studies of cases from a variety of regions and countries (e.g., Zartman 1995; Stedman et al. 2002) and large-sample comparative studies (Fortna 2004; Hartzell and Hoddie 2007; Druckman and Wagner 2019). Findings from these studies shed light on the conditions – both within and outside the negotiating room – for concluding and sustaining peace agreements. An example of important findings comes from the comparative study conducted by Downs and Stedman (2002). Focusing on a set of 16 peace agreements concluded mostly during the early 1990s, these investigators showed that implementation was largely a function of the difficulty of the conflict environment surrounding the talks. Less successful implementation occurred in more difficult conflict environments. Another variable, willingness of neighboring powers to intervene, had virtually no impact on implementation. Missing from this study, and generally from research on settling civil wars, is the role played by justice. This gap was filled by several studies on justice and the stability of peace agreements. A first study focused on distributive justice (DJ) in the agreements. A second study concentrated on procedural justice (PJ) in the negotiation process. Both studies utilized original systems for coding justice. The DJ codes consisted of key words in the agreements that signaled each of the four principles: equality, equity, compensation, and need. The PJ codes consisted of evidence in primary and secondary accounts of the negotiation process that reflected each of the four principles: fair treatment transparency, fair representation, and voluntary decisions. The development and implementation of these coding systems facilitate the evaluation of hypotheses about relationships among the justice and stability/durability concepts. The coding process converted the justice concepts into variables such as the extent to which each DJ or PJ principle was central to the agreement or was emphasized during the negotiation process. These “conversions” facilitate performing statistical tests that evaluate hypothesized relationships: For example, the more central DJ (or PJ) principles are in the agreement (or in the process), the more stable the agreement. The results of the statistical analyses can then be used to construct models that depict the way that the set of variables interact through time across the cases: for example, PJ principles in the process lead to DJ principles in the agreement which, in turn, results in a stable agreement. A more recent study expanded the scope of this research by adding the concept of durable societal peace measured over a period of 8 years (Druckman and Wagner 2019). This study also extended the sampling from 16 to 50 peace agreements. Each of these studies is reviewed followed by a discussion of implications for the connection between justice and peace.

Distributive Justice and Stability Building on the Downs-Stedman data set, Druckman and Albin (2011) coded the 16 peace agreements for four DJ principles: equality, proportionality, compensation, and need. These particular principles are emphasized in both theoretical and

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empirical research, and actual negotiation practice (see e.g., Albin 2001; Deutsch 1985; Konovsky 2000). Druckman and Albin also developed coding categories for types of agreements, namely, whether they were forward-looking (FL) or backwardlooking (BL). Complete texts of all the agreements were assembled from web documentation for coding DJ and FL/BL. The agreements varied in length from 5 (the agreement between the government of Nicaragua and YATAMA) to 52 pages (the agreement between the Republic of Rwanda and the Rwandese Patriotic Front). Although longer texts are likely to provide more opportunities for statements that relate to justice to appear, our emphasis on centrality of the principles, rather than frequency of their appearance in the text, reduces the problem. Each agreement was examined for the presence of each DJ principle – equality, proportionality, compensation, or need. Three other variables were included in the data set: implementation (failure, partial success, and success), difficulty of the conflict environment (number of warring parties, likelihood of spoilers, number of soldiers, and access to disposable resources), and willingness of neighbors to intervene in the conflict or to provide resources. This study evaluated a number of hypotheses. The literature presents competing hypotheses about how DJ relates to stability – that basing agreements on DJ either increases (based on arguments about root causes of internal conflict) or decreases (based on arguments about negotiating norms) their stability. These hypotheses were reconciled by including the difficulty of the conflict environment. The authors hypothesized further that the root causes argument holds in less difficult environments; the normative argument holds in more difficult conflict environments. Variation among the cases on the conflict difficulty variable provided an opportunity to evaluate these contending hypotheses. Hypotheses were also evaluated concerning the effects on stability of each of the DJ principles, which we considered as being either forward (equality and proportionality) or backward (compensation and need) looking. In particular, the forwardlooking principles were expected to occur more frequently than backward-looking principles in the agreements. They were also expected to produce more stable agreements. A final hypothesis posited that forward-looking outcomes – which may include forward-looking justice principles – would be more stable than outcomes which deal primarily with the past. The results can be summarized as follows. The strongest relationship was between the difficulty of the conflict environment and stability: Less stable agreements occurred in more difficult environments (r =
0.65). A moderately strong correlation was obtained between justice and stability (r = 0.56). However, these relationships changed when partial correlations were calculated. A slightly reduced correlation between difficulty and stability was obtained when justice was controlled (from
0.65 to
0.57). A reduced correlation was also obtained between justice and stability when difficulty was controlled (from 0.56 to 0.46). Similar results were obtained from a regression analysis that included the difficulty, justice, and stability variables. These variables form a cluster as indicated by the results of a factor analysis. The willingness variable did not load on this factor, nor did it produce any significant correlations with the other variables.

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These findings suggest that when justice principles are central to an agreement, the impact of more (less) difficult environments on stability is reduced (enhanced). In technical terms, justice was shown to mediate the relationship between the difficulty and stability variables. This means that DJ contributes to the stability of peace agreements. That contribution is indirect in the sense of reducing the negative effects of intense conflicts on stability or increasing the positive effects of less intense conflicts. These findings provide some support for the root causes argument: addressing issues of DJ in outcomes contributes to the shelf life of an agreement. They do not support the normative argument: addressing DJ issues did not interfere with implementation of the agreement. Further investigation provided additional clarification for these findings. Analyses conducted on each of the four DJ principles revealed that one principle in particular accounted for the relationships between difficulty, DJ, and stability. This was the principle of equality, which was also the most frequently-occurring principle in the agreements. When equality was analyzed separately, the same relationships among the variables emerged: like DJ, equality was shown to mediate the relationship between difficulty of the conflict environment and stability. In fact, the relationships between each of the other variables and equality were stronger than they were when DJ (measured as an aggregate of the four principles) was used as the justice variable in the analyses – the DJ-stability correlation was 0.56; the equality-stability correlation was 0.76. The inclusion of the other principles actually depressed the relationships with the difficulty and stability variables. Each of the other DJ principles (proportionality, compensation, and need) showed very weak relationships with stability. Thus, equality accounted for (or mediates) the relationship between DJ and stability. These findings are summarized in Fig. 1. They suggest that the relationship between difficulty (referred to as an independent variable [IV]) and stability (referred to as the dependent variable [DV]) depends on equality principles (referred to in Fig. 1 as the mediator [M]). Thus the negative effects of difficulty on stability are

M Principle of Equality

IV Difficulty of Conflict

DV

Direct Effect

Fig. 1 The mediating effect of equality on agreements

Stability of Agreement

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reduced when equality is central to the agreement; they are increased when equality is not central to the agreement. The variable referred to as forward and backward-looking (FL/BL) outcomes was also analyzed. The findings show a strong relationship between this variable and stability: More forward-looking outcomes are more stable (r = 0.66). However, that relationship was also shown to be accounted for by the equality principle: When equality was statistically controlled, the relationship between FL/BL and stability decreased dramatically (from 0.66 to 0.38). The mediator analysis showed a significant indirect effect for equality (Sobel’s z = 1.96, p u({a, d}) ¼ 11 and therefore {b,c} being preferred to {a,d} for utility function u0(.), which is also consistent with the ordinal preferences, one gets u0({b, c}) ¼ 8 < u0({a, d}) ¼ 9. Hence {a,d} is preferred to {b,c}. The second property that we focus on is envy-freeness, perhaps the most important condition in the fair division literature (Brams and Taylor 1996). Intuitively, an allocation is envy-free if each player weakly prefers her own set of items to the other player’s set. This ensures that there is no pressure on the players to swap their sets of items with other players and guarantees a certain kind of stability. Given our ordinal Table 1 Pareto-optimality Pi a b c d

u(.) 10 8 6 1

u0(.) 7 5 3 2

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approach, however, we must define envy-freeness carefully. Of course, the concept can be easily applied if every player receives exactly one item. For example, if X ¼ {a,b} and the preferences are aPAb and bPBa, respectively, then there is one obvious envy-free allocation, namely, assigning {a} to A and {b} to B. Should the players receive larger sets of items, then things are getting more complicated and preferences over X are necessary. The extension of envy-freeness to larger sets without detailed preference information over X, therefore requires a more thorough elaboration. Similar to our previous discussion on lifting preferences over X to preferences over X, in the literature the focus is on item-wise comparisons between different sets. This concept has been called “pairwise dominance” by Brams and Fishburn (2000), Brams et al. (2003), Edelman and Fishburn (2001), Bouveret et al. (2010), and Aziz et al. (2015), and “ordinal fairness” by Pruhs and Woeginger (2012). Intuitively this means that a set S is pairwise dominated by set S0 if for every item x  S there is an item y  S0 such that y is preferred to x by the player. Hence, formally envy-freeness can be written as follows: Property 2 (Envy-Freeness) An allocation π is envy-free (EF) iff there exist injective mappings fA : π(A) ! π(B) and fB : π(B) ! π(A) such that xPAfA(x) for all x  π(A) and xPBfB(x) for all x  π(B).1 This definition of EF is rather strong in the sense that it holds for all cardinal utilities consistent with the ordinal preferences. Therefore, it is sometimes called necessary envy-freeness. In analogy to Pareto-optimality, there also exists the concept of possible envy-freeness, where it is sufficient that there exists at least one cardinal utility representation that leads to envy-freeness (see, e.g., Aziz et al. (2015)). Obviously, envy-freeness is a property that cannot be satisfied in all situations. Consider again the previous example in which X ¼ {a,b}, but now assume that both players strictly prefer a over b. Then no allocation is (even possibly) envy-free. If π(A) ¼ {a} and π(B) ¼ {b} then B envies A, if the allocation switches items, then A envies B. There is another property that can be important in the fair division of indivisible items. It is concerned with a maximin concept, i.e., with guaranteeing the best possible outcome for the worst off player. This can be seen in the tradition of Rawls (1971), where – behind a veil of ignorance – one might ask that the procedure takes into account explicitly the worst off player. One possibility to do so is to look at the lowest ranked item of a player’s received set of items. Whenever we are in situations where, e.g., a team very much depends on its weakest link, this seems to be a reasonable demand. In principle, this property, called maximinality, does not

1

There may be several distinct injective mappings that guarantee EF. In addition, it is not necessary that the injective mappings fA and fB are inverses. Should EF be guaranteed by a bijection, then this can be done using a canonical bijection in the following form: Order A’s assigned items according to A’s preference and then order B’s items according to A’s preference. The bijection maps the kth item on the first list to the kth item on the second list.

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depend on any explicit extension of the players’ rankings. It can easily be determined from the ranks of Pi for all x  π(i). Property 3 (Maximinality) An allocation π is maximin (MX) iff there is no other allocation π 0 such that max i  fA,Bg r i ðπ 0 ðiÞÞ < max i  fA,Bg r i ðπ ðiÞÞ. In the literature one also finds a second maximinality property based on the widely-used Borda score which assigns points to the items according to their positions in a player’s ranking. This can be seen as a sort of cardinalization of a player’s ordinal preferences. Hence it is possible, assuming additive preferences, to assign a value to any set of items a player receives. Based on those values one can also require an allocation to maximize the minimum value of the sets of items assigned to the players. This is called Borda maximinality and, e.g., discussed and applied in Kilgour and Vetschera (2017, 2018), Baumeister et al. (2017), and Darmann and Klamler (2016).2 Obviously, other properties can also be given a Borda-type definition, e.g., Kilgour and Vetschera (2018) use the properties of Borda-efficiency and Borda envy-freeness. Clearly, allocations that satisfy the ordinal versions of the above properties need not satisfy the Borda versions of it and vice versa. Kilgour and Vetschera (2018) show that in case of four items, whenever an allocation exhibits the ordinal properties, it also exhibits the Borda properties, whereas the contrary only holds in approximately half of the allocations. Interestingly, this relationship reverses when the number of items increases, because for 12 items, only 17% of the allocations satisfying the ordinal properties also satisfy the Borda properties, whereas it is about 75% for the other way round. Many other properties also have been discussed, usually originating in the cakecutting literature, such as proportionality or equitability. In principle, those properties do not apply in situations with purely ordinal preferences as assumed here. Equitability requires that an allocation assigns exactly the same utility to each of the players (and therefore needs precise cardinal utility information). Proportionality demands that, in case of q players, the allocation assigns to each player a share that she values at least 1/q of the total resource. However, certain properties can – at least to some extent – be transformed to the present ordinal framework. For example, Aziz et al. (2015) use concepts based on the stochastic dominance relation and apply it to envy-freeness and proportionality. In that respect, they are able to determine properties alluding to certain fairness ideas in different forms of strength. In addition, they investigate the necessary computational effort to check for the existence of allocations satisfying the respective properties. Finally, a very prominent property in the fair division literature (used in particular by economists in the field of mechanism design) is strategy-proofness, i.e., that telling the truth is a dominant strategy for all players. This is of course a rather strong

2

See also Darmann and Klamler (2019) for a critical discussion of using the Borda count to rank sets of items.

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condition and usually too strong to be satisfied by procedures in the literature on the fair division of indivisible items. Moreover, it is often based on the assumption that players have complete information about the other players’ preferences. However, if it is assumed that players are not fully informed about other players’ preferences, and they are sufficiently risk-averse, then a weaker property might be of interest. It requires that only announcing her true preferences guarantees a player a 50% share, i.e., a player (weakly) prefers her set of items to the other player’s set of items. In principle it says, that misstating one’s preferences might backfire in case a player makes a mistake concerning the other player’s preferences (see also Klamler (2014) for the possible impact of small mistakes when using certain voting rules). In particular, for a twoplayer situation, we say that a procedure is truth-inducing if sincerity is the only strategy that guarantees a player a 50% share for any preferences of the players. Vetschera and Kilgour (2013) analyze the strategic behavior for a special class of fair division procedures allowing the players to use various different strategies. In general, our goal now is to find allocations that satisfy, insofar as possible, the three aforementioned properties. Because the application of the above properties might not be possible otherwise, our focus will mostly (but not always) be on complete, balanced allocations. Hence, we assume that there is an even number of items, i.e., n is even, and n/2 of the n items are assigned to A, and the other n/2 items are assigned to B.

What Is Possible? Before we look in detail at fair division procedures, it may be important to see what are the restrictions of the framework used in this study in terms of which results can actually be achieved. As mentioned in the previous section, fair division is based on players’ ordinal rankings over the set of items, X. In particular, it is envy-freeness, as defined above, which might be out of reach even for more than two items. Consider the following example: Example 2 Let there be two players, A and B, and a set of items X ¼ {a, b, c, d, e, f}. The preference rankings of the players, (PA,PB), are given in the first two columns of Table 2.

Table 2 Envy-Freeness PA a b c d e f

PB b c d e a f

P0A

P0B

P00A

P00B

a b c d e f

b c a f e d

a b c d e f

b c d a f e

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Obviously, in case the players have the same item bottom ranked (here item f ), there is no complete allocation which guarantees envy-freeness, because one of the players will receive item f and hence there does not exist a one-to-one function as used in the definition of envy-freeness. This also occurs in other situations. Consider the
ranking profile P0A , P0B presented in the third and fourth column of Table 2. Either player A or player B has to get two out of the top three items (which are the same for both players). Again, no one-to-one function can be generated to guarantee envyfreeness. Finally, consider ranking profile ðP00A , P00B Þ. Allocation ({a, c, e}, {b, d, f}) does satisfy envy-freeness, because there are one-to-one functions for both players such that every item in a player’s own set is preferred to an item in the other player’s set. The problem that one of the above properties can never be satisfied occurs only with envy-freeness. Pareto optimality and maximinality can (also jointly) always be satisfied. Intuitively, for any preference profile one can always find the rank at which all items come up in either one of the rankings of the two players. Assign all items below that rank in the ranking of one player to the other player. Finally, assign the remaining items in such a way that no Pareto improvement is feasible. Because this is always possible, such an allocation does exist in all cases. Kilgour and Vetschera (2018), in their computational study, analyze for up to 12 items how frequently the above properties are satisfied in all balanced allocations. The fractions do decline rapidly with the number of items, showing that only about 10% of the balanced allocations are envy-free even for problems with four items. In the case of 12 items, almost none of the balanced allocations do satisfy envy-freeness or Pareto-optimality, whereas still around 18% of the allocations are maximin. Hence, in some sense, finding allocations that satisfy all of the above properties becomes finding a needle in a haystack. Getting back to envy-freeness, how can we guarantee whether an envy-free allocation does exist or not? Brams et al. (2014) provide simple conditions that can be used to identify the existence of envy-free allocations in a two player situation. Definition 1 (Condition C(k)) The set of A’s top k items is identical to the set of B’s top k items, i.e., SkA ¼ SkB . Returning to the above example, with preferences given in Table 2, in ranking 3 profile (PA,PB) it
is the case that C(k) is only satisfied for k ¼ 5 and k ¼ 6. In ranking 0 0 profile PA , PB it is only satisfied for k ¼ 3 and k ¼ 6. Finally, in ranking profile ðP00A , P00B Þ the condition is satisfied for k ¼ 4 and k ¼ 6. There is, however, a precise difference in when satisfying the above condition guarantees envy-freeness. This can be stated in the following condition:

It is obvious that for k ¼ n the condition C(n) always has to be satisfied, because the top n items have to be the same for both players by definition.

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Definition 2 (Condition D) Condition C(k) fails for every odd value of k.4 Brams et al. (2014) prove that the existence of a complete, envy-free, and maximin allocation and the satisfaction of condition D are equivalent. Hence, this provides a simple, and also computationally easy, way of determining whether the application of any of the procedures discussed below can lead to an envy-free and maximin allocation at all. When looking at individual players, it is also easily possible to determine whether a player envies the other player or not. In that respect, one only has to compare the assigned set of items to a player with her preference ranking. A player does not envy the other player if for any odd rank in the preference, at least half of the items up to that rank are assigned to that player, because then a one-to-one function, as used in the definition of envy-freeness, can be generated. Going back to player A’s preference PA in Table 2, assigning set {a,b,e} does not create envy for player A. At rank 1, the item a (and therefore more than half of the items up to that rank) is assigned to A. At rank 3, a and b are given to A, and therefore again more than half of the items up to that rank. Finally, at rank 5, {a,b,e} is allocated to A, hence three of the first five ranked items, which also is more than half of them. In contrast, the set {a,d,e} allocated to A might create envy because at rank 3 only one (item a) out of the first three items is assigned to A. Hence, there exist utility values consistent with the ordinal rankings that make A envy B. Whether, in general, envy-free allocations are possible or not, also depends on how highly the preferences of the players are correlated. Higher correlation usually leads to fewer possibilities for “good” solutions with respect to the properties discussed before. Kilgour and Vetschera (2018) analyze the performance of various procedures based on the correlation between preferences. In addition, they show – using computational simulations – that the fraction of allocations satisfying all of the above properties quickly decreases with problem size, i.e., the number of items to be divided.

Procedures In this section we will introduce and discuss various procedures used for the allocation of indivisible items. One approach would be to explicitly look at the complete rankings ≿A and ≿B of the players as, e.g., done by Herreiner and Puppe (2002). Their procedure, called descending demand uses the idea of fallback bargaining by Brams and Kilgour (2001) and simultaneously goes down the individual rankings until for the first time the respective demands of the two players can both be satisfied. The procedure provides a Pareto-optimal but not necessarily envyfree allocation. 4

Brams et al. (2016) provide an even simpler condition (called condition DS) which restricts the application of condition D to specific values of k.

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As we have discussed before, ranking all subsets is a difficult task. However, it allows players to present their preferences in a precise way, i.e., all sorts of complementarities and substitutabilities can be expressed. Denying a direct expression of preferences over X, a very elegant approach, called adjusted winner (AW), has been devised by Brams and Taylor (1996). They consider their procedure to be applicable in all sorts of real-world situations, such as divorce settlements, divisions between heirs, or negotiations between companies thinking about a merger, just to name a few. In their procedure, they allow the players to assign values to the single items and assume the previously discussed additivity condition to hold. The procedure, however, relies on one additional and essential assumption, namely, that eventually one of the items can be divided if necessary (whichever item this is). This could be seen as restrictive, but it also enables the satisfaction of attractive properties such as Pareto-optimality, envy-freeness, and equitability. In addition AW is also attractive with respect to the computational effort necessary to calculate a solution because it can be considered computationally easy. Let us now introduce the adjusted winner procedure in detail: Procedure 1 (Adjusted Winner) 1. Each player receives 100 points to be distributed among the items. Based on the assigned points, each item is provisionally allocated to the player that assigned more points to it. In case of a tie, the item is allocated randomly. 2. Add, for each player, the values of the items provisionally allocated. If the sum is equal for both players, the provisional allocation becomes the final allocation. In case the sums are different, certain items will be transferred. Start with the item that has the lowest point-value ratio, i.e., the lowest ratio of all the items allocated to the player with the currently higher total sum when dividing its assigned value by the value assigned by the other player. Now the new total sums are determined. Should it still be higher for the first player, the item with the nextlowest point-value ratio is transferred. Is it the same, the procedure terminates. Proceed to the final step, if, after the transfer, the receiving player has a higher total sum. 3. Divide the last transferred item between the two players such that the total sums of the players are equal. The following example illustrates the functioning of the AW-procedure: Example 3 Let there be two players, A and B, and 7 items, X ¼ {a, b, c, d, e, f, g}, to be distributed among the players. The value attached to an item x  X by player i is given by vi(x) and stated in the second and third column in Table 3. The last column gives the value ratio vA(x)/vB(x) for the items provisionally allocated to player A (which originally receives more points than player B). Given the points assigned to the items by the players, according to step 1 each player receives the items that she values more than the other player. Hence, player A is provisionally assigned the set of items SA ¼ {b, c, e, g} and player B the set of

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Table 3 Application of AW-procedure Item a b c d e f g

vA(.) 10 20 30 5 15 10 10

vB(.) 20 12 20 10 5 25 8

vA(.)/vB(.) – 1.67 1.5 – 3 – 1.25

items SB ¼ {a, d, f}. This gives a total sum of values of 75 to player A and 55 to player B. Because those values are different, step 2 requires to transfer an item (or several items) from A to B starting with the item which has the lowest value-ratio vA(x)/vB(x), i.e., item g with a value-ratio of 1.25. After the transfer, the new allocation is S0A ¼ fb, c, eg and S0B ¼ fa, d, f , gg with new total sums of 65 and 63, respectively. Hence, as those values are still not equal, we have to continue by transferring the item with the next lowest value-ratio, item c. As a full transfer from A to B would make B the player with the larger total sum, the procedure moves to step 3 and item c becomes the item to be divided. This is done by calculating the share to be transferred such that the total sums of the players are equalized. Formally this means to solve for α in the equation 20 + 15 + (1  α)  30 ¼ 63 + α  20, leading to α ¼ 0.04. Therefore 4% of item c need to be transferred from A to B. This leads to total values of 63.8 for both players. As shown by the example, there is an obvious trade-off between the attractiveness of the AW procedure in satisfying many interesting properties and the necessity that all items are, in principle, divisible. Should this possibility of dividing every single item not exist, then things become more complicated. In addition, the procedure requires that players are able to assign precise values to the items. Again, in case this is not reasonable, an alternative needs to be found. But what are the options in case any of the above problems of (1) not being able to rank all sets of items in the descending demand procedure, (2) not being able to eventually divide an item, and (3) not being able to assign precise values to the item as in the AW procedure, are binding? A simple class of procedures that overcomes those problems, at a certain cost, is introduced in the following subsection.

Picking Procedures Assume a group of children wants to play basketball. Obviously, they have to split themselves into two teams. So, how are they usually doing this? A very common approach is that two team leaders are selected and then they sequentially pick players from the available pool of remaining children. Hence, if the team leaders are called A and B, then such a sequential procedure can be seen as a sequence ABABABAB. . ., meaning that A picks the first child, then B picks a child from those left, then A picks

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again, and so on. The procedure that lets the players alternatively pick from the remaining items can be stated as follows: Procedure 2 (Picking Procedure) 1. Player A chooses an item from the remaining items. If there are no items left, stop the procedure. 2. Player B chooses an item from the remaining items. If there are no items left, stop the procedure. Otherwise return to step 1. Of course, this process can easily be extended to more than two players and is, in principle, very simple to apply. We can illustrate the functioning of the procedure using the following example: Example 4 Assume two players, A and B, a set of six items, X ¼ {a, b, c, d, e, f} to be allocated, and strict rankings PA and PB over the six items for the two players which are the same, given in the first two columns of Table 4: If the procedure is given by the sequence ABABAB, then A picks a first, then B picks b, then A picks c, and so on. The outcome of this procedure will be the allocation ({a, c, e}, {b, d, f}). Obviously, the allocation is Pareto-optimal (as any sincere allocation would be in that example), but it is not envy-free according to the definition given before. Actually, it is not even possibly envy-free, as there is no utility function respecting the ordinal preference of player B for which the set {b, d, f} is considered of higher value than the set {a, c, e} as long as no complementarities and/or substitutabilities exist. If, however, the preferences were completely the opposite as in preference profile
P0A , P0B , then A would first pick a, B would pick f, A then b, and so on. The final allocation is, therefore, ({a, b, c}, {f, e, d}). Again, this allocation is Pareto-optimal, but now also envy-free. Although picking procedures are computationally easy, the first situation in the previous example shows an immediate fairness problem of the above procedure. Obviously, the player going first (A in the example) has an advantage. There is a possibility to avoid such problems by changing the sequence in which the players can pick the items. It seems reasonable to compensate the player who cannot pick first by giving her two picks in a row. Hence the sequence might look like ABBAAB. Table 4 Preference rankings – picking procedure PA a b c d e f

PB a b c d e f

P0A

P0B

P00A

P00B

a b c d e f

f e d c b a

a b c d

b c d a

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In case both players have the same strict ranking, this would lead to the allocation ({a, d, e}, {b, c, f}) which is not necessarily envy-free, but possibly envy-free. Picking procedures also have the advantage that despite their simplicity they always guarantee Pareto-optimal outcomes. In general, Brams and King (2005) show that an allocation is Pareto-optimal if and only if it can be obtained from a sequence of sincere choices by the players. Hence, any picking procedure leads to a Paretooptimal allocation. Given the simplicity of such procedures using picking sequences, it would be interesting to analyze the social welfare consequences of different picking sequences. Bouveret and Lang (2011) determine for various different welfare functions and preference distributions, what are the optimal picking sequences. Picking procedures are, however, easily manipulable (see, e.g., Brams and Taylor (1999)) as demonstrated by the following example: Example 5 Consider preference profile ðP00A , P00B Þ in Table 4. If A goes first according to her true preferences, then she will start by choosing item a, then B will choose b, A will again choose c and finally d is assigned to B. This leads to an allocation of {a,c} to A and {b,d} to B. However, if A chose b in the first round, then B would have to choose c. Hence, A would take its top-ranked item a in the second round leaving d for B. The final allocation would therefore be {a,b} to A and {c,d} to B. Because {a,b} is preferred to {a,c} by player A, such a manipulation would be beneficial to A (but makes B worse off).

Contested Pile Procedures Further procedures have been devised to allocate the indivisible items in a series of stages. But, instead of acting sequentially as in picking procedures, now in each stage the players simultaneously request a certain item (or a specific number of items). The procedure then determines whether the item is actually allocated or shifted into a contested pile (CP) which may or may not be dealt with in a later stage. Brams and Taylor (1996) introduce a very simple procedure that aims at allocating items only insofar as they are not contested. The final allocation is therefore incomplete as some of the items are left aside. The procedure, called BT, works as follows: Procedure 3 (BT) 1. The players (A and B) simultaneously name their most preferred item of those not yet allocated. 2. In case the players name different items, each item is assigned to the player who named it. In case they name the same item, it is assigned to the contested pile. 3. If there are items not yet allocated to the players or the contested pile, move to stage 1. Otherwise stop the procedure.

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Let us apply BT in the following example: Example 6 Let there be two players, A and B, and a set of four items, X ¼ {a, b, c, d}. The
following Table 5 provides two different preference profiles, (PA, PB) and P0A , P0B : Consider preference profile (PA, PB). In step 1, A names item a and B item b. Hence, step 2 of the procedure assigns a to A and b to B. As there are still items c and d left, step 3 requires the procedure to restart with step 1. Now both players name item c, which is therefore put into the contested pile. Because there is only one item (d) left, both name this item which again is put into the contested pile. Hence, the final allocation is incomplete, giving a to A, b to B, and {c, d} to CP. Actually no item is allocated to a player in case the preferences are identical as in
preference profile P0A , P0B of Table 5, because all items are contested. The example shows the problem of the BT procedure. It may be highly incomplete depending on what the preference profile looks like. This, of course, depends again on how strongly the preferences are correlated. Nevertheless, the BT procedure seems rather unsatisfactory. In the literature, two approaches have been undertaken to tackle the problem of incompleteness. One, called AL and introduced by Brams et al. (2014), aims at reducing the size of the contested pile by allocating the items in a more elaborated way. The second, called undercut procedure and devised by Brams et al. (2012), tries to allocate the contested pile in a certain way. Let us first start with AL, defined in Brams et al. (2014), and here presented in a slightly simpler version: Procedure 4 (AL) 1. Let t ¼ 0. 2. If no unallocated items remain, stop. If one unallocated item remains, place it in CP and stop. Otherwise, compare A’s and B’s most preferred unallocated items. If they are the same, go to step 3. If they are different, assign each player its most preferred item, set t ¼ t + 1, and repeat step 2. 3. Let the unallocated item, that both players most prefer, be x, called the tied item, and let yi1, yi2, . . . represent, in order of i’s preference, i  {A, B}, the unallocated items that i finds less preferable than x, called the compensation items. Table 5 Preference rankings – BT PA a b c d

PB b c d a

P0A

P0B

a b c d

a b c d

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4. Consider the assignment of x to B and the first compensation item, yA1, to A. Such an assignment is feasible as long as the number of items (defined as stB) assigned to B (including x) or unassigned, that A prefers to the compensation item it receives, yA1, is at most t, i.e., stB  t. If stB > t, then no assignment of x to B is feasible and move to step 5. If stB  t, then check for assignments of other compensation items to A in descending order until, for the first time, stB > t . Continue for all feasible assignments by setting t ¼ t + 1 and moving back to step 2. 5. Consider the assignment of x to A and the first compensation item, yB1, to B. Such an assignment is feasible as long as the number of items (defined as StA) assigned to A (including x) or unassigned, that B prefers to the compensation item it receives, yB1, is at most t, i.e., stA  t. If stA > t, then no assignment of x to A is feasible and move to step 6. If stA  t, then check for assignments of other compensation items to B in descending order until, for the first time, stA > t . Continue for all feasible assignments by setting t ¼ t + 1 and moving back to step 2. 6. If neither the assignment of x to A nor to B is feasible, then put x in CP. Return to step 2 for the remaining unallocated items. What can be observed is that AL more carefully checks whether an item should be assigned to the contested pile than BT does. In principle, it does not only depend on whether the players name the same item but also on what their preferences exactly look like. The difference can be seen in the following example: Example 7 Let X ¼ {a, b, c, d}, C
X denote the contested pile, and players A and B have preferences as stated in profile (PA,PB) of Table 5. As discussed before the BT allocation of BT is SBT A ¼ fag, SB ¼ fbg and C ¼ {c, d}. Applying AL, however, we first assign a to A and b to B. In step 2, both players next prefer item c. Moving to step 3, for player A there is only one more item (d ) which is less preferred than c. However, if we assigned d to A, there are 2 > t ¼ 1 items (b and c) that A prefers to d and are not assigned to A. Hence, we cannot assign d to A. If we assigned d to B, there is only one item (c) which B prefers to d and is not assigned to B. This AL assignment is therefore feasible. The final AL allocation is SAL A ¼ fa, cg , SB ¼ fb, d g and C ¼ Ø. Thus, the example shows, that there are situations where AL provides a complete allocation while BT does not. Brams et al. (2014) show, that under AL always at least as many items are allocated to the players than under BT. In addition, an AL allocation is a maximal EF allocation, i.e., there is no other envy-free allocation which allocates more items to the players. Both, AL and BT, are also locally Pareto-optimal, i.e., if we only consider the items assigned to the players, there is no other assignment of exactly those items that dominates the AL or BT allocation. This restriction is necessary, because in cases of a non-empty contested pile, any distribution of the items in the contested pile would always lead to domination if all items are considered valuable. One downside of the procedures, which is, however, a general problem, is their manipulability. Should the players have complete information about the other player’s preferences, then there are occasions in which a player can benefit from misstating her preferences.

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The second approach to reduce the incompleteness of the BT allocation is to eventually (if possible) distribute the items in the contested pile among the players. Brams et al. (2012) do so by using the undercut procedure (UP) which is based on the concept lying behind the ultimatum game, in which one player (say A) proposes a division of money and the other player (say B) can either accept the division or reject it. UP uses an extension of this by allowing player B not only to reject the proposal but also directly implement a division which “undercuts” the original division. For example, if A proposes to divide 100 dollar by giving 70 to A and 30 to B, then B could directly implement a division of 69 to B and 31 to A by undercutting A’s proposal. From a game-theoretic point of view, this would lead to two subgameperfect Nash equilibria. Either A proposes a 50–50 split and B accepts, or A proposes a 51–49 split and B undercuts with a 50–50 split. Now, UP consists of two stages, the query steps in which items are allocated either to A, B, or the contested pile and the stage in which the items in CP are distributed. The query steps are actually identical to the BT procedure, which has been discussed before. For the distribution of the items in CP, however, a few additional concepts are required. Because UP needs to compare sets of items in a specific way, the following definitions are necessary to formally define UP. The first definition compares sets of items in a simple way based on the ordinal preference information. Definition 3 Take any two subsets S, T
C. We say that T is ordinally less than S if T  S or if T can be obtained from S, or a proper subset of S, by replacing items originally in S by equally many lower-ranked items (see also Taylor and Zwicker 1999). It will be important to know whether players get individual shares they value at least 50% in their own view. For sets of indivisible items such a concept can be defined as follows: Definition 4 For any set S
C, let S denote the complement of S, i.e., S [  S ¼ C and S \  S ¼ Ø. Player i regards S as worth at least 50% if S≿i  S, i.e., she finds S at least as good as its complement S. Obviously, when looking at sets of items, the precise value of the sets cannot be determined without at least attaching values to the items and assume certain additivity conditions. However, given the previous two concepts, one can define a very useful set of items, called minimal bundle, which has a value “close” to 50%. Definition 5 A player regards a subset S as a minimal bundle if (i) S is worth at least 50%, and (ii) any subset T  C that is ordinally less than S is worth less than 50%. Given the above definitions, the rules of the undercut procedure (UP) can now be stated as follows (see also an extension by Aziz (2015) allowing for more general properties to be satisfied):

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Procedure 5 (Undercut Procedure) 1. Apply the BT-procedure to the set X. This leads to an assignment of the items either to player A, to player B, or to the contested pile, C. 2. If the contested pile is empty, i.e., C ¼ Ø, the procedure ends. Otherwise, both m players identify all of their minimal bundles in C, denoted by Cm A and CB , respectively. m 3. If Cm A ¼ CB , there is no envy-free allocation of the contested pile unless they consider a bundle S and its complement S as minimal bundles, i.e., S,  S  Cm A and S,  S  Cm B . In this case, give S to one player and S to the other player. Otherwise the procedure ends without a division of the contested pile. m 4. If Cm A 6¼ CB , let them order their minimal bundles from most to least preferred. Randomly a player (say A) announces her top ranked minimal bundle T  Cm A . If m 0 also T  Cm , then B announces her top-ranked minimal bundle, T  C . Repeat B B m this if necessary. As Cm A 6¼ CB , eventually one minimal bundle of one player will not be a minimal bundle of the other player. This becomes the proposal. 5. Assuming the proposal to come from player A, player B has two options: (i) accepting the complement of player A’s proposed minimal bundle (the best response if it is worth at least 50% to her) or (ii) undercutting player A’s proposal, i.e., taking for herself the best subset that is ordinally less than player A’s proposal, in which case the complement of player B’s subset is assigned to player A. The procedure ends. Let us illustrate UP with the following example: Example 8 Assume a set of items, X, and two strict rankings over X of the two players which, after application of BT, leave a contested pile of C ¼ {a, b, c, d, e}
X. If we assume sincere behavior, then both players rank the items in the contested pile the same, e.g., aPibPicPidPie for i  {A, B}.5 Consider a situation in which the minimal bundles are such that fa, bg  Cm 2Cm A and fa, bg= B . Moreover, let m fb, c, d, eg  CB . If A offers the division ({a, b}, {c, d, e}), i.e., bundle {a,b} to player A and bundle {c,d,e} to player B, then player B will reject this proposal because the set {c,d,e} must be worth less than 50% given that {b,c,d,e} was a minimal bundle for her. Hence player B will undercut by proposing ({b,d,e},{a,c}), i.e., bundle {a,c} to herself and bundle {b,d,e} to player A. Because fb, c, d, eg  Cm B , bundle {b,d,e} must be worth less than 50% and therefore {a,c} is worth more than 50% to player B. As fa, bg  Cm A , bundle {a,c} must be worth less than 50% to player A and hence {b,d,e} is worth more than 50% to her. This guarantees an envy-free division of the contested pile. If, in addition, we assume positive responsiveness (a

5

Observe that, after application of BT, the items in the contested pile are ranked in the same way by the two players (but not necessarily having the same positions in the original rankings of all items before applying BT).

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weaker condition than additivity), i.e., if, for S \ S0 ¼ Ø and T \ T0 ¼ Ø, S ≿ T and S0 ≿ T0 then S [ S0 ≿ T [ T0, the final allocation under UP is also envy-free. Brams et al. (2012) prove that there is a nontrivial envy-free split6 of the contested pile if and only if the sets of minimal bundles of the players are not identical, i.e., one player has a minimal bundle that is not a minimal bundle of the other player. In addition, in this case UP implements an envy-free split. Obviously UP is not strategy-proof, as can be easily shown (see, e.g., Brams et al. 2012). The following example indicates, however, that UP is truth-inducing, i.e., a player could be worse off (and therefore receive a set of items valued less than 50%) by misstating her preferences. Example 9 Suppose that fag  Cm A , i.e., {a} is a minimal bundle for player A, but A proposes the split ({a,b},{c,d,e}), where, obviously, fa, bg= 2Cm A . There are two possibilities now for player B: (1) If {c,d,e} is worth at least 50% to player B, she will accept the proposal and player A is better off than had she told the truth. (2) If, however, B undercuts (because {c,d,e} is less than 50% for B), the new split would definitely have to be ({b,d,e},{a,c}). This leads to the bundle {b,d,e} assigned to A, which she values less than 50%. Because {a} was a minimal bundle, {b,c,d,e} was less than 50% already. Vetschera and Kilgour (2013, 2014) discuss and analyze contested pile procedures. In particular, Vetschera and Kilgour (2013) is concerned with the strategic behavior in contested pile procedures. They specify various different strategies that players could have when applying the procedure. Using computer simulations, they show that strategic behavior can indeed have an impact on the performance of contested pile procedures. The impact, however, can be mixed, i.e., it is not necessarily negative neither with respect to efficiency nor to envy-freeness. Among their considered manipulation strategies, they were able to show that it is not necessarily the most sophisticated strategy that has the largest effect, at least under certain assumptions about the number of items and the correlation among players’ preferences. Vetschera and Kilgour (2014) focus on some general features of contested pile procedures and show that the undercut procedure outperforms alternative procedures in fairness and efficiency. Using their experimental framework, especially for a moderate (but not too small) size of the contested pile, UP seems to be a promising approach. One particular problem though is the number of minimal bundles, which increases exponentially in the size of the contested pile, and this size very much depends on whether the players’ rankings of the items are highly correlated or not. If, on the other hand, the contested pile is very small, then, however, there is a significant chance that the undercut procedure will not provide a solution. For example, in case the contested pile contains five items, there is only a 50% chance

6

An envy-free split is trivial if each player values its subset at exactly 50%.

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that a solution is found, i.e., a minimal bundle for one player exists which is not a minimal bundle for the other player.

Procedures Without Contested Piles Although the use of contested piles can take the pressure from having to assign all items (at least immediately), there exist rather simple procedures that do guarantee envy-freeness, efficiency, and maximinality whenever allocations satisfying those properties exist. However, they usually will terminate whenever “good” allocations do not exist at all. Hence, their outcomes may also be incomplete.7 The first procedure was introduced in Brams et al. (2016), called singles-doubles procedure (SD). It is based on two simple concepts, namely, items called singles and doubles, which can be defined based on the maximin rank m, which, for any ranking profile (PA,PB) is given by m(PA, PB) ¼ maxx  Xmini  {A, B}ri(x), where ri(x) is the rank of item x in Pi. The definitions of singles and doubles are as follows: Definition 6 Let the maximin rank be m < n. An item is called a single if it is among the top m items for one player but not for the other player. It is called a double if it is among the top m items for both players. The procedure can now be stated in the following way: Procedure 6 (Singles-Doubles-Procedure) 1. Determine the maximin rank m. 2. Identify the singles and assign them to the respective players. Stop the procedure in case all items were singles and therefore have been allocated. 3. For each player, choose her most preferred unassigned double. If those are different, assign them accordingly. If it is the same double, check for the player who can be assigned her second-most preferred unassigned double while still guaranteeing envy-freeness. This can be easily done by checking whether at each odd rank k < n in a player’s ranking she receives strictly more than half of the items from her ranking up to that rank. Eventual ties are broken at random. If no allocation of that form can be made, terminate the procedure. 4. Return to step 3. Note that step 3 is similar to steps 4 and 5 in the AL-procedure. Brams et al. (2016) show that if the players’ preferences admit a complete EF allocation, then there is also a complete maximin EF allocation which will be found by the SD procedure. The SD procedure can be illustrated with the following example:

7

See Kilgour and Vetschera (2018) for an extension of the procedures that provide complete allocations in all cases.

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Table 6 SD-procedure

PA

PB

PA⬘

PB⬘

a

b

a

b

b

c

b

c

c

f

c

d

d

d

e

a

f

e

PA⬘⬘

PB⬘⬘ c

c d

d

d

a

Example 10 Let there be two players, A and B, and X ¼ {a, b, c, d, e, f}. The preference profile (PA,PB) is given in Table 6: The rankings of the players imply that the maximin rank is five, indicated by the horizontal line. That is, every item comes up in either A’s or B’s ranking up to that position. Let us first check whether an envy-free allocation does exist (see also the discussion in section “What is Possible?”). Hence, we have to check for every odd rank k whether the sets of items up to k for the two players are identical or not. For k ¼ 1, we see that {a} 6¼ {b}, for k ¼ 3 it is the case that {a, b, c} 6¼ {b, c, f}, and for k ¼ 5 we get {a, b, c, d, e} 6¼ {b, c, f, d, a}. Therefore, an envy-free allocation (which also has to be maximin) is possible. Given the maximin rank, it can be observed that there are two singles, items f (for player B) and e (for player A). Thus, we first assign the singles to the corresponding players. The remaining rankings of
the doubles are stated in profile P0A , P0B . Now, choosing the most preferred doubles, i.e., a for A and b for B, we see that they are different and can be assigned to the respective players. Profile ðP00A , P00B Þ provides the ranking of the remaining two doubles, c and d, which is the same for both players. Now, c has to be assigned to A, because otherwise A would possibly envy B given that at rank three there are more items assigned to B (items b and c) than to A (item a). Hence the final allocation is (a, c,e) to A and {b,f,d} to B. This is a Pareto-optimal, maximin and envy-free allocation. Obviously, SD might output multiple outcomes. However, any of those allocations satisfies the desired properties. One possible extension of the SD-procedure is to iteratively apply it to the reduced preference profiles of the players whenever some of the items have been assigned. This procedure, called iterated singles-doubles procedure (ISD) has been developed in Brams et al. (2016) and can be represented as follows: Procedure 7 (Iterated Singles-Doubles-Procedure)
1. Let t ¼ 0 and P0A , P0B be the ranking profile with m0 being the corresponding maximin rank.

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2. For PtA , PtB and mt determine the singles and assign them to the respective players. Stop the procedure in
case all items have been assigned. 3. Set t ¼ t + 1 and let PtA , PtB be the new ranking profile over the reduced set of items. If the lowest ranked items in PtA and PtB are different, go back to step 2, otherwise proceed to step 4. 4. For each player, choose her most preferred unassigned double. If those are different, assign them accordingly. If it is the same double, check for the player who can be assigned her second-most preferred unassigned double while still guaranteeing envy-freeness. This can be easily done by checking whether at each odd rank k < n in a player’s ranking she receives strictly more than half of the items from her ranking up to that rank. Eventual ties are broken at random. If no allocation of that form can be made, terminate the procedure. The functioning of ISD and its difference to SD can be illustrated in the following example: Example 11 Let there be two players, A and B, and X ¼ {a, b, c, d, e,
f, g, h, i, j}, i.e., there are ten items to be assigned. The preference profile P0A , P0B is given in Table 7:
The original ranking profile P0A , P0B has a maximin rank of m0 ¼ 9. Hence there is one single for A, item i and one single for B, item j, which are assigned accordingly.
Eliminate the assigned items to get to the reduced ranking profile P1A , P1B with maximin rank m1 ¼ 5. Allocate the singles to the players, i.e., {a,e,d} to A and {f,g,h} to B. Again, eliminate the
assigned items from the allocation process to get the new ranking profile P2A , P2B . The maximin rank now is m2 ¼ 1. Assigning the singles accordingly leads to a final allocation of {a,b,d,e,i} to player A and {c,f,g,h,j} to player B. As can be verified, this allocation is envy-free, Pareto-optimal and maximin. However, applying SD to the above situation leads to a different allocation, namely, {a,b,c,d,i} to A and {e,f,g,h,j} to B, which also satisfies the discussed properties. Table 7 ISD-procedure P0A

P0B

P1A

P1B

P2A

P2B

a b c d e f g h i j

h g f c b a e d j i

a b c d e f g h

h g f c b a e d

b c

c b

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In a recent study, Kilgour and Vetschera (2018) provide simulation results for SD and ISD, comparing them with many other procedures (some of them also discussed in this survey). One of their conclusions is that with respect to finding many of the “good” allocations (in case they exist), SD and ISD seem to be superior to most of the other procedures. In particular, for 12 items SD finds about 60% of the “good” allocations and about 4% of such allocations which many other procedures do not find. Another interesting procedure is the Trump rule introduced by Pruhs and Woeginger (2012). It is based on the idea of allocating items to a player that 2l1 relatively are ranked lower by the other player. Before stating it in detail, let Si n determine the set of player i’s first 2l1 ranked items, for l  1, . . . , 2 . The procedure now works as follows: Procedure 8 (Trump Rule) 1. Let l ¼ 1. 2. Allocate to A the item x  S2l1 which is least preferred by B among the items in A 2l1 SA . which is least preferred by A among the items in 3. Allocate to B the item y  S2l1 B . S2l1 B 4. If it was not possible to allocate different items to the two players, stop the procedure. The procedure failed. If all items in X have been allocated, stop the procedure. Let l ¼ l + 1. Return to step 2. The Trump rule provides an envy-free allocation whenever such an allocation exists. However, it does not work (or at least will be incomplete) whenever such an allocation does not exist and might output allocations which are not maximin. In addition, it might provide two different allocations depending on which player starts in the procedure. Let us illustrate the procedure with the following example: Example 12 Let there be two players, A and B, and X ¼ {a, b, c, d, e, f}. The preferences of the two players are as given in Table 8: Starting with player A, we consider the case l ¼ 1 and therefore the set S1A ¼ fag. Obviously the worst item for B within this set is a. Allocate this item to A. Because S1B ¼ fcg, and c is the worst ranked item for A from this set, assign c to B. Continue Table 8 Trump-procedure PA a b c d e f

PB c b f d e a

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with l ¼ 2 and the sets S3A ¼ fa, b, cg and S3B ¼ fc, b, f g. The worst available item for B from S3A is b, which is assigned to A. The worst available item for A from S3B is f, which is assigned to B. Finally, for l ¼ 3, consider the sets S5A ¼ fa, b, c, d, eg and S5B ¼ fc, b, f , d, eg. Following the Trump rule, this assigns e to A and d to B, leading to a final allocation of {a,b,e} to A and {c,f,d} to B. Observe that a change in who starts the procedure will make a difference. If player B goes first, then, for l ¼ 1, c is assigned to B and a to A. For l ¼ 3, f is allocated to B and b to A. Finally, for l ¼ 5, B receives e and A receives d. The final allocation would, for this order, be {a,b,d} to A and {c,f,e} to B. Perhaps an even simpler approach is to only look at the worst available items of a player and sequentially assign them to the other player without restricting the set of items to be looked at as in the Trump rule. This has been followed by Brams and Taylor (1999) and will be called bottom up rule. As the Trump rule, the bottom up rule will at most output two different allocations depending on who will be assigned the first item. In addition, it has the advantage of always providing a complete allocation, i.e., there will never be items left unassigned. To formally define it, let Xl be the set of items still available in round l, where X1 ¼ X. Given the restriction of Pi to Xl, let xli denote the lowest ranked item for player i in Xl, i.e., xli ¼ fx  Xl : r i ðxÞ > r i ðyÞ for all y  Xl}. The procedure works as follows: Procedure 9 (Bottom Up Rule) 1. Let l ¼ 1. 2. Allocate to A the item xlB  Xl, i.e., B’s least preferred item among X1. Set l ¼ l + 1. 3. Allocate to B the item xlA  Xl, i.e., A’s least preferred item among X1. Set l ¼ l + 1. 4. If all items have been assigned, stop the procedure. Otherwise return to step 2. Interestingly, despite its simplicity, the bottom up rule, in contrast to the Trump rule, always provides maximin allocations. However, it may fail on envy-freeness even if an EF-allocation exists. The following example illustrates the procedure: Example 13 Let there be two players, A and B, and X ¼ {a, b, c, d, e, f, g, h}. The preferences of the two players are as given in Table 9:

Table 9 Bottom-up-procedure PA a b c d e f g h

PB h g f b c a e d

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We start the procedure by assigning player A the item from X1 ¼ X which is lowest ranked by player B, i.e., item d. Then from the items in X2 ¼ X\{d}, we assign to player B the lowest ranked item by player A, i.e., item h. Continuing this until all items have been assigned, leads to the set {a,c,d,e} allocated to player A and the set {h,g,f,b} allocated to player B. If player B starts instead of player A, then the allocation will be {a,b,d,e} to A and {h,g,f,c} to B. Observe that both allocations are maximin, whereas applying the Trump rule, one of the allocations (starting with player B) will lead to an allocation which is not maximin.

Procedures for More than Two Players The procedures discussed so far are based on situations in which only two players are involved, with the exception of picking procedures which can be easily extended to more than two players. Although this might be the standard case for many negotiations, it seems of interest what happens in situations with more than two players. Brams et al. (2015) introduce a simple sequential algorithm, called SA, assuming the number of items to be a multiple of the number of players (to ensure the possibility to check for certain properties) and each of the players having a strict ranking over the set of items. Procedure 10 (SA-procedure) 1. Start with round one. Descend the ranks of the two or more players, moving down one rank at a time. Stop at the first rank at which each player can be given a different item at or above this rank. This is called the stopping point for that round. The rank that is reached is its depth, which is the same for each player. At this depth, assign an item at or above this depth to each player in all possible ways (there may be only one). Hence, this may give rise to one or more SA allocations. 2. On subsequent rounds, continue the descent, increasing the depth of the stopping point on each round. At each stopping point, assign items not yet allocated in all possible ways until all items are allocated. 3. Whenever all items have been allocated, if SA gives more than one possible allocation, choose an alloction which is Pareto-optimal and, if possible, envy-free. Let us illustrate SA with the following example: Example 14 Let I ¼ {A, B, C}, X ¼ {a, b, c, d, e, f, g, h, i} and the rankings of three players be given in Table 10. Descend the ranks of the three players. The first stopping point occurs at depth 1 (first horizontal line). Assign a to A, e to B, and c to C. Continue with the descent. At depth 2, we have the second stopping point (second horizontal line), giving b to A, h to B, and d to C. Continue the descent. At depth 3, we cannot give different items to the player, because C already has c and A already obtains a. This is also the case for depth 4 and depth 5. At depth 6 (third horizontal line), however, g can be assigned to B, i to C, and f to A. The final allocation is therefore {a,b,f} to A, {e,h,g} to B, and {c,d,i} to C.

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Table 10 SA preference profile PA a b c d e f g h i

PB e h a b f g c d i

PC c d i a b e f g h

As can be seen, the SA-allocation is Pareto-optimal, i.e., there is no other allocation that makes at least one player better off without making anyone else worse off. The allocation is also maximin, because the maximin rank is six and the lowest ranked item to any player is f to A and g to B which are both in sixth rank in the respective rankings. There is a downside that the allocation is not necessarily envy-free. Player B might envy player A, because there is no one-to-one mapping of B’s items to A’s items such that B always prefers her own item to the one it is mapped to. This is problematic insofar that there exists an envy-free allocation not found by SA, namely, ({a,b,g}, {e,h,f}, {c,d,i}). However, this allocation is not maximin, because A receives g which is her seventh ranked item. The SA-procedure, although very easy to apply, may normatively be problematic. There is, however, no convincing procedure yet, which works for three or more players. It is the case that, in general, SA satisfies neither of the properties specified in this survey whenever more than two players are involved. On the other hand, for exactly two players, Brams et al. (2015) show that SA produces at least one allocation that is Pareto-optimal and, if an envy-free allocation exists, at least one of the SA allocations will be envy-free and Pareto-optimal. For more than two players, there is another procedure based on the fairness concept of proportionality (discussed in section “Formal Framework and Properties”), i.e., the requirement that among q players, each player receives a share she values at least 1/q in her own view. An even weaker condition has been introduced by Budish (2011), which he called maximin share. It is based on the idea of using the cake-cutting procedure cut-and-choose for the division of indivisible items. Assume that a player (say A) is allowed to divide the items into q different piles, knowing that all the other q–1 players will choose one of the piles before player A. The best she can guarantee to herself in such a situation, i.e., the lowest valued pile among the q piles, is called her maximin share. The maximin share condition now requires that the allocation of a procedure should give a player at least her maximin share. Obviously the maximin share can be very low in cases of only a low number of items which are also valued very differently by a player. Budish (2011) introduces a mechanism based on the competitive equilibrium from equal incomes (CEEI), called approximate CEEI, which approximates the ideal conditions of

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efficiency, envy-freeness, and strategy-proofness. Kurokawa et al. (2018) show that there are allocations in which maximin shares cannot be guaranteed. However, they provide an algorithm that guarantees each player a value of at least 2/3 of her maximin share. Further results on maximin shares can be found in Bouveret and Lemaitre (2014).

Conclusion The goal of this survey was to collect and discuss fair division procedures that could be useful in the negotiation over the division of indivisible items. The ten procedures introduced provide, in principle, elegant ways to resolve such fair division problems. There are, however, restrictions in the applicability of such procedures. Those have been analyzed with respect to three major properties in the fair division literature, Pareto-optimality, envy-freeness, and maximinality. Based on an investigation of what actually can be achieved in this setting, it is shown which of the properties can be satisfied by the procedures. Mostly the focus was on rudimentary preference information, namely, the individual ordinal rankings over the items. Two important additional aspects have been discussed, strategy-proofness and computational complexity. Strategy-proofness in its strongest form can, in principle, not be satisfied by the above procedures. However, milder forms such as being truthinducing will sometimes be guaranteed. Concerning computational complexity, the procedures are computationally easy from an algorithmic point of view and usually do not require excessive effort from the players with respect to preference elicitation (probably with the exception of the undercut procedure). Of course, depending on the preference information available, different – and probably new – procedures could be devised. This could perhaps lead to better procedures satisfying more of the relevant properties in the literature. First attempts in that direction have been discussed by referring to procedures such as approximate CEEI. Clear recommendations about which procedure to use in practical problems are hard to give and might depend on the type of preference information available. The adjusted winner procedure seems definitely attractive but needs cardinal preference information and the potential divisibility of all items, requirements that might not be satisfied in many situations. One option to single out “good” procedures can be seen in simulation studies as, e.g., undertaken by Kilgour and Vetschera (2018). Based on their study, SD and ISD seem to be good and simple alternatives. Finally, certain attempts of practical applications have been made by devising online tools. A major website (www.spliddit.org), containing tools for various different fair division scenarios, has been provided by Ariel Procaccia (see Caragiannis et al. 2019). It is based on the CEEI and guarantees envy-freeness up to one item, i.e., a player would not envy another player if one of the other player’s items was removed. Obviously, because negotiations and group decisions become ever more important, further research will be necessary to improve the qualities of existing procedures and provide convincing arguments for its use in real-world applications.

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Cross-References ▶ Agent Reasoning in AI-Powered Negotiation ▶ Group Decisions: Choosing a Winner by Voting ▶ Group Decisions: Choosing Multiple Winners by Voting ▶ Negotiation as a Cooperative Game ▶ Procedural Justice in Group Decision Support ▶ Sharing Profit and Risk in a Partnership ▶ Supporting Community Decisions

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Brams SJ, Kilgour DM, Klamler C (2014) Two-person fair division of indivisible items: an efficient, envy-free algorithm. Not AMS 61:130–141 Brams SJ, Kilgour DM, Klamler C (2015) How to divide things fairly. Math Mag 88:338–348 Brams SJ, Kilgour DM, Klamler C (2016) Maximin envy-free division of indivisible items. Group Decis Negot 26:115–131 Brandt F, Conitzer V, Endriss U, Lang U, Procaccia AD (eds) (2016) Handbook of computational social choice. Cambridge University Press, New York Budish E (2011) The combinatorial assignment problem: approximate competitive equilibrium from equal incomes. J Polit Econ 119:1061–1103 Caragiannis I, Kurokawa D, Moulin H, Procaccia AD, Shah N, Wang J (2019) The unreasonable fairness of maximum nash welfare. ACM Trans Econ Comput 7(3):1–32 Darmann A, Klamler C (2016) Proportional Borda allocations. Soc Choice Welf 47:543–558 Darmann A, Klamler C (2019) Using the Borda rule for ranking sets of objects. Soc Choice Welf 53:399–414 Edelman PH, Fishburn PC (2001) Fair division of indivisible items among people with similar preferences. Math Soc Sci 41:327–347 Herreiner D, Puppe C (2002) A simple procedure for finding equitable allocations of indivisible goods. Soc Choice Welf 19:415–430 Kilgour DM, Vetschera R (2017) Comparing direct algorithms for two-player fair division of indivisible items – a computational study. Available at SSRN: https://ssrn.com/ abstract¼2997431 Kilgour DM, Vetschera R (2018) Two-player fair division of indivisible items: comparison of algorithms. Eur J Oper Res 271:620–631 Klamler C (2010) Fair division. In: Kilgour DM, Eden C (eds) Handbook of group decision and negotiation. Springer, Dordrecht, pp 183–202 Klamler C (2014) How risky is it to manipulate a scoring rule under incomplete information? Econ Bull 34:1214–1221 Klamler C (2019) Fairness concepts. In: Congleton RD, Grofman B, Voigt S (eds) The Oxford handbook of public choice, vol 1. Oxford University Press, New York, pp 715–734 Kurokawa D, Procaccia AD, Wang J (2018) Fair enough: guaranteeing approximate maximin shares. J ACM 65:1–27 Lang J, Rothe J (2016) Fair division of indivisible goods. In: Rothe J (ed) (2016): economics and computation: an introduction to algorithmic game theory, computational social choice and fair division. Springer, Berlin, pp 493–550 Moulin H (2003) Fair division and collective welfare. MIT Press, Cambridge, MA Procaccia AD (2016) Cake cutting algorithms. In: Brandt F, Conitzer V, Endriss U, Lang J, Procaccia AD (eds) Handbook of computational social choice. Cambridge University Press, New York, pp 311–329 Pruhs K, Woeginger GJ (2012) Divorcing made easy. In: Kranakis E, Krizanc D, Luccio F (eds) FUN 2012, LNCS, vol 7288. Springer, Berlin, pp 305–314 Rawls J (1971) A theory of justice. Harvard University Press, Cambridge, MA Robertson J, Webb W (1998) Cake-cutting algorithms. A K Peters, Natick Rothe J (ed) (2016) Economics and computation: an introduction to algorithmic game theory, computational social choice and fair division. Springer, Berlin Sönmez T, Ünver MU (2010) Course bidding at business schools. Int Econ Rev 51:99–123 Taylor AD, Zwicker WS (1999) Simple games: desirability relations, trading, pseudoweightings. Princeton University Press, Princeton Thomson W (2007) Fair allocation rules. Working paper no. 539, University of Rochester Vetschera R, Kilgour DM (2013) Strategic behavior in contested-pile methods for fair division of indivisible items. Group Decis Negot 22:299–319 Vetschera R, Kilgour DM (2014) Fair division of indivisible items between two players: design parameters for contested pile methods. Theor Decis 76:547–572 Young HP (1994) Equity: in theory and practice. Princeton University Press, Princeton

Sharing Profit and Risk in a Partnership Yigal Gerchak and Eugene Khmelnitsky

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wilson’s Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Contract with Risk-Neutral Partners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two Partners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partnership Versus Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple Partners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linear Contract with Two Risk-Averse Partners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exponential Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Power Function Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear Contract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optimality Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solution Method for Risk-Neutral Partners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solution Method for the NBS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Asymmetric Formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

112 113 114 115 117 118 120 120 122 124 126 127 128 129 132 133 133

Abstract

The setting up of a new partnership involves negotiation. Would-be partners must agree on a scheme for dividing uncertain future profits (or losses). We consider partnerships of two or more partners where initial investment is equal, and the negotiated division depends only on the partners’ attitudes toward risk, their beliefs concerning future profit, and their alternatives (i.e., the disagreement point). We propose several schemes. First, an asymmetric approach starts with one party making a decision that maximizes its expected utility while respecting Y. Gerchak (*) · E. Khmelnitsky Department of Industrial Engineering, Tel Aviv University, Tel-Aviv, Israel e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_46

111

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the other’s individual rationality. The other two schemes are symmetric and based on negotiation; they rely on the Nash bargaining solution and the KalaiSmorodinsky bargaining solution, respectively, and their unbalanced versions. We provide general definitions and highlight some special cases. Keywords

Group decision and negotiation · Fairness · Group behavior · Nash bargaining contracts · Kalai-Smorodinsky solution · Jazz history · Optimal control

Introduction A partnership, sometimes referred to as a “syndicate” (Wilson 1968), is an arrangement in which two or more individuals cooperate to advance their mutual interests and share the profits and liabilities of a business venture. It is an important example of GDN and multidimensional sharing. Such partnerships are especially common in human-capital-intensive professional services (Levin and Tadelis 2005). Various arrangements are possible: all partners might share liabilities and profits equally, or some partners’ liabilities may be limited (e.g., Levin and Tadelis 2005). A partner might accept less than half the profit for reduced risk. In a broad sense, a partnership is any cooperative endeavor undertaken by multiple parties. These parties can be governments, nonprofits, businesses, individuals, or a combination, and the goals of partnership can vary widely. Borch (1962), to whom Wilson (1968) attributes a pioneering contribution, considered such issues in the context of reinsurance markets. There may or may not be a written agreement governing the partnership, but it is generally considered a good idea to lay out specific terms at the outset, so that any disagreement can be settled according to predetermined rules. In some jurisdictions such an agreement is legally required. Partnerships are widespread in common law jurisdictions such as the United States, Great Britain, and the Commonwealth, especially in professional services industries. Partnerships with informal or formal contracts have existed for centuries. A famous early case was the Hanseatic League (eleventh to fifteenth centuries), where a ship sailing from one member city to another would carry not only its own cargo but also freight for other members of the League. The academic investigation of the economics of partnerships and contracts essentially started in the late 1960s (Wilson 1968; see also Brousseau and Glachant 2002). Our settings are partnerships where the partners, whether of complementary or similar skills, can be assumed to always exert high effort, since their individual reputations and income outside the partnership depend on the success of the partnership. Thus, our setting is simple in that it has no “action” or incentive aspects and thus no moral hazard. Also, the partners in our models are not the stereotypical “one partner provides ‘sweat equity’ while the other is (only) an investor.” Examples include a law firm as well as performers and their managers/agents.

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We do not seek “fair division” of profits (Klamler, “The Notion of Fair Division in Negotiations,” in this volume). Our intent is to “explain” these contracts in terms of the partners’ risk attitudes and beliefs about future profits, both of which may differ. We ask what type of preferences and beliefs, and relationships among them, give rise to, general or special, affine linear contracts. We pay particular attention to conditions for the optimality of linear contracts, and even of a constant wage to one party, as was the case in famous contracts involving jazz musicians and their managers between Duke Ellington and Irwin Mills (1926–1939) and between Louis Armstrong and Joe Glaser (1935–1969) (Ward and Burns 2000, p. 214). This review will focus on, and compare, three approaches for dividing uncertain future profit: 1. Leader-follower. Initially, one party proposes a take-it-or-leave-it contract to the other. The proposal will maximize the proposer’s expected utility, subject to an individual rationality constraint on the expected utility of the other party. A famous contract of this type from the history of jazz motivated this model. This approach is applicable to only some of the scenarios. 2. Nash bargaining solution. This division is known to satisfy some attractive axioms (Nash 1950) and to be the limit of a sequential bargaining process (Rubinstein 1982, Binmore et al. 1986). We assume here that an analyst, who knows the partners’ preferences, beliefs, and disagreement values, is trying to predict the outcome of (Nash) bargaining. 3. Raiffa-Kalai-Smorodinsky solution (Kalai and Smorodinsky 1975). Similar to the Nash bargaining solution, the K-S solution also satisfies some attractive axioms. The review starts with the simplest scenario and gradually adds generalization. Initially, we shall pay particular attention to risk-neutral partners and the commonly used affine (“linear”) contracts. These approaches are connected to both cooperative and noncooperative game theory – see Kibris (“Negotiation as a cooperative game,” in this volume) and Chatterjee (“Negotiation as a non-cooperative game,” in this volume). We then extend the three approaches to risk-averse partners, nonlinear contracts, and asymmetric version of the bargaining solutions. For general references on game theory and bargaining, see Friedman (1986) and Muthoo (1999).

Wilson’s Model Wilson (1968) considers a group of individual decision-makers who must make a common decision under uncertainty that will result in a future payoff to be shared jointly among them. The decision process is analyzed when the partners have diverse risk tolerances and/or diverse probability assessments of the value of uncertain payoff. More specifically, a common decision denoted α is chosen, and then, depending upon the random outcome ξ, the resulting payoff x = p(ξ, α) is shared among the members. For example, a group invests its capital of $1 in a project that will return an uncertain amount ξ per dollar invested. The group can borrow (or lend)

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capital in any amount α at a certain cost of h, so a payoff x = (1 + α)ξ
αh is available, and the decision problem is to choose an optimal amount of debt and to determine the sharing rule. A sharing rule of a group of n partners is a set of functions {ci(x, ξ| α), i = 1, . . ., n} (we changed the original Wilson’s notation to be consistent with the notation used in this chapter) such that Xn

c ðx, ξjαÞ i¼1 i

¼ x for all ðx, ξÞ:

ð1Þ

For each partner i, there exists a utility function ui(c) assumed to be increasing, continuous, strictly concave, and differentiable, u0i ðcÞ > 0, u00i ðcÞ < 0, and a probability distribution function Fi(ξ) that represents the beliefs of the partner with regard to the future outcome. The probability density function is denoted by φi(ξ). The criterion for choosing a sharing rule is that it must be Pareto optimal, i.e., such that there is no alternative sharing rule which would increase the expected utility of some partner(s) without decreasing the expected utility of any other partner. Based on the convexity argument, a necessary and sufficient condition for Pareto optimality of the sharing rule was proven by Wilson. It states that there exist nonnegative weights {λi(α), i = 1, . . ., n} such that the sharing rule is obtained as a solution of the problem that maximizes the weighted expected utilities Xn

λ ðαÞEi ðci ðx, ξjαÞÞ i¼1 i

ð2Þ

subject to constraint (1). Having determined the sharing rule for each decision α, the best decision is then obtained by maximizing the Lagrangian function formed from the objective and constraints of problem (2) (see also Kadan and Swinkels 2013). Examples in Wilson’s paper present the optimal sharing rules developed for specific cases of exponential and power utility functions and normally or gamma distributed partners’ beliefs. The sharing rule in these cases is linear in the payoff x and the outcome ξ. The next sections of this chapter are not concerned with the choice of α and focus on determining the sharing rule (contract) in the context of the three types of decision-making described in the previous section. We assume also that x = ξ. Therefore, in our notation φi(x) is the pdf of the profit, X, which represents the beliefs of partner i. Ei(X) denotes the expected profit, Ei(X)  0, so the partnership is expected to Pbe profitable. What we are looking for is the shares of the partners, ci(x), such that ni¼1 ci ðxÞ ¼ x.

Linear Contract with Risk-Neutral Partners This section assumes linear sharing rules, i.e., ci(x) = pix + Ki 8i, as most contracts used in practice are linear, and risk-neutral partners, ui(c) = c.

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Two Partners Leader-follower (see Gerchak and Khmelnitsky 2019a): Here the problem is one of determining a contract, which aims at maximizing the expected utility of the initiating partner (partner 1) subject to a given expected utility of the other one (“individual rationality”). Partner 1 is assumed to know the other’s attitude toward risk and beliefs. We denote by B the expected utility guaranteed to partner 2. So the problem is J LF ¼ maxp,K E1 ðpX þ K Þ

ð3Þ

subject to E2 ðð1
pÞX
K Þ ¼ B, 0  p  1:

ð4Þ

The solution of this problem is  p¼

1,

if E1 ðXÞ > E2 ðXÞ

0,

if E1 ðXÞ < E2 ðXÞ

 ,K ¼


B,

if E1 ðXÞ > E2 ðXÞ

E2 ðXÞ
B,

if E1 ðXÞ < E2 ðXÞ

:

ð5Þ

So the more optimistic partner will receive the whole revenue and transfers a constant amount to the other. NBS with a zero disagreement point (see Gerchak and Khmelnitsky 2019b): J NBS ¼ maxp,K fE1 ðpX þ K Þ  E2 ðð1
pÞX
K Þg

ð6Þ

subject to 0  p  1. The Hessian matrix of the objective function is  H¼


2E1 ðXÞE2 ðXÞ


E1 ðXÞ
E2 ðXÞ


E1 ðXÞ
E2 ðXÞ


2

 :

Since H’s determinant,
(E1(X)
E2(X))2, is negative, the objective JNBS is a saddle-point function, and, as a result, the maximum is attained either at p = 0 or at p = 1, as follows:  p¼

1, 0,

8 1 > <
E1 ðXÞ, if E1 ðXÞ > E2 ðXÞ if E1 ðXÞ > E2 ðXÞ 2 : ,K ¼ 1 > if E1 ðXÞ < E2 ðXÞ : E2 ðXÞ, if E1 ðXÞ < E2 ðXÞ 2

ð7Þ

Again, the more optimistic partner receives the whole revenue. By comparing the LF and NBS strategies, we observe that if B > 12 max fE1 ðXÞ, E2 ðXÞg, the NBS is better for partner 1. He should give up the leadership and bargain instead.

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K-S with a zero disagreement point (see Gerchak and Khmelnitsky 2019c): J KS ¼ maxp,K E1 ðpX þ K Þ

ð8Þ

E1 ð X Þ E2 ð X Þ ¼ : E1 ðpX þ K Þ E2 ðð1
pÞX
K Þ

subject to

ð9Þ

The solution of this problem is  p¼

¼

1,

if E1 ðXÞ > E2 ðXÞ

0,

if E1 ðXÞ < E2 ðXÞ

8 E1 ðXÞE2 ðXÞ > > <
E ðX Þ þ E ðX Þ , > > :

1

2

,K

if E1 ðXÞ > E2 ðXÞ

E1 ðXÞE2 ðXÞ , if E1 ðXÞ < E2 ðXÞ E1 ðXÞ þ E2 ðXÞ

:

ð10Þ

Yet again, the more optimistic partner receives the whole revenue. By comparing the NBS and K-S strategies, one obtains that the partner that has a higher expected utility would prefer the K-S solution, since under the K-S contract his revenue is greater than that under the NBS. Figure 1 illustrates the dependence of K on E1(X), as given in (10).

Fig. 1 The transfer payment, K, in the K-S scheme (eq. (10)) for E2(X) = 3 (bold line), E2(X) = 5 (thin line), and E2(X) = 7 (dashed line)

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Partnership Versus Independence This section determines conditions under which doing business in partnership, as discussed in the previous section, has an advantage over doing business alone. Denote by Y1 and Y2 the profit of partners 1 and 2, respectively, when working alone. Both partners benefit from the partnership if the expected revenue in partnership is not smaller than the expected revenue when working alone. That is, pE 1 ðXÞ þ K  EðY 1 Þ and ð1
pÞE2 ðXÞ
K  EðY 2 Þ: By substituting p and K of the three profit-split schemes from section “Two Partners” into the above inequalities, we find that the partnership benefits both if max fE1 ðXÞ, E2 ðXÞg  EðY 1 Þ þ B

and

B  Eð Y 2 Þ

ðLeader-FollowerÞ;

ðNBS Þ; max fE1 ðXÞ, E2 ðXÞg  2  max fEðY 1 Þ, EðY 2 Þg   Eð Y 1 Þ Eð Y 2 Þ max fE1 ðXÞ, E2 ðXÞg  ðE1 ðXÞ þ E2 ðXÞÞ  max , ðK-SÞ: E1 ðXÞ E2 ðXÞ Figure 2 presents the three regions in the (E1(X), E2(X)) domain where the partnerships benefit both partners under the NBS or K-S scheme.

Fig. 2 Region A, neither NBS nor K-S benefit; region B, both schemes benefit; region C, NBS benefit, K-S does not. Here E(Y1) = E(Y2)  E(Y )

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Multiple Partners When there are more than two partners, each will deposit to, or withdraw from, a pool that clears at the end. Partner i receives ci ðxÞ ¼ pi x þ K i , P P where ni¼1 pi ¼ 1 and ni¼1 K i ¼ 0. Kibris (“Negotiation as a cooperative game,” in this volume) has argued that, with n partners, the procedures of calculating the NBS and K-S solutions are the same as for two partners. Leader-follower: J LF ¼ max pi ,Ki E1 ðp1 X þ K 1 Þ

ð11Þ

Ei ðpi X þ K i Þ ¼ Bi , i ¼ 2, . . . , n, Xn Xn pi  0, p ¼ 1 and K ¼ 0: i i¼1 i¼1 i

ð12Þ

subject to

ð13Þ

By substituting Ki from constraints (12) into (11), the solution of this problem is obtained as follows:  pi ¼

1,

if i ¼ i

0, otherwise

, where i ¼ argmaxj Ej ðXÞ

K i ¼
pi Ei ðXÞ þ Bi , i ¼ 2, . . . n, K 1 ¼


Xn i¼2

Ki,

a similar solution to that of the case n = 2. NBS: Here we shall introduce disagreement points. Let di denote the disagreement point P of partner i. We assume that Ei(X) > di  0 8 i and max i Ei ðXÞ > nj¼1 d j. Note that if Ei(X)  E(X) and di  d for all i, then this condition becomes E(X) > nd, so it will not be satisfied for a large n. The NBS is J NBS ¼ max pi , K i

Yn i¼1

ð Ei ð pi X þ K i Þ
d i Þ

P P subject to pi  0, ni¼1 pi ¼ 1, ni¼1 K i ¼ 0: The maximization of JNBS w.r.t. Ki for any given pi yields K i ¼
pi Ei ðXÞ þ

1 Xn 1 Xn p E ð X Þ þ d
d: j i j j¼1 j¼1 j n n

Sharing Profit and Risk in a Partnership

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By substituting these Ki into JNBS, we have J NBS ¼

 Xn n 1 1 Xn p E ð X Þ
d : j j j j¼1 j¼1 n n

The maximum of JNBS w.r.t. pi is attained at the index corresponding to the largest expected beliefs, i.e.,  pi ¼

1, if i ¼ i ,where i ¼ argmaxj E j ðX Þ: 0, otherwise

So the most optimistic partner receives the whole revenue. By substituting these pi into Ki, the latter is 8 n
1  >

: 1 Ei ðXÞ, otherwise: n



@K i @d i

1 ¼ n
1 n > 0 . Note that all partners receive same expected revenue, n   P P Ei ðXÞ
nj¼1 dj , which is decreasing in nj¼1 d j . By comparing the LF and

So

NBS that partner 1 prefers bargaining over leadership if Pn we observe Pn strategies, 1 n
1  i¼2 Bi > n i¼1 d i þ n Ei ðX Þ and has the opposite preference otherwise. Example 1 For n = 2 and i = 1, 1 K 1 ¼ ðd1
d2
E1 ðXÞÞ, 2 which is negative, and K2 =
K1. ∎ Clearly, if n is large enough, the expected revenue becomes negative. K-S: From its definition, the K-S solution is closest to the ideal point (E1(X), . . ., En(X)) among all feasible points in the expected revenues domain that lie on the line which connects the ideal point and the disagreement point of the partners (d1, . . ., dn). Such a line is presented by the equations  Ei ðXÞ
Ei ðpi X þ K i Þ Ej ðXÞ
Ej pj X þ K j  ¼ 8i, j: Ei ð p i X þ K i Þ
d i Ej p j X þ K j
d j

ð14Þ

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P As in the NBS case, we assume that Ei(X) > di  0 8i and max i Ei ðXÞ > nj¼1 d j. The minimization of the distance to the ideal point subject to constraints (14) and the constraints Xn Xn pi  0, p ¼ 1, K ¼0 i¼1 i i¼1 i is solved by

 pi ¼

1,

if i ¼ i

0, otherwise

, where i ¼ argmaxj Ej ðXÞ:

Then 8 > > > >
> j¼1 Ej ðXÞ
Ei ðX Þ > > : Ei ð X Þ
ð Ei ð X Þ
d i Þ P n  E ð X Þ
d , j j j¼1

if i ¼ i otherwise:

Linear Contract with Two Risk-Averse Partners Exponential Utilities Suppose that the beliefs of the partners are distributed exponentially, ϕi ðxÞ ¼ λi e
λi x, x  0, and the utility functions of the partners are also exponential, ui ðcÞ ¼ ui ð1
e
μi c Þ, i = 1, 2, where λi, μi, and ui are given positive parameters. Leader-follower: The solution of the problem is obtained analytically:

 μ 2
λ1 þ λ2 1 u2
B μ1 μ2 þ λ1 μ2 þ λ2 μ1 c1 ðxÞ ¼ x þ ln  : μ2 u2 μ1 þ μ2 λ2 ðμ1 þ μ2 Þ Note that if λ1 = λ2 + μ2, then c1 ðxÞ ¼

 1 u
B λ2 þ μ 2 ln 2  , μ2 u2 λ2

that is, a fixed wage contract, where partner 1’s share is constant, is optimal. Note also that the parameters of the exponentials are limited to be in the range λ2
μ1 < λ1 < λ2 + μ2; otherwise the share of one of the partners decreases with x.

Sharing Profit and Risk in a Partnership

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NBS (see Kihlstrom et al. (1981)): The solution of this problem is c1 ðxÞ ¼

E ðXÞu1 λ1 μ1 μ2
λ1 þ λ2 1 xþ ln 2 : μ1 þ μ2 E1 ðXÞu2 λ2 μ2 μ1 þ μ2

If μ1 = μ2  μ, then by substituting the expected utilities

E1 ðXÞ ¼



 2λ1 e
μK 2λ2 eμK 1
u , E ðX Þ ¼ 1
u λ1 þ λ2 þ μ 1 2 λ1 þ λ2 þ μ 2

1 in the previous expression and solving for K, one obtains K ¼ 2μ ln λλ12 . That is, if λ2 > λ1, then partner 1 transfers the constant payment (
K) > 0 to partner 2 on the account of receiving a greater share from the future profit, p > 1/2. On the other hand, if λ2 < λ1, then partner 2 transfers the constant payment K > 0 to partner 1 and receives a greater share from the future profit, i.e., p < 1/2. K-S: The K-S condition (9) is generalized to account for utility functions and disagreement points as follows:

E1 ðu1 ðXÞÞ
E1 ðu1 ðcðXÞÞÞ E2 ðu2 ðXÞÞ
E2 ðu2 ðX
cðXÞÞÞ ¼ : E1 ðu1 ðcðXÞÞÞ
d 1 E2 ðu2 ðX
cðXÞÞÞ
d2

ð15Þ

Let d1 = d2 = 0 and K = 0, i.e., c(x) = px. Then the K-S condition reduces to the following quadratic equation: ðλ2 μ1
λ1 μ2 Þp2
λ1 ðλ2 þ μ2 Þð1
2pÞ ¼ 0: The unique solution of the latter equation, such that 0  p  1, is p¼

1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : λ2 ðλ1 þ μ 1 Þ 1þ λ 1 ðλ2 þ μ 2 Þ

It can be shown that p is increasing in λ1 and μ2 and decreasing in λ2 and μ1. That is, the partner’s share decreases in own risk aversion and in own mean of believed distribution. It is increasing in the other partner’s risk aversion and its mean of believed distribution. Now let c(x) = px + K. An analytic expression for the K-S solution is available for some specific cases of the problem parameters. If, for example, μ1 = μ2  μ, then

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• If λ1 < λ2 (i.e., E1(X) > E2(X)) and μ < λ2
λ1, then

p ¼ 1 and K ¼

1 ln μ

λ2
λ1 þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðλ1 þ λ2 Þ2 þ 4λ1 μ 2ð λ 2 þ μ Þ

;

• If λ2 < λ1 and μ < λ1
λ2, then qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 λ2
λ1 þ ðλ1 þ λ2 Þ þ 4λ2 μ ; p ¼ 0 and K ¼ ln μ 2λ2 • Otherwise 1 λ2
λ1 þ and 2 2μ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!# 4λ1 λ2 ðλ1 þ μÞðλ2 þ μÞ λ 2
λ 1 þ ðλ2
λ 1 Þ2 þ : ðλ1 þ μpÞðλ2 þ μð1
pÞÞ p¼

" λ þ μ ð 1
pÞ 1 K ¼ ln 2 μ 2λ2 ðλ2 þ μÞ

Another case where an analytic solution can be derived is the limit when μ1 ! 0 and λ1 = λ2  λ, μ2 = 1. In such a case, partner 1’s utility tends to zero regardless of the contract, and the K-S problem is solved by maximizing the expected utility of eK partner 2. The solution is p = 1 with a negative K that solves λ ¼ 1
K
e K . In the opposite limit case where μ2 ! 0 and μ1 = 1, the K-S contract is p = 0 with a e
K positive K that solves λ ¼ 1þK
e
K . Note that in the previous limit the same λ is obtained for –K.

Power Function Utilities Consider power utility functions, ui ðcÞ ¼ ða þ cÞαi , c >
a, a  0, 0 < αi < 1, and uniformly distributed identical beliefs Xi~U[0, 1]. For the utility functions to be properly defined, the value of K must be bounded by
a  K  a. NBS: The problem is J NBS ¼ max p, K

subject to 0  p  1.

ð1 0

ða þ px þ K Þα1 dx 

ð1 0

ða þ ð1
pÞx
K Þα2 dx

Sharing Profit and Risk in a Partnership

123 2

J NBS Since JNBS is concave w.r.t. K for all a, p, α1, and α2 (this is shown by @ @K 2  0), we first calculate K from the first-order optimality condition. Then, the value of p is calculated numerically. In the limit case where α1 ! 1 and α2 ! 0, the solution is K = a and p = 1. In the opposite limit case where α1 ! 0 and α2 ! 1, the solution is K =
a and p = 0. For intermediate values of α1 and α2, a numerical approximation is shown in Figs. 3 and 4 for a = 2. K-S: The K-S condition (15) here becomes

   ð1
pÞ ð1 þ aÞ1þα2
a1þα2 ða þ K þ pÞ1þα1
ða þ K Þ1þα1    ¼ p ð1 þ aÞ1þα1
a1þα1 ð1 þ a
K
pÞ1þα2
ða
K Þ1þα2 : In the limit case where α1 ! 1 and α2 ! 0, the multiple solutions of the K-S problem are 1 K ¼ ð1
pÞ, 0  p  1: 2 In the opposite limit case, where α1 ! 0 and α2 ! 1, the multiple solutions of the K-S problem are

Fig. 3 Bold, thin, and dashed lines are for α2 = 0.2, 0.5, 0.8, respectively

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Fig. 4 Bold, thin, and dashed lines are for α2 = 0.2, 0.5, 0.8, respectively

p K ¼
, 0  p  1, 2 both independent of a. As expected, K decreases in p, and in the latter limit case, K is negative and becomes more negative as p grows. For intermediate values of α1 and α2, a numerical approximation of the unique solution of the K-S problem is shown in Figs. 5 and 6 for a = 2.

Nonlinear Contract This section assumes that the contract between the two partners is not necessary linear, i.e., the share of each partner may depend on the profit, x. What we are looking for is c1(x), the share of partner 1, as a function of realized profit x. The share of partner 2 is then x
c1(x). The additional constraint c01 ðxÞ ¼ wðxÞ,

0  wðxÞ  1

ð16Þ

is required so that the shares of the two partners do not decline when the profit grows (see (Gerchak and Khmelnitsky 2019a) for an example where without this constraint c1(x) is not monotone).

Sharing Profit and Risk in a Partnership

Fig. 5 Bold, thin, and dashed lines are for α2 = 0.2, 0.5, 0.8, respectively

Fig. 6 Bold, thin, and dashed lines are for α2 = 0.2, 0.5, 0.8, respectively

125

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Optimality Conditions Consider the LF problem. Its formulation has a canonical form of optimal control, (e.g., Hartl et al. 1995). The optimality conditions of the problem state that if w(x) is the optimal control, then there exists a costate variable, ξ(x), that satisfies the following conditions: • The optimal control maximizes the Hamiltonian function, H, at each x: wðxÞ ¼ arg max H,

ð17Þ

H ðxÞ ¼ u1 ðc1 ðxÞÞφ1 ðxÞ þ ψu2 ðc2 ðxÞÞφ2 ðxÞ þ ξðxÞwðxÞ

ð18Þ

where

and ψ is a constant. • The costate equation is ξ 0 ðxÞ ¼


@H ¼
u01 ðc ðxÞÞφ1 ðxÞ þ ψu02 ðx
c ðxÞÞφ2 ðxÞ: @c

ð19Þ

The maximization of the Hamiltonian (18) relates w(x) to ξ(x) as follows: 8 if ξðxÞ > 0 < 1, wðxÞ ¼ 0, if ξðxÞ < 0 : :  ½0,1 , if ξðxÞ ¼ 0

(20)

Equation (20) indicates that the optimal contract, c1(x), consists of a sequence of arcs, each of one of three categories: • The entire marginal profit is allocated to partner 1, c01 ðxÞ ¼ 1 (type 1 arc). • The entire marginal profit is allocated to partner 2, c01 ðxÞ ¼ 0 (type 2 arc). • The marginal profit is divided between the two partners, 0 < c01 ðxÞ < 1 (singular arc). The last category is termed singular, since the division of the profit over the arc cannot be explicitly determined from the Hamiltonian maximization, and additional analysis is required. Let a singular arc occur at an interval [x0, x1]. Then, at that interval, ξ(x) = 0 and ξ0(x) = 0 for all x  [x0, x1]. Now, from (19) we obtain u01 ðc1 ðxÞÞφ1 ðxÞ ¼ ψu02 ðx
c1 ðxÞÞφ2 ðxÞ,

ð21Þ

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127

the condition that solves for c1(x). Following that w(x) is obtained from (16) (see details of the solution method in Gerchak and Khmelnitsky (2019a)). Having determined the value of w(x) on each arc category, we identify subintervals of x, where the singular arcs can potentially occur, and connect the subintervals with the type 1 and type 2 arcs by solving the system of state-costate differential eqs. (16) and (19). The details of the method can be found in Khmelnitsky (2002).

Solution Method for Risk-Neutral Partners Consider a scenario where the two partners are risk neutral, u1(c) = u1  c and u2(c) = u2  c. The optimal solution consists of arcs of types 1 and 2 only. No singular arcs occur, since from the solution of the costate equation it follows that ψ ¼ u1 =u2 and ξðxÞ ¼ u1 ðF2 ðxÞ
F1 ðxÞÞ,

ð22Þ

and the singular arc condition, ξ(x) = 0, does not hold. With respect to (20), the number of arcs equals the number of times the difference F2(x)
F1(x) changes sign (plus one). The following case exemplifies a closed-form solution of the problem. Example 2 Let the beliefs of the partners be distributed normally with equal mean, μ, but different standard deviations, σ 1 and σ 2. For σ 1 smaller than σ 2, F1(x) < F2(x) for x < μ, and F1(x) > F2(x) for x > μ. From (20) and (22), it follows that the optimal c1(x) consists of a sequence of two arcs, 2 ! 1, with the switching point located at the common mean (since F1(x) and F2(x) are equal at μ), i.e.,  c1 ðxÞ ¼

x þ C
μ, if x < μ , c 2 ðxÞ ¼ C, if x  μ



μ
C, if x < μ x
C, if x  μ

where the constant C is obtained from the expected utility of partner 2, ðμ

1 ð

u2 ðμ
CÞφ2 ðxÞdx þ

u2 ðx
CÞφ2 ðxÞdx ¼ B, μ


1

2 as C ¼ μ
uB2 þ pσffiffiffiffi . Now, the expected utility of partner 1 is 2π

ðμ

1 ð

u1 ðx þ C
μÞφ1 ðxÞdx þ
1

μ

 B σ
σ u1 Cφ1 ðxÞdx ¼ u1 μ
þ 2pffiffiffiffiffi 1 : u2 2π

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Y. Gerchak and E. Khmelnitsky

The opposite case, σ 1 > σ 2, is considered similarly, and the expected utility of partner 1 for both cases is

 B jσ
σ j u1 μ
þ 1pffiffiffiffiffi 2 : u2 2π The expected utility of partner 1 grows linearly with the absolute difference between the standard deviations no matter whose belief uncertainty is higher, which is not so intuitive. ∎

Solution Method for the NBS The optimality conditions for the NBS can be derived by means of calculus of variations (e.g., Weinstock, 1974). The conditions state that if c1(x) solves the problem, then u01 ðc1 ðxÞÞ ¼ u02 ðx
c1 ðxÞÞ

φ 2 ð x Þ E1 φ 1 ð x Þ E2

8x,

ð23Þ

where E1  E(u1(c1(X))) and E2  E(u2(X
c1(X))). We note that the optimality conditions (23) are identical, up to a constant multiplier, to the optimality conditions (21) of the LF formulation, that is, despite the LF model positing different roles for the parties – a maximizing principal and a “passive” (though rational) agent, unlike the “symmetric,” predictive, NBS model. By differentiating (23) w.r.t. x, one obtains the following differential equation for c1(x):

c01 ðxÞ ¼

u002 ðx
c1 ðxÞÞ

φ 2 ð xÞ E 1 φ0 ðxÞφ1 ðxÞ
φ01 ðxÞφ2 ðxÞ E1 þ u02 ðx
c1 ðxÞÞ 2 φ 1 ð xÞ E 2 E2 φ21 ðxÞ : φ ð x Þ E 1 u001 ðc1 ðxÞÞ þ u002 ðx
c1 ðxÞÞ 2 φ 1 ð xÞ E 2 (24)

A solution of (24) is used as a singular arc in the solution method that connects arcs of types 1 and 2 similarly to the LF solution. Example 3 The beliefs of the partners are distributed normally, Xi~N(μ, σ i), with mean 10, and unequal standard deviations, σ 1 = 1.51 and σ 2 = 1.5. The utility ic , with the parameters, A1 = 5, A2 = 5, B1 = 7, and B2 = 3. functions are ui ðcÞ ¼ BAi þc Figure 7 presents an approximate numerical solution of the NBS, which consists of a single arc on the interval x  [0, 20]. The expected utilities of the partners are 2.24 and 2.93, respectively. We observe that the two shares grow nonlinearly. Because of the higher spread of beliefs, σ 1 > σ 2, and the fact that u2(c) > u1(c) for all c, partner 1’s share is almost always larger than that of partner 2. ∎

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129

Fig. 7 Numerical approximation of the partners’ shares in Example 3

Asymmetric Formulations NBS: The asymmetric NBS is the solution of the maximization problem (Kalai 1977): n o J ¼ max ½E1 ðu1 ðc1 ðX ÞÞÞ α  ½E 2 ðu2 ðX
c1 ðX ÞÞÞ 1
α , cðÞ

(25)

which gives one partner more weight than to the other. If the disagreement points are unequal, that too reflects the partners’ unequal power. The greater the parameter α, 0  α  1, the higher the relative weight of partner 1. When α = 0.5, one obtains the symmetric NBS discussed in the previous sections. Assume identical utilities and beliefs and a proportional contract c1(x) = px. By differentiating the objective function, we obtain the first-order optimality condition: xð1

α

0

xð1

u ½px φðxÞxdx  x0

xð1

u½ð1
pÞx φðxÞdx ¼ ð1
αÞ x0

xð1

u½px φðxÞdx  x0

u0 ½ð1
pÞx φðxÞxdx:

x0

(26) Isolating α and differentiating α w.r.t. p, assuming that Ðx1

Ðx1

u0 ½px ϕðxÞxdx > 0 and

x0

u0 ½ð1
pÞx ϕðxÞxdx > 0, one can show that dα/dp > 0. Therefore, dp/dα > 0.

x0

That is, the higher the priority of a partner, the greater that partner’s share.

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The symmetric solution, p = 1/2, does not necessarily satisfy (26). The optimal p depends on the shape of the utility function, on the belief distribution, and on α. Example 4 For exponential utilities, u(c) = 1
e
λc, and normally distributed beliefs, X~N(μ, σ), the optimal p as a function of α is shown in Fig. 8. Figure 9 plots the optimal expected utilities of the partners in this case. ∎ Example 5 Consider a linear contract with transfer, c(x) = px + K, under the assumption of risk-neutral partners, ui(c) = ui  c, and arbitrarily distributed beliefs with positive means, E[X1], E[X2] > 0. The first-order optimality conditions result in the following three cases: • If E[X1] = E[X2], then the multiple solutions are given by K ¼ ðα
pÞE½X1 , 0  p  1: • If E[X1] > E[X2], then p = 1 and K =
(1
α)E[X1]. • If E[X2] > E[X1], then p = 0 and K = αE[X2]. In all three cases, K increases with α. In the first case, K decreases with p. ∎ K-S: An asymmetric version of the K-S solution was proposed by Dubra (2001). In our notation and assuming that d1 = d2 = 0, Dubra writes

Fig. 8 Optimal p for λ = 0.5, σ = 1, μ = 3, and μ = 9 in Example 4

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131

Fig. 9 Optimal expected utilities of the partners, E1 and E2, in Example 4, where λ = 0.5, σ = 1, μ = 3 and μ = 9

E2 ðu2 ðX
cðXÞÞÞ ¼ λE1 ðu1 ðcðXÞÞÞ

E2 ð u 2 ð X Þ Þ , E1 ð u1 ð X Þ Þ

“allowing” λ to take any value in [0, 1). Similar to section “Linear contract with risk-neutral partners,” the K-S solution is obtained by solving the following optimization problem: max c1 ðÞ E1 ðu1 ðc1 ðXÞÞÞ,

ð27Þ

subject to E2 ðu2 ðX
c1 ðXÞÞÞ ¼ λE1 ðu1 ðc1 ðXÞÞÞ 0

E2 ðu2 ðXÞÞ , E1 ðu1 ðXÞÞ

d c ðxÞ  1: dx 1

ð28Þ ð29Þ

The solution of (27)–(29) for risk-neutral partners and a linear contract, c1(x) = px + K, is as follows: • For equal means, E1(X) = E2(X), the multiple solutions are given by K¼



 1
p Ei ðXÞ, 0  p  1, i ¼ 1, 2: 1þλ

ÞE2 ðXÞ , i.e., K is • For E1(X) > E2(X), the solution is p = 1 and K ¼
λ EE1 ð1XðXÞþλE 2 ðXÞ negative. ÞE2 ðXÞ , i.e., K is positive. • For E1(X) < E2(X), the solution is p = 0 and K ¼ EE1 ð1XðXÞþλE 2 ðX Þ

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The dependence on λ is given by E1 ðXÞE2 ðXÞ dK ¼
max fE1 ðXÞ, E2 ðXÞg < 0: dλ ðE1 ðXÞ þ λE2 ðXÞÞ2

Example 6 c1(x) = px + K, ui ðcÞ ¼ ða þ cÞαi , c >
a, 0 < αi < 1, a  0, and Xi~U [0, 1]. For the utility functions to be properly defined for all x  0, the value of K must be bounded by
a  K  a. The asymmetric K-S condition (28) becomes    λð1
pÞ ð1 þ aÞ1þα2
a1þα2 ða þ K þ pÞ1þα1
ða þ K Þ1þα1    ¼ p ð1 þ aÞ1þα1
a1þα1 ð1 þ a
K
pÞ1þα2
ða
K Þ1þα2 :

ð30Þ

Generally, no analytical solution of (30) is available. For some specific cases, we note that: • If p is set at zero, any K satisfies (30). Objective (27) tends to ða þ K Þα1 , which in the relevant range is maximized for K = a. • If p is set at 1, any K satisfies (30). Objective (27) is ð1þaþK Þ1þα1
ðaþK Þ1þα1 , 1þα1

which is maximized for K = a. • If K is set at zero, α1 = 0 and α2 = 1, then (30) becomes     λð1
pÞp ð1 þ aÞ2
a2 ¼ p ð1 þ a
pÞ2
a2 : This is solved for p = 0, p = 1, and p = (1 + 2a)(1
λ), if 0  p  1. The expected utility of partner 1 (see (27)) equals 1 for all p. However, the expected utility of partner 2 varies and is maximized for p = 0, which, therefore, determines the K-S solution. Since here p = K = 0, partner 1 receives nothing, and partner 2 receives all the profit. Þα2 • If K is set at zero, and a = 0, then from (30), we have that p satisfies ð1
p ¼ λ. pα1 1 • Note that dp dλ ¼
λ

pð1
pÞ α1 ð1
pÞþα2 p

< 0: ∎

Concluding Remarks Partnerships are a common arrangement whether the partners’ skills are complementary or similar. While their relations are not ones of agency, a scheme for dividing uncertain future profits has to be devised in advance. We model such decisions primarily through bargaining concepts. As such, this is a problem of

Sharing Profit and Risk in a Partnership

133

negotiation. Each partner is expected to earn more than without the partnership. We emphasize linear contracts and consider partners with different risk attitudes and beliefs. For example, one partner may receive 30% of the profit and receive a transfer of $1 M from the other. Natural avenues for future research include: • Profit sharing when partners generate their own revenue, as well as joint revenue. • Generalizing Dubra’s two-player asymmetric K-S solution to more players. • Cost allocation according to partners’ individual revenue. Here the costs have to be paid from realized, rather than expected, revenues. Finally, the motivation for creating partnerships should enter the picture. If partners have similar skills (e.g., lawyers, physicians), the motivation is risk-sharing and economies of scope.

Cross-References ▶ Negotiation as a Cooperative Game ▶ Non-cooperative Bargaining Theory ▶ The Notion of Fair Division in Negotiations

References Binmore K, Rubinstein A, Wolinsky A (1986) The Nash bargaining solution in economic modelling. Rand J Econ 17(2):176–188 Borch K (1962) Equilibrium in a reinsurance market. Econometrica 30(3):424–444 Brousseau E, Glachant J-M (2002) The economics of contracts: theory and applications. Press, Cambridge University Dubra J (2001) An asymmetric Kalai-Smorodinsky solution. Econ Lett 73:131–136 Friedman JW (1986) Game theory with applications to economics. Oxford University Press, Oxford, UK Gerchak Y, Khmelnitsky E (2019a) Partnership’s profit sharing: linear and non-linear contracts. Int Game Theory Rev 21. https://doi.org/10.1142/S0219198919400085 Gerchak Y, Khmelnitsky E (2019b) Bargaining over shares of uncertain future profits. EURO J Decis Processes 7:55–68 Gerchak, Y, Khmelnitsky E (2019c) Profit sharing via the Kalai-Smorodinsky solution, working paper Hartl RF, Sethi SP, Vickson RG (1995) A survey of the maximum principles for optimal control problems with state constraints. SIAM Rev 37:181–218 Kadan O, Swinkels JM (2013) On the moral hazard problem without the first-order approach. J Econ Theory 148(6):2313–2343 Kalai E (1977) Nonsymmetric Nash solutions and replications of 2-person bargaining. Int J Game Theory 6(3):129–133 Kalai E, Smorodinsky M (1975) Other solutions to Nash’s bargaining problem. Econometrica 43 (3):513–518 Khmelnitsky E (2002) A combinatorial, graph-based solution method for a class of continuous-time optimal control problems. Math Oper Res 27:312–325

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Kihlstrom R, Roth AE, Schmeidler D (1981) Risk aversion and solutions to Nash’s bargaining problem. In: Moeschlin O, Pallaschke D (eds) Game theory and mathematical economics. Elsevier North-Holland Publishing Company, Amsterdam, pp 65–71 Levin J, Tadelis S (2005) Profit sharing and the role of professional partnerships. Q J Econ 120(1):131–171 Muthoo A (1999) Bargaining theory with applications. Cambridge University Press, Cambridge Nash J (1950) The bargaining problem. Econometrica 21(1):128–140 Rubinstein A (1982) Perfect equilibrium in a bargaining model. Econometrica 50(1):97–109 Ward GC, Burns K (2000) Jazz: a history of America’s Music. Knopf. Random House Inc., New York Weinstock R (1974) Calculus of variations with applications to physics and engineering. Dover Publications, New York Wilson R (1968) The theory of syndicates. Econometrica 36(1):119–132

Part III The Context for Group Decision and Negotiation

Advances in Defining a Right Problem in Group Decision and Negotiation Melvin F. Shakun and Bilyana Martinovski

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Defining a Right Problem in Group Decision and Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Spiritual Rationality Validation Test for a Right Problem/Solution for an Agent” in Shakun (2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Right Decision for the Group and a Larger Society” in Shakun (2013) . . . . . . . . . . . . . . . . . . Communication as a Producer of Connectedness with the Other . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shift of Attention Produces Higher Value Common Ground and Problem Restructuring . . . Redefinition of Communication as a Producer of Connectedness with the Other . . . . . . . . . Empathy, Reciprocal Adaptation, and Interactive Alignment as Producers of Connectedness with Otherness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example of Connectedness in Communication Through Reciprocal Adaptation and Interactive Alignment in Positive Empathy Exchanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Connectedness with the Other in Negative Emotion Contexts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

138 138 139 141 141 142 144 147 149 152 154 154 155

Abstract

Not all group decision and negotiation agreements are right solutions. In order to take a right decision and find a right solution to a problem, one has to first of all define the right problem. This chapter presents the evolution of a dynamic problem – restructuring for definition of right problem/solution in group decision and negotiation and its manifestation in communication. It starts with a summary of the M. F. Shakun Leonard N. Stern School of Business, New York University, New York, NY, USA e-mail: [email protected] B. Martinovski (*) Center for Cognitive Semiotics, Lund University, Lund, Sweden e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_27

137

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framework for Evolutionary Systems Design and the Connectedness Decision Paradigm Validation Test and then goes through seven ways in which communication, as a cognitive semiotic process, produces connectedness with the Other, namely, shift of attention, common ground, redefinition of communication, empathy, interactive alignment, theory-of-mind reasoning, and reciprocal adaptation. Keywords

Group decision · Negotiation · Problem · Solution · Communication · Connectedness · Emotion · Spirituality · Rationality · Adaptation · Cognitive semiotics · Empathy

Introduction Not all group decision and negotiation agreements are right solutions. In order to take a right decision and find a right solution to a problem, one has to first of all define the right problem. This chapter presents the evolution of a dynamic problem – restructuring for definition of right problem/solution in group decision and negotiation and its manifestation in communication. It starts with a summary of the framework for Evolutionary Systems Design and the Connectedness Decision Paradigm Validation Test and then goes through seven ways in which communication produces connectedness with the Other, namely, shift of attention, common ground, redefinition of communication, empathy, interactive alignment, theory of mind reasoning, and reciprocal adaptation. This chapter relates to other chapters on ▶ “Behavioral Considerations in Group Support”; ▶ “Role of Emotion in Group Decision and Negotiation”; ▶ “Procedural Justice in Group Decision Support”; ▶ “Group Decision Support Practice “as it happens””; and ▶ “Negotiation Process Modelling: From Soft and Tacit to Deliberate.”

Defining a Right Problem in Group Decision and Negotiation Shakun (1992) defines a right problem/solution in group decision and negotiation based on cognition, affective feeling (emotion) and evolutionary generating procedures, in particular a heuristic controls/goals/values referral process for problem restructuring within a general modeling framework, Evolutionary Systems Design (ESD). With ESD, a problem representation consists of two evolving hierarchies of purposes/values – hierarchies 1 and 2 – see hierarchies 1 and 2 here, taken from Shakun (2013) (Fig. 1 and 2 below). Shakun (2010) reviews Shakun (1992) and evolves a spiritual rationality definition of a right problem to include spirituality in addition to cognition and emotion (and other consciousness manifestations – intuitions), as well as the ESD heuristic referral process.

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Fig. 1 Hierarchy 1

Shakun (2013) builds on Shakun (2010) to evolve and simplify the spiritual rationality validation test within an evolved Spiritual Evolutionary Design Framework, the Connectedness Decision Paradigm, CDP (see Fig. 3 below). Following CDP, One represents all there is. Two represents the process of all there is. Two emerges (manifests) from One as agents. An agent constitutes energy/ matter/consciousness (awareness) integrally bound. Agents may be natural (e.g., humans, animals, insects, plants) or artificial (e.g., computers, robots). Here the main focus is on human agents. Connectedness is an experience of unity – a dynamic unity relation experience of an agent. In emerging from One, an agent has an inherent overriding purpose (intended desired result of action in Two). This purpose is to experience connectedness with One (spirituality) – to live Two as One. In practice, a purpose surrogate for connectedness with One is often used. As desired results, purposes may be generally called values, i.e., purposes/values. Spirituality is the highest value.

“Spiritual Rationality Validation Test for a Right Problem/Solution for an Agent” in Shakun (2013) For an agent, if a purpose 1 is reasonable with regard to producing a purpose 2, i.e., the purpose 1/purpose 2 binary purpose relation is reasonable or rational for that agent. For an n-ary purpose relation, rationality means production among purposes in the n-ary relation is reasonable. While rationality is properly associated with cognition,
hence, the term cognitive rationality based on cognitive reasoning – intuition (such as emotion) is also involved in judging rationality (reasonableness) of a purpose relation.

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Fig. 2 Hierarchy 2 Coalition (group) preference: compromise solution

Coalition preference structure (game theory, social choice, concession-making)

Individual preferences

Individual preferences structures

Criteria

Goal/criteria relation

Goals

Technology

Controls (decisions, actions)

All there is Self Hierarchy 1 Right Decision

Problem Definition

ValidationTest

Hierarchy 2

Spiritual Problem Solution Rational

Other

Fig. 3 Decision validation test

For validating spiritual rationality of an n-ary purpose relation, an agent using cognitive reasoning and intuition judges whether the relation is (1) rational and (2) a producer of connectedness with One (or a surrogate purpose). A problem/solution represented by hierarchies 1 and 2 is an n-ary purpose relation.

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Suppose an agent uses a trial arrived at compromise solution found by the group in his private group problem representation (Shakun 2013, Sect. 7) – hierarchies 1 and 2 – and tests this problem/solution to validate spiritual rationality. Successful validation means the agent has validated a right problem/solution. The solution constitutes a right decision for the agent. An individual agent could require that in order for his trial arrived – at problem/ solution to give a right decision for him, the decision also be right for some or all other agents in the group, and this could be the case for any and all individual agents. In any case, if an individual agent judges that a trial arrived at solution is not right for him, the group could continue problem solving to arrive at an evolved solution that is right for him. Figure 3 below shows the Spiritual Evolutionary Design Framework with the Connectedness Decision Paradigm Validation Test. The above discussion of spiritual rationality and its validation clarifies/simplifies an earlier presentation by Shakun (2010).

“Right Decision for the Group and a Larger Society” in Shakun (2013) If each individual agent validates the rightness of his trial arrived at problem/ solution, then the group has defined a right solution, i.e., a right decision for the group. In practice, a trial arrived at solution could still be chosen – or another solution adopted – based on some accepted procedure from game theory, social choice, or concession making (Hierarchy 2). If the solution selected is right for many agents in the group, it could be said to be right widely for members of the group. Right widely generally does not apply to solutions adopted using some non-accepted procedure, if non-accepted by at least many group members – as coercive use of hard power. Going beyond the problem-solving group, a larger society may consider an adopted group solution or some other solution. Interested agents in the larger society will have their own problem representation of purpose relations in some form (not necessarily using CDP hierarchies 1 and 2) and test the group solution for rightness using some validation test (not necessarily spiritual rationality). If a solution is right for many agents in a larger society beyond the problem solving group, then the solution is right widely for the society.

Communication as a Producer of Connectedness with the Other In hierarchy 1, connectedness with One (spirituality) is the highest value. Below this are high-level values (Shakun 2013) that can serve as surrogates for connectedness with One. Here we focus on high-level value, connectedness with the “Other” – other agents – as a purpose surrogate for connectedness with One. We look at communication as a producer of connectedness with the Other and connectedness as a producer of right problem representation/solution. Connectedness with Other or with One is thus one among other purposes of communication, which can be studied

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within cognitive semiotics. Here we describe seven ways in which communication produces connectedness with the Other: Shift of attention (Martinovski 2010) Common Ground (Martinovski 2000, 2007; Martinovski and Traum 2003; Martinovski et al. 2007) Empathy (Martinovski and Marsella 2006; Martinovski and Mao 2009) Interactive alignment (Martinovski 2013b) Reciprocal adaptation (Martinovski 2013a) Theory of Theory of Mind: mirroring, simulation, convention (Martinovski 2007; Iacoboni 2005; Christov-Moore and Iacoboni 2015) Definition of communication (Martinovski 2014; Martinovsky 2015)

Shift of Attention Produces Higher Value Common Ground and Problem Restructuring In the following example, we have a judge, a defense counselor, and a prosecutor engaged in a specific kind of negotiation bound to the context of courts of justice, namely, a plea bargain. The transcription of the authentic interaction is part of Maynard’s corpus with the following transcription note: [] denote overlap, ¼
latching, _ – emphasis, Jge – Judge, Def – Defense counsel, Prs – Prosecutor. Plea bargains in the USA usually do not involve a judge. However, since in many cases deals are struck between the parties, which do not result in respect and application of relevant laws, some states decided to include a judge as a mediator in the plea bargain in order to improve the application of the law. Thus, on one hand, we have the court of justice rational goal to improve the justice process and outcome; on the other hand, we have the rational goal of the participants to reach a less costly agreement. The negotiators have to agree if they would settle or if they would go to a jury trial, and if they would settle what law is to be applied and respectively, what penalty. The excerpt below shows the end of the negotiation. The parties have agreed to settle but not on what law is to be applied and what penalty. The question is if the defendant is to serve prison or jail time or pay a penalty. If he has repeatedly struck a police officer, the law requires more severe penalty than a fee. The prosecutor has found that the defendant has a prior conviction for the same crimes he is arrested for, namely, striking a police officer and disturbing peace. The law is not on the defense counsel’s side, and we see him using negative emotions such as anger, ridicule, indignation, sarcasm, and threats; his good relation with the judge and an unsubstantiated social prejudice claim as counter-arguments. If the law is to be applied, the defense would have to agree to jail time and may bargain the amount of time in jail. After a few cycles of strategically emotionally loaded interactive duel, the parties end up in a stale mate manifested by silence on line 14 (the most relevant to the analysis lines are in bold). At that point, on line 20, the mediator, in this case a judge, whose purpose is to assure the proper application of the law, prompts one of the prosecutors to make a decision and a concession. However, the mediator is not

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asking the prosecutor what is lawfully binding; he is suggesting a rational, “reasonable” solution. Example 1 Plea Bargain Negotiation 1. Prs: He has ub a: one prior. (0.3) conviction in this jurisdiction 2. with thee uhm (0.8) sheriff's office, of of interestinly 3. enough. u:v striking a public officer and of disturbing peace. 4. Def: Will you knock it off. ((disgusted tone)) (0.5) You wanna make 5. a federal case out of this¿ 6. Prs: N:o, [I I just] think [that that i]t's it's not uh this uh¼ 7. Def: [ ˙h h h ] [ h h m ] 8. Prs: ¼happy go lucky chap's uh first (1.0) encounter with uh um (1.8) 9. Def: [Statistic]ly if ya got black skin:. you ar (0.2) you ar (.)¼ 10. Prs: [( )] 11. Def: ¼hhighly likely to contact the police. I think 12. uh:substantially more likely than if you're white. i:s [6 n ' t he] 18. Les: REE-> [6 what] do you sa:y. {0.3} 19. Joy: PEG-> oh isn't he drea:dful. 20. Les: PEE-> eye-:-:s: {0.6} 21. Joy: PEG-> what'n aw::f'l ma::[7:::n] 22. Les: PEE-> [7 ehh] heh-heh-heh 23. Joy: PEG-> oh:: honestly, I cannot stand the man it's \ just {no[8 :}] 24. Les: RPEE-> [8 I] bought well I'm gon' tell Joyce that,ehh[7 heh ]¼ 25. Joy: [9 ( )]¼ 26. Les: RPEE¼[9 heh-heh he-e] uh: eh [10 eh hhhhh] 27. Joy: PEG-> ¼[10 O H : : : :.] I do think he's dreadful 28. Les: PEE-> tch oh: dea-r 29. Joy: PEG-> oh: he r[11 eally i]:s, 30. Les: RPEE-> [11 he dra-]ih-he (.) took the win' out'v my sails c'mpletel(h)y . 31. Joy: REG-> I know the awkward thing is you've never got a ready a:n[12 swer have you. that's ri:ght, ] 32. Les: REE-> [12 no: I thought'v lots'v ready a]nswers a:fterward[13 s], 33. Joy: REG-> [13 yes] that's ri::gh[14 t]. 34. Les: REG-> [14 yes] . 35. Joy: REG-> but you c'n never think of them at the ti:[15 me a:fterwards I always think. oh I should've said that. or I should've said thi]s.

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36. Les: REG-> [15 no:.no:. oh y e s e h- r i : g h t.] {0.7} 37. Joy: REGE-> b[16 ut] I do:'nt think a'th'm at the ti:me 38. Les: REG-> [16 mm:]. ehh huh huh {0.8} 39. Joy: oh:: g-oh 'n I think carol is going, t'the [17 meeting t'ni g h t,]

Emotive reciprocal adaptation is manifested linguistically most expressively when Joy offers elicited empathy on line 15 and Les implicitly accepts it on line 16. The exclamations on lines 15 and 16 are similar; Les starts her exclamation with a similar sound to this of Joy “oo” and continues with a slight differentiation. In that sense, the speakers align with each other in tone and sound, starting with an imitation, although the functions of the utterances are different. Then starts a separation of parallel and reactive empathy (Martinovski 2007). On lines 17, 19, 21, 23, 27, and 29, Joy gives examples of what is meant by parallel empathy, i.e., she expresses a mirrored feeling or disapproval of the person by whose actions Les feels hurt, in that way mirroring Les’ dislike of this person’s actions. In that sense, this is a parallel form of entering into each other’s frame of reference, i.e., of reciprocal adaptation through emotional alignment. On line 30, Les expresses her internal distress, which changes the character of the elicited empathy, i.e., line 31 illustrates reactive empathy. This empathy type is realized here with a role play simulation expressed by the use of the generalizing pronoun “you,” which is another linguistic formulation of the reciprocal adaptation mechanism. The tag question is an elicitor of consent, which again turns the roles around: Joy is supposed to be the empathy giver, but she often becomes the empathy elicitor as a form of empathy giving. On line 35, Joy exchanges the impersonal “you” with a reference to herself, voicing Les’ internal discomfort and embarrassment for which she seeks empathy. This voicing is expressed as a quotation of internal dialogue. Thus Joy internalizes Les’ inner state, i.e., she displays reactive emotive empathy. This exchange of roles and positions is part of the reciprocity ritual. Line 35, however, is an example of verbalized simulation process, which is in the lines of theory of theory of mind rather than interactive alignment theory. On line 37, Joy has taken Les’ internal position and talks about her own experiences, which is another example of cognitive reciprocal adaptation. Les now functions both as a receiver and a giver of empathy; the process has reached its climax, and suddenly on line 39, Joy announces a completely new topic. The adaptation is at first more somatic, uncontrollable, and then becomes more cognitive as the speakers turn to comparisons of experiences and mental representations of experiences. In this empathy process, both speakers verify, confirm, and reconfirm for each other the legitimacy of their experiences, values, and attitudes, and in the processes, they often mirror each other’s verbal actions. The empathy process in Example 1 is fulfilled: there was elicitation, giving, and acceptance of empathy, and there was also identification (e.g., line 31), incorporation (e.g., line 35), reverberation (e.g., line 37), and finally detachment (line 39). The sudden change at the end of Example 1 and the repetitive turn of the roles in the process of empathizing suggest that the empathy process is rather rehearsed and therefore ritualistic. We observe interactive alignment but also

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theory of mind building processes during empathy exchange. Interactive alignment has diverse linguistic manifestation, e.g., exclamations, tone of voice, tag questions, parallel, and reactive empathy forms. Interactive theory of mind building manifests at the incorporation and reverberation empathy stages and takes the form of explicit reasoning from the other’s point of view through generalized pronouns. Thus, reciprocal adaptation as a producer of connectedness with the Other which is a condition for taking a right decision according to the decision validation test illustrated by Figure 3. is realized in this ritualistic informal empathy exchange by frequent interactive alignment and a few final more complex interactive theory of theory of mind (TToM) processes.

Connectedness with the Other in Negative Emotion Contexts In comparison to friendly sharing and empathy exchange, a plea bargain is a more formal activity, which involves strategic and tactical interaction, where the parties have opposing goals. It is a negotiation where participants have conflicting roles and goals. Pickering and Garrod predict manifestations of misalignment or disconnectedness in such activities). Reciprocal adaptation or the procedure by which participants gradually enter each other’s frame of reference may realize in different ways (Martinovski and Marsella 2006; Martinovsky 2015; Martinovski et al. 2007). Rather than claiming that there is resistance to adaptation, the plea bargain data analyzed below indicate that there is adaptation even in negative contexts. In Example 1 above, the prosecutor offers facts, which aggravate the guilt of the defendant and indirectly suggest a harsher verdict. He does that after refusing to respond to empathy elicitation by the defense counsel. For the sake of clarity, we cite below part of Example 1 as Example 3. The defense counsel interprets the prosecutor’s stance taking as a challenge (see lines 204–6 below) and responds with a sudden explosive expression of anger, contempt, and a threat (line 207 below). This emotional reciprocal adaptation takes a form of mirroring: a calm and sober threat to his client’s interests is met with an emotionally loaded counter-threat. On top of that, the defense repeats lexically the prosecutor on lines 216 and 220 below with mocking intonation. This is good lexical alignment but no cooperation and no success in communication, in the sense of communication as alignment. In the sense of communication as a meeting with otherness, this is good communication, because it expresses otherness. Rather than getting into the other’s frame of reference and accepting it, the defense counsel gets into the other’s frame of reference, rejects it, and, with the emotional display, blames the other party. Thus, there is adaptation in negative terms, but it is not in the interactive alignment format but rather as a wellplanned rational ToM and semiotic process, predicting and preventing other’s interactive moves and reactions (as described by the defense counsel himself in the “intermission” phase) and that way arriving to a right decision by redefining the problem and putting it through both rational and connectendess tests.

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Example 3 Plea Bargain Negotiation

204 Prs: He has ub a: one prior. (0.3) conviction in this jurisdiction 205 with thee uhm (0.8) sheriff's office, of of interestinly 206 enough. u:v striking a public officer and of disturbing peace. 207 Def: Will you knock it off. ((disgusted tone)) (0.5) You wanna make 208 a federal case out of this¿ 209 Prs: N:o, [I I just] think [that that i]t's it's not uh this uh¼ 210 Def: [ ˙h h h ] [ h h m ] 211 Prs: ¼happy go lucky chap's uh first (1.0) encounter with uh um (1.8) 212 Def: [Statistic]ly if ya got black skin:. you ar (0.2) you ar (.)¼ 213 Prs: [( )] 214 Def: ¼hhighly likely to contact the police. I think 215 uh:substantially more likely than if you're white.you¼ 101 Jge: ¼[((thrt clr)) ] 102 Def: ¼[start talkin'] to each other through clenched< teeth. 103 [And after about ] five ] minutes of (.) challenging each¼ 104 Jge: [ ah hih!hihhih] ( )] 105 Def: ¼other to go [to trial, and I know 'at 'e doesn't try any¼ 106 [((sound of small item dropped on table)) 107 Def: ¼ca(h)ses see(h)ee, [˙hh o(h)nly r(h)eason's I g(h)otta go to¼ 108 Jge: [( ) 109 Def: ¼trial a[gainst one'a his new kids, r(h)ight?¼ 110 Jge: [˙hhh 111 Jge: ¼Huh!¼ 112 Def: ¼˙hh Or [(hi)his (n- old pro like) mister Franklin, ˙hhh¼ 113 ( ): [( ) 114 Def: ¼And so I finally tried to get the conversation around t(h)a what 115 we were talkin' about. like sett'lin' the ca(h)ase ˙hhh It 116 ˆworks.probably 123 better one fortyeight than a six fortyseven ef< if you wanna 124 be very stric[t about it. 125 Def: [Wull I- thu- I see it as a six forty seven ef. 126 uh: 'e didn' lay hands on any officers, ˙hh if he 'adn't been 127 so ˇdrunk I assume nothing none'uh this woulda ha:ppened. 128 ˙hh[h 129 Prs: [W[ell I130 Def: [I don't think it's worth any jail time no matter what it 131 is. (("no" is garbled)) 132 Prs: I was being academic when I said that. [I ]uh: I I think¼ 133 Def: [ Oh,]

After restructuring the problem by laughing with the judge and flattering, dominating, and ridiculing his opponent, Def suggests his own version of a settlement value, which is of completely different kind: not jail but a very low fine. He does that by following the entertainment and ridicule line of argument, where he invents a new version of a legal term word (line 157–8) and then playfully offers a mocking apology (161,163): Extract 5. 157 Def: [Okay, uh: twenny fi dollar fine?I made it up.[I'm sor]ry.I didn't¼ 162 Prs: [Yih got-] 163 Def: ¼look at the diction-I made up a [ w o rd. 1, then the respective negotiation process is said to be progressive. Theorem 3 Protocols with a positive path of effects of impacts of explicit and tacit knowledge are convergent. The proof results directly from the assumption that the set of feasible solution is nonempty and bounded.

General Remarks and Future Research Tacit and explicit knowledge jointly underlie proposals in negotiation. While explicit knowledge contributes to formal models and its recommendations, observed negotiation processes may reveal deviations of model-based recommendations from real proposals. These deviations reflect inaccuracy of the pre-negotiated common problem structure resulting in limited access to full information and the impact of tacit factors. In this paper we classified negotiations with respect to the appearance of such deviations and identified a class of progressive negotiation processes which converge. The analysis dealt with iterative restructuring of negotiation models driven by the evaluation of outcomes of proposals resulting from explicit and tacit experiences. The process of restructuring used the BIP – a typical interactive procedure based on solving a series of linear programs. The procedure is controlled by declarations of parties on their aspirations and acceptable concessions formed in natural language. The presented approach proves the possibility of merging subjective views, dynamic change of parties’ preference in the course of negotiation, and both – explicit and tacit knowledge to create recommendations for a compromise. This issue was identified in literature and resulted in numerous but separately analyzed aspects. The presented approach integrates these perspectives. It copes with

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subjectivity reflecting interactivity of the decision processes and provides general statements on the appearance of tacit knowledge impacts in deliberate models. The example shows the possibility to analyze practical problems in this framework, but limited space forced us to postpone a detailed description of the negotiation process which directly follows general formulae for the example situation. Several simplifications were adopted here. Sometimes they were made for the sake of simplicity (e.g., two-party case), sometimes to be able to prove the existence of solutions (linearity of vector objective functions and constraints), and sometimes to be able generate these solutions (in BIP). This narrows the range of applications but not at the cost of generality of approach from a point of view of decision theory. A many-party case or different interactive procedures may be used for analysis of deviation observed in negotiation protocol. Linearity assumption may be weakened to include (quasi)convexity. Finally, the presented model identifies some challenging extensions. The first one is to identify common axioms for interactive procedures and to prove for an axiomatically defined class generalized theorems shown here for BIP. The presented formalism enables a second extension related to the introduction of negotiation games using techniques of experimental economy to explain deviations exhibiting the appearance of tacit knowledge. Here the key question concerns a link between measurable human physiological reactions and tacit experiences revealed in deviations from protocols. Physiological reactions recognized as signs of tacit knowledge intervention can facilitate interpretation of deviations and trigger the process of learning aimed at improvement of deliberate models. Context analysis can direct the information search and thus guide learning. Relevant information is presented in other chapters of the handbook.

Cross-References ▶ Group Support Systems: Concepts to Practice ▶ Impact of Cognitive Style on Group Decision and Negotiation ▶ Looking Back on Decision-Making Under Conditions of Conflict ▶ Methods to Analyze Negotiation Processes ▶ Multicriteria Methods for Group Decision Processes: An Overview ▶ Multiple Criteria Decision Support ▶ Multiple Criteria Group Decisions with Partial Information About Preference ▶ Role of Emotion in Group Decision and Negotiation ▶ Systems Thinking, Mapping, and Group Model Building

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Holistic Preferences and Prenegotiation Preparation Tomasz Wachowicz and Ewa Roszkowska

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prenegotiation Preparation – Negotiation Template and Its Evaluation . . . . . . . . . . . . . . . . . . . . . . . Multiple Criteria Decision Aiding and Two Ways of Preference Elicitation . . . . . . . . . . . . . . . . . . Formal Methods for Indirect Evaluation of Negotiation Template . . . . . . . . . . . . . . . . . . . . . . . . . . . . . UTASTAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MARS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Software Support of Prenegotiation Preference Elicitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eNego System and Empirical Findings from Using Hybrid Holistic Prenegotiation Support . . . The System and Its Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Module for a Hybrid Holistic Approach to Prenegotiation Preference Elicitation . . . . The Use of the Evaluated Scoring System in the Bargaining Support in eNego . . . . . . . . . . The eNego Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

One of the activities within the prenegotiation preparation phase is to create an analytical basis for decision support in negotiations. This is done by defining the structure of the negotiation problem, called negotiation template, and eliciting the negotiators’ preferences. As a result, the negotiation offer scoring system is determined, which allows evaluating and comparing the offers, measuring the scale of concessions and their reciprocity and visualizing the negotiation T. Wachowicz (*) Department of Operations Research, University of Economics in Katowice, Katowice, Poland e-mail: [email protected] E. Roszkowska Faculty of Economics and Finance, University of Białystok, Bialystok, Poland e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_64

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progress. The negotiation analysis suggests using the simplest decision support methods here, which are often based on preference aggregation paradigm, such as direct rating. Some recent experimental works, however, indicate various cognitive and technical problems that may occur when such an approach is used. Therefore, in this chapter, the issue of using an alternative approach to score the negotiation template is discussed, which implements a preference disaggregation paradigm and operates with holistic preference declarations. Various options that may be used for designing the holistic prenegotiation preference elicitation protocol are discussed, and the results of implementing one hybrid holistic protocol in the eNego bilateral negotiation support system are presented. Keywords

Negotiation · Multiple criteria analysis · Negotiation support system · Preference modeling · Negotiation process

Introduction Negotiations are complicated decision-making processes (Thompson 2015). In these processes, the parties are involved (two or more) who usually appear to have conflicting interests, and therefore they are jointly trying to find a solution that would satisfy – at least to some extent – their goals. This requires a mutual understanding of the counterpart’s needs and acknowledging the necessity of making concessions, which inherently makes a problem of developing an adequate negotiation approach. The false assumption regarding such an approach is that it may be either soft or hard (Fisher et al. 2011). In fact, neither of these approaches is considered efficient, as they are focused on some social and psychological elements of negotiation game and parties (people) themselves, rather than on the potential value that may be created when the problem under consideration is solved. To know what this value can be and how it may be divided among the parties, the detailed knowledge of the problem, its components, and context is required, which should be processed and analyzed to identify creative options for agreement. This involves extensive analytical work, and cannot be effectively done during the negotiation process. Therefore, the theory of negotiation recommends the parties to conduct a prenegotiation preparation before getting involved in the actual bargaining (Zartman 1989; Peterson and Lucas 2001). From the behavioral perspective, it allows the parties to build the bridges between the conflict they face and prospects of future cooperation, learn about the counterpart, reduce the uncertainty, assure that the concessions will be requited, and organize the internal support. From the formal perspective, which is more focused on decision making aspects of the process, it allows to operationalize and quantify the elements of the negotiation problem, such as issues and options to be negotiated in the form of negotiation template, as well as

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precisely elicit the negotiator’s preferences for all these elements. The latter, however, requires some decision-making and cognitive skills. To prevent negotiators from making errors or falling into certain metal biases during the preference elicitation, it can be facilitated using various decision aiding methods (Young 1991; Raiffa et al. 2002) that preferably should be tailored to the decision maker’s (DM) cognitive style (see the chapter ▶ “Impact of Cognitive Style on Group Decision and Negotiation”). As a result, the formal scoring systems can be built that represent the parties’ goals and needs, which may be used for the asymmetric and symmetric support of negotiators in their search for agreement. Most of the prenegotiation protocols used for structuring and evaluating the negotiation problem operate with the classic multiple criteria decision aiding (MCDA) techniques (see chapter ▶ “Multiple Criteria Decision Support”) that are based on the preference aggregation approach (Raiffa 1982; Keeney and Raiffa 1991; see also a broader discussion on the problem modeling in chapter ▶ “Negotiation Process Modelling: From Soft and Tacit to Deliberate”). They assume that the negotiators, being skilled decision makers, can easily describe their preferences on the atomic level (i.e., for the very basic elements of the negotiation problem) in a quantitative way (using numbers). Such preferences can be then aggregated to determine the preferences over the negotiation offers, which are the packages of selected options. One of the most frequently used methods to support negotiators in their prenegotiation tasks is the direct rating (DR) method, which assumes that negotiators assign the numerical scores to the options that describe their preferences in a cardinal way (see e.g., Edwards and Barron 1994). It is implemented in such negotiation support systems like Inspire (Kersten and Noronha 1999), Negoisst (Schoop et al. 2003) or SmartSettle (Thiessen and Soberg 2003). Despite DR’s simplicity, some electronic negotiation experiments revealed its drawbacks resulting from limited cognitive capabilities of negotiators. The negotiators found it challenging to operate with numbers of abstract interpretation (desirability scores, utilities, satisfaction levels) and were unable to map the predefined preference information about issues’ importance precisely and reliably into the direct rating scorings systems (Roszkowska and Wachowicz 2014a, 2015a). Moreover, some in-class experiments on multiple criteria decision making proved that decisionmakers were averse to use quantitative evaluations. Having the possibility of choosing, they very rarely describe their preferences in a purely quantitative way using strong scales (in 16% of situations only). Contrary, they are willing to define them qualitatively in the verbal, linguistic, or pictorial way (57%) (Roszkowska and Wachowicz 2014b). Finally, specific technical nuances in the implementation of the DR approach in NSS may cause errors resulting from simple heuristics, such as unintentional blindness (Kersten et al. 2017). Naturally, some other techniques could be used to prenegotiation preference elicitation support, which also makes use of the preference aggregation paradigm. The Analytic Hierarchy Process (AHP), for instance, releases the decision-makers from operating with numbers while declaring preferences (Satty 1980). It is based on the series of pair-wise comparisons of the elements of negotiation problem using a

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nine-point verbal scale. AHP relies on the supposition that humans are more capable of making relative judgments rather than the absolute ones. An example of using AHP for multi-actor decision-making may be found in the chapter ▶ “Group Decision Support Using the Analytic Hierarchy Process.” However, the main drawback of AHP is that it may be used mainly in the cases of negotiation problems with a limited number of issues and possible options, and spanning the preference elicitation results made on some salient examples of options on the whole continuous scale may be troublesome (Brzostowski et al. 2012). In a series of papers (Wachowicz et al. 2012; Wachowicz and Błaszczyk 2013; Roszkowska and Wachowicz 2015b), TOPSIS method was also considered in the perspective of evaluation negotiation offers. In TOPSIS (Technique for Ordering Preferences by Similarity to Ideal Solution), options rates are replaced with the distances measured to the reference aspiration and reservation packages, which reduces the negotiator’s workload significantly. It allows additionally, to handle the problem of evaluating new packages that can appear in the negotiations, that fall behind the negotiation space defined in prenegotiation by the parties. However, using distance measures instead of subjective preferences requires making strong assumptions regarding the individual preferences of negotiators, so the risk occurs that the offers’ evaluations may not be precise. The theory of multiple criteria decision aiding offers an alternative support approach that is based on preference disaggregation-aggregation paradigm (Jacquet-Lagreze and Siskos 2001; Matsatsinis and Grigoroudis 2018). In this approach, it is assumed that the DM’s preferences may be inferred from the preferential information provided by them at the aggregated level (holistically). In the negotiation context, this requires preferences to be declared for some examples of negotiation offers (full packages), which are then decomposed by some analytic procedures to determine a system of scores for all atomic elements of the negotiation problem (e.g., the system of value functions). Hence, the evaluation of any negotiation offer, not only those evaluated by the negotiators, is possible. The holistic approach is considered to be less cognitively demanding as the decision-makers are asked to compare some alternative solutions that may really occur in the decision problem they face, which is more natural than comparing the single abstract options without their broader context (Corrente et al. 2013; Kadziński and Tervonen 2013). In this chapter, we discuss the issue of using the holistic disaggregation-aggregation paradigm in the multi-issue prenegotiation preparation process. We describe first the prenegotiation preparation phase and formalize its part related to problem structuring (template design), preference elicitation, and determining the negotiation offer scoring system (template evaluation). This also includes a brief description of preference elicitation by means of classic aggregation mechanism, that is, the direct rating. Then, we consider other options that can be used for template evaluation with a particular focus on holistic methods. We describe two selected methods based on preference disaggregation-aggregation approach in detail, that is, the most known UTA (UTilities Additives) (Jacquet-Lagreze and Siskos 1982) and MARS (Measuring Alternatives near Reference Solutions) (Górecka et al. 2016). Then, we show how these methods are used in the group decision and negotiation support systems.

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We describe in detail the eNego system (Wachowicz and Roszkowska 2020), its construction and functionalities it offers to negotiators in prenegotiation preparation by integrating some concepts of UTA and MARS. Finally, we show the experimental results that investigate the accuracy of the scoring systems determined by the negotiators using the hybridized holistic approach (implemented in eNego) with those determined with the classic aggregation approach, that is, the direct rating mechanism. They also examine the issues related to the ease of use and cognitive demand of the holistic approach in prenegotiation. The results are interesting, as they show the holistic approach to be not as low cognitively demanding as it is suggested in the literature. Quite contrary, the preference elicitation process conducted by means of a holistic approach may occur to be more time consuming and tiresome than the one conducted with the use of classic approach, yet this is a trade-off for the higher scoring system accuracy of the former.

Prenegotiation Preparation – Negotiation Template and Its Evaluation The broad definition of prenegotiation conceives it as the period in relations between the parties, in which the negotiation (bargaining) is considered (and often adopted) as a means to achieve their goals (Tomlin 1989). It is often perceived as an initial diagnostic phase of the negotiation process, the goal of which is to move parties from conflicting to cooperative perceptions and behaviors and increase this way the chances for success in actual bargaining (Saunders 1985; Zartman 1989), that is, in solving their joint decision-making problem (Thompson 2015). This requires preparation and gathering information about all important elements of the conflicting situation, the negotiation problem, the stakeholders involved, their interests, and the situational context. As prenegotiation shapes the negotiation strategy and approach, it is considered to have a crucial impact on the bargaining process and outcomes (Peterson and Lucas 2001; Peterson and Shepherd 2011). Therefore, it should be performed with adequate diligence and adequacy. There are many suggestions regarding how to conduct prenegotiation and organize the preparation activities (Lewicki et al. 2003; Peterson and Shepherd 2010). The most general recommendation divides prenegotiation into three phases (Raiffa et al. 2002). In the first phase, the negotiator is supposed to prepare alone, to build a big picture of the forthcoming negotiations as privately seen from their own perspective. In phase two, a joint meeting with the counterpart(s) is suggested to be organized, which allows verifying the private opinion about the problem and counterparts. In view of new knowledge gained in phase two, during phase three, the negotiator is supposed to think alone again and build their general strategy for the forthcoming negotiation. The issues for consideration in all three phases of the prenegotiation were summarized in the form of a prenegotiation checklist by Simons and Tripp (2003). The items from their checklist grouped into four categories are shown in Fig. 1.

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Prenegotiation preparation

Negotiator

   

Problem Negotiation issues Alternatives Issue importance (preferences)  BATNA  Reservation levels

Counterpart

Situation

Relationship

 Additional issues they may value  Issue importance (preferences)  BATNA  Reservation levels  Your target (when all the above considered)

 Deadlines (who is not flexible with regard to time)  Fairness norms used in argumentation  Topics to avoid and the response strategy for them

 The consequences of strategy undertaken (are our negotiation repetitive?)  Trust issues  Strategies and tactics your counterpart may use  Limits in authority  Agenda

Fig. 1 Prenegotiation checklist. (Source: based on Górecka et al. 2016)

A quick reading of the checklist allows distinguishing two groups of blocks that are concentrated on two separate elements of prenegotiation activities: recognizing the negotiation problem (blocks: negotiator and counterpart) and elaborating prescriptions for negotiation behavior (blocks: situation and relationship). The first group is of particular interest from the viewpoint of decision making and decision support in negotiations and consists of two steps. Step 1 is focused on building a detailed structure of the negotiation problem by identifying the possible issues to be negotiated, defining the feasible resolution levels (options) for these issues, and specifying the possible alternatives for the negotiation agreement. To help negotiators in defining the negotiation problem and its structure various problem structuring methods may be used, for example, the cognitive mapping (Eden 2004; Mingers and Rosenhead 2004) or the elements of PrOACT (Problem, Objectives, Alternatives, Consequences, Tradeoffs) approach (Hammond et al. 1998). The examples of the use of the cognitive mapping to adequate problem structuring and evaluation may be found in other chapters of this Handbook, for example, ▶ “Group Support Systems: Concepts to Practice,” ▶ “Procedural Justice in Group Decision Support.” Step 2 requires the analysis of such a problem from the viewpoint of the negotiator’s interests, that is, setting their goals, aspiration and reservation levels, and identifying this way a structure of their preferences that may be used to evaluate the alternatives (e.g., in the form of the scoring system). This two-step process is called by Howard Raiffa a designing and evaluating the negotiation template (Raiffa et al. 2002), and it resembles the process of structuring and analyzing the multiple criteria decision-making problem of sorting or choice problematic for a single decision-maker (Figuera et al. 2016). Note that similarly the group decision making processes are structured and evaluated – see the chapter ▶ “Multiple Criteria Decision Support.” To define the template formally, negotiators need to identify the set of negotiation issues as well as the sets of feasible resolution levels for these issues. Note,

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however, that some negotiation issues may be quantitative and have a continuous character, which makes it impossible to define finite and countable sets of their resolution levels. In such a situation, it is recommended to focus on the subset of selected salient options only, which discretizes the problem and makes it easier to analyze. Therefore, we define a negotiation template in the form of the following m + 1-tuple: n o T ¼ G, fXi gi¼1,...,m : n o where: G ¼ {gi}i ¼ 1, . . ., m denotes a set m of issues and Xi ¼ xij

ð1Þ

j¼1,...,ni

is a set of

ni salient options for issue gi. The salient options from template T are considered as potential resolution levels that comprise the negotiation offers. Therefore, without loss of generality, the set of feasible offers A may be defined as a Cartesian product of all m sets of feasible options, that is, Y A¼ Xi : ð2Þ i¼1,...,m

To compare the offers from A, the negotiator’s preferences for various resolution levels that comprise the sets Xi in the template T need to be declared. Additionally, some assumptions have to be made regarding how these preferences may be processed, that is, the preference model should be set up. Classically, the negotiation analysis uses an additive preference model (Raiffa 1982), which implicitly assumes that the preferences are independent among the issues (Keeney and Raiffa 1976). Consequently, the preferences are represented by marginal value functions v0i : Xi ! V ithat allow to represent the quality of an option xij in a form of numerical rating v0i xij . If v0i functions are unbounded, they represent the differences in issue importance only implicitly. Sometimes, however, the negotiator may wish to declare the issue weights explicitly. In such a case, the weights wi  0 are defined such as i¼ 1,. . ., mwi ¼ 1 and the marginal value functions are represented in a scaled form, v00i xij  ½0; 1. The global value function V, which can be used to evaluate negotiation offers a  A, is an additive aggregate of marginal value functions: V ð aÞ ¼

X i¼1,...,m

X

  j j z ð a Þ  v i xi , j¼1,...,n i i

ð3Þ

where: zij ðaÞ are binary switchers indicating if the option xij comprises offer a (1) or not (0); and vi ¼ v0i for unbounded preference declarations or vi ¼ wi v00i , if weights are declared and scaled marginal value functions used. Note, however, that if randomization between options in Xi is possible, zij ðaÞ can be a real number describing the fraction of option xij that is used to describe the performance of offer a.

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Thus, the additive scoring system can be represented in the simplified form: S¼

n   o vi xij

i¼1,...,m; j¼1,...,ni

 :

ð4Þ

Using additive scoring systems to score negotiation offers is very convenient and straightforward. Therefore, even if the conditions for preference additivity and independence are violated, in some situations, the use of the additive scoring system may be reinstated by, for instance, redefining the set of issues (Keeney and Raiffa 1991). However, if the preferences have a more complicated structure, for example, are defined by means of pseudo-criteria or outranking relations, the scoring system, as defined in Eq. (3), cannot be determined. Nevertheless, there may still be possible to use some analytic techniques to generate the global scores for offers, though, not in the form presented in Eq. (4). Designing and evaluating the template in prenegotiation by each party is crucially important from the viewpoint of decision making and decision support, both symmetric and asymmetric, that can be provided to the parties during the bargaining phase (Raiffa 1982). First, each feasible offer that is put on the negotiation table may be scored and compared to the others (including BATNA) while searching for an acceptable agreement. The trade-offs between issues may be easily captured, helping to build the most efficient concessions strategy. The dynamics of the negotiation process can also be visualized for the parties in the form of negotiation history graphs depicted in the evaluation spaces of each negotiator individually. They show the scale and reciprocity of concessions made by the negotiator and their counterpart. If software support is considered, the scoring system may be used to suggest the negotiator an offer to be submitted as a balanced response to the offers submitted and received earlier (Kersten and Lai 2007; see also the chapter ▶ “E-Negotiations: Foundations, Systems, and Processes”). The software support system, or a human third party, may also use the evaluated templates of both negotiators to support them symmetrically. The arbitration may be offered to the parties who were unable to negotiate an agreement themselves, for example, by suggesting some fair solutions externally (Brams 2003). For those who achieve the compromise, the postsettlement improvements of the negotiated agreement may also be suggested to assure the final agreement will be efficient. The extensive possibilities for negotiation support that may be offered based on the scoring systems defined in prenegotiation require the process of designing and evaluating the negotiation template to be conducted diligently to assure an accurate representation of the conflict situation. In the next section, we will consider various possibilities that are offered with this regard by the decision theory.

Multiple Criteria Decision Aiding and Two Ways of Preference Elicitation Multiple criteria decision analysis refers to the complex problems of choice, ranking, sorting, or description of the alternatives evaluated by means of multiple, usually conflicting criteria (Roy 1996; see the chapter ▶ “Multiple Criteria Decision

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Support”). These problems need to be solved according to the decision maker’s judgments or preferences (Figuera et al. 2016). The goal of the choice problem is to select the single best alternative or reduce the group of alternatives to a subset of equivalent “good” ones. In the ranking problem, alternatives should be ordered from the best to worst. The order may be partial when incomparability is acceptable or complete. In sorting (classification) problems, the goal is to assign the alternatives into ordered and predefined performance groups, called categories. This approach is also used in ranking problems with a multitude of alternatives. They are first grouped into categories, which are then ordered according to specific ranking rules. Finally, the goal of the description problem is to provide a detail description of alternatives and their consequences, to make the problem better understood by the decisionmaker. In general, multiple criteria decision analysis consists of three elementary steps: determining the structure of the decision problem, expressing and modeling decision-maker preferences, and finally synthesizing the DM’s preferences and developing recommendations regarding the alternatives. On the first step of multiple criteria decision analysis, given a set of alternatives A ¼ {a1, . . ., an} and the set of criteria G ¼ {g1,. . ., gm} the performance values (options) aji are determined. They constitute a so-called decision matrix [aji]j ¼ 1, . . ., n; i ¼ 1, . . ., m. It is equivalent to what was described in the negotiation context as the process of designing the negotiation template T with the associated set of feasible negotiation offers A (see section “Prenegotiation Preparation – Negotiation Template and Its Evaluation,” formulas 1 and 2). Step 2 requires preference declarations and modeling. Three main models are usually used in this step (Greco et al. 2001; Słowiński et al. 2002): functional, relational, and rules-based. The functional model is based on Multi-attribute Value Theory (MAVT) or Multiattribute Utility Theory (MAUT), the latter when the uncertainties are considered. Various MAVT-based methods synthesize the preferences information in a global value function (Keeney and Raiffa 1976), as described in section “Prenegotiation Preparation – Negotiation Template and Its Evaluation.” Such an approach has two main advantages. Firstly, by assigning the global score to alternatives, the complete order of alternatives (ranking) is obtained, which allows comparing alternatives from the set A univocally. Secondly, the MCDA methods based on MAVT are fully compensatory. It means that a good score on one criterion can compensate for a bad score on another one. From the viewpoint of building the negotiation offer scoring system, those properties are valuable and desirable (see section “Prenegotiation Preparation – Negotiation Template and Its Evaluation”). The most popular methods based on MAVT are SMART (The Simple MultiAttribute Rating Technique) (Edwards and Barron 1994), SAW (Simple Additive Weighting) (Churchman and Ackoff 1954), TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) (Hwang and Yoon 1981), MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) (Bana e Costa and Vansnick 1999), AHP (Saaty 2008), UTA (Siskos et al. 2005a). The relational model has a representation in the form of an outranking relation (Roy 1996). The outranking methods are based on comparisons between pairs of

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alternatives and verification whether one alternative is at least as good as the other. The global outranking relations synthesize the single-criterion preference relations between each pair of alternatives. It allows considering one alternative to outperform another but may leave some alternatives incomparable. The incomparability implies that a complete ranking is not always possible, and such ranking is referred to as partial. Contrary to MAVT-based methods, the outranking ones are non-compensatory, that is, a good score on one on one criterion cannot compensate for a bad score on another one. The properties of outranking methods, as mentioned above, make the application of them to the evaluation of negotiation template T limited, as no trade-offs and concessions among offers could be determined. The most known of outranking methods are ELECTRE (Elimination and Choice Expressing Reality) (Roy and Bouyssou 1993; Figuera et al. 2016) and PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluations) (Brans 1982; Figuera et al. 2016). Various variants of their algorithms allow them to be used both for choice (i.e., ELECTRE I, PROMETHEE I), ranking (i.e., ELECTRE III, IV, PROMETHEE II with veto), and classification (i.e., ELECTRE TRI, PROMETHEE TRI, and CLUSTER) problems. The rule-based framework of DM’s preferences is a new approach to MCDA, being an alternative for MAVT and outranking approaches (Greco et al. 2001; Figuera et al. 2016). Decision-maker preference information is represented in terms of exemplary decisions. Next, the decision rule preference model is built implementing preference information that is processed by the rough set mechanisms, which result in the series of “if. . ., then. . .” rules. This approach can be applied to any type of decision problem, that is, choice, sorting, or ranking. Apart from preference model selection, the issue of preference information provided by DM is also of vital importance in step 2 of multiple criteria decision analysis. There are two paradigms used for processing preference information, that is, the aggregation and disaggregation ones (Figuera et al. 2016). The preference aggregation paradigm assumes that parameters of the preference aggregation model are known a priori, while the global preferences are not. Therefore, it requires of DM the direct and explicit declarations of all these parameters, such as the issue weights, options’ scores, preference, or indifference thresholds. Let us note that the preference aggregation approach assumes that the DMs are cognitively skilled and know the principles of preference elicitation and decision aiding quite well, and hence understand the true meaning of all the model parameters and the consequences of their declaration on the performance of decision model. The most popular methods based on direct preference information are DR, AHP, TOPSIS, or PROMETHEE methods. The preference disaggregation paradigm, on the other hand, uses indirect or holistic preference information. It assumes that the parameters of the preference model (unknown a priori) may be determined out of global preferences declared by the DM for some examples of reference alternatives (AR) (Siskos et al. 2005b; Greco et al. 2010; Matsatsinis et al. 2018). The indirect preference elicitation is considered by some researchers (Corrente et al. 2013; Kadziński and Tervonen 2013) to be cognitively easier and less demanding. However, it must be noted that in the

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disaggregation approach, the problems with univocal identification of parameters of the preference model may occur. Usually, many various sets of such parameters exist that reproduce the holistic preferences correctly, which makes the problem of choosing the most representative (best) one (Figueira et al. 2009; Greco et al. 2011). The examples of the methods based on the indirect preference elicitations are UTA, MARS, or GRIP methods (Figueira et al. 2009). In step 3, the preference information is aggregated according to the preference model. The MCDA methods differ in the mathematical algorithms utilized to aggregated preferences. There are even several guidelines that can be useful for choosing the most appropriate method for the multiple criteria decision-making problem (Gershon 1981; Guitouni and Martel 1998; Saaty and Ergu 2015). Their selection and use may also depend on the decision-makers’ cognitive abilities. Figure 2 summarizes the process of the decision analysis of multiple criteria decision problems. Designing and evaluating the negotiation template by the negotiator is, in principle, equivalent to structuring and analyzing the multiple criteria decision-making problem in which the ranking is built based on cardinal scores. Therefore, the above schema may be simply considered as the prenegotiation preparation algorithm to determine the negotiation offer scoring system. One may note that apart from the classic approach recommended by the negotiation analysis, there is an alternative path that can be used in prenegotiation preparation, which implements the indirect preference declarations by the negotiator. Therefore, in the following sections, we will describe the principles of this approach in detail as well as selected algorithms for indirect negotiation template evaluation

Determining the structure of the decision problem

Decision problem

Expressing and modeling decision maker preferences

Preference elicitation

Direct preference elicitation

Synthetizing the DM’s preferences and developing recommendations

Aggregation model (e.g. DR, AHP, TOPSIS)

Indirect preference elicitation

Disaggregation (holistic) model (e.g. UTA, MARS, GRIP)

Decision recommendation

Fig. 2 Multiple criteria decision analysis process

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and will show how it may be used to support the negotiators when implemented in the negotiation support system.

Formal Methods for Indirect Evaluation of Negotiation Template There are many methods based on holistic indirect preference declarations that can be suggested for supporting the process of negotiation template evaluation (Matsatsinis and Grigoroudis 2018). Below, we present two of them, namely UTASTAR (Siskos and Yannacopoulos 1985) and MARS (Górecka et al. 2016). The first one allows outlining the nuances of the general mechanism of the process of scoring system construction and the potential problems one may encounter while using a preference disaggregation approach. MARS implements different disaggregation mechanisms but also shows how the major problem with defining the decision examples may be solved.

UTASTAR Out of many methods that use the holistic preference declarations, UTA seems to be most well-known and popular. This method was proposed by Jacquet-Lagreze and Siskos (1982) to aim at inferring one or more additive value functions from a given ranking on the reference set of alternatives. The early concept of UTA has been improved, extended, and adapted to many different decision-making situations resulting in a formation of the whole family of UTA methods. Below we describe the algorithm of the UTASTAR method (Siskos et al. 2005b; Matsatsinis et al. 2018), which conveys the basic principles of the UTA approach most comprehensively and straightforwardly and is used later by us to build the hybrid holistic approach, implemented in eNego system. It consists of the following steps: Step 1. Determining the problem structure. The problem structure is defined, as previously in section “Prenegotiation Preparation – Negotiation Template and Its Evaluation,” by the set n ofo criteria G ¼ {g1, . . ., gm}, the set of resolution levels (options) of criteria X ¼ xij

i¼1,...,n; j¼1,...,ni

and the set of alternatives A ¼ {a1, . . .ap}. Step 2. Defining the set of reference alternatives RS  A. The set RS consists of those alternatives which make no difficulties in evaluation to DM. Step 3. Providing the preference information on a set of reference alternatives RS in the form of complete rank order. Step 4. Building a set of additive value functions compatible with the DM’s preference declaration (preference disaggregation). The rank order of alternatives from RS declared by the DM is used to formulate the following linear program (LP):

Holistic Preferences and Prenegotiation Preparation

min ðzÞ ¼ subject to :

267

XjAR j k¼1

½σ þ ðak Þ  σ  ðak Þ,

Δðak , akþ1 Þ  δ, if ak  akþ1: Δðak , akþ1 Þ ¼ 0, if ak  akþ1 Xm Xαi 1 w ¼ 1, i¼1 j¼1 ij

ð5Þ

wij  0, σ þ ðak Þ  0, σ  ðak Þ  0, where: σ +(ak)/σ (ak) – are the overestimation and underestimation errors for the global rating of offer + 1) is a difference in ratings for offers ak and  ak,Δ(ak,ak  ak + 1, and wij ¼ v xi jþ1  v xij is a difference in ratings for two subsequent resolution levels of issue i. By solving the linear program, the ratings vij of each option of each issue are obtained. If an alternative solution occurs, some LP subproblems are defined and solved to find the set of univocal ratings. Step 5. Setting up the global value function V based on the results of the preference disaggregation process. In the vast majority of situations solving the linear problem (5) may result in two different solutions: one with z ¼ 0, and another, where z > 0. In the former case, the nonempty set of value functions exists that is compatible with the DM’s preferences, and the global value function V is determined as an average of those that can be determined from series of LP subproblems that maximizing the values of options for subsequent criteria. If z > 0, there is no single set of value functions that fit the DM’s preference declarations, hence the latter need to be verified (steps 3 and 4 repeated). Step 6. Ranking alternatives from the set A using the global value function V. The following example illustrates the application of the UTASTAR procedure for the evaluation of the negotiation template and scoring the negotiation offers. Example 1 Let us assume that seller and buyer negotiate the conditions of the potential business contract, where the following negotiation issues and their resolution levels are discussed: • Unit price (in €): 70; 60; 50; 40; 30, • Time of payment (in days): 7;14; 21, • Returns conditions: “7% defects and 4% penalty”; “5% defects and 2% penalty”; “4% defects and no penalty.” We will build the scoring system for the negotiation template defined above for the seller party using the UTASTAR method. From the seller’s point of view, the criterion price is a benefit issue, while the time of payment is a cost issue. For the returns conditions, the seller provides the following verbal evaluations: VP – “7%

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defects and 4% penalty”; AV – “5% defects and 2% penalty” and VG – “4% defects and no penalty,” where VG – very good, AV – average, VP – very poor. This completes step 1. In step 2, the reference set has to be designed. It should be easy for DM to evaluate, but on the other hand, it should be informative enough, that is, all the options from the template should be represented in it. We will consider two alternative reference sets in this example RS1 and RS2 (see Table 1). In our example, RS1 is simply a copy of RS2 with two additional offers added (shaded in Table 1). In step 3, the seller builds the rank order of offers from RS1 and RS2, respectively (Table 1, columns 1–3). Note that building such an order requires the seller to make a series of comparisons between pairs of offers and answer simple questions “do I prefer alternative a or b?” No cardinal intensities of the preferences need to be specified. In step 4, the LP is built to disaggregate the ordinal preferences provided by the seller. For both reference sets, the LP models resulted in a nonempty set of value functions (z ¼ 0). The global value functions determined out of the ordinal preferences for exemplary offers are shown in Table 1, while the option ratings (the explicit scoring systems S) – in Tables 2, 3, and 4. Table 1 Rank order and rating of offers obtained by UTASTAR Rank order 1 2 3 4 5 6 7 8 9

RS1

RS2

(70,21,AV) (40,7,VG) (50,21,VG) (40,14,VG) (40,7,AV) (60,14,VP) (30,21,VG) (40,7,VP) (30,21,AV)

(70,21,AV) (40,7,VG) (50,21,VG) (60,14,VP) (30,21,VG) (40,7,VP) (30,21,AV)

Rating RS1 69.7 68.2 66.6 50.6 40.2 39.2 38.2 30.0 19.1

Rating RS2 71.9 41.8 31.2 30.1 28.5 13.3 11.7

Table 2 Marginal value function for issue price Price vi for RS1 vi for RS2

30 0.0 0.0

40 18.8 2.0

50 28.4 2.7

60 36.9 18.8

70 50.6 60.2

Table 3 Marginal value function for issue time of payment Time of payment vi for RS1 vi for RS2

7 11.2 11.3

14 2.3 11.3

21 0.0 0.0

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Table 4 Marginal value function for issue returns Returns vi for RS1 vi for RS2

VG 38.2 28.5

AV 19.1 11.7

VP 0.0 0.0

As one can see, the results obtained (the scoring systems) differ for each reference set. This difference is the effect of changing the informativeness of the reference set, which we mentioned while describing the UTASTAR procedure. Adding two more offers that the negotiator is willing (or recommended by the supportive facilitator) to evaluate change the system rather significantly. The weight of the issue of returns, for instance, is changed of almost ten rating points. The rating of the option of 14 days of delivery also changes dramatically, from 2.3 to 11.3. Similarly, the shape of marginal value functions of options of price differs significantly in both systems. These differences show the need for careful design of the reference sets in the UTASTAR algorithm, as adding or removing a single offer may profoundly affect the form of scoring system obtain. It also shows that some mechanisms for verification of the scoring system’s quality at the disaggregated level may be required to make sure that such scoring system accurately represents the negotiator’s preferences. There are also other issues, more technical ones, that should be of interest when implementing the UTASTAR method. For instance, the value of the calibration parameter δ that describes the minimal difference between the ranked alternatives or the αi, describing the number of sections into which the marginal value function (assuming to be partially linear) is divided for each issue. More extensive discussion over these technical problems may be found in Wachowicz and Roszkowska (2020).

MARS The MARS method is also a multiple criteria preference elicitation approach that can be used to evaluate the negotiation template. However, it differs from UTASTAR in the scope of preferential information that can be provided by the negotiator, as well as predefines for them the reference set of offers for evaluation (Górecka et al. 2016). It consists of five following steps: Step 1. Determining the problem structure. As in the case of UTASTAR, the problem needs to be defined first for the MARS approach in the form of the sets G, X, and A. Step 2. Defining the reference set of alternatives for evaluation YnIRS. The set YnIRS is precisely predefined for the DM and consists of: (1) Ideal Reference Solution (IRS), which is an alternative comprised of the best options for all the criteria and (2) alternatives near to ideal reference solution (nIRS), which consist of the best options for all the criteria except one. The reference set YnIRS is built based on the recommendations of the ZAPROS procedure

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(Moshkovich et al. 2016) and consists of alternatives that are easy to compare, since they differ at most in two criteria only and require of the DM to compare a single tradeoff and choose the one that cost them less. Step 3. Pairwise comparison of alternatives from YnIRS. In MARS, the MACBETH-like semantic categories are used for alternatives comparisons. The ordinal scale may be applied, with judgments like {“more preferable,” “less preferable,” “equally preferable”} or verbal scale describing the strength of preference between the alternatives under consideration {“no,” “very weak” (d1), “weak” (d2), “moderate” (d3), “strong” (d4), “very strong” (d5), “extreme” (d6)}. It is also possible to use additional intermediate levels describing the DM’s hesitation between the major categories in verbal scale, for example, “between very strong and extremely strong” (d5–d6) (see Bana e Costa et al. 2016), similarly to AHP. Step 4. Solving the linear program corresponding to the comparisons performed using the MACBETH algorithm. The obtained scores form the Joint Cardinal Scale (JCS) with the alternatives from YnIRS scored on the 0–100 scale. Step 5. Determining the option ratings out of JCS. The procedure requires to assign the scores to all options that form IRS equal to 100 (each). Each non-ideal option receives the score equal to the score of the nIRS alternative, which it comprises. Step 6. Determining the alternatives’ global values V. The global scores of alternatives can be determined from the following formula: Vðak Þ ¼

m X

ð100  JCSki Þ

ð6Þ

i¼1

where JCSki is the rating of the option that comprises an offer ak for ith criterion (determined in step 5). Let us note that in the MARS procedure, the scores reflect the distances to the Ideal Solution. Thus, the smaller the score, the better the alternative is. The scores obtained from the MARS algorithm may be easily transformed into the range [0; 1] by applying one of the normalization formulas. Example 2 We consider the same negotiation problem, as described in Example 1. The seller is building the negotiation offer scoring system using the MARS algorithm. In step 2 the reference set YnIRS was determined for the negotiator. The Ideal Reference Solution IRS ¼ (70, 7, VG) and the set YnIRS consists of nine offers YnIRS ¼ {a1 ¼ IRS, a2, . . ., a9}, which are presented in Table 5 in column 2. In step 3, the seller compares the ideal offer IRS and the offers from the set YnIRS using a predefined semantic scale. The results are presented in Table 6. As described in the algorithm, the comparison of offers is made verbally, in terms of the tradeoffs, for example, comparing a2 ¼ (70, 14, VG) with a6 ¼ (50, 7, VG) requires of the seller answering a question: “do I prefer to concede of 20 for price or

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Table 5 YnIRS and the ratings of its elements Number offers a1 ¼ IRS

Offers (70,7,VG)

JCS 100.00

a2 a3 a4 a5 a6 a7 a8 a9

(70,14,VG) 70,21,VG) (70,7,AV) (60,7,VG) (50,7,VG) (40,7,VG) (70,7,VP) (30,7,VG)

92.59 85.19 77.78 74.07 51.85 40.74 37.04 0.00

Options 70 7 VG 14 21 AV 60 50 40 VP 30

Option rating 100.0 100.0 100.0 92.59 85.19 77.78 74.07 51.85 40.74 37.04 0.00

Table 6 MACBETH-like comparisons in MARS approach Offers a1 a2 a3 a4 a5 a6 a7 a8 a9

a1 No

a2 d2 No

a3 d2 d2 No

a4 d3 d2–d3 d2 No

a5 d3 d2 d2 d1 No

a6 d3 d3 d3 d3 d3 No

a7 d4 d4 d3 d3 d3–d4 d2–d3 No

a8 d4 d4 d3 d3 d3 d1–d2 d1 No

a9 d5 d5 d5 d5 d5 d4 d3 d3 No

of 7 days for the time of payment, and of how much?” In our example, the seller consider the concession of 7 days (a2) to be moderately better (d3) than a concession of 20 EUR (a6). In step 4, using the MACBETH algorithm, we obtain the cardinal scores JCS for each offer (see column 3 in Table 5). These scores are assigned to the options comprising the offer (step 5), see columns 4 and 5 in Table 5. In step 6, the global values of the offers are determined, which shows the concessions necessary to make when moving from the ideal offer IRS to another. For the best offer V(IRS) ¼ 0, while for the worst one: V(30, 21, VP) ¼ (100  0) + (100  85.19) + (100  37.04) ¼ 177.77. For other offers from ak  A, we have: 177.77 V(ak) 300. For instance, the value of offer (50, 14, AV) is calculated based on its options’ ratings from Table 5: V(50, 14, AV) ¼ (100  51.85) + (100  92.59) + (100  77.78) ¼ 77.78. Consequently, conceding from the offer (50, 14, AV) to (30, 21, VP) will cost the seller 100 points, which is quite a significant amount taking into account the rating scale range from 0 to 177.77. Comparing both methods based on the holistic approach, that is, UTASTAR and MARS, we can conclude that they do not enforce the negotiators to operate with

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abstract and interpretatively unclear scores that should be assigned directly to the elements of the negotiation template. However, MARS allows negotiators to declare more detailed information about their preferences than UTASTAR, as the 12-point verbal scale may be used to declare the differences in offers quality. This may allow obtaining more precise scoring systems than when rank order is only defined (as in UTASTAR). MARS advantage is also a predefined reference set, which releases the negotiator from defining it themselves. Additionally, the alternatives in reference set are constructed to cover all the options from the template. It assures that the option ratings will be determined by the method directly, and not from the linear interpolation of neighboring options (or by copying the score of neighboring option, as it often happens in UTASTAR). However, there is one drawback of such an approach. The number of reference offers in big negotiation problems (consisting of many issues and feasible options) may be too big for the DM to evaluate them reliably, without any cognitive errors and inconsistencies. An interesting solution might be fusing some elements of these methods and, additionally, to hybridize them with some other concepts of preference declarations for tuning the results and obtaining more precise scoring systems. However, it seems clear that for the reasons related to the technical complexity of the algorithm, practical use of such approaches is only possible, if the prenegotiation protocols that use holistic (or hybrid holistic) approaches are implemented in software support systems.

Software Support of Prenegotiation Preference Elicitation Defining the template and sketching out the general preferences for its elements may not seem a challenging task for the negotiators. However, from the technical viewpoint, determining the scoring system may require some analytics and computations that are related to the specificity of the preference model, especially when the preferences are declared holistically, and the parameters of preference models need to be inferred. Therefore, starting from the late 1980s, the software negotiation support systems are designed to support this part of prenegotiation preparation (Kersten and Lai 2007). These systems, mostly used in training and teaching negotiations, implement the prenegotiation protocols that are adequately tailored to the preference models P and the types of preference information S. There are many examples of negotiation support systems that use either direct or holistic preference declarations. For instance, systems such as SmartSettle (Thiessen and Soberg 2003) or NegoCalc (Wachowicz 2008) are based on the models of additive preferences and implement the even swaps method (Hammond et al. 1998) to elicit the structure of negotiators’ preferences. The users define their preferences directly for the decomposed elements of the negotiation template. The protocols are based on the series of comparisons of tradeoffs between subsequent issues and derive this way the cardinal scores vij for all salient options xij under consideration. Web-Hipre (Mustajoki and Hamalainen 2000), which offers a group decision support facilities,

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also elicits the parties preferences using a disaggregated template and combines MAVT and AHP. The Mediator system (Jarke et al. 1987) is an example of the group decision support tool that implements the notion of evolutionary system design. There is an individual single-user support module implemented in the Mediator system that is used in prenegotiation to elicit the parties’ preferences. This module operates with a mixed aggregation-disaggregation approach embedded in MAVT philosophy according to the algorithm proposed earlier in the PREFCALC system (JacquetLagrèze 1990). Within the aggregation step, the negotiators define the issue weights explicitly (wi) and then the system automatically generates the option values using a predefined quadratic scoring function. In disaggregation step, a subset of offers is chosen and ranked by the negotiator, for which the UTA algorithm is implemented to derive the option and issue values. Then, the compromise preference model is set up by the negotiator, who may manually tune both weights and option scores, as well as go back to step 2 and reset the rank order to compute new modified UTA-based scores (Jacquet-Lagreze and Shakun 1984). Inspire (Kersten and Noronha 1999), one of the first and the most well-known web-based negotiation support systems, operates with a preference elicitation protocol designed in the opposite way to the Mediator’s one. Its prenegotiation protocol is based on the hybrid conjoint measurement (Angur et al. 1996). This is a two-step procedure that starts with a direct declaration of preference for issues (wi) and options (vij ) by means of SMART-like scores assignments (Edwards and Barron 1994). Then, in step two, the list of exemplary offers AR  A is presented to negotiator together with their global ratings v(AR) resulting from vij values declared by the negotiator. If negotiator does not agree with such aggregated values, they may be changed to reflect the global scores of offers more accurately veðAR Þ. Using these new scores Inspire performs the preferences disaggregation process that uses the principals of conjoint analysis. This way, the new adjusted option and issue ratings are determined (e vij ) and used for further bargaining and postsettlement support. A similar solution is implemented in the Negoisst system (Schoop 2010). NegoManage (Brzostowski and Wachowicz 2014) also makes use of the holistic approach in preference declarations. However, it hybridizes it with the idea of clustering and kernel density estimation (Parzen 1962). The system starts from the negotiator’s declarations of the indifference surfaces, which represent some selected classes of offers of the same quality (categories). They are defined using an advanced linguistic scale without any numerical declarations. Then, the negotiator is asked to give examples of offers from each surface, but NegoManage supports them by providing an algorithm for the automated generation of such offers. Finally, to build the scoring system, the probability distributions of belonging to the surface are determined out of the examples. These distributions, combined with the surface’s scores derived from linguistic declarations, allow evaluating any feasible negotiation offer from within the template. As we can see, the holistic judgments are quite often used in the negotiation support systems for prenegotiation evaluation of the negotiation template. They are, however, often hybridized with other concepts and notions of preference

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declarations, as if the former requires additional support to be efficient. In the next section, we will describe in detail the recently designed negotiation support system called eNego and provide some empirical findings on the use and usefulness of the hybrid holistic preference elicitation mechanism that is implemented in it.

eNego System and Empirical Findings from Using Hybrid Holistic Prenegotiation Support The System and Its Organization eNego is an online negotiation support system used for negotiation teaching and research.1 It is designed to support bilateral synchronous or asynchronous multiissue negotiations and helps negotiators in their prenegotiation and bargaining activities. eNego is controlled by the administrator, who may easily set up the system according to the experimental or teaching requirements. For every single negotiation or the whole negotiation experiment (series of negotiation instances), the negotiation protocol needs to be settled that consists of the series of steps and activities that are going to be performed by the system’s users during the negotiation process. It allows to include all the important support elements in the negotiation process as well as schedule some additional tasks, for example, the pre- and postnegotiation questionnaires that allow gathering some additional information about the system use and its evaluation. eNego operates with a database of negotiation cases with explicitly predefined negotiation templates, which are assigned to the experiments by the administrator. The system does not offer negotiators any support tools for joint template design and modifications. Consequently, the prenegotiation preparation in eNego is limited to the facilitation of the individual evaluation of the negotiation template. Various methods and their hybrids may be used in eNego to support the negotiators in template evaluation. They are coded as separate modules and included in the negotiation protocol by the administrator. During the bargaining phase, eNego helps negotiators in building and exchanging negotiation offers and messages and visualizes the negotiation history. No postsettlement analysis and support have been implemented in the system so far, but the system is module-built, and any designed postsettlement mechanism may also be included in the eNego negotiation protocol by the administrator when coded. The system also provides an administrator with certain support mechanisms that allow them to manage the users and experiments, for example, tools for automated users registration for groups, setting up the negotiation dyads within and between groups, or messaging with participants. A simple tool for designing new questionnaires is also offered. Finally, the data extraction module is designed to help the

1

https://web.ue.katowice.pl/enego/

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Fig. 3 eNego – organizational schema

administrator to retrieve the specific data regarding the negotiation process and users. The general organizational schema of the eNego system is presented in Fig. 3.

The Module for a Hybrid Holistic Approach to Prenegotiation Preference Elicitation Out of various preference elicitation algorithms implemented in eNego, one uses the notion of holistic preference declarations. It is an algorithm similar to the one used in the PREFCAL system for Mediator group decision support and hybridizes disaggregation and aggregation approaches. For its disaggregation part, the UTASTAR algorithm was used, yet it includes the MARS-based way for determining the set of reference alternatives. Some additional elements of preference elicitation are also implemented in the prenegotiation protocol to handle the potential nonmonotonous preferences. The whole algorithm consists of four steps (Wachowicz and Roszkowska 2020): • Step 1. Calibrating the preference monotonicity for negotiation issues To determine the correct scoring system out of holistic declarations, the negotiators need to define the monotonicity of their preferences. To avoid false assumptions, in eNego, the negotiator declares the best and worst options for each issue in the template. If not extreme options are selected as best, the marginal value functions are considered to be unimodal, and the corresponding constraints are added to UTA model to assure maximal value for the best option with increments

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Fig. 4 Prenegotiation protocol in eNego – step 1

possible on the slope between worst and best, and decrements – after moving from best option to the edge of the feasible range. The interface of declaring worst and best options in eNego for simple four-issue contracting negotiations is shown in Fig. 4. • Step 2. Rank ordering the predefined MARS-based reference offers (disaggregation step) Based on the idea of MARS, the set of reference alternatives is built using the previous definition of the best options for each issue from step 1. The negotiator is asked to rank these alternatives according to the descending order. The comparison should not be cognitively too demanding, as the alternatives differ in two options of two issues at most. In eNego, the list of alternatives is presented to the user, which are the active drag-and-drop elements. The user may easily build the rank order reflecting their preferences by reorganizing the list using the mouse (Fig. 5). As the disaggregation engine implemented in eNego is based on UTASTAR, no intensities of preferences are required to be declared. • Step 3. Tuning the ratings of template elements (decomposed level) eNego runs the linear program built according to the modified nonmonotonous UTASTAR model (for details see Wachowicz and Roszkowska 2020).2 When no single set of marginal value functions compatible with the preferences declared in steps 1 and 2 can be found by the optimization algorithm (the goal functions describing the scale of over and under-estimations of the offers is greater than

2

The changes are technical, and were focused on determining a standardized scoring system for the negotiation template, therefore we do not discuss them in detail in this chapter.

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Fig. 5 Prenegotiation protocol in eNego – step 2

zero), eNego displays the warning to the user. It suggests the negotiator goes back to the previous steps of preference declarations and adjust them to eliminate potential inconsistencies, as the rating system determined and displayed to the user does not preserve the rank order of offers. The negotiator may also do a manual tuning of the scoring system displayed using direct rating approach and change the option values vij disaggregated in previous step (Fig. 6). The process of resetting the rank orders and direct tuning the cardinal values is iterative and may be repeated until the negotiator feels satisfied with the scoring systems. • Step 4. Analyzing the global scores of selected alternatives (aggregation step) When the rating system is finally set by the negotiator in the iteratively repeated steps 1–3, its results are presented at the aggregated level to show the consequences of its use. Some selected offers from the negotiation space A are listed accompanied by their global scores. The negotiator is asked to compare the offers and verify if their ratings reflect the differences in their quality (strength of the preferences) adequately (Fig. 7). If they feel unsatisfied with the global ranking and ratings, they may go back to any of the previous steps and modify their preference declarations, both at an aggregated or disaggregated level.

The Use of the Evaluated Scoring System in the Bargaining Support in eNego As described in section “Prenegotiation Preparation – Negotiation Template and Its Evaluation,” the scoring systems are used by the parties not only to set up their priorities and quantify their goals, which helps the party to understand the

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Fig. 6 Prenegotiation protocol in eNego – step 3

Fig. 7 Prenegotiation protocol in eNego – step 4

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negotiation better. It may also be utilized by any third party to support the negotiators during the bargaining phase. So does the eNego, offering the negotiators the user interface divided into four segments (Fig. 8). The first segment (left-top corner) displays the negotiation process dynamics in the form of the negotiation history graph. Offers sent by both parties are depicted here by two separate series on the timeline with the rating values they assure to the supported negotiator (asymmetric perspective of one party). This allows the negotiator to compare the concession strategies as well as to measure their reciprocity. The top-right segment can be used to select new offers, as responses to the current negotiation status. When the target value of the new offer is typed to the text-box left to the negotiation history graph, or a slider below it is used to change this value, eNego prints the list of offers near to this target value in the top-right box (“Exemplary offers”). The negotiator may use one of the eNego suggestions for new offers or compose one themselves using the bottom-left segment. It consists of a list of drop-down boxes that present the list of options for each issue. As negotiator manipulates with these options, they may observe how the value of the offer changes to themselves (“Total” line shows the value of the scoring function for the offer under consideration). Finally, the bottom-right section provides the users with a classic text-box, which can be used to send the messages to the counterpart. The system tracks the status of each negotiation and informs the parties about offers sent by their counterparts. The

Fig. 8 eNego – UI for the bargaining phase

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standard notification is sent via email. However, if both negotiators are active in the system, the recipient receives a short message in a pop-up window, which prevents them from sending their own offer (which may be being composed at that time) without reviewing the one that has been just sent by the counterpart. The history of the negotiation process can always be recalled from the drop-down menu “Show schedule,” which consists of all the tasks scheduled by the eNego administrator as well as some fixed elements of the support process.

The eNego Experiments The negotiation experiments are organized in the eNego system as the elements of the academic courses each semester starting from 2018. Four runs of experiments have been organized so far, in which the participants were undergraduate, graduate, and postgraduate students from three Polish universities. Apart from didactic purposes, there are also the research goals of these experiments. They are focused on studying the use and usefulness of decision support mechanisms in software supported negotiations. Below, we describe two experiments organized in eNego, in which a hybrid holistic disaggregation-aggregation prenegotiation preference elicitation approach was implemented, and the quality of the results obtained (i.e., the scoring system accuracy) was compared to those determined by means of the classic approach that utilizes the direct rating method. In both eNego experiments, the same bilateral multi-issue negotiation problem was used, which was based on the original Cypress-Itex negotiations once implemented in the Inspire system (Kersten and Noronha 1999; Vetschera 2007). There were two parties in eNego negotiation, the bicycle producer and the parts supplier, negotiating a new contract for the delivery of rear-wheel gears. Four issues were to be negotiated: price, time of delivery, time of payment, and returns. For each issue, sets of feasible options were defined that made the following negotiation template (Table 7). The students played the roles of agents negotiating on behalf of principals. In prenegotiation, the case description and confidential preferential information were displayed to each agent. The latter described in detail the goals and priorities of the principals. This information was also visualized by means of pie charts. Part of such information for bicycle producer is shown in Fig. 9. Table 7 Negotiation template for bicycle negotiations in eNego Issues to negotiate Price (in US$) Delivery time (in days) Payment (days after delivery) Returns policy

Options $3.45; $3.75; $4.05; $4.35; $5.00 20; 30; 45; 60 Upon delivery; 14; 30; 60 Any defects, no penalty; 3% defects, no penalty; 5% defects, 2% penalty; 7% defects, 4% penalty

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Fig. 9 Description of principals’ preferences in eNego negotiations

The eNego negotiators were asked to read the case description and then follow the prenegotiation preference elicitation process (as described in subsection “The Module for a Hybrid Holistic Approach to Prenegotiation Preference Elicitation”). When building the scoring systems, they were asked to represent their principal priorities most accurately. After completing their prenegotiation activities, the parties were moved to the bargaining phase. They were asked to negotiate following the principals’ instructions and settle with a satisfying agreement. In such a context of representative negotiations, the agency theory identifies several personal incentives that may influence the agents and cause them to act not following their principals’ goals, such as their individual aspirations, objectives, and self-interest (Jensen and Zimmerman 1985; Lee and Thompson 2011). However, these nonessential issues can be reduced or eliminated by increasing the relational attachment between the principal and the agent, for example, by rewarding the agent’s effort and engagement (Jacobides and Croson 2001). Since the participants of the eNego experiment were students, who were taking part in the academic courses on negotiation and decision making, we decided to link the rewarding system with their final course performance. For all the students in our study, the experiment was the only evaluated activity that made the final course grade, and 30% of this grade came from the quality of prenegotiation preference elicitation. In both eNego experiments (studies 1 and 2), the students were given handouts and introductory lectures regarding the essence of prenegotiation preparation, preference elicitation, and the use of the eNego system. However, in study 2, before the experiments, the students participated in series of in-class laboratories, during which the process of determining the scoring system by means of the holistic approach was additionally explained and practiced using Excel and purposely designed add-in. The purpose was to show the students the machinery of the preference elicitation

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process and the nuances related to the influence of the preference declarations on the scoring system quality. As the goal of our study was to analyze the effects of the prenegotiation support, we focused only on measuring the accuracy and similarity of the scoring systems the eNego users built to the preferential information provided in advance. The bargaining results were of no interest for this study. Technically, the reference scoring systems in eNego were build based on the circle sizes and were considered to represent the principal’s preferences in an ultraprecise way. Then the scoring system of each agent was compared to the reference scoring system of the corresponding principal using the notions of ordinal and cardinal accuracy (for details see Wachowicz et al. 2019; Wachowicz and Roszkowska 2020): • Ordinal accuracy is an index that measures to what extent the rank order of the template elements in an agent’s scoring system is similar to the rank order in the principal’s scoring system. The measure is scaled to the range [0;1], where 1 reflects full concordance of the agents scoring systems (all ranks are the same as in principal’s one), while 0 reflects the perfect discordance. Conceptually, the measure is based on the Kendall rank correlation and matching index. • Cardinal accuracy measures the discrepancies in the strength of preferences between the agent’s and the principal’s scoring systems. It uses the notion of Manhattan distance. The absolute values of differences in ratings of all options in principal’s and agent’s scoring systems are determined and added. Such an aggregate measure depends on the template size. Therefore, it is standardized using an average accuracy simulated for randomly defined scoring systems. As the results, the agent’s scoring system that perfectly reproduces the agent’s one has a cardinal accuracy equal to one, while the scoring system similar to average random one – accuracy equal to zero. Apart from the objective results measured by means of the quality of scoring systems obtained, we also tried to verify the subjective users’ evaluation of the preference elicitation process offered in the eNego system. Therefore, we used postnegotiation questionnaires in which such an opinion was gathered using both open and close questions (the latter, with a predefined five-point Likert scale). As a reference point to the objective results obtained, we used the data from similar bilateral negotiation experiments conducted earlier in the Inspire system – study 3 (see Roszkowska et al. 2017). In study 3, the contract negotiations were conducted, the template of which was similar in size and structure of the principal’s preferences. Four issues were analyzed, for two of which the principal’s preferences were monotonically increasing, while nonmonotonous unimodal preference functions represented two others. For study 3, we have selected the participants for which the same rewarding system was used, as in eNego studies 1 and 2. Note that in Inspire, a hybrid conjoint measurement is used to determine the scoring systems, which consists – conversely to eNego – of aggregation-disaggregation approach. However, analyzing the written reports of study 3 participants, we did not find the

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information about the usage of the second step of the approach. Consequently, we assume that they did not change the global values of offers determined on the basis of the option values provided by them directly, nor they run the conjoint analysis to change the initial scoring system. Therefore, we will consider the scoring systems from study 3 as determined by means of a classic direct rating approach (for decomposed negotiation template directly). We had 69 students in study 1, and 112 in study 2. In study 3, there were 165 students selected from the Inspire dataset that fulfilled the requirement described above. As a consequence, in all the studies, the students came from one university and classes taught by one teacher. Hence, we eliminated the potential influence of the organizational culture and differences in teacher characteristics and styles on the experimental results (Wachowicz et al. 2018).

Results The average ordinal and cardinal accuracy indexes for all three studies are presented in Table 8. It is clearly seen that the hybrid holistic approach to prenegotiation preference elicitation and determining the scoring system accurately reflecting the negotiator’s preferences gives better results than the classic direct rating that operates with a disaggregated template only. The average ordinal accuracy, which simply shows to what extent the agent’s scoring system reflects the rank order of preferences defined by the principal, is higher in study 1 and 2 than in study 3. These differences are significant (the value distributions in study 1 vs. study 3 differ at p ¼ 0.003 and in study 2 vs. study 3 at p ¼ 0.001 in the Mann-Whitney U test). The same tendency can be observed for cardinal accuracy, which is the lowest in study 3 and the highest in study 1. Here, however, the differences are not significant ( p > 0.414). We see then that by using the hybrid holistic approach, the higher accuracy of scoring systems and – consequently – the more reliable bargaining support is possible. The hybrid approach protocol, however, is more extensive and requires more time to complete. Therefore, we asked the participants in studies 1 and 2, how do they evaluate the hybrid holistic approach and how they compare it to the direct rating, which they know from handouts and lectures. The results are shown in Table 9. The subjective evaluation of the use of the hybrid holistic approach implemented in eNego is fairly average and quite similar in both studies. The most enthusiastic opinion we observe in both studies for the user interface used to organize preference Table 8 Average values of ordinal and cardinal accuracy indexes Experiment Study 1 (hybrid holistic approach, no training) Study 2 (hybrid holist approach + training) Study 3 (classic direct rating approach)

Average accuracy of agent’s scoring system Ordinal Cardinal 0.941 0.724 0.954 0.736 0.901 0.715

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Table 9 The average answers for the postnegotiation evaluation questionnaire in eNego experiments

Question The whole preference elicitation process in eNego was cumbersome and time-consuming It was difficult for me to build a ranking using the predefined alternatives If I had an option, I would use a different set of alternatives to compare The drag-and-drop interface for boxes with offers examples was unintuitive and inefficient I would prefer to assign the issue and option ratings myself just from the very beginning, without any preceding holistic declarations

Average answer Study Study 1 2 4.28 5.04 4.72 4.19 5.23

4.77 4.49 5.31

3.49

4.31

Seven-point Likert scale used in the questionnaire: 1 – totally agree,. . ., 7 – totally disagree

declarations at the holistic level (step 2 in the holistic disaggregation-aggregation approach), but it is still only one point higher than average. The most surprising is the final opinion on using the hybrid holistic approach versus the classic direct rating (as it was in study 3). Here, the users in study 1 are even slightly more prone to use the classic approach than the alternative holistic approach. However, when the awareness of this approach increases (study 2), the users seem to accept its inconveniences more, presumably expecting better and more reliable results it will produce. For this question, the difference in evaluation is significant (3.49 vs. 4.31, at p ¼ 0.02). Similarly, significant is the difference in the opinion regarding the workload and difficulty of this approach (question 1). Although in both studies, the prenegotiation protocol was the same, the participants in study 2 evaluated it more optimistically as less tiresome and time-consuming, that their colleagues in study 1. Again, the better knowledge of the method itself seems to ease the strictness of its evaluation. The differences in evaluations for the remaining answers, though always higher in the case of study 2, occurred not significant.

Summary In this chapter, we discussed the issue of prenegotiation preparation and its facilitation by using the decision support mechanisms based on the holistic preference declarations. Such an approach requires the negotiator to express a general opinion regarding the quality (value, desirability) of some selected negotiation offers, by comparing the complete packages (future contracts). No precise declaration of preferences on the disaggregated level, that is, for atomic template elements, is required. Holistic comparisons, however, seem to be a typical situation the negotiators face during the negotiation process. They need to compare the offers submitted in subsequent negotiation rounds to the negotiation table, evaluate the trade-offs they require and consider, which of them is better. They also compare the offers with

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BATNAs and the aspiration and reservation packages, to check if their goals are met. Therefore, using the holistic comparisons in the phase of the prenegotiation preparation seems to be a natural prequel to what is going to happen during future bargaining. Thus, understanding the general philosophy and mechanisms related to holistic preference declarations seems to be crucial from the viewpoint of their proper use in the process of determining the reliable and accurate scoring systems for the negotiators. We have started the discussion with the description of the prenegotiation preparation phase and its stages related to negotiation template definition and evaluation to show how important they are for the future negotiation support, understanding the parties’ approach, measuring the concessions, and their reciprocity and searching for the balanced and fair solutions. We outlined the classic negotiation support approach that is based on direct rating and preference aggregation paradigm and potential problems with its use related to the cognitive limitations of the decision-makers. Therefore, we sketched out the broader perspective on how the prenegotiation preparation may be organized alternatively. We focused mostly on the approach based on preference disaggregation mechanism, which releases the negotiators from cognitively challenging declarations through numbers or quantitative comparisons, often considered as unintuitive. Out of many methods based on the holistic preference declarations, we showed two: UTASTAR and MARS. The former one is one of the first methods designed to implement the preference disaggregation approach and uses the most straightforward preference statements in a form or rank order. However, its results heavily depend on many technical issues, such as the size of the reference set and the mixes of the alternatives it is comprised of, or the quantitative tunning parameters describing the number of breakpoints of marginal value function or differences in values among the reference alternatives. Another problem is the multitude of compatible value functions the UTASTAR identifies based on the holistic declarations of DM, for which determining the mean values may result in losing some important information that was not explicitly and precisely declared by the decision-maker due to operating with rank orders only. For this reason, we have presented another approach, that is, MARS. First, its algorithm operates with a predefined set of reference alternatives to be evaluated by the negotiators. The construction of such a set is precisely defined, and based on the declaration of best resolution levels for each negotiation issue. Second, the mechanism for offers’ comparisons, based on notions of MACBETH, allows defining the strengths of preferences, not only their order. Therefore, more reach preferential information is provided, and more reliable scoring systems may be determined out of it. The advantages of both these methods motivated us to design the negotiation support system called eNego, in which a hybrid prenegotiation preference protocol was implemented. This protocol derives not only form the notions of UTASTAR and MARS but also introduces some debiasing mechanisms to reduce the cognitive effort and help negotiators to obtain accurate and reliable scoring systems. We presented the general design of this system, as well as the functionalities it offers during the prenegotiation phase.

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Finally, we investigated whether such a hybrid holistic approach performs better than the classic one that uses the notion of direct rating. In two experiments, we compared the performance of eNego negotiators with an earlier study conducted in the Inspire system, where direct rating was used. It occurs that using hybrid disaggregation-aggregation approach results in the scoring systems better fit to the negotiators’ preferences both on the ordinal and cardinal level. The results may not be spectacular with respect to cardinal errors but differ significantly for ordinal accuracy. However, the subjective evaluation of the hybrid holistic approach by the eNego system users is not particularly enthusiastic. It is better for the users to whom the holistic idea was explained in detail, and the training of its use was offered before eNego negotiation. However, generally, this still shows that the holistic approach may not be so cognitively easy, as some researchers suggest it. Some additional effort and time may be required to be spent on prenegotiation preparation to make such a holistic approach effective.

Cross-References ▶ A Group Multicriteria Approach ▶ Advances in Defining a Right Problem in Group Decision and Negotiation ▶ Group Decision Support Using the Analytic Hierarchy Process ▶ Group Support Systems: Concepts to Practice ▶ Impact of Cognitive Style on Group Decision and Negotiation ▶ Multiple Criteria Decision Support ▶ Negoisst: Complex Digital Negotiation Support ▶ Negotiation Process Modelling: From Soft and Tacit to Deliberate ▶ Procedural Justice in Group Decision Support Acknowledgments We thank Prof. Gregory Kersten from Concordia University for his inspiring contribution and support in earlier research related to measuring the accuracy of negotiation offer scoring systems in the principal-agent negotiations. The research presented in this chapter was partly supported by the grant from the Polish National Science Center (2016/21/B/HS4/01583).

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Context and Environment in Negotiation P. J. van der Wijst, A. P. C. I. Hong, and D. J. Damen

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The “Home-Field” Advantage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Negotiation and the Role of Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environment and Behavior: Mindset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environment and Behavior: Nature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environment and Behavior: Creativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environment and Negotiation Behavior: The Present Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Participants and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional Analyses: Mood, Stress Level, Trust, Satisfaction, and the Virtual Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environment and Negotiation: Gender . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Home Advantage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Diplomats carefully choose the location where international negotiations will take place, since this is reported to influence the negotiation process and outcomes. However, the general role of environmental factors in negotiations has received P. J. van der Wijst (*) Department Communication and Cognition, Tilburg University, Tilburg, The Netherlands e-mail: [email protected] A. P. C. I. Hong · D. J. Damen Tilburg University, Tilburg, The Netherlands e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_57

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little attention, with the exception being studies on “home-field” advantage, mostly in the domain of sports. Insights from different disciplines indicate that in other contexts, the environment may influence human interaction too. Studies from environmental psychology provide ample evidence of the positive impact nature, both green (forests) and blue (coast, lakes), has on well-being, mind-set, and creativity. A literature study on the role of environment is followed by an experimental study in which the effect of the environment on negotiations is examined. In a virtual reality laboratory, the location of a beach and an office were created, in which participants had to carry out face-to-face negotiations with either distributive or integrative characteristics. The results show that the environment predominantly affected psychological variables: negotiating at the beach increased positive emotions and reduced the stress experienced in the negotiation. However, the different locations did not lead to different negotiation outcomes. The implications of the environment for negotiations are discussed, as well as the possibilities virtual reality technology offers in this respect. Keywords

Negotiation · Context for negotiation · Cognition · Communication · Empathy · Environment · Negotiation process · Virtual reality

Introduction Site selection in negotiations can be a critical variable. The location will have an impact on the protocol used and – if it takes more time – on the food served, on the location where to spend the night, and even on the dress codes. Although these factors might not be decisive for reaching a good deal, the practitioner’s guidelines for doing business abroad do mention that the location of the negotiation is a factor that should not be underestimated (Mayfield et al. 1998; Ghauri 1986). Generally, it is considered more beneficial to negotiate in a location that not only offers bargainers various practical advantages but also increases their feeling of being comfortable. In most cases, the location that ignites these feelings is taken to be the negotiators’ “home” location. The familiarity of being in one’s own environment has been argued to increase people’s confidence in competitive situations, with studies reporting its effectiveness in both the field of sports and distributive negotiations (Brown and Baer 2011). To our knowledge, however, the general impact of the environmental context on negotiators’ success during the negotiation (be it distributive or integrative) has received little attention thus far. The effect of the environment on human behavior has also been studied in order to assess its effect on factors of health, people’s mindset, and creativity. These studies range from the environmental effects on well-being due to the creativity of the design of the office space, the presence of plants, and being immersed in nature or in a coastal environment. These variables have been shown to reduce stress, to restore the attention level, and to increase the creativity at which we perform tasks.

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Although these beneficial effects of the environment on people’s (mental) health have not been studied in the context of negotiations, it is conceivable that the results also pertain to the negotiation setting. In a distributive bargaining situation, negotiators’ mindset is often competitive, and strategies to increase the pressure on a counterpart may not always be ethical. As a result, the stress level of negotiators in a distributive negotiation is likely to be high. The question thus arises as to whether and how a natural environment will have a restorative effect in that setting. In turn, integrative negotiations benefit from a high level of creativity of the parties involved. Hence, it seems reasonable to assume that a natural environment also contributes to more successful integrative negotiations (see also chapter ▶ “Negotiation Processes: Empirical Insights”). This chapter focuses on the question how the environmental context in which a negotiation is being held influences the bargaining process and the outcome of the negotiation. In the first part of this chapter, we will discuss relevant literature on the effect of environmental factors on the process and outcome of negotiations. We will start by discussing the findings from the literature on the effect of the environment on human behavior, starting with the home-field effect in sports and negotiations. Then we will turn our attention to studies on the effects of the environment on our mindset in general. Since many studies specifically focus on the effect of a natural environment, its impact on our well-being and creativity will be discussed separately. This section is followed by the description of our experimental study in which we manipulated the environment of the negotiation by means of virtual reality. In our experimental study, we varied the negotiation environment and compared the effectiveness of distributive and integrative negotiations that were located either in an office or in a beach setting. We conclude this section by discussing our findings and by providing suggestions for future research.

The “Home-Field” Advantage The effect of location on performance received most attention in the context of sports. In almost every sport, players prefer playing “at home” (at the home field), in their own stadium and with their own fans cheering them to victory. This preference is not without basis. Several studies have shown that under balanced conditions between playing at home and elsewhere, more than 50% of the matches played at home are won (Courneya and Carron 1992; Pollard 2002; Thomas et al. 2004; Allen and Jones 2014). Although no conclusive factors have been found that might explain the homefield advantage, studies have shown that factors like fatigue (Schwartz and Barsky 1977) and familiarity with the home field (Snyder and Purdy 1985) did not account for the home-field effect on players’ performance. Schwartz and Barsky (1977) showed that players’ fatigue caused by traveling was unlikely to cause the homefield advantage because no significant differences were found in players’ performance between first- and second-half season data. In turn, the learning factor of

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being more familiar with sporting at your own field could also not explain the homefield advantage, as the advantage has been documented for sports having highly similar playing grounds in every city (Snyder and Purdy 1985). Moreover, the presence of the home crowd as a factor explaining the home-field advantage has also been questioned. Pollard (2002), for instance, showed that home matches of cricket in the United Kingdom also displayed a home advantage, although the crowd during a cricket match is known for their discrete, almost inaudible support. Studies have also investigated the psychological factors involved in the homefield effect on players’ performance. The most frequently investigated factor is players’ stimulated confidence in their performance due to them playing at home. Bray et al. (2002), for instance, found that female hockey players report higher levels of self-confidence and self-efficacy prior to playing at home and lower levels of stress (see also Bray and Martin 2003, Terry et al. 1998, and Thuot et al. 1998). However, other studies have also shown that the intense support of the crowd can be detrimental to that confidence since it can increase players’ desire not to fail, thereby decreasing players’ athletic performance (Allen and Jones 2014; Jordet and Hartman 2008; Butler and Baumeister 1998). Besides confidence, other psychological factors have been studied in relation to the home advantage, predominantly in the context of sports, but without finding important effects. For instance, different levels of anxiety did not influence the level of soccer players in a home match or away (Duffy and Hinwood 1997; Bray and Martin 2003), nor was the mood of professional rugby players influenced by the location of the game (Polman et al. 2007). Although Thelwell et al. (2006) found a home-field effect on the mood of inexperienced soccer players, the authors also showed that experienced players’ mood was not affected by playing at home or away. Hence, it still remains to be investigated which factors contribute to the homefield effect.

Negotiation and the Role of Location From a consideration of the impact of the environment in sports to considering it in the context of negotiations is not a big step. The negotiation process and outcome are often described in sport terms, with competitive approaches and winners and losers (see also chapters ▶ “Negotiation Processes: Empirical Insights” and ▶ “Non-cooperative Bargaining Theory”). However, we do not know much about a possible home-field advantage in negotiations. In the vast field of studies on all the variables that can have an impact on the process and outcome of negotiations, the question of where the negotiation takes place received surprisingly little attention. Hosting the negotiation might not only be logistically beneficial to negotiators by increasing their control over the situation – ranging from the food served to the better access to information and specialists – but it might also play an important psychological role in negotiators’ belief in their competence (Salacuse and Rubin 1990). Within the field of cross-cultural negotiations, the role of the location where the negotiation takes place is considered to play a non-negligible role (e.g., Moran and Stripp 1991

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in Brown and Baer 2011; Griffin and Daggatt 1990). Although only briefly mentioned in most discussions of cross-cultural negotiations, it is widely assumed that negotiating “at home” in a cross-cultural or international negotiation is more comfortable for a negotiation party (Peak 1985; Weiss 1994; Peleckis 2014). This belief has also been reflected in Chu et al.’s (2005) study under experienced business negotiators. In Chu et al. (2005), the majority of the negotiators believed themselves to be better off negotiating at their own “turf,” with negotiators to feel more comfortable (71%), more confident (66%), and more successful (59%) negotiating at home than elsewhere. In addition, 69% of the Chu et al.’s (2005) experienced negotiators reported to consider themselves to be at a clear advantage when they are able to decide the negotiations’ location. Chu et al.’s (2005) findings were reflected in an experimental setting by Brown and Baer (2011) who were, to our knowledge, the first to examine the underlying factors explaining the home advantage in negotiations in a controlled empirical setting. In a series of buyer-seller experiments, in which they manipulated a “resident” condition versus a “visitor’s” condition, Brown and Baer (2011) compared the negotiation effectiveness of the participants to the one in a neutral condition. The home-playing negotiators outperformed the visiting negotiators. The visitors also did worse than the negotiators in the neutral condition, meaning that in the distributive setting Brown and Baer tested, the negotiators in the home situation not only were best off, but the visiting negotiators even suffered from the “away” disadvantage. The effect was partially mediated by confidence, which suggests that the residential advantage is strongest when it yields a sense of confidence in the negotiator’s mind.

Environment and Behavior: Mindset As we can conclude from the studies discussed above, the “home” environment in negotiations or even in sports increases the confidence of those who are acting in that “home” situation. If we take a look at the effect of the environment on human functioning in a broader organizational context, we can see that the home-feeling is important in more than just negotiation contexts. The physical spaces in which we spend most of our (working) time have an effect on our well-being and our functioning. The founder of scientific management, Frederick Taylor (1911), realized the importance of the organizational environment for an effective workflow. He was convinced that the organizational workspace should not distract from the essential tasks at the workplace. Personal belongings at the workplace, like pictures or plants, were considered to be distractive. The idea that workplaces should only consist of the necessary equipment needed to carry out the primary tasks is referred to as the “lean” approach to the management of workspace. Although the lean approach is still very common and has strong support from the “lean management” school (Gabriel 1997; Holweg 2007), its merits are mostly based on case studies (Haberkorn 2005; Knight and Haslam 2010a, b; Haslam and Knight 2010; Tapping and Dunn 2006; Mann 2010). More recent developments in management have shown that the optimal relationship between

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the physical characteristics of the workplace and the productivity of its occupants is not a lean one. On the contrary, employees perform best when they can identify with their workplace (Knight and Haslam 2010a; Nieuwenhuis et al. 2014; Brown 2009; Brown et al. 2005; Gosling et al. 2002). The experiments in the study by Knight and Haslam (2010a) showed that, compared to a lean office, an enriched office increased productivity and that an office space personalized by the participants themselves yielded even the best results. A possible explanation for this “enrichment” effect could be that decorating one’s own office space allows the worker to identify more with the space and have a greater idea of privacy and permanency (Baldry 1997). Furthermore, if an employer allows his workers to personalize their workplace, employees are argued to feel more respected by their management and to be more motivated. Knight and Haslam (2010b), Nieuwenhuis et al. (2014), and Greenaway et al. (2016) all refer to Tajfel and Turner’s (1979) social identity theory to explain the effect of the personalized workplace on employees’ mindset. Feeling more at home in one’s workplace has been shown to lead to a higher identification with the organization and to a stronger in-group feeling with the team members. As a result, motivation will increase, thereby stimulating employees’ productivity (see Van Knippenberg (2000) for a discussion on social identification and its impact on motivation in an organizational context). The relationship between organizational identification and job satisfaction has been confirmed by numerous studies (Worchel et al. 1998; Kreiner and Ashforth 2004; Van Dick 2004). Hence, managing the characteristics of a work location can have a positive spin-off on employers’ identification with the organization. The importance of office space properties is also more and more recognized by designers and architects. Yet, the psychological importance of that space received relatively less attention. Pierce and Brown (2019) relate the importance of a personal workspace to the construct of psychological ownership. Having a home at work – a personal workspace – becomes a part of who we are and of whom or what we identify with it. The more an office space allows for personal and private identification, the better the chances for psychological ownership for the employees and, hence, for a greater work satisfaction and motivation.

Environment and Behavior: Nature Besides the option to personalize one’s work environment, the proximity of nature can help to increase work effectiveness. Many studies have shown that the presence of nature in general is beneficial for our well-being. It works out positively on our memory and attentional capacities (e.g., Tennessen and Cimprich 1995, Berto 2005, Berman et al. 2008, Cimprich and Ronis 2003, Tabrizian et al. 2018, and Kjellgren and Buhrkall 2010), and it has been reported to have positive health effects and to help recover from stress (Bengtsson and Grahn 2014; Tyrväinen et al. 2014; Grahn and Stigsdotter 2010; Stigsdotter et al. 2017; Ward Thompson et al. 2012). Even patients in a hospital with a view on greenery recover more quickly and report having less pain (Beukeboom et al. 2012). Given the generally positive impact of

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nature, it is not surprising that people strongly prefer natural environments over urban environments (Kaplan and Kaplan 1989; Van den Berg et al. 2007; Meidenbauer et al. 2019), and this preference is similar across cultures (Kaplan and Yang 1990). In their leisure time, people are willing to travel far to experience nature or to pay extra for a hotel room with a view at the seashore. Also at periodic activities – like weekly markets – a green environment has a positive effect on the social encounters and the length of the visit (Annerstedt et al. 2013; Aram et al. in press). Nature has also been demonstrated to have a beneficial effect on work-related performances and work-related well-being. This holds for the location of the office, for instance, with a forest or park nearby, but also for the presence of plants inside the building or the office room (Grinde and Patil 2009). The plants have a positive effect on the emotional state and the experienced stress of office workers and as a result on their task performance (e.g., Bringslimark et al. 2007 and Dravigne et al. 2008). The positive effect of a natural environment has been associated with Attention Restoration Theory (ART; Kaplan 1995). Spending time in a natural environment, or even watching it on pictures or on a screen, can increase concentration capacity afterward. ART states that nature offers distractive stimuli, such as trees, beaches, and clouds, that allow the human mind to wander spontaneously and without effort, thereby reducing the impact of unwanted stimuli like stress or strong negative emotions (McMahan and Estes 2015; Ulrich et al. 1991). The restorative effect of nature has been attributed to the ease at which these natural stimuli can be processed. Comparison of natural and urban environments confirms the restorative effects of nature (Hartig et al. 2003). Within the literature on the health effects of a natural environment, a distinction is made between green (e.g., parks, woods) and blue (e.g., beaches, lakes, rivers) environments. Interestingly, the majority of the studies on health effects concern green spaces. Blue spaces received less attention, although the restoration effect of being near or at the water seems to be at least as important. That is, Gascon et al. (2017) conducted a systematic literature review of studies focusing on the health effect of blue space. Although the results were mixed and inconclusive, people living near blue spaces, notably in coastal areas as opposed to urban areas, reported a better general health (e.g., White et al. 2013 and de Vries et al. 2003), doing more physical activities (e.g., Ball et al. 2007 and Bauman et al. 1999) and having a greater psychological well-being (Alcock et al. 2015). These studies combined indicate the importance of the natural environment on people’s general well-being and mindset.

Environment and Behavior: Creativity While the favorable effect of green and blue spaces on our well-being has been validated in a great number of studies, the question as to what extent the space we are in affects our creativity has received far less attention. Several studies indicate that the presence of nature is also beneficial for tasks that require creativity. Ceylan et al. (2008) conducted a survey among managers to study their experiences with the office space they were working in. The managers reported that the presence of plants

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in a room was considered a creativity enhancing attribute. This experience of the managers as reported in the study of Ceylan et al. (2008) is confirmed by Shibata and Suzuki (2004) who studied the effect of the presence of one single plant in an office as opposed to a shelf with magazines, on the performance level in a task which required creativity. Furthermore, they also assessed the plant’s effect on mood. The presence of the plant resulted in a better task performance, although this effect was restricted to the female participants only and independent from mood. In a study by Raanaas et al. (2011), the positive effect of the presence of plants was found both for men and women. Atchley et al. (2012) took a more intense approach to the possible effect of the natural environment and sent groups of hikers for 4 days into the wild in different parts of the United States, deprived of all technology, including cell phones, in order to study the effect of the immersion in nature on their creativity. They observed an increase in creativity of 50% compared to a group of hikers who performed the same task before they left for the forest. The results are attributed to the attention restoration effect of the low-arousal stimuli nature offers (ART), but the authors do not exclude the possibility that having been deprived of mobile phones and other technologies for 4 days may have stimulated their creativity. Furthermore, it should also be noted that the sample of the study by Atchley et al. (2012) consisted exclusively of females. Oppezzo and Schwartz (2014) investigated the effect of physical activity on creativity and compared walking on a treadmill to walking on the green campus of the university where the study took place. The walking exercises improved the performance on the creativity task, but walking outside on the green campus produced the strongest positive effect. The physical activity of walking outdoors was crucial in their study, since being driven over the green campus in a wheelchair resulted in considerably less creativity. Interestingly, the green campus effect was also gender specific and stronger for females. The results of Shibata and Suzuki (2004), Atchley et al. (2012), and Oppezzo and Schwartz (2014) indicate that it would be worthwhile to study the interaction between gender and the effects of a natural environment more systematically. The question of how much or how long the exposure to nature should be has also received serious attention. The level of immersion in the green environment has been hypothesized to interact with the restoration or the increased creativity resulting from it. De Kort et al. (2006) varied the immersion in nature by presenting participants in their study a nature film on different screen sizes, after a stress-inducing task. Physiological measures, based on skin conduction and heart rate measures, indicated that the arousal caused by the stress task decreased faster when watching nature in front of a big screen. Subjective measures, such as self-reported affect, did not interact with screen size. Self-reports from the participants indicated that both levels of immersion led to complete restoration. Palanica et al. (2019) investigated creativity and the level of immersion in either a natural or an urban environment. They compared full immersion, operationalized as being outdoors in a natural setting, with being indoors, either watching a two-dimensional video or having a 3D virtual reality experience. Interestingly, in the indoor setting, the nature experience, irrespective of the medium, enhanced creativity more than the urban experience, but no difference was found between being outdoors in a nature and urban setting.

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The authors conclude that the experience of being outdoors suffices to stimulate creativity. Furthermore, the level of creativity in outdoor nature did not differ from the one in the 2D and 3D nature presentations, and the authors suggested this could be a signal of a ceiling effect for nature.

Environment and Negotiation Behavior: The Present Study As we signaled in the introductory part of this chapter, much is still unknown about the impact the environment can have on negotiations. Mostly anecdotal evidence from diplomacy and an incidental experiment (Brown and Baer 2011) indicate that a homefield advantage similar to the one in sports does occur. Negotiating “at home” increases confidence. Case studies from intercultural and diplomatic negotiations show that both home, away, and neutral grounds have their pros and cons (see also chapter ▶ “Negotiation Processes: Empirical Insights”). The studies discussed above, mostly found in the discipline of environmental psychology, provide useful insights that can be very relevant for the assessment of the impact environment or location can have on negotiations. The design of our workspace influences our mind, our well-being, and, as a result, the effectiveness of our functioning. A personalized workspace and the presence of nature increase productivity. The “green” and the “blue” factors have been regularly shown to produce a positive effect on our well-being. It allows a better restoration from stress and it increases creativity. Interestingly, the natural elements in the environment do not necessarily need to be real or outdoors. Videos or virtual reality presentations of nature scenes have a positive effect too. The positive effects of a natural environment reported above have, to our knowledge, never been tested for negotiations. Negotiations, especially in a competitive distributive setting which require claiming value, can be a stressful activity. Integrative negotiations on the other hand particularly ask for creativity in order to create value (see also chapter ▶ “Negotiation Processes: Empirical Insights”). Environmental factors could therefore be very relevant for both types of negotiations. It is strictly speaking not surprising that the environment or the location has not often been studied in relation to negotiations. They mostly take place in an office space, and, although it is not difficult to imagine that negotiators come to creative solutions over a break stroll in the garden or a park, we do not know of studies comparing the effect of the two types of environment on distributive and integrative negotiations. In order to assess the environmental effect, an experimental setting has been designed in which we studied negotiation simulations taking place in a regular office setting and in a natural environment. The different locations were realized in a virtual laboratory (see method below), in which an office room was designed and, as a contrast, a beach setting with the appropriate sounds and the waves or office windows projected on the walls. The environment of the beach was chosen because it was expected to contrast most with the office space. In these two settings, participants had to negotiate either a distributive case or a case that contained integrative potential. We expected positive effects of a natural environment, including “blue space,” on the stress level and creativity. More concretely, we expected the beach setting to have a positive effect on the stress level, the mood, and the creativity of the negotiators which

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should be reflected in a better joint negotiation outcome in the integrative negotiations (chapter ▶ “Impact of Cognitive Style on Group Decision and Negotiation”). The office setting, on the other hand, was expected to produce common phenomena, such as a greater “fixed-pie” bias. This would lead to more competitive outcomes in the distributive case and to lower joint outcomes in the integrative case. We also expected negotiators in the office setting to report higher levels of stress and more negative mood levels (chapters ▶ “Role of Emotion in Group Decision and Negotiation” and ▶ “Impact of Cognitive Style on Group Decision and Negotiation”). Furthermore, we investigated possible moderating effects of the negotiation space on relational variables that are particularly relevant for negotiations: the experienced trust, fairness, and personal liking (chapters ▶ “The Notion of Fair Division in Negotiations,” and ▶ “Procedural Justice in Group Decision Support”). It was hypothesized that on top of the reduced stress and increased creativity, the beach setting would create an atmosphere which would also contribute to a more positive relational outcome. The following description has been reproduced from our 2017 paper with kind permission of the International Conference on Group Decision and Negotiation. To examine whether and how the negotiation process was affected by the location and type of the negotiation, we set up an experiment in which participants negotiated the terms of a working contract during a job interview in an office space or at the beach, in dyads, face-to-face. The location was manipulated in the DAF Technology Lab1 of Tilburg University, in order to increase the validity of the study. The lab enables the creation of very realistic virtual reality environments. For the purpose of this study, a realistic office and beach setting was programmed. The addition of office furniture versus deck chairs and sand increased the validity. We used a 2D application in which the setting (office or beach) was projected by eight beamers from the ceiling on all four walls of the room (see Figs. 1 and 2). The realism of the setting was enhanced by accompanying sound and motion of the setting. In the office location, participants heard a moving ventilator and office sounds in the background, whereas in the beach setting, they heard sounds of moving waves reaching the beach, and they saw a sailing ship passing by at the horizon.

Method Participants and Design One hundred sixty-two undergraduate students (81 dyads) from Tilburg University participated in the experiment as part of a course requirement. Participants’ average age was 23.40 years (SD = 3.02), and they were randomly assigned to one condition in a 2 (location: office or beach)  2 (negotiation type: distributive or integrative) between-subjects design. The dependent variables were the negotiation outcome

1 For more information about the DAF Technology Lab, see https://www.tilburguniversity.edu/ campus/experiencing-virtual-reality/

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Fig. 1 The beach environment projected on the walls of the virtual laboratory

Fig. 2 The office environment projected on the walls of the virtual laboratory

(individual profit, joint profit), satisfaction about negotiation process, and outcome, mood, stress, and trust and mutual liking).

Materials The negotiation case designed for the study was a job interview between an employer and a future employee, who had to agree on three items: the salary, the

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length of the contract, and the number of vacation days. A payoff matrix was created in which for each option of the three items, a different payoff in gains was indicated. This allowed to create a distributive and an integrative negotiation case. In the distributive setting, the payoff matrix for both parties was completely mirrored with the most beneficial item and option for a negotiator being the opposite for the counterpart. In the integrative setting however, the importance of the items was not the same for both parties. In this case the employee had a relatively higher payoff for the salary options, whereas it was more important for the employer to limit the contract length as much as possible. This difference resulted in an integrative potential which could be reached by logrolling.

Procedure Upon arrival in the virtual reality beach or office, participants were introduced to each other, and they were told that they would perform a negotiation with each other consisting of a job interview. The roles of employer and future employee were randomly assigned to the participants, and participants in the office setting were told that the negotiation took place at the office of the employer. After having been informed about the study, participants signed a consent form and completed a first questionnaire that contained demographic background variables and items that assessed participants’ mood and stress level. After completing this questionnaire, the participants were given written information about the negotiation case. Participants were given a maximum of 10 min to prepare for the negotiation. Before entering the lab, they had to make a short test of calculating the total payoff of several offers in order to check whether they understood the payoff matrix. Furthermore, they had to write down their planned first offer. Finally, they could enter the lab and the negotiation started. Participants negotiated about the offers of each item. During the negotiation they used the payoff matrix to assess the payoff of the offer they received and the counteroffers they made. After approximately 15 min, participants had to decide if they would come to an agreement and, if so, what the negotiated outcome was for each item. After the negotiation ended, they had to indicate on a special form whether they had an agreement and, if so, what the final offer was for each item. Then the participants were asked to fill out a questionnaire that assessed their stress level, and mood again, and satisfaction about the process and outcome, and relational variables (experienced formality, trust, fairness, and mutual liking). After having completed this questionnaire, participants were thanked for their participation and were fully debriefed via email approximately 2 weeks after the end of the experiment.

Measures Mood Participants’ mood was measured before and after the negotiation and consisted of 12 items on a 5-point scale (1 = very slightly or not at all, 5 = extremely) that were

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adopted from the original Positive and Negative Affect Schedule (PANAS) (Watson et al. 1988). Six items measured positive affect (PA: interested, strong, determined, happy, excited, and proud), and six items measured negative affect (NA: afraid, nervous, scared, irritable, weak, and ashamed). Cronbach’s alpha for the positive affect scale was 0.79 (M = 2.88, SD = 0.72) for the pre-measurement and 0.84 (M = 3.15, SD = 0.84) for the post-measurement. Cronbach’s alpha for the negative affect scale was 0.70 (M = 1.66, SD = 0.56) for the pre-measurement and 0.68 (M = 1.56, SD = 0.56) for the post-measurement.

Stress Level Stress level was measured prior to and after the negotiation and consisted of one question on a 7-point Likert scale (1 = very relaxed, 7 = very tense). The mean score on this scale was 3.64 (SD = 1.52) for the pre-measurement and 4.65 (SD = 1.86) for the post-measurement. Satisfaction Participants’ satisfaction was measured with two items: one item assessed their satisfaction about the process of the negotiation and one item assessed how satisfied they were with the result of the negotiation. Both items were measured on a 5-point Likert scale (1 = completely disagree, 5 = completely agree). The average score for process satisfaction was 4.13 (SD = 0.91) and for outcome satisfaction 4.11 (SD = 0.94). Trust A single item (“I think my counterpart was trustworthy”) measured the perceived trustworthiness of the participants, on the same 5-point Likert scale (1 = completely disagree, 5 = completely agree) and had a mean score of 4.20 (SD = 0.86). Virtual Reality Experience In order to assess the effect of the virtual environment in the eyes of the participants, we asked them to rate four statements (e.g., “The virtual environment was realistic; – distracting; – influenced the negotiation; “after a while I forgot being in a virtual environment”) and to indicate their experience on four contrastive statements (“the virtual environment was “formal vs informal; relaxing vs energizing; discouraging vs stimulating; professional vs unprofessional”).

Results Joint Gain and Outcome Difference In a first analysis, we tested whether the beach setting would lead to higher joint gains than the office setting in integrative negotiations. To examine this, we performed a 2 (location: beach or office)  2 (negotiation type: distributive or integrative) ANOVA, with joint gain as the dependent variable. The joint gain was computed by summing up the payoff gains for each party (i.e., employee and employer). The means can be found in Table 1.

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Table 1 Means and standard deviations (between parentheses) for joint gain as a function of negotiation location and type Integrative negotiation Distributive negotiation

Beach 15,677.79 (333,29) 14,560.00 (387.26)

Office 15,762.50 (432.97) 15,400.00 (397.31)

Table 2 Means and standard deviations (between parentheses) for outcome difference as a function of negotiation location and type Integrative negotiation Distributive negotiation

Beach 322.22 (290.45) 505.00 (585.42)

Office 358.33 (405.79) 408.89 (288.80)

A marginal main effect for the negotiation type was found: negotiations with integrative potential yielded higher joint gains (M = 15,720.14, SD = 273.20) than the distributive negotiations (M = 14,980.00, SD = 277.41), F(1, 78) = 3,61, p = 0.061, η2 = 0.04. No effect for negotiation space nor interaction between negotiation type and location was found, Fs < 1,41, ps > 0.239. The beach setting did not lead to the expected higher joint gains in integrative negotiations than the office space. In the second analysis, we examined whether differences in outcome between negotiators would be more pronounced in distributive negotiations taking place in the office than at the beach. To examine this, we performed a 2 (location: beach or office)  2 (negotiation type: distributive or integrative) ANOVA, with outcome difference as the dependent variable. The outcome difference was computed by subtracting the payoff gains for each dyad2. The means can be found in Table 2. No main effects for office setting and negotiation type were found, nor an interaction between location and negotiation type, Fs < 1.51, ps > 0.223. Thus, contrary to our expectations, differences in outcome between negotiators were not more pronounced in distributive negotiations taking place in an office as compared to the beach.

Additional Analyses: Mood, Stress Level, Trust, Satisfaction, and the Virtual Environment We examined whether the beach or office setting would influence the negotiators’ mood, stress levels, trust, and satisfaction (see Table 3 for an overview). We conducted two mixed ANOVAs on participants’ mood, the dependent variables being one on positive affect (PA) and one on negative affect (NA). In both analyses, location (beach or office) and negotiation type (distributive or integrative) were Since the outcome difference could be positive or negative, we first squared the differences and then square rooted the result to end up with an outcome difference that was positive.

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Table 3 Means and standard deviations for mood, stress, trust, and satisfaction as a function of negotiation location and type Location Negotiation PosMood pre PosMood post NegMood pre NegMood post Stress pre Stress post Trust Satisfaction process Satisfaction outcome

Beach Distributive M SD 3.01 0.70 3.18 0.90 1.57 0.58 1.54 0.54 3.69 1.37 4.43 2.02 4.26 0.80 4.05 1.08 3.93 0.99

Integrative M SD 2.98 0.69 3.34 0.81 1.51 0.49 1.40 0.46 3.26 1.48 4.58 1.74 4.17 0.85 4.32 0.89 4.36 0.76

Office Distributive M SD 2.61 0.80 2.81 0.82 1.83 0.57 1.65 0.62 3.58 1.59 5.11 1.56 4.17 1.02 3.89 0.82 3.94 0.95

Integrative M SD 2.81 0.70 3.12 0.74 1.87 0.54 1.81 0.60 4.23 1.50 4.67 2.09 4.23 0.76 4.10 0.79 4.16 1.00

entered as the between-subjects factors and time of measurement (i.e., pre-measurement and post-measurement) was entered as the within-subjects factor. The first analysis showed that participants had a more positive mood after the negotiation (M = 3.15, SD = 0.84) than before it (M = 2.88, SD = 0.73 F(1, 154) = 29.51, p < 0.001, ηp2 = 0.16). Furthermore, participants generally had a higher positive mood in the beach negotiations (M = 3.13, SD = 0.71) than in the office negotiations (M = 2.84, SD = 0.73; F(1, 154) = 6.03, p = 0.15, ηp2 = 0.04). Regarding participants’ negative affect, the analysis revealed that they had a less negative mood after the negotiation (M = 1.56, SD = 0.56) than before it (M = 1.66, SD = 0.56), (F(1, 154) = 6.21, p = 0.014, ηp2 = 0.04). Thus, overall, the beach setting yielded a more positive mood than the office setting, and negotiations in general increased participants’ positive moods and decreased their negative moods. However, negotiating at the beach or office did not influence the development of the participants’ positive and negative mood differently (i.e., increase or decrease), and this also did not depend on the type of negotiation. The stress the negotiators experienced increased significantly after the negotiation F(1, 153) = 30.28, p < 0.001, ηp2 = 0.17. Furthermore, although only marginally significant, the general stress experienced at the beach was slightly lower than in the office F(1, 153) = 3.06, p = 0.082, ηp2 = 0.02. The negotiators in the integrative setting were more satisfied with the outcome results than the ones in the distributive setting, F(1, 158) = 4.84, p = 0.029, ηp2 = 0.03. No main effect for location nor interaction between negotiation type and location was found for satisfaction with results, Fs < 0.53, ps > 0.470. As for the satisfaction about the process, no main effects for negotiation type nor location nor interaction were found, Fs < 1.84, ps > 0.177. The perceived trustworthiness of the counterparts was relatively high (M = 4.20; SD = 0.86) and was not affected by the location nor by the negotiation type, Fs < 0.30, ps > 0.586. The evaluation of the virtual environment the participants had been negotiating in yielded the following picture. The virtual beach was considered more distracting

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(t(160) = 2.34; p = 0.021), more relaxing (t(160) = 5.39; p < 0.001), and more informal (t(160) = 16.65; p < 0.001) than the virtual office. Vice versa, the virtual office was evaluated as more realistic (t(160) = 2.64; p = 0.009) and more professional (t(160) = 14.14; p < 0.001) than the virtual beach. Furthermore, when in the virtual office, participants indicated having less problems forgetting they were in virtual space (t(160) = 2.50; p = 0.013).

Environment and Negotiation: Gender We ran additional analyses to verify whether male and female participants experienced the location of the negotiation differently. Different studies on environmental effects noticed gender differences, although they studied the effect of green locations and not blue ones, like the beach in the present study (Shibata and Suzuki 2004; Oppezzo and Schwart 2014). Gender did not have an effect on the joint outcome nor on the outcome differences, and no interaction was found with negotiation type nor with negotiation location, Fs < 1.72, ps > 0.235. The mood measurements taken at the end of the negotiations indicated that irrespective of the experimental condition, males report a more positive mood than females (M(male) = 3.35, M(female) = 2.94; F(1,154) = 9.07, p = 0.003, ηp2 = 0.06). No interactions were found for gender and negotiation type nor for location. No effects were found for negative mood either (Fs < 3.74, ps > 0.055). As for the experienced stress, gender did not interact with the difference between the pre- and post-negotiation measurements, negotiation location, nor negotiation type (Fs < 3.34, ps > 0.069). So the development of stress during the negotiations was similar for males and females. However, if we take a look at the stress post-measurement only, a significant interaction was found between gender and negotiation location. Female participants felt more stress in the office location (M(female) = 5.50; SD = 0.304) than at the beach (M(female) = 4.33; SD = 0.238), whereas this was the same for the male participants (office: M(male) = 4.22; SD = 0.326; beach (M(male) = 4.78; SD = 0.304)). Gender did not interact with negotiation location in the assessment of the level of informality (F(1,153) = 0.29; p = 0.59), but it did with negotiation type (F(1,153) = 6.81; p = 0.010, ηp2 = 0.04). Female participants reported a higher informal atmosphere in the integrative negotiations than males (M(female) = 4.24; SD = 0.154; M(male) = 3.25; SD = 0.175), whereas in distributive negotiations, no difference was found (M(female) = 3.81; SD = 0.156; M(male) = 3.69; SD = 0.181). Male and female participants did not differ in the assessment of trust of their counterpart. No interaction with negotiation location or negotiation type was found (Fs < 0.265, ps > 0.608). They also did not differ in their satisfaction with the results nor with the process, and this also did not interact with negotiation location or negotiation type (Fs < 2.932, ps > 0.089).

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In general, male and female participants appreciated the virtual environment equally. Females, however, thought negotiating at the virtual beach was more relaxing than in the office (M(beach) = 5.15, SD = 0.119; M(office) = 4.06; SD = 0.153), whereas males did not feel this distinction that strongly (M(beach) = 4.81, SD = 0.153; M(office) = 4.42; SD = 0.165; F(1,153) = 5.742; p = 0.018). All in all, gender did not strongly moderate the negotiations. Females appreciated negotiating at the beach more than in the office, and for men, the location did not really matter.

Home Advantage In the office location scenario, the negotiator taking the role of the employer explained that they received the employee in their home office. For obvious reasons, this was not the case at the beach location. Although the instructions did not explicitly mention or trigger a “home-field” advantage in the office, this might have been the case. However, no effect for the role of the negotiator (employer versus employee) was found and no interaction with the location where the negotiation took place.

Discussion In the virtual environment study, we explored the possibility that the negotiation location would influence the mindset and the mood of the negotiators. This effect would be reflected in the negotiation process and outcome and interact with the type of negotiation. We argued that the joint gains in the integrative negotiations taking place at the beach would be higher than in the office location. We expected the differences in outcome between negotiators would be more pronounced in distributive negotiations taking place in the office. However, the results of the study did not support our expectations. The joint gain in the integrative negotiation was indeed higher than in the distributive negotiation, but this was the same for the beach and the office, and this most probably was the result of the different payoff settings. Also, the outcome difference was the same for distributive negotiations taking place at the beach and in the office. The influence of the environment apparently did not reach the negotiation process and outcomes. In contrast, the study did indicate that the location of the negotiation influenced negotiators’ mood. Although in general the participants were in a better mood after the negotiations than before, this effect was most pronounced for the beach setting. The general stress level the participants experienced was higher after the negotiations than before, but this tended to be less for the negotiations taking place at the beach. More precisely, this difference could be attributed to female participants who experienced more stress than men in the office location. We know from negotiation studies which include the gender factor that women tend to be less at ease and are often worse off than men at the negotiation table (Stuhlmacher and Walters 1999;

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Mazei et al. 2015), so the higher stress for women in the office setting may be an indication of this gender effect. On the other hand, the stress level the female negotiators experienced on the beach setting was considerably lower than in the office and at the level of the male negotiators. This indicates quite convincingly that the beach setting has a stress-reducing effect on women in an otherwise stressful situation. As far as we know, the present study was the first in which a Virtual Reality Lab was used to examine the possibilities it offered to change the environment in which a negotiation took place. We created a beach and an office setting and found that both locations yielded different experiences, indicating that the manipulation had been successful. Other studies which included VR applications to observe the effects of the environment primarily used “green” environment instead of the “blue” one used in the present study. Although we do not have a fundamental reason to expect different results, it would be interesting to replicate the present study with a green VR environment, such as a forest or park. Furthermore, we also lack information on the impact of a “real” green or blue environment on the negotiation process and variables. A control condition at the realistic office and beach situation was lacking in this study, and this makes generalizations to those real settings difficult. So, the present study is just a first and modest step toward a better understanding of the impact of environmental factors on negotiation behavior. Still, the effect that the location had on negotiators’ emotions (mood) and perceptions (stress) variables offers interesting new opportunities to further study the effects of mood on negotiations and, more precisely, mood which is not induced by negotiation variables or by the interaction with the counterparts (see chapter ▶ “Role of Emotion in Group Decision and Negotiation”). This makes a Virtual Reality Lab an interesting tool to integrate in research into the environment and negotiation and an interesting addition to the studies investigating the use of digital media in negotiation settings (see chapter ▶ “Communication Media and Negotiation: A Review,”). In the VR study, the participants were, during the entire negotiation, at the virtual beach or in the virtual office. However, the environment could also be important as a factor outside the negotiations. As we have seen above, Attention Restoration Theory (ART) suggests that a natural environment or even natural elements at a specific location offer stimuli that allow the mind to be distracted and to wander, and this would help to recover from stressful experiences or from tasks that demand intensive concentration and creativity. It could be argued that especially the beach negotiation in the VR laboratory implied that the participants were not only exposed to the distracting stimuli of the waves but also to the requirements the negotiation imposed on them. A proper testing of ART would be to have negotiators, before taking their place at the negotiation table, make an individual walk through a park or along the beach. This could be done either before the negotiation itself or during a break, and this could be a real stroll or a VR stroll, after which they reenter the negotiation with a refreshed mind. It should further be noted that the creativity required for a successful integrative negotiation in the VR study was limited. A more complex case would be more appropriate for the assessment of the impact of the environment on creativity.

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Numerous studies have shown that a natural environment nearby has a beneficial effect on our well-being and this effect ranges from quicker physical recovery from medical issues to a mindset that is less prone to stress and more open for positive emotions. The present study confirmed these findings for negotiations, which were experienced as less stressful when carried out at the beach. The negotiators in the beach setting also reported stronger positive emotions. The VR setting of the beach was clearly realistic enough to produce the same positive effects. Positive emotions have been shown to contribute to agreements in integrative negotiations (Carnevale and Isen 1986; Baron 1990; Baron et al. 1990; Thompson et al. 1999). A positive mood enhances the willingness to look for shared interests and for options to create value instead of claiming value. A positive mood has been experimentally stimulated in different ways, such as by receiving positive feedback from the counterpart, but also by means of little presents, or by showing fragments of a popular series like “Friends.” The present study provides good arguments to further investigate the moderating role of a natural environment in integrative negotiations. The home-field advantage, which has been shown to hold for negotiations too (Brown and Baer 2011), was not a factor we included in the VR study. However, given the fact that the home-field advantage is particularly relevant for intercultural and international negotiations, in future studies the VR lab could be used to create locations which are representative for different cultures and contribute to the validity of studies of intercultural negotiations between members of different cultures. The technology of the VR lab could also be used to study the individual personalization factor in the home-field paradigm. Negotiators could relatively easily create their preferred “home” location where they could receive the counterpart. The session at home could be alternated with session at the counterparts’ home, which would enable researchers to study this factor in a very controlled way. As the studies on office design illustrate, the possibility to personalize the location or space where work or, here, a negotiation will take place offers interesting opportunities to learn more about the effect of the environmental factors. From our inventory of studies on the role of location and environment on negotiations, it could be concluded that whether it is caused by a “home” situation, an office design that allows personalization, a room decorated by plants or having a view on green spots, or a green or blue environment in general, the positive effects reported that are relevant for negotiations or other conflict-solving interactions such as a mediation reside in the positive mindset that results from those environmental factors. The studies that focus on this area are very scarce (Brown and Baer 2011), and the robustness of the findings from disciplines like environmental psychology is a convincing argument to continue this line of research. A distinction should then be made between two conditions in which the location or environment could influence a negotiation. Firstly, the environment can serve as a means to enhance the concentration, mood, and well-being before and in between (parts of) a negotiation. After the exposure to the environment, negotiators would then rejoin the “normal” negotiation table. This would allow to further assess the validity of theories like the Attention Restoration Theory. Secondly, the effect of the environment that “hosts” the negotiation needs to be studied. Although in the present study, the approach of

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the negotiation simulation in the VR lab and its outcome were relatively limited, the fast-growing possibilities that the technology of virtual reality offers allow us to study a great variety of environmental factors pertinent to negotiations, ranging from creating vast landscapes to producing detailed stimuli in the direct negotiation space. Those stimuli could range from stress-reducing or stress-increasing mechanisms to, for instance, the distracting presence of people interested in the outcome of the negotiation like in labor/employer negotiations, which in the future might be located in a forest or beach, real or virtual.

Cross-References ▶ Communication Media and Negotiation: A Review ▶ Impact of Cognitive Style on Group Decision and Negotiation ▶ Negoisst: Complex Digital Negotiation Support ▶ Negotiation Processes: Empirical Insights ▶ Non-cooperative Bargaining Theory ▶ Online Dispute Resolution Services: Justice, Concepts, and Challenges ▶ Procedural Justice in Group Decision Support ▶ Role of Emotion in Group Decision and Negotiation ▶ The Notion of Fair Division in Negotiations Acknowledgments We thank TICC for granting us permission to use the DAF Technology Lab. The DAF Technology Lab is partially funded by a philanthropic donation from the PACCAR Foundation/DAF Trucks and with funding from the European Union, Op Zuid, the Ministry of Economic Affairs, the Province of Noord-Brabant, and the municipalities of Tilburg and GilzeRijen (PROJ-00076) awarded to Tilburg University. The usual exculpations apply.

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Neuroscience Tools for Group Decision and Negotiation Adiel Teixeira de Almeida, Lucia Reis Peixoto Roselli, Danielle Costa Morais, and Ana Paula Cabral Seixas Costa

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Foundations of Neuroscience and Its Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neuron and the Information Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neuroscience Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Strengths and Weaknesses of Neuroscience Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Behavioral Neuroscience and GDN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Behavioral Experiments for Decision-Making with Neuroscience Tools . . . . . . . . . . . . . . . . . . . . . . Using Neuroscience for Understanding Decision-Making Process . . . . . . . . . . . . . . . . . . . . . . . . Contributions from Neuroscience Researches for Negotiation Process . . . . . . . . . . . . . . . . . . . . Using Neuroscience Behavioral Studies to Modulate Decision-Making Methods . . . . . . . . . . . . Conclusions and Future Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Neuroscience is a new and interdisciplinary field, so it is no surprise that its ideas and principles have been applied in many different contexts. Group decision and negotiation is one area in which neuroscience may be especially helpful. One goal

A. T. de Almeida (*) · L. R. P. Roselli · D. C. Morais CDSID – Center for Decision Systems and Information Development, Universidade Federal de Pernambuco, Recife, PE, Brazil e-mail: [email protected]; [email protected]; [email protected] A. P. C. S. Costa CDSID – Center for Decision Systems and Information Development, Universidade Federal de Pernambuco, Recife, PE, Brazil Departamento de Engenharia de Produção, Federal University of Pernambuco, Recife, Brazil e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_53

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is to understand how actors’ interactions are registered directly in the brain, to identify affective factors, and thereby to explain humans’ ability or inability to evaluate the actions and intentions of others. Also, neuroscience tools provide broad and deep knowledge of the cerebral mechanisms. In the context of group decision and negotiation, these tools can be used to explain how decisions have been made, allowing the development of theoretical models. Thus, this chapter aims to demonstrate the use of the neuroscience approach to support group decision and negotiation, and to provide a better understanding of human preferences, develop new insights into multi-attribute decision processes, and improve decision support systems. Keywords

Group decision and negotiation · Neuroscience · Preference modeling · Multiple attribute decision-making

Introduction A variety of neuroscience methods have been used to investigate neural systems, allowing the development of an understanding of the neural mechanisms that support decisions. Understanding the human brain and behavioral responses can help to explain the heterogeneity seen when people act individually and interact, that is, understanding the underlying mechanisms by using neural data to make better predictions about human behavior. Besides, it is possible to understand how actors’ interactions register directly on the reward system of the brain, as affective factors and the ability to evaluate the intentions of others play an important role. In this context, the neuroscience approach can help understand the behavior of decision-makers (DMs) when Multi-Criteria Group Decision Making/Aiding (MCGDM/A) or Negotiation Support Systems are presented, in order to improve the group decisions and negotiation (GDN) approach. Neuroscience has advanced in large part because of the many types of equipment and tools to provide physiological measures that have been developed. Aligned with the use of mathematical models for individual and group decisions, the data collected using neuroscience tools, which uncover cognitive biases and neural activities, enhance knowledge of GDN processes. Behavioral considerations for GDN are highlighted in [Eden, Behavior Considerations in Group Support], [Salo et al., MCDA methods for Group Decision Processes], and [Corrente et al., Multiple Criteria Decision Support]. This chapter discusses some of the equipment and tools used in this area, and the relation between behavioral neuroscience and aspects of GDN. Also, many applications of behavioral experiments are collected and investigated, with special focus on their applications to GDN. Finally, some future challenges for the field of GDN are discussed.

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Foundations of Neuroscience and Its Tools Glimcher and Fehr (2014) noted that in the last century, the study of human behavior was classically based on two approaches, neurological, and physiological. In the neurological approach, human or animal patients with brain lesions were studied and their behavioral deficits correlated with their neurological lesions. The physiological approach involved the study of the brain, correlating direct measurements of biological states, such as the triggering of action potentials in neurons, changes in blood flow, and changes in neurotransmitters to events in the outside world. This type of approach was extremely limited, since the physiological measurements were invasive, restricting their use to anesthetized animals. In the 1960s to 1980s, scientific advances led to an expansion and fusion of these two approaches, and models of psychology began to be used to understand the relationship between the brain and behavior. These advances made it possible to carry out studies by taking measurements on conscious animals. At this time, two problems were faced by researchers: the excess of models and the scarcity of data. The attempts to solve these problems led to the revolution in cognitive neuroscience. In this revolution, the study of decision-making has been highlighted, being one key to understand the emergence of areas in neuroscience such as neuroeconomics, neuroIS, consumer neuroscience, decision neuroscience, behavioral neuroscience, neuromarketing, management neuroscience, and organizational neuroscience. Theories as risk-based decision-making and emotion-based decision making (Bechara et al. 1994; Macmillan 2002; Glimcher and Fehr 2014) aroused in the scientific community an interest in behavioral studies in humans. Initial studies on decision-making were associated with brain damage. A better understanding of the relationship between mental and neural function in humans awaited the development of methods to visualize human brain activity noninvasively, such as functional magnetic resonance imaging (fMRI) (Kwong et al. 1992; Ogawa et al. 1992). With the development of neurophysiological tools, scholars in many disciplines have begun to consider measuring human brain activity during decision-making. In the following sections some basic concepts and a brief description of the equipment and tools used in neuroscience are presented.

Neuron and the Information Processing The neuron is the central element of the nervous system. It is an electrically excitable nerve cell that receives, processes, and sends information. The operation of a neuron is not only based on electrical impulses, but also chemical signals that enable the communication of one neuron with another (Müller-Putz et al. 2015).

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Information processing happens in the cell body. The information is transported to the dendrites through an axon, and at the end of an axon are terminals that receive electrical signals and send chemical substances to the synapse; these chemical substances are called neurotransmitters and are the basis for communication among neurons (Müller-Putz et al. 2015). For any and all mental processes, neural networks must be active. It is estimated that the human brain comprises 100 billion neurons, with each neuron having, on average, 10,000 connections to 10,000 other neurons (Müller-Putz et al. 2015). Fabiani et al. (2007) explain that the electrical activity that results from the activation of only one neuron is very small; however, it is possible to measure the joint activity of vast number of neurons. Neurophysiological tools make it possible to measure neural activity in different ways, as will be presented in the next section.

Neuroscience Tools The neurophysiological tools used in neurosciences can be classified into two major groups: psychophysiological tools and brain imaging tools (Dimoka et al. 2012). According to Dimoka et al. (2012), the applications and equipment used for each group can be classified as follows: (a) Psychophysiological tools Eye-tracking: Measures where the eye is looking (eye position) or the eye’s motion relative to the head (eye movement). Skin conductance response (SCR): SCR tools measure activation in the sympathetic nervous system, which changes the sweat levels in the eccrine glands of the palms of hands (or feet or arms). Facial electromyography (fEMG): Measures muscle activity in the form of electrical impulses spawned by muscle fibers during contraction from two main facial muscles, the corrugator supercilli and zygomaticus. Electrocardiogram (EKG): Measures the electrical activity of the heart from the skin, i.e., how many times the heartbeats in a minute. (b) Brain imaging tools Functional magnetic resonance imaging (fMRI): A noninvasive method that reflects neural activity by measuring changes in blood oxygenation and blood flow. Positron emission tomography (PET): Measures metabolic activity by representing neurochemical changes using radioactive tracer isotopes that are detected by a PET scanner. Electroencephalography (EEG): Measures electrical brain activity, using detectors on the scalp, from extracellular ionic currents that are caused by dendritic activity. Since the individual electrical potentials are very small, EEG captures the sum of the potentials of millions of neurons that follow a similar spatial orientation. Magnetoencephalography (MEG): Measures electrical brain activity similarly to an EEG, but measuring changes in magnetic fields caused by brain activity.

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The temporal resolution of MEG is comparable to EEG; however, MEG has lower spatial resolution. MEG is more effective in registering activity in deeper brain structures than an EEG, but does so at a lower spatial resolution and accuracy than fMRI.

Strengths and Weaknesses of Neuroscience Tools Dimoka et al. (2012) discuss the importance of understanding the strengths and weaknesses of neurophysiological tools in developing valid studies. The main strength of neurophysiological tools is the ability to collect data, especially data that cannot be manipulated. In some experiments, individuals may tend not to be truthful, for example, being able or unwilling to answer questions involving feelings and emotions, as is very common in GDN processes. In these situations, neurophysiological tools receive signals that describe processes that are not consciously carried out. These signals can be measured in real time, while the individual performs a task or responds to a stimulus and can help in better understanding of cognitive overload in the decision-making process. On the other hand, these tools also present weaknesses that need to be carefully considered in any study. Among the weaknesses, we highlight the artificial scenario that is created in the experimental context in which neurophysiological tools are used, which may limit the validity of the studies. As an illustration of this artificiality, we mention fMRI and PET scanners that are in general cylindrical whole-body tubes that completely change the environment in which the individual would perform a task or make a decision. Most neurophysiological tools use sensors in the human body that can induce stress and bias. Eye-tracking tools often require individuals to wear special equipment such as goggles or a helmet. Neurophysiological data may also not be so easily interpreted. The ocular scans, for instance, can be related to complexity or the difficulty of performing the task as well as interest in the task or the attribution of importance to the stimulus (Raynor 1998). Thus, neurophysiological measure may have more than one meaning, making it difficult to interpret. Another difficulty is the collection and analysis of the data. The amount of data collected is usually very large, and much of the data preprocessing for noise removal (artifacts) such as those caused by undue movements of individuals during the experiment needs to be performed manually.

Behavioral Neuroscience and GDN Multi-Criteria Group Decision Making/Aiding (MCGDM/A) and the Negotiation Process are different approaches that have many similarities and cannot be totally dissociated (Kilgour and Eden 2010). In this context, there are some recent advances in the neuroscience approach that bring insights applied to them, conjointly and separately.

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Table 1 A broad view of neuroscience studies for on group decisions and negotiation Subject Group decision processes

Negotiation processes

Topic Multiattribute decisions

Other features Game theory Interaction processes Emotions Cooperation and competition Cultural differences

References Nermend (2017), Hunt et al. (2014), Trepel et al. (2005), Barberis and Xiong (2009), Goucher-Lambert et al. (2017), Sylcott et al. (2013), Ravaja et al. (2016), Linkov et al. (2012) Brocas (2012), Preuschoff et al. (2006), Kuhnen (2015) Krueger et al. (2008), Hollmann et al. (2011), Rilling et al. (2002) Lee (2006, 2008), Fehr and Camerer (2007), Gęsiarz and Crockett (2015) Bechara and Damasio (2005), Liu et al. (2016), Tabibnia et al. (2008) Balconi and Vanutelli (2018), Lee et al. (2018) Briley et al. (2014), Wawra (2009), Kubota et al. (2012)

Related to Group Decision Making/Aiding, the principal aspect discussed is preference modeling. Of course, from the behavioral point of view, studies related to the investigation of how a decision-maker (DM) individually demonstrates his/her preferences will be evaluated. It does not usually make sense to aggregate the DMs’ preferences, since the individual characteristics will be mixed, and the DMs will ignore their individual preferences in order to generate the group preferences. On the other hand, for the negotiation process, the focus is on the participant’s integration process, using the support of game theory (von Neumam and Morgenstern 1953) to evaluate the behavior in negotiation, and investigating some factors that can affect the negotiation process (Raiffa 1982). An overview of reference studies of neuroscience on group decisions and negotiation are presented in Table 1. Recent advances in Neuroscience can enrich these themes and improve the processes developed from behavioral studies about DMs. A search of the literature points out many of the highlights regarding group decisions and negotiation processes. Group Decisions: • Dorsolateral prefrontal cortex plays an important role in MCDM/A (Krawczyk 2002). • Emotion is presented when participants analyze pairwise comparison (Nermend 2017). • Within attribute comparison strategy is used instead of complete integration of values (Hunt et al. 2014). • Environmental impact has more importance than esthetic feature (GoucherLambert et al. 2017). • Mental effort is positively correlated to visual processing (Goucher-Lambert et al. 2017).

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• Emotion is presented in the trade-off evaluation process (Sylcott et al. 2013). • Accumulation of information until brain is prepared to select an alternative (Brocas 2012). • InverseS-shaped curve is associated with emotions of fear and hope (Barberis and Xiong 2009). Negotiation Process: • Reinforcement learning might be used to calculate expected utility (Krueger et al. 2008). • Emotional self-regulation and reward processing strongly influence game choices (Hollmann et al. 2011). • Emotions support advantageous decisions (Bechara and Damasio 2005); • Emotions expressed are similar in online interaction and off-line interaction (face to face) (Liu et al. 2016). • Extreme emotions generally bring unsuccessful results for trades (Liu et al. 2016). • Competitive conditions, inspired by positive feedback, improve outcomes (Balconi and Vanutelli 2018). • In cooperation scenario, participants make decisions more accurately (Lee et al. 2018). • Empathy is an important element in an intercultural communication (Wawra 2009). • Emotions can support identification of the role of race and influence in decisionmaking processes (Kubota et al. 2012).

Behavioral Experiments for Decision-Making with Neuroscience Tools Using Neuroscience for Understanding Decision-Making Process According to Sanfey et al. (2006) and Weber et al. (2007), how we make decisions is a research question interesting many areas of knowledge, such as economics, psychology, and marketing. Despite the vast interest and research on this theme, the neuroscience approach can provide a special contribution based on the investigation of the neural process involved in human and animal decisions. Experiments using neuroscience tools can provide powerful insights that can enrich the investigations of the decision-making process by these areas (Linkov et al. 2012; Nau 2007). Therefore, this approach aggregated to other areas of knowledge can offer many improvements for the techniques and methods existing. The relation between decision-making and the brain system is complex and has been briefly described by Brocas (2012). According to Brocas, the first processing of outside stimuli by the brain is done in the primary sensory cortices, when the neuronal cell-firing and synaptic connectivity create the representation of the received information that will be interpreted and executed, in form of responses,

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by the motor cortex. The prefrontal cortex, which deals with cognitive tasks, has an important role in decision-making process. Related to the prefrontal cortex, Krawczyk (2002) commented about the higher influence of this area in many subprocess related to decision-making, describing functions that each part of the cortex develops during the decision process. Reward values and affective information related to attributes and alternatives are processed in the orbitofrontal and ventromedial areas; reflection about multiple pieces of information and the characterization of their quality is processed in the dorsolateral area. The categorization of conflicting options is processed in Anterior and Ventral Cingulate Cortex. In this chapter, the author investigated many types of decisions, in terms of multiattribute decisions the dorsolateral prefrontal cortex (DLPFC) presents an important role in the integration of information to generate the decision.

Analyzing Multiattribute Decision-Making Process Nermend (2017) presented an experiment to evaluate a car selection problem with six alternatives and six criteria (price, look, fuel consumption, trunk space, maintenance cost, and insurance cost). A web system was designed to control the activities developed in the decision process when participants solved the problem using the Analytic Hierarchy Process (AHP) method. In this study, an electroencephalogram (EEG), galvanic skin response (GSR), and heart rate measure (HR) were used to measure brain and body responses. The aggregation of body sensations with brain activation were used to enrich the study and investigate the decision-makers’ behavior further, allowing it to be correlated with additional factors. Thus, via the GSR results, it was possible to observe the presence of emotion when participants analyzed pairwise comparisons in AHP. Another paper related to the theme was Hunt et al. (2014). The paper investigated, using fMRI and a computational model, a decision with three alternatives and two attributes. The conclusion suggested a within-attribute comparison strategy was used instead of complete integration of the values. With the fMRI data, it was observed that the intraparietal area was related to the attribute competition while the medial frontal cortex is related to the integration of consequences. These two papers were specifically related to the MCDM/A field and bring important insights to the preference modeling process. The first one commented about the presence of emotion in the decision-making, which is a challenge to some areas, such as economics, of how to model this behavior and include it in the decision process. Although there is a presence of emotions in group decisionmaking field, it is possible to suppose that emotions have more impact in the negotiation process because of the integration aspect presented. In this context, the presence and role of emotions are commented on in more detail in section “Analyzing Emotions.” The second study presented an interesting reflection about the how multicriteria evaluation is processed in the brain, suggesting that a multiattribute scenario can be processed by a comparison of the values inside each attribute instead of the integration, which is the basis of the most common MCDM/A model. However, instead of

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these insights, much more has to be studied and discovered to understand coherently the nuances of decision-making process in the brain. According to Hunt et al. (2014), the neural basis of important aspects presented in multi-attribute decision-making has not been integrally studied yet. Some studies used Neuroscience to investigate the neural process through the lens of prospect theory (Kahneman and Tversky 1979). Trepel et al. (2005) summarize the neural systems related to components of utility and prospect theory from many studies using human and animals. Two representations of utility were investigated: decision utility, which is related to weight of an outcome in a decision in the context of reward and punishment, can be characterized as anticipation, and experience utility, which is related to hedonic experience, can be reported in real time or in retrospective evaluations. These two representations of utility involve different brain systems. For the former representation, studies suggest that the following systems are involved: the dopamine system, ventral striatum, prefrontal cortex, and amygdala. The dopaminergic system seems to be the first representation of decision utility. The ventral striatum may be related to the representation of the anticipated reward’s magnitude. The prefrontal cortex is subdivided into different roles in decision-making: the dorsolateral prefrontal cortex (DLPFC) is important for conservation and operation of cognitive representations and planning future actions based on those representations, and the ventromedial prefrontal cortex (VMPFC) seems to be related to anticipatory responses to losses. Finally, the amygdala is extremely related to processing emotion and learning characteristics for negative outcomes. For the latter representation, results indicated that the striatum and orbital and ventromedial prefrontal cortices are presented for processing of experienced rewards and the amygdala for processing experienced losses. The striatum is divided in dorsal striatum, which receives inputs from dorsal and lateral prefrontal cortices, and is related to processing experienced rewards, and the ventral striatum, which receives inputs from limbic structures and the VMPFC, and as discussed above is related to anticipation of rewards and experience of rewards. An interesting comment provided in this paper is related to the investigation of the inverse S-shaped curvature, in terms of overweighting for low probabilities and underweighting for high probabilities, in prospect theory. Explanations for this curvature may include emotional aspects such as fear or hope. The first aspect can be represented in underweighting of high-probability for gain and overweighting of low-probability for losses, and the second for the opposite rationality. The authors affirm that the neural systems to explain this phenomenon are not currently known, but the amygdala can be involved for fear and the ventral striatum for hope. Another study related to the use of prospect theory was developed by Barberis and Xiong (2009) in order to investigate the origin of the disposition effect, a common phenomenon in trading. The disposition effect is a fundamental characteristic of trading, represented by the larger propensity to sell a stock that has gone up in price than one that has gone down. A reason presented to use prospect theory to investigate the disposition effect can be explained by the investor behavior to buy or sell stocks when gains and loss are presented. The reasoning used was if a stock has risen in value

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and the investor was risk-averse over gains, he/she can be inclined to sell their stock. But if a stock has gone down in value and the investor is risk-seeking over losses he/she is inclined to hold on the stock. In this context, two applications of prospect theory are considered, the first involving applying the prospect theory to annual stocklevel trading profits and the second to understood gains and losses. The results indicate the second application predicts the disposition effect more consistently. Some studies were seen in the multicriteria scenario but related more specifically to consumer preferences for products; even not related specifically to MCDM/A context they presented interesting insights. Goucher-Lambert et al. (2017) developed an experiment using fMRI in which participants had to select between different water bottle options evaluated in terms of three criteria: form, function, and price. The authors include the sustainability perspective in the problem and conclude that environmental impact (function) has higher importance for the participant than the esthetic feature (form and price) of the product. The mental effort spent in the decision problem was evaluated. Using the fMRI data it was possible to observe that areas related to visual processing were more activated when esthetic features were evaluated and represented a higher mental effort. This result can be associated to the higher quantity of information presented in this step, mainly generated in the evaluation of form characteristics. The reaction time (RT), i.e., the time spent until the DM makes a decision or expresses a preference, was also calculated in each step of the process. The results suggested that participants spent less time evaluating environmental features than the others, and a possible explanation was the moral connotation associated to sustainability feature, thus being more of a necessary choice. This can also be confirmed by the activation in brain areas related to self-referential behavior, i.e., the knowledge of the responsibility for your actions and how others will interpret your actions. In the same context, Sylcott et al. (2013) developed an experiment to evaluate the form and function of products using fMRI. From results it was possible to note that when these two attributes coexist, a different and more complex neural process was applied, compared to the process presented when only one attribute was evaluated. According to the authors, the trade-off evaluation between the attributes generated activations in areas that are emotion-oriented, suggesting that emotions were also presented in multicriteria decision-making approaches. Finally, Ravaja et al. (2016) investigated the decision process when brand and price were evaluated for packages of products using an EEG and SCL. Based on the results, it was possible to observe a greater activation in the left frontal cortex in the predecision phase, which anticipates a positive decision to acquire a product and the presence of emotion and motivation when a previously selected choice was evaluated. Conjointly with the results of Sylcott et al. (2013), a lower motivation effect was presented when trade-offs had to be done. Even not related specifically to the MCDM/A approach, these studies in consumer preferences presented interesting insights into the MCDM/A approach. The study of (Goucher-Lambert et al. 2017) brings an interesting result about the positive correlation of mental effort and the visual processing, being useful to develop and improve Decision Support Systems (DSS). This paper also presented the RT

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evaluation, a possible analysis to be applied in MCDM/A methods in order to investigate difficulty and fatigue in the process, which has received a great deal of attention in many studies Brocas (2012). Also, in the context of decision-making approach, but not related specifically to a common MCDM/A method or problem, Linkov et al. (2012) used a method termed Weight of Evidence (WoE), to quantify which data observed were more likely given to one or another alternative, thus enabling the more compatible alternative to be selected. This method can be used when different sources of information were presented to a DM that needed to be aggregated and compared in order to generate the decision. The authors divided the method into five phases and investigate the neural process presented in each one. The first phase was related to the quantification of evidence to support the selection of an alternative. The authors commented that the evaluation of conditional probabilities is developed by the brain following statistical decision theory. Thus, this process is able to select the optimal alternative, which balanced speed and accuracy. The authors also highlighted the importance of the investigation of conditional probabilities for many decision situations, such as political decisions, suggesting that for many situations, the organization of information, as is made in the brain, can be a clue to support the process. An important tool mentioned by the authors were graphics which can be included in the process because of the advantage of separation of information and facility to visualize what is special in a decision process. The graphical visualization in MCDM/A fields is also being studied in de Almeida and Roselli (2017a) and Roselli et al. (2018a, 2019a). Related to the second phase, comparing the evidence processed, the authors commented about the separate process developed by the neurons to treat different sources of information, highlighted that the organization of the data is very important. The MCDA approach was also commented on as an important approach that permits high-quality information be used to support the best alternative selection. However, many practical challenges are still present in this field in order to organize and compare information to generate solutions. The third phase was related to the generation of the decision. For this process, neuroscience research suggests that the brain accumulates relevant information by an additive function until is prepared to select the final action/response. The brain can calculate the trade-off between speed and accuracy, finding an adequate level for these factors. The authors comment that this trade-off process can be applied in many decisional situations, suggesting it is important to improve the efficiency of decision process by the selection of a level of uncertainty that would be acceptable in a specific situation. The fourth phase was related to the subjectivity presented in the decision-making process. Neuroscience studies suggest that the objective and subjective aspects are aggregated to generate a response and the subjective factors present an important role in the process because they are responsible to guide behavior. Thus, these factors cannot be absent, and their modulation is a continuous challenge to decision-making field, being improved over and over by the knowledge bring for neuroscience researches.

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Finally, the last phase studied was adaptation to new information. The authors comment that the brain presents many learning processes that are responsible to update information and improve future decisions. This aspect is important in decision-making, being supported and implemented by mental processes such as reinforcement learning rules. The authors conclude by affirming that the neuroscience studies can be important to investigate the nature of decision-making process in general way. In the field of political decisions, the authors allege that the insights provided can contribute to deal with irrationalities and inefficiencies presented in these kinds of decisions. In this study, it is possible to observe a similarity with the phases presented and the steps of many MCDM/A methods, which were also commented on by the authors as an important approach to aggregate the information. The paper suggested an interesting relation of speed and accuracy provided by the brain, i.e., the brain is responsible to evaluate that trade-off. Also, the brain can accumulate information until is prepared to make a decision. In this context, a question can arise, how much information is necessary to make a decision? This question is relevant to investigate in order to improve the methods developed making them more efficient and realistic.

Analyzing Other Features in the Decision-Making Process Other studies not specifically related to MCDM/A context are collected below in order to complement the investigation of preference modeling in MCDM/A field. In Brocas (2012), an experiment was developed using an economic model. In the experiment, participants had to choose between actions a and b, which were subjected to two possible corresponding states of nature, A and B. If the correct action was selected and the state of nature corresponding is presented, a benefit was given. Thus, a model was built, imagining that the participant has a time T to select the alternative. If the participants select it in a time lower than T, the participant received an indication about the state of nature and can update their beliefs. According to the experimental evaluation, waiting and accumulating more information provided to the DM better evidence about the decision. However, it was suggested that the optimal thresholds vary over time, so as time goes by it becomes less beneficial to wait and more urgent to make a decision. Thus, the accumulation of information was observed as a process developed by the brain. Although the presentation of the thresholds was not defined exactly in this study, this might be a challenge to neuroscience and decision-making approaches. The investigation of this threshold can provide important improvements in methods already presented in the literature. Other studies looked at decisions made when risk was present. Risk underlying decisions is very common in our daily life. This field has been studied by economists and psychologists for a while, but likely the most promising research is about the investigation of neural processes presented in these decisions (Trepel et al. 2005). Some neuroscience research has investigated the rewards and learning process in decision-making approach. These aspects were also investigated in decisions under risk. In this context, Preuschoff et al. (2006) developed an experiment involving risk and reward for a task evaluation. The results suggested that the dopaminergic system

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was presented in the evaluation, but activation was different for these two aspects. Related to expected reward the activation was immediate, and for risk was late. In order to investigate financial decisions, Kuhnen (2015) concluded that asymmetries in brain activation were found when financial decisions were presented. According to the author, this result can be explained by the loss aversion behavioral. In summary, it is possible to observe the application of neuroscience in prospect theory and its contribution to understanding human behavior. An important conclusion was the inverse S-shape, suggesting the correlation of this common feature with emotions. Based on all papers presented above, it is possible to observe the wide range of application for the neuroscience approach in the decision-making field. For MCDM/A context, some papers were found bringing some interesting insights, but for now there are still many opportunities for future research. Now the negotiation process will be explored.

Contributions from Neuroscience Researches for Negotiation Process In the negotiation process, art as well as science is present. The art is symbolized by personal characteristics that can have power to determinate better solutions. The science is represented by mathematical models and strategic thinking, which can be applied in order to bargain the best compromise between the participants (Raiffa 1982). A mathematical approach to modeling rationality is game theory (von Neumann and Morgenstern 1953), which can be used to support and improve the negotiation process (Macmillan 1992). According to Krueger et al. (2008), game theory offers a mathematical formalization for strategic choices, and this approach has recently become the focus of the neuroeconomics approach to negotiation as well. Neuroeconomics tries to investigate economic theory in detail based on neural mechanisms using information provided by the brain to update economic theory. This approach has inspired many changes in economy theory, providing challenges to standard economic perspective, which in many cases assumes that decisions processes are solved by a simple and coherent utility maximization. Neuroeconomics conclusions suggest that brain processes are motivated by the interaction of multiple systems (Camerer et al. 2004; Glimcher and Rustichini 2004; Camerer 2007).

Using Game Theory Studies to Investigate Negotiation In the context of Neuroeconomics, game theory can be used to investigate the negotiation process from the point of view that negotiation can be similar to a game when participants are involved in a conflict, making decisions, and tradeoffs based on the reaction of the opponent and are guided by rules. Thus, using experiments for games can be an exciting idea to develop experiments for negotiation and generate insights for this field.

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Game theory studies social decisions, i.e., decisions that involve choices by more than one decision-maker, where the outcome received by a party depends not only on its choices, but also the choices of others. In game theory, a decision problem may be described as alternatives and a payoff matrix, and players maximize their payoff. However, many studies have demonstrated that in the real world, players do not always achieve the best outcome, and neuroscience can help to explain why, considering the presence of many factors in the decision problem (Lee 2006). In this context, papers that develop experiments using famous games were presented and the neural process investigated. Krueger et al. (2008) reviewed famous games experiments and the neural mechanism presented in them. The authors concluded that in experiments it can be possible to note two major systems: a valuation-choice system and a shared social system. The investigation of the first one, which is related to the development of trade-offs in the game, suggested that the heuristic of reinforcement learning might be used to calculate the expected utility for different choices. For the second one, it was observed that factors such as empathy could be used to understand opponent behavior. Hollmann et al. (2011) investigated the ultimatum game (UG). This game is characterized by in the beginning is divided an amount of money for the players, after that, the proponent player offers some quantity of money to the other, who can accept or reject the offer. If the offer is accepted by the other player, both players divide the money offered. However, if the offer is not accepted, none of them receive the money. According to the maximization of the utility, the rational thinking is the proponent offers a small sum of money and the responder accepts it. However, the results suggest that this behavior did not occur and low offers (representing 10–20% of the total money received) were rejected in more than 50% of the cases. In order to investigate the UG, trying to predict the participant behavior before the partner presented their response, the authors developed an experiment using fMRI. The results suggested that areas related to emotional self-regulation and reward processing presented a strong influence in the game. Moreover, signals from the blood oxygen level-dependent (BOLD) was indicated as a very good predictor for the acceptation/rejection of offers. Also using fMRI, Rilling et al. (2002) developed an experiment to investigate women playing the Prisoner’s Dilemma game. The results suggested that mutual cooperation behavior was associated with brain areas related to reward processing and this behavior was responsible to motivate the participants to continue being cooperative instead of being purely self-interested in the game. The results found for these researches suggested that humans are not totally rational or follow the standard concepts developed by the standard economic theory. According to Lee (2006), although the economic theory considers the human as a rational agent, neuroscience studies suggested that humans can approximate the optimal solution using heuristics that can be motivated by an emotional process or lived experience. Therefore, many factors can be present in social decision-making, influencing the way that games are commanded. These factors are focus of much neuroscience research in order to understand decision behavior (Krueger et al. 2008).

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Analyzing the Interaction Process in Negotiations According to Hollmann et al. (2011), the negotiation process is a complex process that involves a mutual interaction between the partners. The negotiation process can be characterized as a social decision, and these decisions are dynamic since humans have to investigate and estimate partner behavioral to update them responses (Lee 2008). In order to continue exploring human behavior in the negotiation process and provide insights into it, it is interesting to investigate the neural process in social decision-making, in a general way, not only in the context of games. Related specifically to neural process in social decisions, Lee (2008) suggested that process regarding to outcome evaluation and reinforced learning was developed in these decisions, and many areas are activated, such as the striatum, insula, and orbitofrontal cortex. Fehr and Camerer (2007) also affirmed that areas related to reward evaluation were activated in human social interaction, such as the striatum and prefrontal cortex. Regulatory mechanisms, such as dopamine and serotonin systems, and hormones, such as testosterone and oxytocin, can also motivate different attitudes during social decision-making. Also, the neural process presented in individual decisions versus social decisions, although similar, present differences in intensity. These differences can be the mechanism to accommodate the social behavior (Lee 2006, 2008). It can be observed that not only the evaluation of outcomes and reinforcement of learning was presented in interaction processes, but the action of many factors can modulate and modify the results in a negotiation interaction. According to Gęsiarz and Crockett (2015), the prosocial behavior can be motivated by many factors, such as altruism, egoism, intuition, deliberation, inborn instincts, learned dispositions, and utility generated from outcomes. Fehr and Camerer (2007) investigated brain activation during human social interaction for altruistic, fair, and trusting behaviors. Several studies on the role of emotions are presented below. Analyzing Emotions In a general way, emotions are a result produced for the brain to respond for a perception about an object or event, which generate modifications to body and brain states (Damasio et al. 1990). Fehr and Camerer (2007) also affirm that the presence of emotions in the evaluation of outcomes (benefits and costs) is required to solve conflicting situations. The study of emotions is not considered in the standard economic theory, but evidence shows that emotions play a key role in decision-making processes. Based on an experiment developed using four decks of cards with different levels of reward and punishment, the participants can choose the cards where two of them offer low reward and low level of punishment, and the other two offers a high reward and a high punishment. In the experiment, participants with a normal ventromedial prefrontal cortex (vmPFC) changed their choices after feeling the high punishments. However, participants with damaged vmPFC kept choosing high punishment decks. The experiment included the mensuration of skin-conductance response (SCR). The

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results indicated that participants with damaged vmPFC had SCR values unchanged even when rewards or punishments were received. Instead of normal vmPFC, participants presented larger SCR values in the initial phase of the experiment, when high punishment was received. These results suggested that the emotions present a special role in the decision-making field, being a preventive behavior to direct correct strategies. In this experiment was possible to note that participants with damaged vmPFC even presented normal intellects but presented difficulty in expressing emotions and because of this have inabilities to make judgments and advantageous decisions in real life (Bechara and Damasio 2005). The presence of emotions in decision-making approaches has been commented on by many papers, but Bechara and Damasio (2005) presented important results. According to them, emotions support advantageous decisions being an important factor between environmental conditions and human decision processes. Liu et al. (2016) investigated emotion in online interactions. An experiment was developed, using 30 traders over a period of 2 years, to analyze if emotions inferred from online messages were correlated to emotions expressed in off-line interactions, i.e., face to face. The results suggested that the emotions expressed were similar in the two types of interactions. In the context of negotiation, this result is very interesting to support the negotiation research based on interaction using negotiation agents, which is commented on later. Liu et al. (2016) also discussed types of emotions and results in trading. Thus, extreme emotions generally bring unsuccessful results for trades, and moderate levels of emotions generate profitable trades. Tabibnia et al. (2008) studied the relationship between happiness in fairness and financial interests. To investigate the theme, the authors developed an experiment that controlled the monetary payoff and provided fair and unfair offers. The conclusions suggested that a higher level of happiness was related to fair offers, resulting in activations in some reward regions of the brain. Also, increased activity in a region related to emotion regulation was presented when unfair proposals were in discussion. However, while the influence of emotions in the decision-making process is suggested by neuroscience research, its absence is a reality in many methods, techniques, and concepts related to decision-making processes. Volz and Hertwig (2016) commented that normative and descriptive frameworks used to model decisions do not consider emotions, and suggested, as an alternative, mapping emotions using existing cognitive frameworks for decision-making. Therefore, emotions might be modulated to be included in decision-making models, of course, this is a challenge to neuroscience and decision-making research.

Using Neuroscience for Analyzing Cooperation and Competition Competition and cooperation are characteristics of the two types of negotiation – distributive and integrative (Raiffa 1982). Various studies have investigated the role of neural process and human behavior in these two forms of negotiation. Many studies consider the importance of cooperation in social decision-making. According to Rilling et al. (2002), cooperation is the basis to construct human social behavior. On the other hand, competition is a common behavior among social

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animals, such as humans (Balconi and Vanutelli 2018). In this context, investigating the neural process behind these two mechanisms is important to understand the human behavior and consequently the negotiation process. According to Balconi and Vanutelli (2018), some previous papers related competition to the actuation of prefrontal and parietal cortex, while cooperation involved the orbitofrontal cortex. Moreover, in order to better investigate these mechanisms, the authors developed an experiment in which participants had to evaluate a selective attention task. Thus, the results suggested that in the competition session the participants presented better performances, especially in the feedback phase compared to the first phase (individual tasks). This result was in line with previous research, which suggested that for competitive conditions the cognitive outcomes were improved compared to cooperative conditions, principally when a positive feedback is received for a winning situation. Moreover, a decrease in inter-brain connectivity was presented for competition phases compared to individual phases. The authors commented that based on neuroscience research it is observed that competitive situations involve less neural mechanisms than cooperative. Lee et al. (2018) also investigated the competition and cooperation behavior trying to distinguish these behaviors. An experiment using fMRI was developed: in this experiment, participants played a Tetris-like game. The results suggested that when cooperation was allowed, the participants were more accurate in solving the game activities than when competition was presented. It is possible to observe that these experiments presented results that are possibly in contradiction, due to the date of these papers is noted that they are quite recent and much more investigation is needed on this topic.

Analyzing Cultural Differences and Other Aspects Additional aspects can be relevant to a negotiation, modifying both the process and the outcome. Examples of aspects that have been studied include cultural and racial differences. In this context, Briley et al. (2014) presented a brief discussion about the use of neuroscience to understanding culture. The authors affirm that differences in culture and communication can influence judgments and decisions performed. Thus, it is very important to better understand these differences to know when they will appear, and consequently influence decisions, and when they will not. In the same context, related to intercultural communication, Wawra (2009), suggested that neuroscience can be an important approach to enrich the research in this field. According to the author, empathy is an important element in an intercultural communication because this emotion allows people to enjoy the experience of learning instead of to be angry at the misunderstandings that can occur. Finally, related to race studies, Kubota et al. (2012) investigated conjointly neural system emotions and decision-making process in the scope of race. According to the authors, emotions are an important aspect that can support the identification about variations in race and influence in the decision-making process. Therefore, again, these papers suggested that emotions present a stronger relation to culture and race differences.

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Using Neuroscience Behavioral Studies to Modulate DecisionMaking Methods According to Korhonen and Wallenius (1997), although past theories explain behavioral aspects in decision-making, many studies do not take it into consideration to modulate methods and systems. Thus, this section highlights the presence of behavior in MCDM/A its contribution to the development of relevant studies for the future generation of MCDM/A society, as interactive methods which the inclusion and modulation of DM behavior (Wallenius et al. 2008). It is worthwhile to mention that some studies have used neuroscience behavioral studies to modulate methods, such as those conducted in order to improve the FITradeoff method (de Almeida et al. 2016). In this section, a brief description is given about the use of neuroscience tools to investigate behavioral aspects in order to modulate FITradeoff method. The FITradeoff method uses the trade-off elicitation procedure (Keeney and Raiffa 1976), with partial information, in a flexible and interactive way, and is freely available at http://www.fitradeoff.org. FITradeoff is cognitively easier and avoid the usual inconsistencies found in the traditional trade-off elicitation procedure, which are usually around 67% (Weber and Borcherding 1993). Regarding the trade-off elicitation procedure (Keeney and Raiffa 1976), neuroscience experiments were performed with this procedure (Roselli et al. 2019b). Thus, based on these experiments, the number of inconsistencies is confirmed. This kind of study, aiming to investigate decision methods and procedures can be classified as Behavioral Operations Research study. In the FITradeoff DSS for choice problematic (de Almeida et al. 2016), several graphical visualizations are presented in order to support the DM during the decision process. These graphics bring flexibility to the process because if the DM desires, a final alternative can be selected based on them, before the entire process had been finished. A few applications can be found that use the FITradeoff method (Carrillo et al. 2018; Frej et al. 2017). In Carrillo et al. (2018), the graphical visualization was used to support the selection of an agricultural technology package and in Frej et al. (2017) to support a supplier selection in a food industry. In this context, based on the importance presented by the graphical visualization in the FITradeoff method and other decision methods, neuroscience experiments have been conducted to investigate the DM behavior when using this kind of visualization. These studies were developed with the purpose of improving the design of the FITradeoff DSS, particularly the human interface of the software, and to obtaining insights for the interaction between analysts (or facilitators) and the DMs (de Almeida and Roselli 2017a). The first experiment presented 24 visualizations mixed in three distinct sequences. These visualizations were built which three, four, or five alternatives and criteria, the majority were bar graphics (being nine with same weights and nine with different weights for the criteria), and the other six types were: spider graphics, bubble graphic, tables, and bar graphic with tables, all with same weights. Regarding this experiment some studies are already presented in the

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literature (Roselli et al. 2017, 2018a, b, 2019a; de Almeida and Roselli 2017b; Roselli and de Almeida 2017). The results for this experiment suggested the random sequence presented the greater number of hits, as well as bar graphics with same weights; the most looked-at criteria were the ones that receive the highest weights. Also, the spider graphic and the tables presented a great hit rate compared to the other types and should be further investigated. Therefore, based on this former result, other two experiments were constructed. One of them, which was constructed in 2018, presented only bar graphic and tables in order to compare the hit rate and the behavioral express when they were evaluated, regarding to this experiment some papers were produced (de Almeida et al. 2018; Roselli and de Almeida 2019a, b). The other was composed by bar graphics, tables, and spider graphics; in this case, the majority of the visualizations were built which two alternatives in order to generate insights for the dominance relation presented in the FITradeoff method for ranking order problematic (Frej et al. 2019), which the study developed (Roselli and de Almeida 2020). Both of these experiments presented 22 visualizations and included the EEG measures in order to investigate different patterns of behavior. Also, they were applied to management engineering students from the Federal University of Pernambuco, and the main task required was to evaluate each visualization and select the best alternative based on the MAVT (Keeney and Raiffa 1976). Based on these studies, two special tools have been proposed: the recommendation rules bases on de Bernoulli distribution with three decision regions and the alpha-theta diagram with behavioral patterns for decisions (Almeida and Roselli 2020).

Conclusions and Future Challenges Thus, this chapter presented some general ways in which neuroscience tools for behavioral studies can make important contributions to the understanding of group decisions and negotiation processes. These studies provide measures of physical and cognitive responses for individual and group decision-making, offering the promise of characterizing aspects that influence how the decision-makers act and interact. In fact, as a new approach to deal with group decisions and negotiation processes, there are challenges to further investigate. It is important to conduct neuroscience testing to fully evaluate the group decisions and negotiation models and to assist in further revision and development. Based on the wide range of applications of neuroscience methods and ideas to GDN processes, many insights into the direction of future research in GDN can be discerned. Related to multicriteria decision-making approach, the main insights provided by the literature presented here is that neuroscientific tools can be used to model preferences as: presence of emotion, comparison of the values inside each attribute instead of the integration, mental effort positive correlated to visual processing, and capacity to brain accumulate information until is prepared to make a decision. The first insight was suggested in many papers as an important aspect presented in

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decision-making field. The modulation and inclusion of emotions in experiments, methods, and concepts is yet a challenge for MCDM/A approach. The second insight is an application to think, expressing the presence and importance of this kind of research in MCDM/A approach. Finally, the third and fourth insights are important to developed DSS, with another reflection: which threshold is adequate to make a decision? For the second theme, from game theory experiments, it was suggested that humans are not totally rational, i.e., not following the standard concepts developed by the economic theory. Many aspects presented in social decision, such as emotions, empathy, cooperation, competition, culture, and racial differences are the focus of neuroscience researches bringing many insights and generating opportunities to future research. As a general comment, the influence of emotions were presented in all these aspects being very important to understand a partner, build a cooperative relationship, support advantageous decisions, and motivate intercultural relations. Therefore, investigation and modulation in negotiation processes is fundamental, even more than in group decisions, since human interaction is the basis of this process. Neuroscience can also contribute to the design of online/offline platforms for group decision-making and negotiation. For group decision-support systems (GDSS), neuroscience tools can be used to measure emotion, attention, and excitement when group members are using these platforms, in order to improve the design of this type of environment. Also, related to negotiation support systems (NSS) physiological tools can be used to assess user reactions when NSSs are used in order to prevent negative reactions during negotiator interaction. In this perspective, many lines of GDN research have been aided by the neuroscience approach and the tools it brings. GDN depends on modeling preferences and making decisions, and will likely continue to rely on neuroscience to refine its modeling processes and further develop its procedures.

Cross-References ▶ Behavioral Considerations in Group Support ▶ Multicriteria Methods for Group Decision Processes: An Overview ▶ Multiple Criteria Decision Support ▶ Role of Emotion in Group Decision and Negotiation Acknowledgments This work had partial support from the Brazilian Research Council (CNPq).

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Part IV Crowd-Scale Group Decisions

Supporting Community Decisions Masahide Horita and Yu Maemura

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MCDM and Other Traditional GDN Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Language Use and Communication in Public Conflicts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spatial Decision Support Systems (SDSS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Public conflicts refer to situations in which members of a community must make or delegate collective decisions with conflicting positions or preferences. The jurisdictions under which such decisions must be made may be legal, informal, or voluntary, but conflicts are “public” in the sense that any decision made will affect all members of a community, to a greater or lesser degree. Research in the field of group decision and negotiation has evolved to address fundamental challenges that emerge when stakeholders tackle public conflicts. Although theoretical and practical challenges still abound for researchers focusing on public conflicts, important progress has been made through problem structuring methods and other GDN techniques that have been applied to some of the largest and most complex public conflicts. A review of promising lines of research reveals that group decision and negotiation research to support community decisions in the public realm has and will continue to produce a unique set of decision support systems, such as support systems that capture linguistic and spatial dimensions.

M. Horita (*) · Y. Maemura The University of Tokyo, Tokyo, Japan e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_44

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Keywords

Group decision and negotiation · Crowd-scale · Discussion and deliberation · Public sector · Multiple participant-multiple criteria · Argumentation · Communication

Introduction Every day we are faced with disagreements over what collective choice should be made, or what course of joint actions should be taken to deal with commonly held public concerns or objectives. No matter how disparate, connected, homogenous, or diverse a group of people may be, private individuals within a society will at some point be exposed to a decision that extends out into the public realm, and can choose to consider how to negotiate so that their preferences can be reflected in the decision. Some examples could include: a decision over a controversial law, a public policy or an international treaty; the planning and implementation of a large-scale project such as public infrastructure or an urban regeneration scheme; regulations over commonpool resources such as water, fish, forests, and natural parks; locational decisionmaking for a not-in-my-backyard (NIMBY) facility; boundary disputes from the international to neighborhood scales; and the provision of public goods such as quality urban environments and social security systems. Public conflicts, or those situations characterized by conflicting interests of individuals over public matters, have been tackled by a range of approaches hitherto developed in the group decision and negotiation (GDN) field. Public conflicts refer to situations in which members of a community must make or delegate collective decisions with conflicting positions or preferences. The jurisdictions under which decisions are made may be legal, informal, or voluntary, but conflicts are “public” in the sense that any decision made will affect all members of a community, to a greater or lesser degree. The scope of public conflicts can be demarcated in contrast with small-scale private or interpersonal conflicts through several distinct characteristics, such as: (i) a large number of decision-makers and/or stakeholders; (ii) complexity caused by the multiplicity of and interdependence between stakeholders’ interests; (iii) uncertainty over the facts and consequences of actions; (iv) diversity in value systems that underlie stakeholders’ interests and goals; and (v) procedural criteria for ensuring legitimacy and other ethical requirements for public deliberation and decision-making. Many GDN techniques and methodologies for managing or resolving public conflicts have been developed for addressing these issues. Firstly, the multidimensionality of stakeholders’ diverse interests and preferences in public conflicts can be tackled by systematically assessing the commonality of interests and preferences, the degree of dissensus and polarization, and the relationships among principal interest groups. A systematic assessment of this information then helps to identify what state of affairs is compatible with whose interests, and how tolerable it is to whom. Without any methodological guidance, such an

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assessment could easily turn unmanageable. Initially one may not be able to see how many of the stakeholders share the same views as himself/herself, or why others are objecting against certain proposals. The number of possible combinations of feasible options may be so large that they cannot even narrow down the scope of a dispute to identify a reasonable set of alternatives. With GDN techniques, however, these activities are methodically structured to aid decision makers. Preference modeling and problem structuring methods, for example, can be used to formalize how each stakeholder preferentially ranks different scenarios and how such preferences are formed by a set of criteria with different weights. The individual preferences can then be aggregated to identify certain scenarios that could gain relatively greater support, clusters of stakeholders with similar or consistent preferences, or an area of deep division as its root causes of the conflict (see chapters ▶ “Group Decision Support Practice “as it happens”” by Franco, and ▶ “Multiple Criteria Group Decisions with Partial Information About Preference” by de Almeida et al., for more practical guidance). Second, the epistemic uncertainty in current states and the consequences of possible actions can be tackled by various simulation techniques, embedding plausible causal relationships between concerned entities. This process, implemented using a cognitive or socio-economic modeling framework, not only addresses factual uncertainty in physical or natural settings, but can also represent humane or social consequences. This includes how the collective choice of a certain scenario would affect the welfare of each member of the public in the short- or long-term, enabling the stakeholders to evaluate and consider the consequences of each possible scenario. As exemplified by a dispute over a potentially hazardous (NIMBY) public facility, some consequences may only be expressed probabilistically or qualitatively, in which case it effectively represents a form of public risk perception attached to each outcome. Third, the diversity in stakeholders’ value systems produces a classic problem for the GDN community, namely the possibility or impossibility of reaching agreement over goals and criteria. In many public conflicts, there is no single authority to impose an ultimate objective function whose optimization can be regarded as a collective goal. Rather, it is through the process of public deliberation and consensus building that participants attempt to identify and define the collective goal, what their social welfare function may be, and why a certain value needs to be weighted more heavily than others. Both pessimistic and optimistic results abound in the literature of public choice theory regarding the prospect of such attempts (see Suzuki and Horita 2017, for a review), which are reflected in some GDN techniques and methodologies introduced below. Fourth, resolving public conflicts usually coincides with procedural requirements that demand a process should formally or informally satisfy a set of ethical criteria. This means those group decision support systems to be introduced into real-world cases must be implemented through ethical approaches, as opposed to merely “engineering” the resolution and forcing it onto the public. In democratic contexts, various GDN techniques and support systems do not represent absolute technocratic solutions, but rather embody attempts to achieve values such as transparency,

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inclusiveness, fairness, and other procedural norms. For example, by publicly sharing information about the entire course of communications among stakeholders, or by visualizing a degree of equity to be imposed on the stakeholders’ division of distributed resources (see chapter ▶ “The Notion of Fair Division in Negotiations” by Klamler), support systems can help to elucidate the relationship between possible resolutions of a conflict and stakeholders’ interests. These are achieved not only by employing the problem structuring/visualizing methods described above, but also by turning to the linguistic aspects of conflict resolution processes, where linguistic information such as participants’ arguments are considered as primary data. Such functions of support systems could be used to prevent the entire conflict resolution process from being “black-boxed,” resulting in a solution that might otherwise be proclaimed as rational only as a consequence of nonaccessible analysis by technical experts. More discussions on procedural justice can be found in the chapter on ▶ “Procedural Justice in Group Decision Support” by Kaur and Carreras. Support systems can also be used to provide sensemaking to stakeholders, enabling them to see, literally, the possible outcomes of a conflict by various visualization techniques. Such techniques could help stakeholders understand what it would mean, for example, if a NIMBY facility such as a nuclear waste disposal plant were to be built nearby. Spatial and social consequences can be scrutinized by visualizing options and outcomes in an intuitively recognizable form. As indeed many public conflicts have a spatial dimension, a specific set of group decision support systems has now emerged to specialize in this field: spatial decision support systems (SDSS) are introduced in more detail in a subsequent section below. The rest of this chapter is structured as follows. The next three sections are divided from the viewpoint of the methodological or technical approaches employed by each group of support systems for managing public conflicts. Section “MCDM and Other Traditional GDN Techniques” reviews problem structuring methods. This is followed by an introduction to linguistic approaches in section “Language Use and Communication in Public Conflicts,” and a review of spatial decision support systems in section “Spatial Decision Support Systems (SDSS).” The last section concludes with a discussion on related issues and future challenges.

MCDM and Other Traditional GDN Techniques Of the earlier applications of group decision support systems for public conflict management and resolution, there is a distinct cluster of work that employs the traditional methods and techniques in GDN, exemplified by use of multicriteria decision-making (MCDM)(Matsatsinis and Samaras 2001; Matsatsinis et al. 2005; Manos et al. 2010). MCDM is of particular help for formulating the relationships among sets of alternatives, stakeholders’ value systems represented as criteria and weights, and their aggregate desirability. While stakeholders in conflict may not easily be able to agree on the common weights of criteria, group decision support systems often own the capability of visualizing consequences of altered user inputs and different aggregation methods so that they can be used as a medium for

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prompting stakeholder dialogue, deliberation, and negotiation. They may also be used to assess the robustness of possible or proposed resolutions of conflict in the form of a sensitivity analysis. There are also methods for reducing potential disagreements. For example, when everyone needs to concede to a certain extent in order to reach a joint agreement, it often matters whether the degree of concession each individual makes is equal or fairly distributed. Since the MCDM framework does provide a method for assessing the gap between one’s desired position and a proposed concession, it is possible to visualize the distribution of concessions made by each stakeholder. Exploring such scenarios with equal or fair concessions from everyone’s viewpoint may contribute to breaking the dead-lock of the conflict (see the chapter ▶ “Just Negotiations, Stable Peace Agreements, and Durable Peace” by Druckman and Lynn, for more cases of real-world negotiations). Many of the systems employing the MCDM approach are complemented by other group support methods and techniques. Uncertainty over consequences of each alternative, for example, is handled with physical models and resulting causal networks of their concerned entities. They can then be integrated into scenario analysis tools to observe possible futures before users of the systems rate them (Cerreta et al. 2012; Duspohl and Doll 2016). It is also possible for stakeholders to see the degree of conflict by sharing how diverse their views are. Degrees of conflict can be represented within the MCDM framework as the distribution of ratings of alternatives, the distribution of weights for criteria, or even the distribution of preferred methods for aggregation. In an intensely divided conflict, the last issue materializes: a conflict over how to resolve a conflict. In the MCDM framework, it is argued that the choice of which MCDM method to use can itself constitute an MCDM problem (Tecle 1992; Bogetoft 1999). While it is well known that employing a different MCDM method could cause a drastically different outcome to be chosen, some have proposed methods for choosing a suitable MCDM method. Tecle (1992) sets out criteria for MCDM methods that are categorized according to their evaluative viewpoints. For example, one might regard the consistency of results as the most important property of a MCDM method, while others may prioritize simplicity in eliciting decision-makers’ knowledge. These procedural conflicts over the preferred criteria for MCDM methods themselves can again be tackled by a system of questions aimed at structuring different decision-makers’ priorities. Other traditional methods and techniques of GDN are also in use. When people disagree over what really is the problem, it often becomes an issue how differently they view and recognize a given situation. When such cognitive and epistemological conflicts at both subjective and intersubjective levels arise, it helps to employ problem structuring methods such as cognitive mapping (see chapter ▶ “Systems Thinking, Mapping, and Group Model Building” by Richardson and Andersen), Bayesian mapping, and other ontology-engineering models (Carmona et al. 2011). On the other hand, when strategic interactions between stakeholders constitute the essence of a conflict that matters, a game theoretic framework is of more relevance. Based on the world-view held by each stakeholder (which itself can be

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collectively shared by the above cognitive methods), a game model can visualize the structure of a public conflict and show where the pursuit of individual interests by the stakeholders will lead them (Fang et al. 2003a, b; Kassab et al. 2006; Sharif and Kerachian 2018; see also chapters ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions” by Kilgour et al., and ▶ “Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives” by Hipel et al.). It can also be used for reverse engineering what change of preferences or invention of new options is needed to achieve a desirable resolution to the conflict. Preference changes or new options are often represented in the form of concessions, compromise, and mutual trust (Kinsara et al. 2015). More information on one of the most significant recent developments in how game theory can be applied to GDN can be found in the chapter ▶ “From Game Theory to Drama Theory” by Bryant. The systems approach in these methods to capture the whole situation from a holistic perspective makes it possible for a large number of stakeholders to deal with a complex conflict with multiple issues and diverse interests.

Language Use and Communication in Public Conflicts Regardless of the number of stakeholders or the level of complexity within a public conflict, interested parties within this context are essentially engaged in predefined procedures in which they are permitted to voice their concerns. Linguistic approaches to the study of GDN processes expose us to studies and research on support system features that utilize or leverage these “voices,” that is, linguistic information, that are produced through various public decision-making processes. There are an increasing number of applications of the linguistic approach that directly utilize the information on how people dispute or negotiate in practice. Inspired by recent developments in fields including artificial intelligence and data sciences, this linguistic turn is now materializing at an operational level. The diverse and nonmonotonic nature of public conflicts is captured in the forms of data models and formal knowledge. Natural language processing (NLP) allows us to use the whole body of public debate as a corpus, from which one can analyze where the conflict truly lies through issue extraction and argumentation analysis. Pragmatic approaches have also proven useful in understanding the communicative strategies of stakeholders involved in complex public processes and revealing how institutional contexts and underlying interests can lead to incongruencies in the parties’ interpretations. The assumed relationship between linguistic data and negotiation outcomes has been confirmed through various studies. Research in this area supports a fundamental and important hypothesis – negotiation outcomes, quality, or substance can be linked to certain patterns or structures within the expressions and linguistic items produced by stakeholders. For example, Sokolova has analyzed textual data of negotiations to reveal how successful e-negotiations can be characterized by the frequent mention of words related to the negotiation process – what they call process-specific information (2006). Similarly, Twitchell has been able to code the

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contents of negotiations to indicate their integrative or distributive characteristics and provide a score to represent this indicator. Interestingly, this score could then be used to reasonably predict the ability for parties to produce agreements during divorce negotiations (Twitchell et al. 2013). However, it should be noted that the textual data analyzed in these studies are structured specific to certain negotiation procedures – e-negotiations are conducted through software and online platforms that produce clear turn-taking between negotiators; and divorce negotiations are a high-stakes and interpersonal situation in which sensitive distributive issues are discussed between self-interested parties. Linguistic insights generated from within these specific contexts are still far from producing lessons that help us understand complex negotiations that often take place within the public sphere. An essential feature of the public decision-making process is represented by the transparency obligations, policies, and practices that require deliberative procedures and information to be made available to the public. Public institutions responsible for organizing, administering, or managing decision-making processes are often mandated to produce and publish transcripts, memos, minutes, and agendas. While most people will not argue that efforts to improve the transparency and availability of public processes are futile or meaningless, their impacts on the quality of decisions or institutional accountability remain questionable. Citizens and stakeholders in the modern information-era are now faced with issues of information overload and may find that critical and important public decisions are often hidden under and obfuscated by the sheer amount of information now available to the public (not to mention the frightening and destructive power of disinformation on the quality of civic dialogue and deliberative processes, which we will not discuss here). Natural language processing (NLP) has emerged as a powerful field for the development of tools to help users interpret such large bodies of textual information. Developments in the field have revealed how linguistic concepts can now be applied to help users interpret complex and vast amounts of textual information in various public contexts, such as food safety (Gillani and Kő 2014), or education (Pandey 2017). Pandey (2017), for example, illustrates how documents within the educational sector can be analyzed for abstract constructs such as “innovativeness.” Their study describes the development of a dictionary of phrases that can be used to identify and extract phrases that represent innovation within letters to the Board of Education from US school districts. Furthermore, the subjective insights contained within a corpus can also be used to produce decision support information, such as preferences (Visser et al. 2012) or rationales (Xiao et al. 2017). Linguistic models can also be utilized to structure decision-making procedures or dialogues (Morge and Mancarella 2014), as well as coordination between parties (Parsons and McBurney 2003). These studies represent admirable attempts at applying specific concepts, structures, or processes to enhance outcomes or improve the quality of information, yet the most fundamental challenge still remains in terms of how citizens should navigate pluralistic values and conflicts within Habermasian processes. While there may be agreement as to the legitimacy of certain procedures and rules surrounding public processes, the cognitive gaps, ambiguity, and conflicting values that

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are unearthed through deliberative processes are a critical issue that is often overlooked or left unresolved. Researchers have attempted to reveal this complexity and to suggest some strategies to combat it, such as a conscious acknowledgement and emphasis on values within public dialogue (Wade 2004). Others have focused specifically on ambiguity in language and discourse, such as Fischhendler (2008), who reveals how vague language can be utilized strategically in political situations, as well as Bamberg (2010), who reveals how complex and ambiguous knowledge production can become as public participation is incorporated into city-planning processes, while highlighting the need for analytical tools to process such complexity. Others have attempted to develop conceptual models to breakdown the structure of arguments and claims (Tian and Cai 2014), while some have been able to uncover fundamental differences in language use between communities involved in environmental conflicts (Webb 2008). Studies of this nature can also illustrate systematically the dynamic and evolving nature of concepts and their meanings within the language of stakeholders (Cobb et al. 2014). In summary, the linguistic studies mentioned here take one of three broad approaches: (i) they apply linguistic concepts to help decision-makers or public stakeholders interpret and navigate the decision-making process, (ii) they utilize linguistic concepts and or approaches to produce information that can be utilized directly in decision-support systems, and (iii) they rely on linguistic framing to reveal the complex, dynamic, and transformative nature of public conflicts. The incorporation of linguistic theoretical concepts into public decision procedures allows us to better understand the “what” of complex conflicts – what has been said, and by who? Naturally, a question that emerges is then, how should we consider the “where”?

Spatial Decision Support Systems (SDSS) It is not coincidental that many examples where DSS have been used for managing or resolving public conflicts exhibit a spatial dimension. The subjects of public conflicts relate to places in which people spend their lives. Common examples of public conflicts of a spatial nature include common resources that people must share with others, the facilities that benefit some, but adversely affect others, and the boundaries that by definition lose an effective meaning without the consent of neighboring parties. Conflict arises over the ownership, access, control, and regulation of those spatial entities due to differing interests of decision-makers. The state of conflict – that is, their emergence, escalation, and resolution – is often visible through the spatial objects of interest; the fact that a controversial facility has been built itself signifies some kind of transition in the conflict situation. These aspects of public conflicts have led decision-makers to employ particular visualization tools, which are now known as spatial decision support systems (SDSS). SDSS typically consists of traditional DSS capabilities, exemplified by MCDA tools, augmented by the capacity to handle spatial information under the platform of geographical information systems (GIS). Thus, with SDSS, conflicting interests can

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Fig. 1 Standard design of a spatial decision support system (SDSS)

be visually projected onto a geographical space – most typically as a map, which has long proved an effective tool for making sense of spatial relations and interactions of our daily activities. A standard design of a SDSS is shown in Fig. 1. Here each location is assessed according to a set of criteria, whose weights can be collectively decided by users. Resulting weights are used for aggregating each layer of the map, showing an overall assessment for each location. Decision-makers can interactively deliberate over the validity of collective weights for the criteria, or the resulting aggregate map. The system may include a model of such interactions among stakeholders within the system, such as a game-theoretic model of strategic interactions or a linguistic model of their arguments. SDSS can be categorized according to their domains of application and their methods for representing public conflicts. In terms of domains of application, numerous examples can be found in the field of water conflicts. Water, undoubtedly one of the most important common resources for human beings and ecosystems, is known to have induced public conflicts over both their use and management at all spatial scales. Technical insights into how water resources exist, distribute, or change in response to various human activities are provided by a number of analytical tools such as hydrologic and other physiochemical models. The merger of such technical capabilities and decision support functions can be found in, for example, Thiessen et al. (1998), who developed an environment for computer-assisted negotiation of water resource conflicts. The typical water conflict between the upstream and the downstream has been captured and used for facilitation by Braga (2000) in a study of integrated water resources planning in Brazil. Different and conflicting interests in water-related objects have been visualized within the MCDA framework, such as the conflict between

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groundwater protection and environmentally hazardous activities (Simon et al. 2004), and that of activities that could threaten the sustainability of an aquifer (Valle et al. 2015). A similar tool that combines GIS and MCDA has been implemented to help manage various agricultural activities to avoid soil erosion in Argentina (Cisneros et al. 2011). At greater spatial scales, examples of application also abound. Molina et al. (2011), in the context of groundwater use in Spain, attempted participatory modeling of group decisions as part of an integrated assessment of the European Water Framework Directive. Applications of SDSS are of course not limited to water resources, but many other natural resources and components of ecosystem management are inherently spatial. Forests often become a subject of conflict as communities wrestle with the challenge of sustainable resource management while exploiting valuable resources to support and enhance their daily lives. DSS specifically designed for this domain include van Noordwijk et al. (2002) and El Wahidi et al. (2015). Coastal management, typified by the conflict between fishery activities and coastal protection measures, has been facilitated with DSS for integrated coastal zone management in the United States (Brody et al. 2004), Spain (Garmendia et al. 2010), and Italy (De Boni et al. 2018). The second major area of SDSS applications is the domain of urban planning. One of the unique characteristics of those applications is that emphasis is placed not only on substantive issues such as the location of a facility or a land use plan, but also on the procedural aspect of planning activities. While there is an increasingly strong orientation towards the consideration of concepts that can help achieve procedural justice in planning processes, such as participation, communication, deliberation, and fair decision procedures, the role of technical tools including SDSS has expanded to create a physical and social platform for visualizing the rationale behind each proposal for resolving a public spatial conflict. Again, Kaur and Carreras’s chapter of this book on ▶ “Procedural Justice in Group Decision Support” most relevantly addresses these issues. An early example is seen in Martin and Bender (1999), where a spatial conflict over land use in an American rural area was first modeled as a noncooperative voting problem, and then subsequently modeled as a cooperative game for achieving the fair redistribution of values to be obtained by mutually cooperative stakeholders. As for an example of applications to the NIMBY problem, Higgs (2006) developed an MCDA-type of SDSS for enhancing public participation in deciding the location of a waste facility. The linguistic approach that is reviewed in the previous section is in fact often employed within the SDSS framework as seen in Horita (2000a, b), Rinner et al. (2006), Higgs (2006), and Simao et al. (2009). This approach can be seen as incorporating stakeholders’ arguments into a conflict model, be it a game model or an MCDA problem, as a medium for public deliberation and consensus building. Many of these examples originate from the “Planning for Real” approach, which was invented originally in the UK as an attempt to democratize the planning processes in the form of a nontechnical toolkit for collecting public views (Neighbourhood Initiatives Foundation 1999). More recent applications enable

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users to engage in such communicative processes over the internet, as can be seen in Mansourian et al.’s development of a system enabling users to participate in urban planning processes (Mansourian et al. 2011). Work in this area claims that the primary objective of these attempts is to establish “local shared values” (Cerreta et al. 2012), which could in turn pave the way for stakeholders to carry out the altruistic or reciprocal actions that are needed to resolve a badly entangled conflict.

Summary and Conclusions This chapter has provided a selective review of research developments on GDN, both theoretical and practical, that apply within the domain of public conflicts. Studies and applications of GDN concepts that pertain to public conflicts have developed alongside the evolving needs of communities and public stakeholders. The origins of support systems for public conflicts can be situated around the transition of research from the development and utilization of formal concepts to analyze public conflicts as a subject of research, to the development of tools and frameworks utilized directly by decision makers as a product of research. This transition is perhaps best exemplified by the development of MCDM, along with other conventional studies endeavoring to represent various fundamental operational properties of decisions and conflicts through preferences, alternatives, cognitive and epistemological models, strategies, and interests, among others. The common transparency requirements for public decision procedures to be applied publicly, or at least for the details to be made available to relevant stakeholders, produces a vast amount of information and linguistic data that can be a subject of study in itself, or an element of group decision procedures that can be enhanced and improved through the incorporation of language features and data analysis. While there is enormous potential for theoretical linguistic insights to contribute to public decision making processes, practical applications will depend upon user demands. Linguistic analysis could help understand complex information in retrospect, or could be used to structure decision procedures in situ. Finally, the incorporation of spatial information can help decision makers understand not just “what” is important, through what has been said, but “where” these issues may be occurring. Efforts within both areas of public decision support systems are examples of additional dimensions being integrated into decision problems and the systems designed to support them. The dimensions mentioned and described here include the complexity of language in public discourse, as well as the spatial dimension. As public bodies are required more and more to develop support systems and mechanisms that can better educate, involve, or provide feedback on the decisions and procedures that are delegated to representative bodies, future system innovations are likely to add, integrate, or virtualize various dimensions into decision support systems.

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Cross-References ▶ Conflict Resolution Using the Graph Model: Individuals and Coalitions ▶ Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives ▶ From Game Theory to Drama Theory ▶ Just Negotiations, Stable Peace Agreements, and Durable Peace ▶ Multicriteria Methods for Group Decision Processes: An Overview ▶ Procedural Justice in Group Decision Support ▶ Systems Thinking, Mapping, and Group Model Building ▶ The Notion of Fair Division in Negotiations

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Rinner C, Balram S, Dragicevic S (2006) Argumentation mapping in collaborative spatial decision making. Collab Geogr Inf Syst:85–102. https://doi.org/10.4018/9781591408451.ch005 Sharif M, Kerachian R (2018) Conflict resolution in construction projects using nonzero-sum fuzzy bimatrix games. Iran J Sci Technol-Trans Civ Eng 42(4):371–379. https://doi.org/10.1007/ s40996-018-0106-3 Simao A, Densham PJ, Haklay M (2009) Web-based GIS for collaborative planning and public participation: an application to the strategic planning of wind farm sites. J Environ Manag 90 (6):2027–2040. https://doi.org/10.1016/j.jenvman.2007.08.032 Simon U, Bruggemann R, Pudenz S (2004) Aspects of decision support in water management – example Berlin and Potsdam (Germany) I – spatially differentiated evaluation. Water Res 38 (7):1809–1816. https://doi.org/10.1016/j.watres.2003.12.037 Sokolova M, Shah M, Szpakowicz S (2006) Comparative analysis of text data in successful face-toface and electronic negotiations (journal article). Group Decis Negot 15(2):127–140. https://doi. org/10.1007/s10726-006-9024-z Suzuki T, Horita M (2017) Convergent menus of social choice rules. In: Schoop M, Kilgour D (eds) Group decision and negotiation. A socio-technical perspective. GDN 2017, Lecture notes in business information processing, vol 293. Springer, Cham, pp 47–60 Tecle A (1992) Selecting a multicriterion decision making technique for watershed resources management. J Am Water Resour Assoc 28(1):129–140 Thiessen EM, Loucks DP, Stedinger JR (1998) Computer-assisted negotiations of water resources conflicts. Group Decis Negot 7(2):109–129. https://doi.org/10.1023/a:1008654625690 Tian Y, Cai G (2014) Modeling claim-making process in democratic deliberation. Concept Model 8824:458–465 Twitchell DP, Jensen ML, Derrick DC, Burgoon JK, Nunamaker JF (2013) Negotiation outcome classification using language features (journal article). Group Decis Negot 22(1):135–151. https://doi.org/10.1007/s10726-012-9301-y Valle RF, Varandas SGP, Fernandes LFS, Pacheco FAL (2015) Multi criteria analysis for the monitoring of aquifer vulnerability: a scientific tool in environmental policy. Environ Sci Pol 48:250–264. https://doi.org/10.1016/j.envsci.2015.01.010 Van Noordwijk M, Tomich TP, Verbist B (2002) Negotiation support models for integrated natural resource management in tropical forest margins. Conserv Ecol 5(2):21 Visser W, Hindriks KV, Jonker CM (2012) Argumentation-based qualitative preference modelling with incomplete and uncertain information (journal article). Group Decis Negot 21(1):99–127. https://doi.org/10.1007/s10726-011-9274-2 Wade SO (2004) Using intentional, values-based dialogue to engage complex public policy conflicts. Confl Resolut Q 21(3):361–379 Webb TJ (2008) Conversations in conservation: revealing and dealing with language differences in environmental conflicts. J Appl Ecol 45(4):1198–1204 Xiao L, Stromer-Galley J, Sándor Á (2017) Toward the automated detection of individuals’ rationales in large-scale online open participative activities: a conceptual framework (journal article). Group Decis Negot 26(5):891–910. https://doi.org/10.1007/s10726-016-9516-4

Crowd-Scale Deliberation for Group Decision-Making Mark Klein

Contents The Need for Crowd-Scale Deliberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Limitations of Existing Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Towards More Effective Crowd-Scale Deliberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deliberation Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Idea Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deliberation Analytics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . From Negotiation to Consensus-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Narrative Reports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crowdsourced Moderation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Task Marketplace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Many of humanity’s most pressing and challenging problems – such as environmental degradation, physical and economic security, and public health – are inherently complex (involve many different interacting components) as well as widely impactful (affect many diverse stakeholders). Solving such problems requires crowd-scale deliberation in order to cover all the types of disciplinary expertise needed, as well as to take into account the many impacts the decision will have. Current approaches to group decision-making, however, fail at scale, producing outcomes that are needlessly suboptimal for all the parties involved. The key questions addressed herein will include (1) why group decision-making M. Klein (*) Center for Collective Intelligence, Massachusetts Institute of Technology, Boston, MA, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_40

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fails in this way, explaining the problems of achieving Pareto optimality and noting the tendency to miss win-win solutions that are not the “dream choices” of any participant, as well as (2) how recent advances in social computing technology can address these failings, for example, through the use of deliberation maps, idea filtering, and crowd-scale complex negotiation. Keywords

Group decision and negotiation · Crowd-scale · Negotiation support system · Argumentation · Pareto-optimal · Preference modeling · Nonlinear utility functions

The Need for Crowd-Scale Deliberation Let us define deliberation as the activity where groups of people (1) identify possible solutions for a problem, (2) evaluate these alternatives, and (3) select the solution(s) that best meet their needs (Walton and Krabbe 1995; van Eemeren and Grootendorst 2003). Deliberation processes have changed little in centuries. Typically, small groups of powerful players craft policies behind closed doors and then battle to engage wider support for their preferred options. Most people affected by the decisions have at best limited input into defining the solution options. This approach has become increasingly inadequate as the scale and complexity of the problems we face has increased. Many important ideas and perspectives simply do not get incorporated, squandering the opportunity for far superior outcomes. While notable advances have been made in terms of enabling medium-scale physically collocated deliberation (see, for example, Fishkin and Luskin (2005)), such engagements are expensive and difficult to arrange because they do not take advantage of the potential of time- and space-distributed interaction using internet technology. We have the potential to do much better by radically widening the circle of people involved in complex deliberations, moving from “team” scales (tens of participants) to “crowd” scales (hundreds, thousands, or more). This is because crowd-scale interactions have been shown to produce, in appropriate circumstances, such powerful emergent phenomena as: • The long tail: Crowd-scale participation enables access to a much greater diversity of ideas than would otherwise be practical: potentially superior solutions “small voices” (the tail of the frequency distribution) have a chance to be heard (Tapscott and Williams 2006). • Idea synergy: The ability for users to share their creations in a common forum can enable a synergistic explosion of creativity, since people often develop new ideas by forming novel combinations and extensions of ideas that have been put out by others. • Many eyes: Crowds can produce remarkably high-quality results (e.g., in open source software) by virtue of the fact that there are multiple independent

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verifications – many eyes continuously checking the shared content for errors and correcting them (Raymond 1999). • Wisdom of the crowds: Large groups of (appropriately independent, motivated, and informed) contributors can collectively make better judgments than those produced by the individuals that make them up, often exceeding the performance of experts, because their collective judgment cancels out the biases and gaps of the individual members (Surowiecki 2005).

Limitations of Existing Work While the Internet now provides the cheap, capable, and ubiquitous communication infrastructure needed to enable crowd-scale deliberation, current technologies (i.e., social media tools such as email, forums, blogs, and so on) generally result in very poor deliberation outcomes, characterized by large volumes of disorganized and low-quality content, haphazard evaluation, toxic interactions, and such debilitating emergent dysfunctions as clique formation, groupthink, polarization, and deadlock (Klein and Convertino 2015; Klein 2012; Tversky and Kahneman 1974; Sunstein 2006; Schulz-Hardt et al. 2000; Cook and Smallman 2007; Bjelland and Wood 2008; Blohm et al. 2011). We can illustrate these deliberation failures using utility diagrams. A utility diagram is a scatter plot where the points represent possible solution to a problem, and the axes represent the value of a solution to the people (“agents”) impacted by it. Figure 1, for example, shows a utility diagram for two agents. The best solutions lie, as we can see, in the upper right of the diagram (the “pareto frontier”). Any solution not on the pareto frontier is worse for both parties (“paretoinferior”) than a pareto solution, and should of course be avoided. Current deliberation technologies tend to produce non-pareto solutions, due to three fundamental issues: Impoverished ideation: Current technologies typically elicit the “dream choices” of individual participants but fare much more poorly at eliciting win-win solutions that maximize the utility for all the stakeholders. We can represent that in a utility Fig. 1 An example of a utility diagram with a pareto frontier

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Fig. 2 Win-win solutions in the utility diagram

diagram as in Fig. 2 where the dotted points represent the win-win solutions that alltoo-often do not emerge from the crowd. There are several reasons for this problem: • Solo ideas: Current tools generally provide no technological support or incentive for crowd members to work together to collaboratively develop new ideas. Many tools use a contest frame which actually dis-incentivizes collaboration. • Unsystematic exploration: Current tools do not inherently foster systematic exploration of the space of potential solutions: there is no tracking of the design dimensions, the options for each dimension, the interactions among candidate sub-solutions, and so on. • Small voices: Excessive redundancy (people often repeat themselves or others in order to win the “attention wars”) means that potentially promising ideas from smaller groups/less vocal individuals can get lost in the crowd. • Extremization: Participants often push extreme versions of their clique’s ideas rather than seek win-win solutions that might give both parties most of what they want. This can occur for several reasons, including tribal signaling, and using controversy to capture crowd attention. • Balkanization: Participants self-organize into subgroups wherein ideas rarely cross-fertilize across groups. This can be caused by social media tools (filter bubbles) or by people’s tendency to find groups they can relate to (homophily). Haphazard evaluation: Current social media technologies do not provide any inherent support or encouragement for systematic, well-reasoned evaluations of solution alternatives. On the contrary, fallacious arguments are often presented as fact and not challenged, undercutting participants’ ability to accurately evaluate which solutions are better than others. It has even been observed that fallacious arguments spread through social media faster and further than accurate ones (Vosoughi et al. 2018). The effect of these deficits in evaluation can be represented as substantial error/ uncertainty in the position of proposed solutions in the utility diagram (Fig. 3). The reasons for this include challenges (e.g., small voices, extremization, and balkanization) we have already discussed, the fact that gathering evaluations from stakeholders can be slow and expensive so many stakeholders are often not consulted, plus the difficulty in tracing where claims in social media come from.

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Fig. 3 Illustration of the impact of haphazard evaluations, in a utility diagram

Fig. 4 Illustration of the impact of decision dysfunctions, in a utility diagram

Decision dysfunctions: Current deliberation technologies can lead crowds to select pareto-inferior solutions even when pareto-superior solutions have been proposed. A typical result is deep resistance to implementation by the losing stakeholders, or deadlock with no decisions made at all. A critical reason for this dynamic is the failure of “zero-sum bargaining” frames when applied to complex decisions (Fig. 4). In many contexts, such as buy/sell negotiations, each party typically starts by taking an extreme position, representing their ideal solution, and then make concessions, as slowly as possible, until they “meet in the middle.” While this can produce pareto-optimal agreements for simple decisions (i.e., with one or a few independent issues and thus monotonic utility functions), our research has shown that it reliably produces highly suboptimal agreements when applied to complex decisions (with many interdependent issues and thus multi-optimum utility functions with local suboptimal traps) (Klein et al. 2003).

Towards More Effective Crowd-Scale Deliberation Effective crowd-scale deliberation can be realized, we believe, by building upon recent advances in social computing, optimization, mechanism design, and other fields. This requires supporting, in an integrated way, the three key stages of the deliberation life cycle:

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• Ideation: Helping crowds develop better solution ideas. • Evaluation: Helping crowds evaluate potential solutions more accurately. • Decision-making: Helping crowds select pareto-optimal solutions. The architecture in Fig. 5 illustrates how this can be done. Participants interact by posting in a “deliberation map” (a tree structure made up of interleaved questions, answers, and arguments, described in more detail below). These users can generate the contributions themselves or “harvest” them from conventional social media. Crowd-based idea filtering algorithms can then be used to identify the most promising solution ideas generated by the crowd, and these ideas become the starting points for consensus-making processes mediated by negotiation algorithms. If the current set of solution ideas do not lead to agreement, the crowd can loop towards further ideation aimed at resolving the limitations of the earlier solution ideas. All this is supported by a suite of deliberation analytics that data-mine the traces of the crowd’s activity and generate customized metrics, alerts and reports to help the participants, moderators, and customers of the deliberation have a much clearer sense of where the deliberation is as well as where and how they can contribute best. A deliberation task marketplace can be used to help ensure that important deliberation tasks (e.g., suggesting answers for a critical question, evaluating a promising answer) are performed by the people who can do them efficiently and well. In the following sections, we will describe, in more detail, work to date on these components.

Idea Filtering

Deliberation Mapping

Analytics Negotiation

Incentives

Metrics

Freetext Discussions Alerts

ParetoOptimal Consensus

Reports

Deliberation Task Marketplace requester system Eric system Nick

Fig. 5 Architecture for our approach

task add-argument factcheck judge rate

post eligible idea xy223 anyone arg 12334 anyone issue 3l74 analysts arg 8786 analysts

bounty 3 2 5 1

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Deliberation Maps The core component of this approach is deliberation mapping (also known as argument mapping) (Shum et al. 2006), a simple but powerful approach wherein deliberations are captured as topically organized tree structures made up of questions to be answered, possible answers for these questions, and arguments (statements that support or detract from an answer or argument) (Fig. 6). Deliberation maps have many advantages. If properly structured, every unique point appears just once, radically increasing the signal-to-noise ratio, and all posts must appear under the posts they logically refer to, so all content on a given question is co-located in the tree, making it easy to find what has and has not been said on any topic, fostering more systematic and complete coverage, and counteracting balkanization by putting all competing ideas and arguments right next to each other. Careful critical thinking is encouraged, because users are implicitly encouraged to express the evidence and logic in favor of the options they prefer (Carr 2003), and the community can rate each element of their arguments piece-by-piece. Users, finally, can collaboratively refine proposed solutions. One user can, for example, propose an idea, a second raise an issue concerning how some aspect of that idea can be implemented, and a third propose possible resolutions for that issue. While deliberation maps have been in use for decades, it is only recently that this concept has been applied to enabling deliberations with crowds (100’s or more participants) rather than just individuals or (small) teams. As an example of crowd-scale deliberation, let us consider the Deliberatorium, which has been under development by the author and his colleagues for over a decade and has been applied successfully to real-world crowd-scale deliberation engagements on such complex and contentious topics as biofuels use, water use in drought regions, and electoral law reform (Klein and Iandoli 2008). It includes tools to enable easy

Fig. 6 Example of a deliberation map

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navigation, rating, and collaborative editing of complex maps, as well as moderation to ensure that the maps remain well-structured even with novice users. We found that the system enjoys short learning curves with “real-world” users and the same high levels of adoption as conventional social computing tools like web forums, making it suitable for use by diverse, open crowds. The moderation burden is light, much lower than would be needed to harvest, post-hoc, discussions hosted by conventional social computing tools. Two moderators were, for example, sufficient to handle the nearly 200 active contributors in our first major evaluation, and most posts (~85%) required no or only minimal moderator input. Using this system, users were able to generate extensive well-organized and high-quality content on complex contentious topics without top-down supervision (Iandoli et al. 2009, 2017; Klein et al. 2012; Spada and Klein 2014).

Idea Filtering A critical challenge with crowd-based deliberation systems is that they tend to produce huge corpuses of ideas of widely varying quality. The role of idea filtering is to eliminate, as much as possible, the “lose-lose” ideas (i.e., ideas that are not pareto-optimal), so the community has the best possible alternatives at hand when it makes its final decisions. A range of techniques have emerged to address this important challenge. Authorbased approaches filter out ideas based on who contributed them, for example, based on their previous behavior (Kittur et al. 2013) or on their responses to “gold questions” that assess their competence (Oleson et al. 2011). This approach is limited, however, by the simple fact that good ideas often come from unexpected sources (Lakhani and Jeppesen 2007). Content-based filtering uses software algorithms to derive metrics for idea quality based on such features as word frequency statistics (Walter and Back 2013; Westerski et al. 2013). Such techniques are fundamentally limited by the fact that current natural language processing algorithms have only a shallow understanding of natural language, and thus can be easily fooled. For this reason, much attention has been given to crowd-based filtering, where human participants are asked to select the top ideas. Such filtering is potentially powerful for two reasons. One is that human crowd members can potentially understand ideas much more deeply than software. A second reason is because of the “wisdom of the crowds” phenomenon: large numbers of people, it has been shown time and again, can collectively make better judgments than the individuals that make them up, often exceeding the performance of experts (Surowiecki 2005). The reason for this is that the errors made by different crowd members, under the correct conditions, are independent and therefore cancel each other out, while the shared “signal” is strengthened by aggregation over many contributions. Despite this promise, existing crowd-based filtering techniques (including voting, rating, ranking, and prediction markets) tend to fail when faced with complex decisions involving large numbers of competing alternatives (Klein and Convertino 2015). For more

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details on such techniques, you can refer to the chapters ▶ “Group Decision Support Using the Analytic Hierarchy Process” and ▶ “Group Decisions: Choosing a Winner by Voting” in this collection. Limited-budget multi-voting (Kessler 1995; Bao et al. 2011) represents one possible way to address these problems. In this approach, which we call the “bag of lemons,” participants are provided with a list of candidate ideas, given a limited number of tokens, and asked to allocate their tokens to the worst ideas (the “lemons”), rather than the best ones. Our empirical evaluations have shown that this kind of filtering is far quicker, as well as more accurate, than rating or traditional (pick the best idea) multi-voting (Klein and Convertino 2015). The reasons for this are simple. First of all, limited-budget multi-voting allows users to use snap judgments to quickly hone in on the ideas that may merit tokens: they do not need to fully evaluate each idea. To identify the worst ideas, moreover, a participant need only find ideas that are clearly deficient with respect to just one important criterion. Picking the best ideas, by contrast, forces you to make judgments about all the criteria, including some you may not be well qualified to assess. The bag of lemons thus greatly reduces the cognitive complexity for participants and allows a crowd to be highly accurate at filtering ideas in situations with multiple criteria, even if none of the crowd members are individually able to evaluate ideas with respect to all the criteria.

Negotiation The steps we have outlined so far help communities identify good candidate solutions for a problem. The next step is for the stakeholders to decide which solution(s) to implement. Since the stakeholders will almost certainly be self-interested, with diverse preferences, this is inherently a negotiation problem. The vast majority of research on negotiation mechanisms has focused on “simple” problems (e.g., with a small number of parties and a small number of independent issues such as price) but are ill-suited to complex negotiations which include many parties, as well as many interdependent issues (Klein et al. 2003). The fundamental issue is that simple negotiations need to deal only with simple (monotonic, single optimum) agent utility functions that can be optimized using hill-climbing, while complex negotiations inherently involve complex (multi-optima) agent utility functions that require radically different optimization techniques (such as simulated annealing, genetic algorithms, particle swarm optimization, and so on). Previous work on complex negotiation mechanisms has, to date, been limited to small problems: typically only 2 agents and 10 or fewer issues. Our team has been working, for over a decade, to define novel algorithms that can handle much larger scale problems. To date, we have developed mechanisms that work successfully for problems with 100 issues and 30 agents, building on such ideas as simulated annealing, genetic algorithms, iterative constraint narrowing, issue clustering, and hierarchical agenda management (De La Hoz et al. 2017; Zhang et al. 2014; Marsa-Maestre et al. 2014; Hattori et al. 2007; Fujita et al. 2014).

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For related work, see the chapters ▶ “Discussion and Negotiation Support for Crowd-Scale Consensus,” ▶ “Supporting Community Decisions,” ▶ “Group Decisions: Choosing Multiple Winners by Voting,” and ▶ “Group Decision Support Using the Analytic Hierarchy Process” in this collection.

Deliberation Analytics Conventional deliberation tools suffer from the problem of “opaqueness,” i.e., it is difficult to get a sense of the “health” of a deliberation. While there has been substantial effort devoted to defining manually coded, post-hoc metrics for deliberations (Stromer-Galley 2007; Steenbergen et al. 2003), only rudimentary real-time metrics have emerged. The core reason for this is that, in current deliberation tools, the content takes the form of unstructured natural language text, limiting metrics algorithms to the analysis of word frequency statistics, which is a poor proxy for the kind of semantic understanding that would be necessary to adequately assess deliberation quality. One important advantage of using deliberation maps is that they enable, by virtue of their semi-formal semantics, far more powerful analytics (Klein 2012), for assessing deliberations and detecting crowd behavior. Some examples of analytics we have been able to implement include: • Maturity: The maturity of a deliberation map can be estimated by gathering statistics on the topology of the map (e.g., breadth and depth of the branches of the map). • Balkanization: This phenomenon, when a crowd self-assembles into cliques that ignore or reflexively down-rate competing ideas, can be detected by applying social network analysis to the interactions in deliberation maps, taking advantage of the interaction type information (e.g., agreement, refinement, disagreement) that deliberation maps provide (Klein et al. 2017). • Non-grounded evaluations: This occurs when users rate posts without accounting for relevant arguments. This can be detected by observing whether users read, and how they rate, the arguments underneath a given deliberation map post. • Groupthink: Groupthink occurs when a crowd converges prematurely on a given (often the first) solution idea, without giving adequate attention to competing ideas. This can be detected at how quickly the variance in attention increases for the ideas addressing an issue in the deliberation map. • User interests/skills: We can develop a model of which topics a user is interested in and expert on by assessing their viewing activity as well as the ratings of the posts they contribute. In addition to being able to monitor the “health” of a deliberation, these analytics can generate alerts that guide users to the parts of the deliberation where they can do the most good. We have implemented, for example, alerts that: • Notify the contributors in a deliberation about new content they may want to review, such as a new argument disagreeing with a point they made, a new

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alternative to an idea they proposed, or a new post that drew attention from someone with similar interests. • Notify the moderators of a deliberation about potential problem areas, such as an issue where balkanization appears, where groupthink appears to be in play, or where users are getting disengaged. • Notify the customers of a deliberation (e.g., the policy makers who convened a deliberation on a given topic) about which parts of the deliberation map appear to be mature and thus ready to transition to a decision process.

Future Work Achieving effective crowd-scale deliberation will require, we believe, extending and adding to the kinds of components described above. Here are some directions we consider especially promising.

Harvesting Huge online communities are already engaged in deliberation using existing social media platforms. While the discussions are often inchoate, they do represent a vast resource of thought and opinion. One ongoing direction for our project is to develop improved tools and processes that help individuals, what we call harvesters, scan existing social media to capture the most interesting questions, answers, and arguments as deliberation maps. We believe that harvesters will be intrinsically motivated by the opportunity to facilitate the world’s access to important knowledge, in the same way that Wikipedia authors are so strongly motivated to create and maintain articles in Wikipedia. Such deliberation maps would in fact represent an important complement to wiki pages, since wikis are notoriously ill-suited (Kittur et al. 2007) to capturing knowledge about the kind of contentious topics that deliberation maps are designed for.

From Negotiation to Consensus-Making While our work to date on nonlinear negotiation represents a significant step towards supporting crowd-scale collective decision making, important challenges remain. Aside from the challenges that need to be addressed for any negotiation – e.g., maximizing the social welfare1 of the outcome, minimizing the cognitive burden on the negotiators, minimizing the amount of private information the negotiators have to reveal, protecting the negotiation process from unfair manipulation – crowd-scale negotiation has the additional challenge of avoiding decisions that alienate portions 1

i.e., the summed utility of the stakeholders involved.

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of the community. Such alienation can undercut implementation of the decisions as well as the future cohesion of the community itself. In this context, therefore, fairness and legitimacy become paramount (Mascarenhas and Scarce 2004). This suggests that future work should adopt nontraditional solution concepts that try to minimize regret rather than just maximize utility.

Narrative Reports Ideally, a deliberation system will make it easy for interested parties to ask overview questions about the emerging content, such as: “what are the issues that divide people most deeply?” or “what are the best-supported ideas for this issue, and why?” The semi-formal semantics of deliberation maps provide unprecedented opportunities to answer such questions algorithmically. One of our project goals is to create such a “narrative generation” capability that realizes this promise (Garcia and Klein 2015). We will, in particular, develop a suite of algorithms that gather the data (including map contents, participation activity, and deliberation metrics) needed to answer different prototypical overview questions about deliberations, and will build upon rhetorical structure theory (Taboada and Mann 2006) to structure this data into clear natural language narrative responses.

Crowdsourced Moderation Because good argument-mapping skills are not universal, moderators help ensure that new posts are correctly structured. Posts, when initially created, are given a “pending” status and can only be viewed by other authors. If a post doesn’t adequately follow the argument map conventions, moderators will either fix it or leave comments explaining what needs to be done. Once a moderator has verified that a post follows the conventions, the post is “certified” and becomes available to be viewed, edited, commented on, or rated by the general user population. The certification process helps ensures well-structured maps and provides incentives for users to learn the argument formalism. Moderators act as honest brokers: their role is not to evaluate the merits of a post but simply to work with authors to ensure that the content is structured in a way that maximizes its utility to the community at large. While our evaluations have shown that the need for moderators is relatively low, they do represent a potential cost and bottleneck to system operation, so we are exploring how moderation could be crowd-sourced, i.e., broken down into a series of easy-to-do micro-tasks (e.g., to check if a new entry repeats a point already in the map) that are distributed redundantly to regular crowd members. We can then use a majority-vote-based mechanism like find-fix-verify (Bernstein et al. 2015) to enable high-quality moderation decisions even with a mixed user population.

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Task Marketplace Existing deliberation systems have no innate mechanism to ensure that the crowd members direct their energies to the activities that generate the greatest value. One promising possible solution is to harness the power of market mechanisms. Crowd members can submit a wide range of deliberation tasks in a task marketplace, e.g., to formalize some free text into the deliberation map, check whether a new map post is correctly structured, contribute arguments for/against an idea, mentor a peer, and so on. Each task will include a virtual currency “bounty” conditional on it being performed properly. This approach has many compelling benefits. • Markets provide a natural incentive for mutual support amongst deliberation participants: if they want to benefit from the crowd, they need to contribute to others as well. • In order to maximize their income, participants are incentivized to bid to take on the tasks that are most important (i.e., have the highest bounties) and that they can perform quickly and well, thereby actualizing an effective task-person matchmaking process. • We can manage priority across different activities simply by adjusting budgets: contributors with bigger budgets can offer bigger bounties and get quicker results. • Participants will have a natural incentive to acquire the skills (e.g., by taking additional training) needed to fill critical (and thus potentially) lucrative gaps in the market.

Conclusions In this chapter, we have described the need for effective crowd-scale deliberation, outlined the limitations of current technologies, and described how these limitations can be transcended by integrating and extending recent advances in deliberation mapping, idea filtering, and complex negotiation. Our hope is that this will inspire other researchers to engage more deeply and creatively in solving these critical challenges.

Cross-References ▶ Discussion and Negotiation Support for Crowd-Scale Consensus ▶ Group Decisions: Choosing a Winner by Voting ▶ Group Decisions: Choosing Multiple Winners by Voting ▶ Participatory Modeling for Group Decision Support ▶ Supporting Community Decisions

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Acknowledgments This work has been supported by the JST CREST program in Japan, the FP7 program in the European Union, the National Science Foundation in the United States, and the Templeton Foundation.

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Discussion and Negotiation Support for Crowd-Scale Consensus Takayuki Ito

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Facilitator-Mediated Online Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Collagree: An Intelligent Crowd-Scale Decision Support System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Facilitator Support Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Incentive Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quality of Opinions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Toward Intelligent Automated Facilitators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Case Studies Using Collagree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Social Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nagoya Next-Generation Total City Planning 2018 (Ito et al. 2015) . . . . . . . . . . . . . . . . . . . . . . Aichi Design League (Ito et al. 2015) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hybrid Discussion Support for Continuous Workshops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aichi Design League 2016 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cyber-Physical Discussion Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lessons Learned: Social Presence of Facilitator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-Agree: Online Discussion Support Based on Automated Facilitation Agent (Ito et al. 2019) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Automated Facilitation Agent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experiment with Nagoya Local Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Good discussions are essential for group decisions, especially when a group is large. But large group discussions are often plagued by antisocial behavior such as flaming, the sending or posting of offensive messages. Fortunately, several T. Ito (*) Department of Social Informatics, Kyoto University, Kyoto, Japan e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_41

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case studies have provided an important lesson: When a large-scale online decision support system with facilitator support functions was deployed in several real-world online discussion cases, no flaming was observed. Thus, for large online discussion groups, good support is critical to establishing and maintaining coherent prosocial discussions. The success of this approach led to the proposal of a facilitator-mediated online discussion model that seems likely to lead discussions in profitable directions, enabling even very large groups to reach good decisions. The ultimate goal is an automated facilitator agent that can help participants exchange viewpoints, negotiate together, and attain reasonable outcomes. There is now good reason to believe that, by supporting productive discussion, the social presence of a facilitator will ensure success in large-scale negotiations. Keywords

Group decision and negotiation · Crowd-scale · Agents · Crowd decision support system · Automated facilitation agent · Online discussion support

Introduction Online discussion platforms are receiving much attention because they seem likely to be a next-generation approach to much-needed open democratic citizen forums. Such forums require systematic methodologies that can efficiently support productive discussions, reasonably integrate ideas, and even achieve consensus. The need for online discussion of important social problems has increased due to the COVID19 pandemic. Intelligent crowd-based decision support systems incorporating facilitator support functions have been deployed in several real-world cases, and have provided several valuable lessons. Several intriguing ongoing projects have inspired researchers to enter this arena. Climate CoLab (Introne et al. 2011; Malone and Klein 2007; Malone et al. 2009b), a well-known web-based project, aims to harness the collective intelligence of thousands of people worldwide to address global climate change. It is supported by a crowd-sourcing platform developed by MIT CCI (similar to projects of Wikipedia and Linux) that enables citizens to work with experts to create, analyze, and select detailed proposals that tackle climate change. The steps of the Climate CoLab system, including proposal creation, finalist selection, proposal revisions, voting, and presentations to potential implementers integrate innovative opinions with crystalized, implementable ideas. Deliveratorium (Gürkan et al. 2010; Iandoli et al. 2007; Klein 2007) is another project where people submit ideas by following an argumentation map, a discussion structure that enables individuals to frame their ideas. Deliveratorium shows the relations among ideas and opinions clearly and fully using structured argumentation maps. This structuring is feasible even if input opinions are completely polarized.

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Various facilitator-mediated online discussions that attempt to lead discussions down more fruitful paths have been proposed. A major problem is that online discussions often degenerate into flaming, the posting or sending of offensive messages. Because flaming phenomena discourage people from engaging in online discussion forums, effective strategies to avoid flaming are needed. Real-world workshops or town meetings usually include a facilitator who coordinates, leads, integrates, classifies, and summarizes discussions, aiming to achieve a consensus. In one series of online experiments, professional facilitators joined the online discussion projects, gaining experience at harnessing internet discussions involving more than 100 participants. It became clear that, to manage large-scale discussion, facilitators need support. As a result of this experience, support functions for facilitators were integrated into the CollAgree system. The use of CollAgree in a range of case studies has provided valuable lessons. One important achievement was that no flaming was observed. Other evidence suggests that the social presence of a facilitator “where social presence refers to the feeling of being socially near another person, no matter where they are located” can greatly affect participant behavior. Based on experience with the CollAgree system, a new discussion support system called D-Agree was developed. It included an automated facilitation agent, software that extracts structures from texts exchanged by participants. Recently, D-Agree was used in social experiments to gather opinions from citizens concerning current issues and future plans relating to the local government of the city of Nagoya, Japan. The remainder of this chapter is organized as follows. Section “Facilitator-Mediated Online Discussion” discusses the importance of facilitators who mediate largescale internet discussions. Section “Collagree: An Intelligent Crowd-Scale Decision Support System” describes the current implementation of CollAgree, and section “Case Studies Using Collagree” presents case studies of its use in online discussions. Section “Lessons Learned: Social Presence of Facilitator” discusses the lessons learned from these case studies and provides further discussion on automated facilitators. Section “D-Agree: Online Discussion Support based on Automated Facilitation Agent (Ito et al. 2019)” presents a brief overview of the large-scale discussion support system, D-Agree, which includes an automated facilitation agent who coordinates discussions, and its use in Nagoya. Finally, Section “Conclusion” makes some concluding remarks.

Facilitator-Mediated Online Discussion Facilitator-mediated online discussion model(Ito 2018) leads discussions to smoother, more efficient results. Online discussion often degenerates into flaming, which is defined as posting or sending offensive messages during a discussion. Flaming has been criticized because it discourages participants from joining online discussion forums, which need more effective ways to avoid it.

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T. W. Malone et al. (2009a) described the importance of a hierarchy for harnessing crowds to produce collective intelligence and classified its genomes into several types based on four categories: Who, Why, What, and How. The following passages borrowed from their work describe the Crowd and Hierarchy Genes as the foundation for the Who category for crowd-based intelligence (collective intelligence): Crowd Gene: “Using the Crowd gene, activities can be undertaken by anyone in a large group who chooses to do so, without being assigned by someone in a position of authority.” “Reliance on the Crowd gene is a central feature of web-enabled collective intelligence systems. In fact, most of the examples include at least one instance of the Crowd gene – at least one task where anyone who chooses to can participate.” Hierarchy Gene: “When the conditions for using a Crowd aren’t met, you can use a Hierarchy (often meaning: management).” “ For instance, if only a few people have the skills you need, and you already know who they are, you can assign the task to them directly. Or if you can’t figure out how to prevent people in a Crowd from sabotaging your goals, you many need to use a Hierarchy instead. In this sense, you can think of the traditional Hierarchy gene as the “default” gene, the one to use when you can’t figure out how to get a Crowd gene to work. For example, since anyone can edit or add/delete articles in the Wikipedia project, its situation resembles the Crowd Gene. On the other hand, these activities are all monitored and overseen by moderators whose actions reflect the Hierarchy Gene. In the Linux project, anyone can generally post and edit source codes, like the Crowd Gene. Linux Torvalds et al. decided which of the numerous modules submitted by people to actually include in the project’s next release, which also resembles the Hierarchy Gene. Using a facilitator as a hierarchy gene for large-scale online discussions has been focused to discourage flaming (Ito 2018). A facilitator (Hunter 2009) is defined as a process guide, someone who simplifies a process or makes it more convenient. A facilitator usually leads collaborative discussions so that members can achieve effective results after discussions. Facilitation enables a group of people to achieve its purpose in its own agreed-upon way. A facilitator is especially critical for collaborative discussions in the world. For example, local governments often hold facilitator-mediated workshops to gather opinions from their citizens. Online discussion should also be mediated by a facilitator and taken in a direction that obtains effective results after discussion. However, no such systems currently exist because the nature of online discussion is completely different from physical (face-to-face) discussion. In online discussions, the amount of participants is usually large, and these people are often located remotely and cannot see each other. Online discussions often become dispersed, multi-threaded, and asynchronous and might branch into many sub-discussions. The response times between posts might be very long, too. On the other hand, physical discussions are continuous, single-threaded, and synchronous. It is very difficult to simultaneously have several threads in real discussions; they must be synchronous because all participants are attending a single discussion thread.

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The existing online discussion systems are usually based on the Crowd Gene. Their characteristics, i.e., dispersive, multi-threaded, and asynchronous, are the features of Crowd Genes. Current online discussion systems often fail to avoid flaming because Crowd Genes fail to diligently discourage it. One obvious way to avoid flaming is to observe and manage discussions from a higher level: by introducing the Hierarchical Gene. But current online discussion systems have no such observation or management function, although Wikipedia and other successful social computing systems do have their own versions of it. Thus, introducing a Hierarchy Gene into online discussions is promising and reasonable. A facilitator was introduced as a Hierarchy Gene into online discussions (Ito 2018). Facilitators manage online discussions and lead and motivate participants to have productive and fruitful discussions. They also observe postings, replies, and other actions by the participants and identify individuals who are engaging in antisocial behavior. Since facilitators can enhance the potential of online discussions, they were installed into the social experiments on online discussions. Then there have not been any flaming in more than ten social experiments (Ito 2018). On the other hand, several real problems have surfaced when introducing facilitators into online discussions. Because of the characteristics of online discussions, human facilitators have difficulty expediting them. Since no actual expert facilitators exist for managing such online discussions, several facilitator support functions have been developed. For example, incentive mechanisms motivate participants to post opinions by assigning points (virtual money) to their actions. Such facilitation support functions have successfully helped facilitators. It also includes intelligent algorithms, e.g., NLP-based analysis of discussion contexts, which can intelligently support facilitators.

Collagree: An Intelligent Crowd-Scale Decision Support System Facilitator Support Functions An intelligent crowd decision-making support system has been developed. It is called Collagree: COLLective, COLLaborative, and AGREEment. Its first version was implemented in 2013, and it has also been upgraded and branched into a couple of slightly different versions. Figure 1 shows a typical user interface accessed by both facilitators and participants. This interface, which supports facilitators, was greatly influenced by these works ①, ②, and ③. The following are its typical functions. ① Agreement or disagreement analysis for a comment is shown. Facilitators can understand whether a discussion thread is positive or negative. ② Keywords are highlighted so that facilitators can understand what ideas are being focused on and which are important. ③ Facilitation tab allows facilitators to input their instructions to participants. ④ Opinions and discussions can be searched and reordered. ⑤ Issue tags can be added by participants to each opinion and comment so that they can search for them later. ⑥ E-mail reminders for participants as well as reminders about future related events.

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Fig. 1 Collagree User Interface. (Source (Ito et al. 2014))

Incentive Mechanisms Incentive mechanisms have received great focus in the field of social computing. Incentives in social network are very effective for efficient information gathering and finding. One of the most well-known success stories about incentives is the 2009 DARPA Network Challenge, where competing teams had to locate ten red weather balloons placed around the continental United States. Using a recursive incentive mechanism that both spread information about the task and incentivized individuals to act, the MIT team won the competition by finding all ten balloons in less than 9 h (Pickard et al. 2011). Incentive mechanisms (Ito et al. 2014; Takahashi et al. 2016) for participants have been developed to harness collective intelligence. Although facilitators, who are one element of a hierarchical management, resemble a top-down approach to produce collective discussions, incentive is a bottom-up approach. What facilitators require from participants who want to contribute to online discussions has been identified (Ito et al. 2014; Takahashi et al. 2016). This is because the information gained by facilitators in online discussions is drastically less than in face-to-face discussions. After several social experiments, such requirements will become more important. Thus, several functions have been implemented so that incentivized participants can post comments/opinions to Collagree. Discussion points are adopted as one of the incentive mechanism (Ito et al. 2015). Figure 2 shows a user interface of Collagree that has an initial incentive mechanism. Users can post opinions/comments through the top boxes. The side bar has functions for showing discussion points, user rankings, highlighted keywords, themes, and participant information. The timeline shows the sequence of opinions and replies. Users can reorder the sequence by points, keywords, etc. By reordering the points, users can easily find particular targets of focus and noteworthy discussions from the timeline. Figure 2 gives a detailed description of the discussion points as an incentive mechanism in Collagree. There are two types of discussion points: action (active) and evaluated (passive). Action points include posts, replies, and agreements, all of

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Fig. 2 Outline of discussion points in Collagree. (Source (Ito et al. 2015))

which are obtained when a user posts, replies, and agrees. It can be expected that these points will encourage users to actively post, reply, and agree. Evaluated points are those to which others replied and with which they agreed. When posted comments are replied to or agreed to, they have been evaluated, suggesting that they have discussion value. Thus, the system gives discussion points to them. It is expected that evaluated points will encourage participants to submit more thoughtful comments to get more replies or agreements. A recursive (or propagating) pointing idea for the agreed points is also adopted, in which if comment X is agreed with, then its ancestor (parent) comments are also evaluated because these ancestor comments might have produced comment X that was agreed with. This incentivizes the participants to solicit agreements and replies.

Quality of Opinions The initial incentive mechanism described in the previous section did not use the quality of opinions. It is observed that facilitators want diverse opinions for different phases in a discussion. For example, in the beginning (divergence) phase, they want to identify a sampling of the variety of opinions; in the final (convergence) phase

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they want to summarize the discussion. Thus, they prefer concentrated and similar opinions. A discussion point function based on the quality of opinions has been developed (Takahashi et al. 2016), as judged by content and posted timing. Five members of the Japan Facilitation Association defined these two elements. Since they also participated as facilitators in past experiments, they were familiar with the system. The method’s setting are summarized in Fig. 3 (right).

Criteria for Quality of Posts – Opinion Content Evaluation Method: Opinions that fit the specific phase (divergence, convergence, or agreement) will be highly evaluated. – Posted Timing Evaluation Method: Quick replies and posts during discussion lulls will be highly evaluated. Evaluation Method of Opinion Content The features of new posts are judged as either a divergence or a convergence. The system uses a word-weighting algorithm (BM25) for its judgments (Robertson and Zaragoza 2009). First, it extracts all the nouns from a new post. Then it extracts the keywords from the previous discussion using BM25. After that, it determines whether noun wi and keyword ej match. When w  ej, M1 points are given to the user. When wi equals ej, Pi n does not equal score e , D points are given to the user. j j¼1 wi is a noun that was extracted from new posts. ej is a keyword that was extracted from document set D ¼ {d1, d2, . . ., dn}. score(ej, D) is the importance of ej calculated by BM25. The sum adopted in this process for all the nouns is Pd, which is an additional discussion point given for opinion content. M1 and M2 in the formula are parameters that can be freely set. M1 corresponds to the divergence, and M2 corresponds to the convergence. For emphasizing divergence, M1 should be higher. For emphasizing divergence, M1 needs to be higher. In contrast, when convergence should be emphasized, M2 needs to be higher. In Collagree, these parameters are changed based on the phase of the discussion: divergence phase: M1 ¼ 0.7, M2 ¼ 20; convergence phase: M1 ¼ 0.5, M2 ¼ 25; agreement phase: M1 ¼ 0.3, M2 ¼ 30. As a result, an opinion that fits the discussion phase will obtain a high rating. Evaluation Method of Timings of Posts A reply within 30 min receives five discussion points. When there are no new posts for more than 3 h, a new post receives ten discussion points. The sum of the additional points on the posted timing is Pt.

Discussion Graphs The initial implementation of Collagree faced problems, including “high viewing cost” and “creating a draft agreement,” according to previous advanced research. “High viewing cost” suggests the number of posted opinions is too unwieldy when a

Fig. 3 Settings of discussion points and past experiment results. (Source (Takahashi et al. 2016))

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discussion becomes large. Therefore, participants have difficulty grasping its contents. “Creating a draft agreement” means that the opinions posted by participants weren’t integrated because of anonymity and asynchronicity, which are features of online discussions. These two problems have been solved by introducing a discussion tree-based discussion method for opinion gathering in large-scale discussions on the web (Sengoku et al. 2016). A discussion tree visualizes a discussion’s flow on the basis of the reply relationships in the conversations to make discussions more efficient. Discussion trees are commonly used as a facilitation tool for face-to-face workshops. The discussion tree method in online discussions was implemented and extended it so that it can support such discussions. Participants can use it to grasp a discussion’s flow and issues and clarify the discussion contents. In addition, it can provide positioning and the mutual relationships of opinions to participants so that they can easily create a draft agreement. A major difference of discussion trees from the argumentation maps used in Deliberatrium (Iandoli et al. 2007; Klein 2007; Malone and Klein 2007) is that the former are generated automatically from chunks of text freely submitted by participants on discussion forums. In addition, the discussion tree uses text-mining techniques to present critical keywords in the discussion contents. These features limit the load imposed on participants when the argumentation map requests them to manually create a logical argumentation structure. Since an automatically created discussion tree edited by facilitators can create an accurate discussion tree, participants can smoothly deliberate by viewing a discussion tree. Figure 4 shows a discussion tree created for each discussion theme in Collagree as well the following functions. The numbers below correspond to the numbers with red circles in Fig. 4: (1) summarizing-opinion display function, (2) opinion-tag adding function, (3) important opinion display function for helping readers grasp discussion content, (4) agree or disagree display function, and (5) clustering of thread functions for

Fig. 4 Discussion tree in Collagree. (Source (Sengoku et al. 2016))

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creating draft agreements. Each function was implemented on the basis of the results of a preliminary experiment with a discussion tree. The discussion tree nodes in Fig. 4 represent each opinion, and the links show the reply relationships. The size of each node denotes the opinion’s significance. The text displayed in the node is a summarized opinion. The node’s color is different for each classification. Blue links denote agreement with an opinion, and red links denote disagreement. Another work (Sengoku et al. 2016) demonstrated experimental results that show the effectiveness of discussion trees.

Toward Intelligent Automated Facilitators The following is the description about the principle of the action selection of facilitators to alleviate the cognitive loads of human facilitators during web-based discussions. It is assumed that a facilitator selects an action that maximizes his/her expected utility corresponding to his/her intention. A previous work (Shiramatsu and Ikeda 2016) described a particular utility function, i.e., the number of non-facilitator utterances in succeeding utterances within a certain period of time, corresponding to the facilitator’s intention to promote active discussions. The expected utility can be estimated with Random Forest Regression, which is trained by a discussion corpus. The experimental results showed that actions selected by the expected utility were consistent with the intention represented by it. However, the actual actions of the human facilitators were inconsistent with the actions selected by the expected utility. These results indicate that it is required to investigate the diverse intentions of facilitators with diverse utility functions. A method for generating facilitator questions from the extracted opinions of discussion participants in the preceding context has been also proposed (Ikeda and Shiramatsu 2017). First, the opinions in it were extracted using clue expressions. A facilitator’s question is generated with pattern-matching rules using the case structure of a predicate in the extracted opinion. This method assumes that an appropriate type of question can be selected with a superficial case structure. The method was evaluated through a subjective experiment. Its results show that the method has the potential to develop autonomous facilitator agents.

Case Studies Using Collagree Social Experiments The evaluation by people in actual fields is the most important aspect for finding valuable insights/ideas that can contribute to society. Several social experiments to evaluate the new ideas on a system with actual people were conducted. Basically, a mini-size laboratory-level experiment to investigate how well these new functions work has been conducted. If they are successful, then the current system was introduced to actual social experiments. If not, the reasons for the failure was

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analyzed, fixed the problems, and applied a new system to another actual field. The following are the review of some social experiments as case studies and focus on the facilitator effects of online discussion and whether flaming occurred.

Nagoya Next-Generation Total City Planning 2018 (Ito et al. 2015) The city of Nagoya in Aichi prefecture has over three million people. After 3 months of preparation with city officials, an internet-based town meeting focused on its planning was created. Nagoya’s mayor announced this project by newspapers and TV as an actual town meeting of the Nagoya Next-Generation Total City Planning for 2018. The experiment ran on the Collagree system for a 2-week period from 12:00 on Nov 19, 2013 to 12:00 on Dec 3, 2013 with nine experts from the Facilitators Association of Japan. The participants discussed the following four categories about their perception of an ideal city based on Nagoya’s plan for 2018: a city where human rights are respected and everyone lives happily; a city that is resistant to disasters where people can live safely; a city with a comfortable urban environment in harmony with nature; and a city with vitality and charm. Over the 2 weeks, Collagree gathered 266 registered participants, 1151 opinions, 3072 visits, and 18,466 views. The total of 1151 opinions greatly exceeded the 463 opinions obtained by previous real-world town meetings. On the right in Fig. 5, the questionnaire results are shown. Both participants and facilitators experienced the importance of an online discussion forum to gather opinions for local government. Any flaming was not found. However, a couple of participants who just posted their own opinions failed to follow the main discussion streams. Even though such actions resemble a kind of flaming, they did not cause any deleterious effects to the other participants or the discussion itself.

Aichi Design League (Ito et al. 2015) A large-scale experiment with local governments in Aichi prefecture was conducted. The participants discussed current city planning issues for the towns and cities in Aichi prefecture, which has over seven million people and around 60 local towns and cities. Representative citizens from the local government offices were gathered. On the first day, guest speakers discussed the city planning issues face-to-face, and then the participants continuously discussed them online for another 10 days. Around 300 opinions from the first 2 days were gathered, and discussions progressed effectively. Figure 6 shows the results and the detailed settings of the social experiment. No inflammatory language or flaming were identified.

Hybrid Discussion Support for Continuous Workshops The use of city development workshops continues to increase, reflecting the need for citizen participation in such legislation. City development workshops have been

Fig. 5 Nagoya Next-Generation Total City Planning 2018: Press conference with Mayor Kawamura and results. (Source (Ito et al. 2015))

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Fig. 6 Aichi Design League: A large-scale Aichi prefecture city-design discussion with Collagree (pictures on right). Before this social experiment, a lab-scale preliminary experiment (on left) was conducted, which shows discussion points that incentivized people to join discussions. (Source (Ito et al. 2015))

carried out continuously over weekly or monthly periods. Even though participants may have opinions or thoughts about discussions during or after the workshops, reflecting on them during workshop discussions is sometimes difficult. In this work, we proposed a virtual-world workshop using Collagree and verified the method’s effects by social experiments in which continuous workshops were conducted by landowners, residents, and students. Discussions were conducted by a consensusbuilding support system during and after the workshops. The discussion data of both real- and virtual-world workshops were analyzed and it gave questionnaire surveys to the participants and identified the effects and problems of the proposed method.

Aichi Design League 2016 In 2016, a large-scale experiment with local governments in Aichi prefecture was conducted (Nishida et al. 2017). It was called “AICHI DESIGN LEAGUE (2016).” The core time mechanism was verified, which provided the time settings for the facilitator and the participants to gather and discuss. The core time was presented to the participants to encourage them to contribute to the discussions during those specific times. The left table of Fig. 7 shows an outline of the experiment. 124 people (21 civil servants and 103 students) participated on October 28. The discussion’s theme was “town planning in 20 years.” This experiment was made in two parts. In “Part 1,” nine civil servants and students presented “town planning in 20 years” in the target areas. In “Part 2,” they discussed on the internet

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Part 1 Lecture by civil servants Date

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Civil servants of nine municipalities in Aichi presented the area and city planning for students.

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(b) Core-time Effect Fig. 7 Aichi Design League 2016. (Source (Nishida et al. 2017))

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using Collagree from October 28 to November 4. The “Divergence phase” was conducted until noon on November 1. The “Convergence phase” was conducted until 8:00 p.m. on November 3. The “Evaluation phase” lasted until midnight on November 5. The core time was set from 10 a.m. to 12 noon on November 1 and 5 to 7 p.m. on November 4. The core time, which was set before the discussion phase changed, was announced 3 days earlier. It was explained that the core time is a period during which everyone was encouraged to join the discussion. For the participants, joining the core times was optional. It was analyzed that the number of daily views and posts to verify how the discussions were influenced by the core time mechanism. The right graph in Fig. 7 shows the transition of the number of daily posts and views. The number of posts decreased after the discussion’s start. However, on November 1, when the core time was set, there were 78 cases, which is over double the previous 35 cases. On November 4, when the core time was set, there were 43 cases, 22 more than the previous 21 cases. The number of views decreased after the start of the discussion. However, on November 1, when the core time was set, there were 1203 cases, 649 more than the previous 554. In addition, on November 4, when the core time was set, there were 1385 cases, 826 more than the previous total of 649. Since the number of posts and views more than doubled compared with the previous day when the core time mechanism was set up, it is concluded that it affected the discussion, which ran continuously until the end. Any flaming activities in this experiment was not identified as well.

Cyber-Physical Discussion Support A hybrid (cyber-physical) environment in which people can simultaneously discuss either online or offline was conducted. A large-scale experiment was conducted in a panel discussion session at an international conference where participants discussed throughãĂĂCollagree and face-to-face communications as usual. The experimental results were analyzed from the following three metrics: participants’ cyber-physical attention, keyword and cyber-physical linkage, and cyber-physical discussion flow. These three analyses results indicated that the methodology effectively supports hybrid large-scale discussions. Two cyber-physical discussion experiments were conducted at the IEEE ICA2017 and AAI2017 conferences and experienced no flaming phenomena at either of them (Fig. 8).

Lessons Learned: Social Presence of Facilitator More than ten real-field social experiments were conducted including the experiments presented in the previous session. In these experiments, no flaming phenomena was identified. Several possible reasons might explain how flaming was avoided in online discussions:

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Fig. 8 Cyber-physical discussion experiment. (Source (Kawase et al. 2018))

Semi-anonymity: In all of the experiments, participants registered under their real names and e-mail addresses. Although the system administrator knew their real names, the other participants (including the facilitators) did not. From the viewpoint of the participants, if they behaved poorly, they could still be identified even without engaging in such activity. But generally, even in such semi-anonymous systems like Twitter, flaming phenomena are very common. Collaborative discussions: In the experiments so far, the discussions were all collaborative. Thus, participants who behaved antisocially were ignored and barred. However, even in such collaborative discussions as on Wikipedia articles, sometime such flaming phenomena can be observed in the general internet world. Social presence (Tu and Mcisaac 2002): This idea, which refers to the feeling of being socially present with another person at a remote location, is largely focused on a very influential factor in social media in the social psychology field. In Collagree, in all the experiments, it was openly informed to the participants that the facilitators were observing the discussions to manage them. Perhaps such a social presence of a facilitator(s) discouraged antisocial behavior by online participants. More work is required on this possibility. Large-scale online discussion systems might be an alternative for democratic systems because they enable people to discuss shared problems and could lead to crowd-scale decisions. Toward such a vision, a facilitator-based online discussion model was proposed, intelligent online discussion systems were implmented, and real-field social experiments were conducted. The problem of flaming is critical in online discussion systems, including web forums, social networking services, and question-answer systems. Because of flaming, some people avoid online discussions.

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As one key idea to attack the flaming problem, a facilitator-based online discussion system was proposed. Actually, to create automated software agents that can function as facilitators is one of the important goals. At this point, human facilitators were employed and provided facilitator support functions. A large-scale online discussion support system with several functions was implemented for aiding facilitators and incentivizing participants to post opinions. It also has a discussion tree function that enables participants to easily grasp the entire discussion view. More than ten social experiments were conducted in actual fields with Nagoya, Aichi prefecture, and international conferences. The experiments were progressing quite well, and most of the participants understood the usability and the possibility of online discussion support systems. The most critical result is that it has not yet had any flaming phenomena in any of the social experiments. One of the insights suggests that the social presence of facilitators is key.

D-Agree: Online Discussion Support Based on Automated Facilitation Agent (Ito et al. 2019) Outline Collagree is an effective online discussion platform with human facilitators. More than 30 experiments (Kawase et al. 2018; Nishida and Ito 2019; Nishida et al. 2017) were conducted after the above experiments, and clarified the critical problems faced by human facilitators. Such discussions often had over a thousand opinions that were posted simultaneously. Many discussion threads became entangled with overlapping opinions. Such elements are characteristic problems for online discussions that are not seen in ordinary face-to-face discussion workshops. In this work, automated facilitation agent (Ito and Shiramatsu 2018) was proposed to manage online discussions. Figure 9 outlines D-Agree. Figure 10 shows the user interface of D-agree. An automated facilitation agent extracts the discussion structure from the texts posted in discussions. The discussion structure represents a discussion’s semantics. The IBIS structure (Kunz and Rittel 1970) was adopted as a discussion framework because the aim is to create discussions through which people can clarify issues, ideas, and debate merits/demerits. IBIS effectively constructs such discussions. Extending any form of argumentative structure is also easy (Lawrence and Reed 2017). Based on the extracted structure, facilitation agents post facilitation messages about a discussion, manage a knowledge database that contains the previous discussion structure, and collect data from other social media.

Automated Facilitation Agent Automated facilitation agent software was implemented and it observes the posted texts, extracts their semantic discussion structures, generates facilitation messages, and posts them to the discussion system. The software also filters inappropriate posts.

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Fig. 9 D-Agree outline. (Source (Ito et al. 2019))

Fig. 10 D-Agree user interface. (Source (Ito et al. 2019))

The facilitation agent consists of two parts: a discussion structure extraction/ visualization mechanism and an observing and posting mechanism. To extract the discussion structure, the deep-learning technologies including BiLSTM (Lample et al. 2016) were used, which first captures meaningful sentences and then important words that are IBIS components: issues, ideas, pros, and cons. After that, it identifies the relations among these IBIS components and unifies these relations and components into one discussion structure. Extracting a discussion/argumentation structure has been widely studied in the argumentation mining field (Lawrence and Reed 2017; Stab and Gurevych 2014a, b; Stab and Gurevych 2017). The main difference between this approach and the argumentation mining field is that this approach is based on IBIS structure, which focuses on facilitation. The IBIS structure includes an issue component, which is different from ordinal argumentation structures. Issue components are critical for facilitation and innovative discussions. Previous papers (Suzuki and Ito 2020; Suzuki et al. 2019; Yamaguchi et al. 2018) describe the technical details. By using the extracted structure, the observing and posting mechanism posts facilitation messages. It has around 200 facilitation rules, which were carefully

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Fig. 11 D-Agree system architecture. (Source (Ito et al. 2019))

Fig. 12 An example of facilitated discussion. (Source (Ito et al. 2019))

collated after consultation with professional facilitators. These facilitation mechanisms have been implemented by Amazon Web Services (AWS). Figure 11 presents the architecture of D-Agree and its user interface. This is done by AWS lambda and CloudWatch, which are sufficiently scalable. Both of English and Japanese as languages are available.

Experiment with Nagoya Local Government From November 1 to December 7, 2018, we conducted a real-world experiment with the Nagoya municipal government. Citizens discussed five themes about their city’s future. There were 15,199 page views, 157 registered participants, and 432 submitted opinions. The main objective was to gather opinions and discussions for a midterm

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draft of the Nagoya City Next-Generation Comprehensive Plan, generated by the Nagoya municipal assembly, the local government, and its offices. The plan had five main themes. Themes 1 and 2 were facilitated by expert facilitators. Themes 3 and 4 were only facilitated by automated facilitation agents. Theme 5 was facilitated by cooperation between humans and agents. The details of the analyzed results were presented in papers (Ito et al. 2019, 2020). Figure 12 shows an actual case where the automated facilitation agent successfully facilitated a discussion among people. A detailed explanation is presented on the right of the figure 12.

Conclusion In this chapter, we discussed Collagree and D-Agree, online forums through which large groups of individuals can exchange opinions and discuss themes. The aim of these systems is to make it easier for the group to reach a consensus. Collagree provides an intelligent mechanism that can support human facilitators. It worked well in several social experiments. But, unfortunately, it was very demanding on human facilitators, who were unable to observe discussions 24 h a day and 7 days a week. The solution appears to be an automated facilitation agent, which can extract discussion structures using deep learning techniques. The new system, D-Agree, worked well in a large-scale experiment in which citizens advised the local government of Nagoya city. Another trial is currently under way in Afghanistan (Haqbeen et al. 2019), where D-Agree is gathering citizen input on the future of Kabul city. We may be close to the ideal version of on-line discussion support, where hundreds of individuals can provide input, come to an understanding, and reach consensus on good, timely decisions and recommendations.

Cross-References ▶ Crowd-Scale Deliberation for Group Decision-Making ▶ Group Decision Support Using the Analytic Hierarchy Process ▶ Participatory Modeling for Group Decision Support ▶ Supporting Community Decisions Acknowledgments The research reported here reflects the contributions and input of many individuals and organizations. The author was supported by the JST CREST fund, Grant JPMJCR15E1.

References Gürkan A, Iandoli L, Klein M, Zollo G (2010) Mediating debate through on-line large-scale argumentation: evidence from the field. Inf Sci 180(19):3686–3702 Haqbeen J, Ito T, Hadifi R, Nishida T, Sahab Z, Sahab S, Roghmal S, Amiryar R (2019) Agent that facilitates crowd discussion. In: Proceedings of ACM collective intelligence, vol 2019

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Participatory Modeling for Group Decision Support Alexey Voinov

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Participatory Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tools and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PM in the Social Media Era . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PM at Different Times and Places . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

There are problems, especially when people are involved, which are hard to define and solve in a unique way. They do not have one clear and unequivocal solution because conflicting values and priorities are involved. When dealing with such problems, it helps to engage as many stakeholders in the process as possible. Participatory modeling is an efficient method for dealing with such problems. It involves stakeholders in an open-ended process of shared learning and can be essential for developing sustainable solutions. While there may be various levels of participation, the process revolves around a model of the system at stake. The model is built in interaction with the stakeholders; it provides formalism to synchronize stakeholder thinking and knowledge about the system and to move toward consensus about the possible decision-making. The process here becomes even more important than the model produced, because the process itself helps to make better decisions.

A. Voinov (*) Center on Persuasive Systems for Wise Adaptive Living (PERSWADE), University of Technology Sydney, Sydney, NSW, Australia University of Twente, Enschede, The Netherlands © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_65

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Keywords

Group decision · Crowd scale · Facilitation · Modeling team · Stakeholders · Biases · Media effects · Model integration

Introduction Participatory modeling (PM) is a way of structuring the deliberative process around some formal models, which are jointly created in this process. There is a lot to learn and share during a well-organized, structured, and documented modeling process. For this reason, PM may be seen as a purposeful learning process for action that engages the implicit and explicit knowledge of stakeholders to create formalized and shared representations of reality (Voinov et al. 2018). Engaging stakeholders in this process can result in better decisions with less conflict and faster progress toward a solution. The bottom-up approach, when the stakeholders play a role in the decisionmaking process, offers a lot of promise, especially in democratic societies, where unpopular decisions are hard to impose and implement in a top-down scheme of events. The co-learning element in participatory modeling creates a background of shared understanding and “levels the playing field” making potentially conflicting stakeholders more likely to come to an agreement. In Behavioral Operations Research, PM can be seen as a useful method to enhance and promote Systems Intelligence (Hamalainen et al. 2018). It is instrumental to connect subjective human preferences, narratives, beliefs, modified by culture, traditions, and social cohesion, with objective data and facts about systems, mutually enriching both.

Participatory Modeling Participatory modeling (PM) stems from the understanding that better decisions are implemented with less conflict and more success, when they engage or even are driven by stakeholders, that is, by those who will be bearing the consequences of these decisions. This leads to a more bottom-up approach where the stakeholders play a role in knowledge generation and sharing, and, possibly, in the decisionmaking process. The drive toward participatory decision-making is primarily fueled by the increasing realization that the more humans impact the environment and the more they attempt to manage natural resources, the more complex and less predictable the overall socio-ecological system becomes and the harder it becomes to find the right decision and to choose the best management practice (Voinov and Bousquet 2010). The idea of PM is very simple. When building a model of a system, we bring together our best knowledge about it. The modeling process inevitably becomes a learning process. This is what modelers usually enjoy the most: starting to understand how the system works. Modeling helps to collect, structure, select the most

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Fig. 1 The stakeholder participation continuum

important information, and leads to better representation of relationships between various causes, drivers, and outcomes. Why not open up the modeling process and invite those who will be using the model to join? Why not share the excitement of understanding with the group of people who are part of the system? Especially since they may also know more about the system than what a modeler would regularly learn from existing publications and reports? Especially since it will be then who are supposed to use the model results to make better decisions? There may be different levels of participation (Fig. 1). We can simply solicit information from the stakeholders, to explain the processes and find the right parameters for our models. Ideally, it is even better stakeholders get involved in the model-building process itself. What is especially valuable is that in this case the people start to consider the model as their own creation, their “baby,” they are more likely to trust it and to use it. In some cases, the stakeholders feel empowered enough to continue participating in the decision-making process itself, a kind of “deep participation,” which usually leads to most positive and lasting results. There has been a proliferation of various clones of stakeholder engagement in modeling, or, rather, of the use of modeling in support of a decision-making process that involves stakeholders. In many cases, the differences are quite subtle and it may seem that various agencies or groups come up with a new term to serve as a recognized trademark for their efforts. In essence, they tend to be doing more or less the same things. For a brief overview of various types of stakeholder-based modeling, as well as some stakeholder processes that do not rely on modeling, see a review by Voinov and Bousquet (2010). With all the diversity of social and environmental conditions, it is hardly possible to come up with a generalized PM strategy. However, some of the basic steps and elements can be identified and are shown in Fig. 2. There are many loops back and

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Fig. 2 The PM cycle. The order and time spent on different steps may change depending on stakeholder decisions and preferences. A more proactive role of scientists and modelers in defining the problems and tasks for scientific inquiry can lead to more meaningful results and policies. Eventually, also more participation in the actual action-taking is essential (Voinov et al. 2016)

forth, and there is no particular order in how the process proceeds. We may need to go back again and again, or jump several steps forward if the goals of the study are already achieved and management decisions are agreed upon. While the order is uncertain, the major components of the process seem to be quite generic. Participatory modeling can also be safeguard from the above-mentioned subjectivity in modeling. In fact, when the model is thoroughly discussed and documented with various, often times conflicting, stakeholders involved, it becomes way harder to bring in assumptions and variables that suit selected purposes, or vested interests. Moreover, stakeholder participation makes the modeling process truly adaptive, so that models can adequately incorporate new information about the systems as it becomes available and adjust to the new goals driven by the decision-making and management needs. The challenges seem to shift into the relational, social dimension of the process that can help us to identify differences and similarities in various case studies, to identify patterns and ways to learn from the experience of the others. PM helps to deal with behavioral issues in modeling (Hämäläinen 2015), by creating means for integrating mental models of stakeholders with existing formal knowledge and data.

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Although there is usually a common structure to PM (cf. Fig. 1), the actual processes and sequence of events vary depending on the goals of the modeling and on the participants involved. PM participants should aim to achieve some general consensus on participatory processes, their mediation, and importantly, on a core set of principles to help guide the discussions and processes. There is no set of principles that will always apply; and there certainly will be multiple ways to implement any given set of core principles, because they always depend on the specific issues and participants involved. However, some general principles of good PM practice are already available (Box 1) (Voinov and Gaddis 2017). Similarly, we can recommend some ideas for group agreements and moderation, as follows (Voinov et al. 2016): 1. A PM process offers some structure to the group process, which can help to document, track, determine the origins, and share information related to the project. This does not necessarily mean that all parties will have to accept, use, or weight the sources of information in the same way. 2. When creating knowledge, beliefs, values, and biases (both individual and institutional) are explicitly exposed (Glynn et al. 2017). Political, ideological, ethical, cultural, or spiritual differences are inevitable between different stakeholders in a PM process. To achieve some form of resolution that is essential for the PM process to proceed and produce useful results, sources of such differences need to be explored and respectfully discussed with the group. 3. In a group there are likely differences in the power of different stakeholders involved, both on institutional or individual levels. They should be explicitly recognized, and when appropriate, possibly compensated for. 4. Further engagement beyond a PM group is required to consider, and respond to the needs of the broader community potentially impacted by the decisions or actions resulting from the PM. This includes acknowledgment of issues important for future generations or other absent parties. 5. Participants may have different degrees of commitment, which should be recognized. Ideally, all participants to the PM process should be seeking follow-up of PM results into meaningful policies and/or community action. The group prepares – and implements (i.e., acts on) – a concrete plan which details actions for follow-up among decision/policy-makers and the affected public. This implies that a PM approach does not terminate with the end of the specific (investment) project, but has an on-going follow-up with specifically identified people, and it includes monitoring and evaluation. 6. Some upfront agreements on the acceptance of PM results and recommended follow-up actions are important, realizing that the PM process will be as fair as possible, but also probably imperfect. Before initiating or proceeding with a PM process, the participants state whether (or not) they will eventually comply with the outcomes of the process, or what further procedures they would require to do so, e.g., a popular referendum, a vote, an approval by a Government agency or a Company Board, etc.

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7. The group agrees on the level of access to the project results and proceedings. Ideally all data should be open-access and models – open-source. There should be clear and transparent documentation provided for the process and the findings (Glynn et al. 2018). This can also help with the issue of acceptance of PM results. Agreement on a set of core principles, such as those listed above, would help establish social norms that can guide PM and contribute to meaningful policy decisions and actions, though they may be hard to achieve and enforce. Most PM activities are voluntary, and therefore it is impractical and infeasible to compel participants to adhere to such social norms, even if they have been explicitly identified early on, or to make them comply with the outcomes or recommendations produced. Nevertheless, the occurrence of subsequent non-compliance, if there had been a previous commitment, would be significant as a pointer to, and critique of, any stakeholders who do not follow the line on consensual social norms and modes of behavior.

Box 1 Some Generic Principles of Good Participatory Modelling

• • • • •

• • • • • • • • • •

Identify a clear problem and lead stakeholders. Engage stakeholders as early and often as possible. Create an appropriately representative working group. Gain trust and establish neutrality as a scientist. Keep it flexible and focus on the process rather than the product. Environmental systems are open in time and space: make the process that deals with them also open and evolving. Promote adaptive management, adaptive modeling, and adaptive decision-making. Maintain societal and scientific openness, and transparency of methods and models. Rely on collaborative research, and open-source models. Know your stakeholders and acknowledge conflict. Select appropriate modeling tools to answer questions that are clearly identified. Mind the people. Always be aware of social and group dynamics, special interests, power, and hierarchies. Facilitate and encourage learning – learn from each other and the process. Go in circles and branch out – go back, reiterate, refine. Incorporate all forms of stakeholder knowledge. Accept a different kind of uncertainty – be certain about uncertainty. Accept non-traditional metrics of success – group validation and verification. Involve stakeholders when presenting results to decision makers and the public.

There are numerous examples of PM processes in the reviews by Voinov and Bousquet (2010) and Voinov et al. (2016, 2018). Also, Gray et al. (2017) dive into many aspects of PM with various case studies.

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Tools and Methods There are a variety of tools and methods used to conduct the PM process (Fig. 3). A survey of about 100 PM practitioners has shown how participants chose methods for their PM projects (Voinov et al. 2018). On the one hand, respondents clearly admit that they choose methods that they are most familiar with: 92% totally agree or strongly agree with this statement. At the same time, 60% claim that they choose the most appropriate methods. This suggests that perhaps researchers choose the projects where their methods-expertise is the most appropriate choice, yet only 35% of our participants said that was a factor. Indeed, the vast majority say that they choose methods based on the problem characteristics (87%) and on the nature of the community involved (73%). These responses are difficult to reconcile. When asked to rate factors in terms of how important each is when selecting a method, all the identified factors were considered important. Time, money, and level of stakeholder involvement required, as well as the availability of data had the

Fig. 3 Tools and methods of participatory modeling (Voinov et al. 2018)

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highest importance. Skills and education of stakeholders were of lower importance in the survey, though still important. Overall, the survey suggests that practitioners consider many things when selecting methods, but that they do not necessarily have a clear hierarchy of criteria or approach for choosing those methods. Their prior experience may often be most important, which means that there is evidence that the so-called hammer and nail syndrome plays a role. Once we profess in a certain method (“the hammer”), we tend to solve all problems using that method (“everything looks like a nail”). Mostly the methods used in PM may be grouped into three clusters, each one used in particular stages of the process. 1. Conceptual (qualitative) stage. A PM process usually first focuses on eliciting what the stakeholders think and know. In Forrester’s (1961) terms, here we try to access the mental database of stakeholders. The interaction is on the conceptual level, and the tools used are mostly for the sake of structuring human interaction and assisting the process of deliberations and information exchange. Next to this are the methods for soliciting data and information from stakeholders. There are also some semi-quantitative methods, which build on direct stakeholder participation, yet employ ways of attaching values to concepts. These can be weights, or estimates, or probabilities. 2. Quantitative stage. Here the process is further developed to quantify some of the variables and interactions between them. The modeling process is advanced by incorporating quantitative data and functional responses into the model. These can be extracted through some machine learning, statistical, techniques directly from data and observations, or they can be based on theory and knowledge accumulated in past exercises. The more we can bring into the process in addition to what stakeholders already know, the more we can expect for the analysis of the system and for understanding its behavior beyond what is already known about it. Quantitative modeling requires some analytical, data processing, and programing skills, which usually means that only some part of stakeholders will be able to participate in and contribute to this stage. 3. Reporting and testing stage. Delivering and presenting results back to the larger group of stakeholders and decision makers in a meaningful and compelling way requires a different set of tools. Now the focus is on visualization, persuasion, framing, and contextualizing the material. While progression within each of the stages is rather smooth, there is a clear disconnect between the methods used in each of the three stages. There is a significant cognitive leap that is required to switch from mental, conceptual modeling to quantitative, computer modeling. Mental modeling mostly operates with concepts. These may not necessarily be easily quantifiable. They may be expressed in various terms, using totally different and mismatching units. There are hardly any rules to limit the variety of concepts and ideas used in mental modeling. This certainly becomes a problem, when formulating a quantitative analog of a mental

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model, when concepts have to be converted into variables, stocks, flows, parameters, functions, and equations. Bringing the science, the computer modeling results back to the stakeholders is another cognitive transition: this time from quantitative, logical, or Kahneman’s (2011) system 2 type of knowledge and information back to something that would appeal to the feelings, to system 1 thinking. One of the challenges of PM is to marry these three stages by developing improved integration techniques connecting mental and computer models. On the one hand, computer interfaces are increasingly covering this gap by providing improved functionality for communicating mental models and ideas to the software implementation and back. On the other hand, there is still much to be done in terms of developing usability techniques specifically focused on the communication lines between mental and computer modeling. Here again it is crucial to recognize the existing biases and beliefs in the group and keep them in mind when preparing the final presentation. While all stages in the PM process assume possible iteration, method and tool selection is crucial because there may be insufficient time or resources available to go back and do the whole PM process once again with another method. The modeling method chosen depends upon, but can also determine, the types of data to be collected and processed. While the “hammer and nail” syndrome always has a negative connotation, past experience certainly matters and, indeed, it may not be bad to use a method that someone is most comfortable with. Besides, there is often considerable overlap between some methods: this only makes it harder to come up with a unique optimal choice.

PM in the Social Media Era Today there are several important trends in the field of PM. Perhaps the most important are the quantitative and qualitative growth of social media, mobile applications, web services, and other means for broader “popular” access to data and information and for wider social participation in creating these data and information. All this creates more potential for an even broader participation of stakeholders in decision-making processes and further expansion of a new approach known as “citizen science” (Voinov et al. 2016). If we are to make decisions on complex problems that affect the future of many people, it makes sense to involve as many people, stakeholders in the decision process. If we want to make sure that interests of as many people as possible are considered, we do want to find a way to get these people involved in a broad discussion of the various options, outcomes, the boundaries of our analysis, the impacts, and the scenarios. What kind of tools we need to engage hundreds, or thousands of people in a discussion about our future? Can we just register their “likes” or “thumbs ups” and “downs”? Or can we also use social media to better inform stakeholders about the different options, the influences, causations, scenarios,

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drivers, and feedbacks? We already see some examples of penetration of participatory modeling tools into citizen science (Gray et al. 2012). On the downside, new opportunities that come from social media still may not immediately translate into better decisions and real actions taken. As observed by Jonathan Swift back in 1710, “it often happens, that if a Lie be believ’d only for an Hour, it has done its Work, and there is no farther occasion for it. Falsehood flies, and the Truth comes limping after it; so that when Men come to be undeceiv’d, it is too late; the Jest is over, and the Tale has had its Effect. . .”1 With the Internet, information can really fly around the world in seconds. Unfortunately, this applies equally well to misinformation. What makes things even worse is that it is also easy to find like-minded people on the Internet and gain further support to the misinformation spread. Moreover, most of the existing social media platforms, say, YouTube or Facebook or Twitter, use algorithms that try to identify your preferences and deliberately select and offer content that matches what you have been looking at in the past. A climate skeptic most likely will be guided to clips that deny climate change, a Trump supporter would most likely be shown clips and tweets coming from other likeminded users. This effect is also known as Balkanization (see ▶ “Crowd-Scale Deliberation for Group Decision-Making” in the chapter by M. Klein, this volume). This increases the likelihood of viewers to stay online by exploiting the confirmation bias, which makes it more pleasant and enjoyable for us to hear or see things which we agree with (Kahneman 2011). This leads to “group think” (Janis 1972; Hämäläinen 2015), which can have a further self-enhancing effect: people are more likely to acquire their knowledge by consulting those who share their values and whom they therefore trust and understand (Kahan 2012). So, by the time truth comes out, it is possible that lies have already established their critical mass of supporters that are now engaged in a positive feedback self-assuring exercise, effectively blocking all the information that would be contradicting the group thinking. The theory in this case does not have to be anything coming from science. Instead it would be the prevailing beliefs, biases, and preferences of the group, the “wishful thinking,” or perhaps the value choices that promise the most comfort – physical, mental, or spiritual. People are still very dependent on their fast system 1 thinking (Kahneman 2011), primarily based on their intuition, “gut feeling,” preconceived notions, beliefs, and biases. This can easily clash with the slow system 2 thinking based on logic, information, knowledge, that which comes from models, data, and analysis. With the new Internet connectivity and the “information highway,” we no longer have to rely on our memory to access facts and data, and we could supposedly spend way more resources on processing those facts and information. But can this avalanche of data actually help us in making better decisions and improving our management, or,

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1710 November 2 to November 9, The Examiner, Number 15, (Article by Jonathan Swift), Quote Page 2, Column 1, Printed for John Morphew, near Stationers-Hall, London. (Google Books Full View)

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instead, it will overwhelm us by the diversity of information and misinformation that is now available, and will only promote particular vested interests, and group ideas? Will we use the abundance of newly available physical and human sensors accessed through the Internet and social media to solve the dire problems of resource crunch (environmental pollution, minerals, energy, space, water, energy – you name it) that we are now facing as a civilization, or will we rather use this information to gain more control for certain groups at the expense of privacy and well-being of other people? This is yet to be seen. The expectation still is that by opening the modeling process to stakeholder participation and by using this participation to educate stakeholders and “level the playing field,” we can create better mechanisms to communicate our biases and beliefs, not just data and information. In doing so, we have a better opportunity to move toward consensus and improved decision-making. The more recent advances in Artificial Intelligence, Machine Learning, and Natural Language Processing offer much hope for a new way to do PM, when stakeholders exchange their ideas in the form of comments on a social media platform. These comments are processed on the fly, generating various visualizations that can translate the flow of ideas and opinions registered into more formal conceptual models, casual loop diagrams, or directly into Fuzzy Cognitive Maps (Anjum et al. 2019). These, in turn, enrich the ongoing discussion, informing the participants about the overall prevailing trends and opinions that evolve. A web-based tool for serious discussions, Discussoo,2 is currently under development, and can be already used to organize a stakeholder process online, harvesting the most relevant concepts from the comments posted, identifying the most important and related trends in the discussion, assigning weights to concepts and interactions between them. For related work, see the chapters ▶ “Discussion and Negotiation Support for Crowd-Scale Consensus,” ▶ “Supporting Community Decisions,” and ▶ “CrowdScale Deliberation for Group Decision-Making” in this collection.

PM at Different Times and Places Will PM work everywhere and always? The history of PM essentially started in the 1960s when Forrester was including managers in building models for business systems. It was boosted in the 1970s by the so-called Sunshine Laws adopted by the US federal and state governments, requiring that meetings, decisions, and records of the regulatory authorities be made available to the public. It was also at that time that the US Army Corps of Engineers called for the broad participation of stakeholders. Broad stakeholder involvement has always been seen as a triumph of democracy, where broad layers of society, in principle, got the opportunity to take part in deciding on various policy and management issues.

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How dependent is PM on the democratic tradition, and what would PM look like in places which are not quite democratic and do not assume wide stakeholder participation in most decisions? Is PM even relevant there? Who would be the stakeholders? How do you work with them? How to organize the process? For example, in China decisions are very top-down. The five-year plan produced by the Communist Party of China (CPC) is pretty much a must for the development of the country and guides all further decisions on lower levels of the government. On top of that, the CPC defines certain strategies like the “Rule of Law” that the 2012 CPC congress reconfirmed, which led to arrests in the highest echelons of power. The party makes decisions in consultation with scientists and experts who identify the best solutions based on their research. Science continues to play an important role in the decision-making process and scientists are well respected and wellfunded. At the same time, people can go to jail for publishing “rumors” on social media (Global Times 2017). People may not, therefore, be too eager to participate in public hearings and debates. The dominant opinion in the West is that democracy is the best and that other countries should simply evolve and develop to also reach that stage, assuming that democracy is to come together with maturity of society as it becomes more open. However, there is evidence that other social arrangements may also be quite productive (Bell 2015). Eric X.Li, a Chinese investor and political scientist, tells us that the system in China is not a democracy, yet it is not bad, and might be even better than democracy in some ways.3 The Chinese system, which Li calls “meritocracy,” has already produced unprecedented development in the country, and there is hardly any reason to expect it to be phased out and replaced by democracy any time soon. Most importantly, he argues that considering and comparing democracy and meritocracy is really not about what is bad or good, what is wrong or right. His main point is that there may be different systems, and not necessarily all that is not democracy immediately means bad, dilapidated, and it is only a matter of time and development for it to get replaced. Democracy may not be the only optimal state of human development. There may actually be several optima. Keep in mind that what we mean by democracy, in the meanwhile, is also changing, gradually deteriorating in some cases, morphing into something that would be more properly referred to as plutocracy. Let us also not forget that China’s meritocracy not only managed to build a prospering economy and eliminate hunger in the country, but also stopped exponential population growth in the country, and is currently leading the transition to low-carbon alternative energy, strongly supporting the Paris accord, unlike some of the exemplary democratic countries. The proliferation of stakeholder participation seems to start in the mid-1970s. At that same time, the notion of “wicked problems” emerged (Rittel and Webber 1973), which recognized that many of the socio-environmental problems do not have solutions in the regular sense because stakeholders cannot agree, judgment is multidimensional, there is no one right solution, only better or worse ones.

3

https://www.ted.com/talks/eric_x_li_a_tale_of_two_political_systems

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Interestingly, this lack of solutions seems to be also a feature of a democratic, deliberative process, where all stakeholder opinions have to be taken into account. Later on, the idea reemerged as “post-normal science,” which technically speaking is almost about the same: we have to deal with problems that are unsolvable in the usual sense; there is much uncertainty in the decisions we have to make, yet stakes are high and science should extend to engage stakeholders. Funtowicz and Ravetz (1993) observe that “one reaction, as among some leading exponents of postmodernity, is despair.” Apparently by the 1970s, we have reached the stage when democracy started to show signs of incompetence and inability to solve some of the urgent problems that society was (and still is) facing. It may seem like participatory research efforts emerged as an attempt to fix democracy and make it functional again. What are our chances of success, and what else has happened in mid-1970s? If we look at the dynamics of per capita GDP and GPI (Genuine Progress Indicator), we see that while GDP continues to grow, GPI levels off at about that time and even starts to decline after that (Fig. 4) (Talberth et al. 2007). At about the same time, income has disconnected with productivity. Before mid-1970s, income was constantly growing together with productivity. After that, while productivity continued to grow, income stagnated, while debt started to increase. This time seems to also coincide with when stakeholders started to gain ground in the decisionmaking processes. It almost looks like we are substituting real well-being and life quality with more participation, giving people the illusion of involvement while nothing really changes for the better. Global GPI/capita & GDP/capita 12,000

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This was also the time when in some Western societies, experts started to lose respect. Science became no longer cool. Scientists were no longer worth trusting. Climate change was labeled as a hoax, which scientists have invented just to get federal funding. The history of climate change denial is an unprecedented crusade against science and scientists, evolving in some of the most democratic and civilized countries, and culminating with the election of the last US president. So what role PM really can play? Is this how we should conduct good science in the post-normal age, or are we just inventing all sorts of ways to prop up democracy, still being sure that there is nothing better possible? To what extent PM really helps in solving problems? Or is it just a way to pretend that we can move toward a solution, while already accepting that since problems are “wicked” they are unsolvable? Should we, perhaps, instead of waiting for democracy to overtake China, also learn something from the meritocracy there? PM in China and similar cases can still be useful. Except here stakeholders will be experts, so working with them and facilitating the process may require a set of different skills and attitudes. In this case, a clone of PM known as collaborative modeling (CM) (Basco-Carrera et al. 2017) may turn out to be more appropriate. CM focuses more on the quantitative part of the PM process, when a model is already available and stakeholders are invited to use it to make the right decisions. Normally, experts would be more likely to accept a state-of-the-art science-based model without questioning it validity. They are more likely to trust other experts and therefore using such already available products would be easier. There are some promising tools available to support this, such as OpenGML (Wen et al. 2017; Chen et al. 2020), which can be used to assist experts in reusing existing models as components and running them together.

Conclusion Over the past 50 years, stakeholder participation in decision-making has rapidly advanced drawing experience and methods from a variety of fields, including operations research, systems analysis, computer science, psychology, and behavioral science. The most exciting part of PM is the interaction of mental models of people with what the computer and software can offer. On the one hand, we have the humans involved in the modeling process, with their qualitative, conceptual, cultural, mental models. These models are largely driven by the intuitive, implicit, tacit knowledge, powered by Kahneman’s “system one” or fast type of thinking. Just like humans themselves constantly change and evolve, while acquiring new knowledge, and personal experience, changing priorities, values, party affiliations, sympathies, so do their mental models and ideas about how systems work. On the other hand, we have the quantitative knowledge collected over many years in many other past case studies, formalized in terms of system models and software code and powered by the analytical and computational ability of the computer. These models are the

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embodiment of “system two” or slow type of thinking, driven by data, logic, experience, and expert knowledge. The PM experience is the marriage of the two types of models, two types of thinking. Clearly, there is a gap between the operations of the two systems. In the domain of human interactions, we face processes that are sometimes difficult to quantify and to account for. For example, there is a well-developed practice of developing surveys and questionnaires to explore human perceptions, values, and to understand their role in the overall system performance. However, we should remember that by only administering these surveys, we might be already changing the system. By just asking a question, we may be changing the answer. In physics this is known as the “observer effect”: the act of observation may have an impact on the phenomenon observed. Clearly here we find some very similar effects. By only asking the question about the value of a certain ecosystem function, we are likely to already increase this value, since some people may have never even though about this function as bearing value. People are driven by many biases and heuristics, which have an impact on human responses, judgments, and actions. The world of computer models is way more structured, formalized, static. This is not to say that there is less uncertainty in the observations we make and in model results we generate. But this is a different type of uncertainty. In ecology, hydrology, or biology, there are more “known unknowns,” whereas in social science we are routinely dealing with “unknown unknowns.” The other problem faced when synching the mental and computer models is that the latter are developed, tested, applied, but rarely well documented, and prepared for reuse and further integration with other models. While there is growing interest in developing tools for model integration and reuse, there is still a long way to go before navigation in this space of models will become simple and intuitive enough. In PM, the stakeholders are launched into this space of models, while at the same time we try to enrich the existing models and algorithms with the knowledge and information provided by the stakeholders. So far there are not many tools that can be offered to assist them. We still see that at some point the stakeholder discussions are stopped, the modelers go behind the scenes, and do their magic, translating the results of workshop deliberations into some model codes, which are now no longer understood by the workshop participants. It is not until the model, the computer spews out the model results in form of maps, graphs, or tables that the results can be brought back to the stakeholders. As in integrated modeling, where we are trying to connect, to link various models as components and make them work in concert, exchanging information and updating each other, here we face the challenge of integrating computer models with mental models. The only integration tool that exists so far for this task is the model interface, though rarely built with this purpose in mind. Something is certainly worth looking at and further developing. Participatory modeling has the potential to integrate meaningful input from stakeholders and decision makers into the modeling process. When executed well, it provides an objective, value-neutral place for a diverse group of stakeholders to contribute information regarding an ecosystem of interest. Even more important is

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the flow of information from science toward stakeholders, from theory to practice, and to action. One of the main problems facing society today is our lack of action on some of the crucial issues that have been identified by scientific research, but science fails to communicate the urgency and need for action to the rest of society. This disconnect remains serious and threatening in several contexts that endanger our future (e.g., climate change, biodiversity, etc.) (Voinov and Gaddis 2017). We argue that nowhere else can science and practice come as close together as in the process of participatory modeling. When stakeholders are already involved in the scientific process, as in the PM process, and when scientists are already directly and actively communicating and collaborating with stakeholders, it takes only a few more steps to directly engage in the political and decision-making process. Scientists should not shy away from taking a more proactive role in identifying the most urgent problems, and then making sure that action is taken to implement the solutions they have identified in real life.

Cross-References ▶ Behavioral Considerations in Group Support ▶ Collaboration Engineering for Group Decision and Negotiation ▶ Group Support Systems: Concepts to Practice ▶ Procedural Justice in Group Decision Support ▶ Supporting Community Decisions ▶ Systems Thinking, Mapping, and Group Model Building

References Anjum M, Voinov A, Castilla Rho J, Pileggi SF (2019) Understanding mental models through a moderated framework for serious discussion. In: 23rd international congress on modelling and simulation, Canberra Basco-Carrera L, Warren A, van Beek E, Jonoski A, Giardino A (2017) Collaborative modelling or participatory modelling? A framework for water resources management. Environ Model Softw 91. https://doi.org/10.1016/j.envsoft.2017.01.014 Bell D (2015) Chinese democracy isn’t inevitable. The Atlantic, May 29, 2015. https://www. theatlantic.com/international/archive/2015/05/chinese-democracy-isnt-inevitable/394325/ Chen M, Voinov A, Ames DP, Kettner AJ, Goodall JL, Jakeman AJ, Barton MC, Harpham Q, Cuddy SM, DeLuca C, Yue S, Wang J, Zhang F, Wen Y, Lü G (2020) Position paper: open webdistributed integrated geographic modelling and simulation to enable broader participation and applications. Earth Sci Rev 207:103223. https://doi.org/10.1016/j.earscirev.2020.103223 Forrester JW (1961) Industrial Dynamics. MIT Press, Cambridge, MA. Reprinted by Pegasus Communications Funtowicz S, Ravetz R (1993) Science for the post-normal age. Futures, September, 739–755 Global Times (2017) Man detained for online gripes about hospital’s food. Global Times 9 (2371):11. www.globaltimes.com.cn Glynn PD, Voinov AA, Shapiro CD, White PA (2017) From data to decisions: processing information, biases, and beliefs for improved management of natural resources and environments. Earth’s Future 5:356–378. https://doi.org/10.1002/2016EF000487

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Glynn P, Shapiro CD, Voinov A (2018) Records of engagement and decision tracking for adaptive management and policy development. In: IEEE International Symposium on Technology in Society (ISTAS) proceedings, Washington, DC Gray S, Chan A, Clark D, Jordan R (2012) Modeling the integration of stakeholder knowledge in socialeecological decision-making: benefits and limitations to knowledge diversity. Ecol Modell 229:88e96. https://doi.org/10.1016/j.ecolmodel.2011.09.011 Gray S, Paolisso M, Jordan R, Gray S (2017) Environmental modeling with stakeholders. https:// doi.org/10.1007/978-3-319-25053-3 Hämäläinen RP (2015) Behavioural issues in environmental modelling – the missing perspective. Environ Model Softw 73:244–253. https://doi.org/10.1016/j.envsoft.2015.08.019 Hamalainen RP, Saarinen E, Tormanen J (2018) Systems intelligence: a core competence for nextgeneration engineers? In: 2018 IEEE international conference on teaching, assessment, and learning for engineering (TALE). Presented at the 2018 IEEE international conference on teaching, assessment, and learning for engineering (TALE), IEEE, Wollongong, pp 641–644. https://doi.org/10.1109/TALE.2018.8615247 Janis IL (1972) Victims of group think. Houghton Mifflin, Boston Kahan D (2012) Why we are poles apart on climate change. Nature 488(7411):255. https://doi.org/ 10.1038/488255a. http://www.ncbi.nlm.nih.gov/pubmed/22895298 Kahneman D (2011) Thinking, fast and slow. Farrar, Straus and Giroux, New York Rittel HWJ, Webber MM (1973) Dilemmas in a general theory of planning. Policy Sci 4(2): 155–169 Talberth J, Cobb C, Slattery N (2007) The genuine progress indicator 2006. Redefining Prog, p 31 Voinov A, Bousquet F (2010) Modelling with stakeholders. Environ Model Softw 25(11):1268– 1281. https://doi.org/10.1016/j.envsoft.2010.03.007. http://linkinghub.elsevier.com/retrieve/pii/ S1364815210000538 Voinov A, Gaddis EB (2017) Values in participatory modeling: theory and practice. In: Gray S, Paolisso M, Jordan R, Gray S (eds) Environmental modeling with stakeholders. Springer International Publishing, Cham, pp 47–63. https://doi.org/10.1007/978-3-319-25053-3_3 Voinov A, Kolagani N, McCall MK, Glynn PD, Kragt ME, Ostermann FO, Pierce SA, Ramu P (2016) Modelling with stakeholders – next generation. Environ Model Softw 77:196–220. https://doi.org/10.1016/j.envsoft.2015.11.016 Voinov A, Jenni K, Gray S, Kolagani N, Glynn PD, Bommel P, Prell C, Zellner M, Paolisso M, Jordan R, Sterling E, Schmitt Olabisi L, Giabbanelli PJ, Sun Z, Le Page C, Elsawah S, BenDor TK, Hubacek K, Laursen BK, Jetter A, Basco-Carrera L, Singer A, Young L, Brunacini J, Smajgl A (2018) Tools and methods in participatory modeling: selecting the right tool for the job. Environ Model Softw 109:232–255. https://doi.org/10.1016/j.envsoft.2018.08.028 Wen YN, Chen M, Yue SS, Zheng PB, Peng GQ, Lu GN (2017) A model-service deployment strategy for collaboratively sharing geo-analysis models in an open web environment. Int J Digital Earth 10(4):405–425

Group Decisions: Choosing a Winner by Voting Hannu Nurmi

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lessons of the Classics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voting Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Agenda-Based Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluating Voting Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Profile Analysis Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Some Fundamental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Context Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods for Reaching Consensus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Best Voting System? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Voting is one of several methods for making group decisions. Many voting systems have been developed for seemingly the same purpose, i.e., to find the collective will. The basic motivation for the study of voting systems is the fact that different systems often produce different outcomes when applied to a given set of voter opinions. In some contexts, we are able to single out plausible outcomes, e.g., candidates that – given a distribution of opinions in the electorate – ought to be elected for the system to be called reasonable or democratic in an intuitive sense. Social choice theorists have developed various plausibility criteria for the evaluation of voting systems. The classic paradoxes of social choice are

This is a substantially updated version of Nurmi (2010). H. Nurmi (*) Department of Philosophy, Contemporary History and Political Science, University of Turku, Turku, Finland e-mail: hnurmi@utu.fi © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_11

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presented and commented upon. The most important criteria used in the assessment of voting procedures as well as the most important results in social choice theory are reviewed and explained. The analysis of opinion distributions has motivated a variety of research techniques that have played an important role in the results of voting theory. While voting theorists typically aim at maximal generality of their results, the application of those results in institution design usually takes place under profile restrictions or other contextual specifications. Hence it is worthwhile to augment the general results with the analysis of performance of various voting rules under practically relevant contextual restrictions. Keywords

Group decision · Context for group decision · Voting · Preferences · Preference modeling · Pareto-optimal · Consensus reaching · No-show paradox

Introduction Voting is a very common way of resolving disagreements, determining common opinions, choosing public policies, electing office-holders, finding winners in contests, and solving other problems of amalgamating a set of (typically individual) opinions. Indeed, group decision-making most often involves bargaining (see chapters ▶ “Methods to Analyze Negotiation Processes” and ▶ “Negotiation Process Modelling: From Soft and Tacit to Deliberate”) or voting, or both. Voting can be precisely regulated, like in legislatures, or informal, like when a group of people decide where and how to spend a Sunday afternoon together. The outcome of voting is then deemed as the collective choice made by group. In this chapter we deal with voting procedures aiming at electing a single winning candidate or policy alternative. The methods used to elect a group of candidates – e.g., a committee or an assembly – are discussed in a separate chapter (see chapter ▶ “Group Decisions: Choosing Multiple Winners by Voting,” in this volume. The decision to take a vote is no doubt important, but so are the questions related to the way in which the vote is taken. In other words, the voting procedure to be applied plays an important role as well. In fact, voting rules are as important determinants of the voting outcomes as the individual opinions expressed in voting. An extreme example is one where – for a fixed set of expressed opinions of the voters – the outcome can be any one of the available alternatives depending on the procedure applied. Consider the following example of the election of a department chair. There are six candidates for the post. They are identified as A, B, C, D, E, and F. Altogether 11 electors can participate in the election. Four of them emphasize the scholarly merits of candidates and find that A is most qualified, E next best, followed by C, then F, D, and finally B. Two electors deem the teaching merits as most important and give the preference order BECFDA. The next three electors focus on

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administrative qualifications and suggest the order DCBEFA. Finally, two electors focus on the applicants’ past success in acquiring external funding and conclude that the order of priority is FCDEBA. These views are summarized in Table 1. Suppose now that the voting method is the one-person-one-vote system where every voter can vote for one candidate and the winner is the recipient of the largest number of votes. This is system is also known as the plurality method or first-pastthe-post rule. Assuming that the voters vote according to their preferences expressed in Table 1, the winner is A with four votes. Plurality system is a very common voting rule, but in many single-winner elections, the aim is to elect a candidate supported by at least a half of the electorate. If one candidate gets more than 50% of the votes, he/she/it (hereafter he) is elected. Otherwise those two candidates with largest number of votes face off in the second round of voting. The winner of this round is then declared the winner. In the Table 1 example, since no candidate is supported by six or more voters, the second round candidates are A and D. In the second round, D presumably adds his vote sum by the votes of the four voters whose favorites are not present in the second round. So, D wins by the plurality runoff method. Suppose that the choice problem is looked upon as a pairwise comparison setting so that the procedure is based on how – on the basis of their expressed preferences – the voters would vote in every candidate pair that can be formed, i.e., how they would vote when A is confronted with B, when B is confronted with C, etc. There are several voting methods that are based on such pairwise comparisons of decision alternatives. They differ in how the winner is determined once the pairwise votes – sometimes called duels – have been taken. Most of these methods, however, agree on electing the candidate that beats all other contestants in pairwise majority comparisons, should there be such a candidate. In Table 1 there is: it is E as this candidate would defeat all other candidates by a majority in pairwise comparisons. It is, by definition, then the Condorcet winner. Whenever a Condorcet winner exists, it is unique (otherwise it could not defeat all other candidates). The voting procedures that always elect the Condorcet winner when one exists are called Condorcet extensions or Condorcet consistent procedures. Up to now we have three different winners depending on which rule is adopted in the example of Table 1. However, candidate C can also win if the Borda count is used. This method is based on points assigned to alternatives in accordance with the rank they occupy in individual preference orderings. The lowest rank gives 0 points,

Table 1 Six candidates, six winners

4 voters A E C F D B

2 voters B E C F D A

3 voters D C B E F A

2 voters F C D E B A

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the next to lowest 1 point, the next higher 2 points,..., the highest rank gives k
1 points, if the number of alternatives is k. Summing the points given to each candidate by all voters gives the Borda score of that candidate. In Table 1 the candidate with the largest Borda score is C. It is possible that even B be the winner. Suppose that the approval voting method is adopted (Brams and Fishburn 1983). This method allows each voter to vote for as many candidates as he wishes with the restriction that each candidate can be given either 1 or 0 votes. The winner is the candidate with the largest number of votes. By making the additional assumption that the group of three voters votes for three of their most preferred candidates (i.e., for D, C, and B), while the others vote for only their highest-ranked one, B turns out as the approval voting winner with five approval votes. Also F can become the winner in Table 1 if the range voting method is being applied with some additional ad hoc assumptions. This method is based on scores given to candidates by voters. These are to be selected from a predetermined range of values, say, from 0, indicating the lowest allowed value, to 15 indicating the largest allowable one. The scores given by each voter to each candidate are then summed and the candidate with the highest score is elected. Making the ad hoc assumption that the nine first listed voters assign the candidates values from 0 (the lowest-ranked candidate) to 5 (the highest-ranked one) consistent with their rankings and that the last two voters use the same assignment for their five lowest-ranked candidates assigning their first-ranked F the value 15, candidate F emerges as the range voting winner with the total score sum of 45. So, by varying the rule any candidate can be elected the department chair if the expressed voter opinions are the ones presented in Table 1. Why do we have so many rules which seemingly all aim at the same goal, viz., to single out the choice that is best from the collective point of view? All rules have intuitive justification which presumably has played a central role in their introduction. The plurality and plurality runoff rules look for the candidate that is best in the opinion of more voters than other candidates. In the case of plurality runoff, there is the added constraint that the winner has to be regarded best by at least a half of the electorate. The systems based on pairwise comparisons are typically used in legislatures and other bodies dealing with choices of policy alternatives rather than candidates for offices. The motivation behind the Borda count is to elect the alternative which on the average is positioned higher in the individual rankings than any other alternative. The approval voting, in turn, looks for the alternative that is approved of by more voters than any other candidate. In range voting the voters are given the opportunity to express not only preferences but also the intensity of preference regarding the candidates. This can be seen as defining the utility of each candidate in a given scale of values. The winner is then the candidate that represents the largest utility sum. Table 1 depicts an ordinal preference profile, i.e., a set of preference relations of voters over decision alternatives. In analyzing the outcomes ensuing from this profile when various methods are used, we have made assumptions regarding the voting strategy of the voters. To wit, we have assumed that they vote according to their expressed opinions, i.e., sincerely. Very often the voters vote strategically, i.e.,

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deviate from their true opinions in voting, e.g., when they think that their true favorite has no chance of being elected. In these situations the voters may vote for their best realistic candidate and act as if their true favorite is ranked low in their preference order. Although voting as such is a very important method for group decisions, the study of voting rules can be given another justification, viz., by substituting criteria of performance for voters in settings like Table 1, we can analyze multiple criterion decision-making (MCDM). So, many results of the theory of voting systems are immediately applicable in the MCDM settings chapters ▶ “Multicriteria Methods for Group Decision Processes: An Overview,” ▶ “Multiple Criteria Group Decisions with Partial Information about Preference,” and ▶ “Multiple Criteria Decision Support,” in this volume).

Lessons of the Classics The theory underlying voting systems is known as social choice theory. It has a long but discontinuous history documented and analyzed by McLean and Urken (1995) (see also Tangian (2014)). While contributions have undoubtedly been made in the medieval times (see, e.g., Hägele and Pukelsheim 2008), the first systematic works on voting and social choice were presented in the late eighteenth century. From those times stems also the first controversy regarding choice rules. It arose in the French Royal Academy of Sciences and has survived till modern times. It is therefore appropriate to give a brief account of the contributions of Jean-Charles de Borda and Marquis de Condorcet, the main parties of the controversy. While both were dealing with social choice, the specific institutions focused upon differ somewhat. Borda’s attention was in the election of persons, while Condorcet discussed the jury decision-making setting. Borda was interested in the choices that would best express “the will of the electors,” while Condorcet wanted to maximize the probability that the chosen policy alternative (verdict) is “right.” Condorcet’s probability calculus, however, turned out to be defective and was soon forgotten. Today he is much better known for his paradox and a solution concept. Also Borda’s contribution can be best outlined in terms of a paradox. Since it antedates Condorcet’s writing, we consider it first. Borda’s paradox is a by-product of the criticism that its author directs against the plurality voting system. Table 2 reproduces the illustrative distribution of opinions of 21 voters over 3 candidates – i.e., the preference profile – used by Borda in his presentation in 1770 (De Grazia 1953). In this table, as in Table 1, voters’ ordinal preferences are in descending order. Table 2 Borda’s paradox 1 voter A B C

7 voters A C B

7 voters B C A

6 voters C B A

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The voters are identified by their preferences over three candidates: A, B, and C. Assuming that each voter can vote for one and only one candidate and votes according to his preferences, A will get 8, B 7, and C 6 votes. Hence, A wins by a plurality of votes. Borda’s main point was that A is not a plausible winner. While it receives the plurality of votes, it is not supported by an absolute majority of voters. More importantly, its performance in pairwise comparisons with other candidates is poor: it is defeated by both B and C with a majority of votes in paired comparisons. A is, in modern terminology, the Condorcet loser. Moreover, A is ranked last by an absolute majority of voters. Surely, a candidate defeated by every other candidate in pairwise contests cannot be a plausible winner. This was Borda’s contention. As a solution to the problem exhibited by the paradox, Borda proposed a point counting system or method of marks (a.k.a. the Borda count). This system was described in the preceding section. One of its advantages is, indeed, the fact that it eliminates the Borda paradox, i.e., the Borda count never results in a Condorcet loser. The fact that it does not always result in a Condorcet winner has been viewed as one of its main shortcomings. In the above setting, C is the Condorcet winner. It is also the Borda winner, but – as was just pointed out – it is possible that the Condorcet winner not be elected by the Borda count. The lessons from Borda’s paradox are the following: • There are degrees of detail in expressing individual opinions and using this information for making social choices. These are important determinants of choices. • There are several intuitive concepts of winning, e.g., pairwise and positional. • These concepts are not necessarily compatible. Even within these categories, i.e., among pairwise and positional conceptions, there are incompatible views of winning. • If an absolute majority agrees on a highest-ranked alternative, both pairwise and plurality winners coincide. • The Borda count is profoundly different in not necessarily choosing the alternative ranked first by an absolute majority. The first lesson pertains to the fact that while plurality voting requires only a minimal amount of information on voter opinions, there are methods, notably the Borda count, that are able to utilize richer forms of expressing opinions. This observation thus poses the question of the “right” form of expressing opinions. The second lesson points to the central observation in Borda’s paradox, viz., “winning” may mean different things to different observers. The view underlying the plurality voting according to which the most frequently first-ranked candidate is the winner is clearly a positional view, but a very limited one: it looks only at the distribution of first preferences over candidates. The Borda count is also based on a positional view of winning: to win one has to occupy higher positions, on the average, than the other candidates. The third lesson suggests that some methods of both pairwise and plurality variety agree – i.e., come up with an identical choice – when more than 50% of

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the voters have the same candidate ranked first. This may explain the absolute majority requirement often imposed on winners in presidential elections. The fourth lesson says that Borda’ proposal differs from many other voting systems in not necessarily electing a candidate that is first-ranked by an absolute majority of voters. Indeed, when the number of candidates is larger than the number of voters, the Borda count may not elect a candidate that is first-ranked by all but one voter. Depending on one’s view on the importance of protecting minority interests, this feature can be regarded as a virtue or vice (see Baharad and Nitzan 2002). The discrepancies among positional procedures can take extreme forms, as shown by Donald G. Saari (1992). Consider the following profile. Let vote-for-m denote a voting procedure where each voter can vote for precisely m candidates and the candidate with the largest vote sum is the winner. In the profile depicted in Table 3, the plurality winner is A, vote-for-two winner is B, vote-forthree winner is C, and the Borda winner is D. More generally, Saari has proven the following theorem. Theorem 1 Saari 1992. Consider the alternative set c1, . . ., cK of at least three elements. Then such a profile exists that alternative cj wins when the voting rule is vote-for-j and this holds for j = 1, . . ., K
1. Moreover, cK is the Borda winner. Somewhat similar – albeit not quite so extreme – discrepancies can be encountered among pairwise procedures as well. Consider Table 4 and three Condorcet extensions: Copeland’s rule, Dodgson’s method, and max-min procedure. The first mentioned elects the candidate that in pairwise majority comparisons defeats more candidates than any other candidate. Dodgson’s method elects the candidate that can be made the Condorcet winner through the smallest number of binary preference switches in individual rankings. The max-min procedure elects the candidate whose minimum support in all pairwise comparisons is larger than that of any other candidate. In Table 4 Copeland’s rule results in a three-way tie between A, B, and C. Each of these defeats two others in pairwise majority comparisons. Table 3 Discrepancy among positional procedures

2 voters A B C D

Table 4 Discrepancy among some Condorcet extensions

10 voters D A B C

2 voters A D C B

7 voters B C A D

2 voters C B D A

1 voter B A C D

7 voters C A B D

3 voters D B C A

4 voters D C A B

420 Table 5 Condorcet’s paradox

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1 voter A B C

1 voter B C A

1 voter C A B

Dodgson’s method yields D as the winner since lifting D from the last rank to the top of one voter’s preference ranking requires only three binary preference switches, while all other candidates require more such switches to become the Condorcet winner. Furthermore, D has the minimum support of 14 in all pairwise comparisons which is the highest minimum. Thus, it is also the max-min winner. Table 4 reveals a somewhat counterintuitive possibility: Dodgson’s method and the max-min procedure may lead to the choice of a Condorcet loser. Condorcet’s paradox is better known than Borda’s. In the literature it is sometimes called the voting paradox, simpliciter. Given the large number of various kinds of paradoxes related to voting, it is, however, preferable to call it Condorcet’s paradox. In its purest version, it takes the form of Table 5. Suppose that we compare the candidates in pairs according to an exogenously determined list (agenda) so that the winner of each comparison survives while the loser is eliminated.1 For all alternatives to be present in at least one pairwise comparison, one needs at least k
1 comparisons, if the number of alternatives is k. Hence, we need to conduct two paired comparisons in the three-alternative case. Suppose that the agenda is (i) A versus B and (ii) the winner of (i) versus C. The winner of (ii) is the overall winner. We notice that just two out of all three possible pairwise comparisons are performed. The method is based on the (in general erroneous) assumption that whichever alternative defeats the winner of an earlier pairwise comparison also defeats the loser of it. If the voters vote sincerely, A will win in (i) and C in (ii). C thus becomes the overall winner. Suppose, however, that C were confronted with the loser of (i), i.e., B. The winner of this hypothetical comparison would B. Prima facie, it could be argued that since it (B) would defeat the former winner C, it is the “real” winner. However, this argument overlooks the fact that there is a candidate that defeats B, viz., A. But not even A can be regarded as the true winner as it is beaten by C. So, no matter which candidate is picked as the winner, there is another candidate that defeats it. The lessons of Condorcet’s paradox are the following: • The winner of the pairwise comparison sequence depends on the agenda. More precisely, any candidate can be rendered the winner of the procedure if one has full control over the agenda.

1

In the theory of voting, the concept of agenda refers to the order in which various policy proposals or candidates are voted upon. The notion is thus more specific than the agenda concept appearing in such expressions as “the European Union has a hidden agenda,” “what do we have on the agenda today,” etc.

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• The paradox implicitly assumes complete voter myopia. In other words, in each pairwise comparison, every voter is assumed to vote for whichever candidate he prefers to the other one. • Splitting rankings into pairwise components entails losing important information about preferences. The first lesson pertains to the importance of agenda-setting power in certain types of preference profiles. When the preferences of voters form a Condorcet paradox, any alternative can be made the winner with suitable adjustment of the agenda of pairwise votes. The second lesson points out an important underlying assumption, viz., the voters are assumed to vote at each stage of procedure for the candidate that is preferable. For example, one assumes that the voter with preference ranking ABC will vote for A in the first pairwise vote between A and B because he prefers A to B. Yet, it might make sense for him to vote for B if he knows the entire preference profile as well as the agenda. For then he also knows that whichever candidate wins the first ballot will confront C in the second one. If this voter wishes to avoid C (his last-ranked candidate) being elected, he should vote for B in the first ballot since B will definitely be supported by the second voter in the ballot against C. So, complete agenda control is possible only if the voters are myopic. In other words, strategic voting may be an antidote against agenda manipulation. The third lesson has been emphasized by Saari (1995, p. 87–88). If the voters are assumed to possess rankings over candidates, it makes no sense to split these rankings into pairs ignoring all the rest of the preference information. Given what we know about the preference profile, a tie of all three alternatives is the only reasonable outcome (assuming that we do not wish to discriminate for or against any candidate or voter). After all, each alternative is ranked first, second, and third by equally many voters. There is no way of making a difference between them other than discriminating for or against some alternative or some voters. The Condorcet paradox emerges not only in cases where the voters submit consistent (i.e., complete and transitive) preference rankings, but it can also pop up in settings where none of the voters has a consistent ranking. In the latter case, the word “paradox” is hardly warranted since no one expects collective preferences to be consistent if all individual preferences are inconsistent. The two classic voting paradoxes have some joint lessons as well. Firstly, they tell us what can happen, not what will necessarily, often, or very rarely happen. Secondly, there are limits in what one can expect from voting institutions in terms of performance. More specifically, the fact that one resorts to a neutral and anonymous procedure – such as plurality voting or the Borda count – does not guarantee that the voting outcomes would always reflect the voter opinions in a natural way. Thirdly, the fact that strategic voting may avoid some disastrous voting outcomes poses the question of whether the voters are (or should be) instrumentally rational (and resort to strategic or sophisticated voting) or wish to convey their opinions in voting (expressive or naïve voting).

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All these issues have been dealt with in the extensive social choice literature of our time. Probability models and computer simulations have been resorted to in order to find out the likelihood of various types of paradoxes (see, e.g., Gehrlein and Lepelley (2017)). The performance criteria for voting procedures have also been dealt with (see, e.g., Felsenthal and Nurmi (2018); Nurmi (1987)). The issue of strategic vs. sincere voting has been in the focus ever since the path-breaking monograph of Farquharson (1969). So, the classic voting paradoxes have been instrumental in the development of the modern social choice theory.

Voting Procedures There is a wide variety of group decision contexts where voting is resorted to, but a basic distinction can be made between settings where a single candidate is to be elected and those where a policy alternative is to be chosen. In addition, there are settings where one looks for a collectively most acceptable ranking over (all or the top-ranked) candidates or a set of collectively best candidates (see chapter ▶ “Group Decisions: Choosing Multiple Winners by Voting,” in this volume). The bulk of voting theory deals with systems resulting in the choice of one candidate or alternative. These are called single-winner voting systems.2 A large number of such systems exist today. They can be classified in many ways, but perhaps the most straightforward one is to distinguish between binary and positional systems. The former are based on pairwise comparisons of alternatives, whereas the latter aim at choosing the candidate that is better – in some specific sense – positioned in the voters’ preferences than other candidates. These two classes do not, however, exhaust all systems. Many systems contain both binary and positional elements or consist of repeated applications of a voting rule. We shall call these hybrid ones. Examples of binary systems are Dodgson’s method, Copeland’s rule, and maxmin method. These were described above. Another binary system is Kemeny’s median (Kemeny 1959). It works as follows. Given a profile of preferences over k alternatives, one first generates all k! conceivable strict preference rankings and compares the support that each one of them has in the profile. The support is obtained by decomposing the generated ranking into pairs and tallying the number of individuals whose ranking of the pair coincides with that of the generated ranking. The generated ranking with the largest support is the Kemeny ranking, and its first alternative is the Kemeny winner. For example, in Table 2 the Kemeny ranking is CBA with the support of 39. Thus, the Kemeny winner is C. Of positional systems we have already discussed two, viz., the plurality system and the Borda count. Also approval voting can be deemed a positional system.

2 A more extensive description of the procedures can be found in, e.g., Felsenthal and Nurmi (2018, Ch. 3).

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Of hybrid systems the best-known is undoubtedly the plurality runoff. It is a mixture of plurality voting and binary comparison. Obviously, this system can be implemented in one round of balloting if the voters submit their full preference rankings in one go. Another known hybrid system is single transferable vote. Its single-winner variant is called Hare’s system. It is based on similar principles as the plurality runoff system. The winner is the candidate ranked first by more than a half of the electorate. If no such candidate exists, Hare’s system eliminates the candidate with the smallest number of first ranks and considers those candidates ranked second in the ballots with the eliminated candidate ranked first as first-ranked. If a candidate now has more than half of the first ranks, he is elected. Otherwise, the elimination continues until a winner is found. A variation of Hare’s method is Coombs’ procedure. It is otherwise similar to the former, but instead of eliminating the alternative with the smallest number of first ranks, it eliminates the candidate with the largest number of last ranks. As in Hare’s method, the winner of Coombs’ procedure is the alternative that is ranked first by more than 50% of the voters. These are but a sample of the voting systems considered in the literature (for a more extensive listing, see, e.g., Felsenthal and Nurmi (2018)). They can all be implemented once the preference profile is given (in the case of approval voting, one also needs the cutoff point indicating which alternatives in the ranking are above the acceptance level). In a way, one may assume that all alternatives or candidates are being considered simultaneously. There are other systems in which this is not the case, but only a proper subset of alternatives is being considered at any given stage of the procedure. There are also procedures that cannot be implemented on the basis of just the preference rankings. The range voting was already described above. Another procedure of this nature is the majority judgment devised by Balinski and Laraki (2011). It is based on the ordinal scaled values that each voter assigns to each alternative. When all grades have been submitted, the median grade of each alternative is determined, and the alternative with the highest median grade is declared the winner. We illustrate this procedure in Table 6 where the grades assigned by 21 voters to 3 alternatives are consistent with the rankings of Table 2 so that grades range from a (the lowest) to h (the highest). The median grades thus obtained yield the ranking BAC which differs from the Kemeny and Borda rankings. Also the winner is different from that ensuing from the Borda count and Kemeny’s median. Finally, it is worth observing that the Condorcet winner, C, is ranked last by the majority judgment procedure.

Table 6 Majority judgment does not elect the Condorcet winner

A B C

1 voter e d b

7 voters h a b

7 voters b g c

6 voters f g h

Median grade f g c

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Agenda-Based Systems It can be argued that all balloting is preceded by an agenda-formation process. In political elections, it is often the task of the political parties to suggest candidates. In committee decisions the agenda-building is typically preceded by a discussion in the course of which various parties make proposals for the policy to be adopted or candidates for offices. By agenda-based procedures, one usually refers to committee procedures where the agenda is explicitly decided upon after the decision alternatives are known. Typical settings of agenda-based procedures are parliaments and committees. Two procedures stand out among the agenda-based systems: (i) the amendment and (ii) the successive procedure. Both are widely used in contemporary parliaments. Similarly as the amendment procedure, the successive procedure is based on pairwise comparisons, but so that at each stage of the procedure an alternative is confronted with all the remaining alternatives. If it is voted upon by a majority, it is elected and the process is terminated. Otherwise this alternative is set aside and the next one is confronted with all the remaining alternatives. Again the majority decides whether this alternative is elected and the process terminated or whether the next alternative is picked up for the next vote. Eventually one alternative gets the majority support and is elected. Figure 1 shows an example of a successive agenda where the order of alternatives to be voted upon is A, C, B, and D. Whether this sequence will be followed through depends on the outcomes of the ballots. In general, the maximum number of ballots taken of k alternatives is k
1. Fig. 1 The successive agenda

the rest A

the rest C B Fig. 2 The amendment agenda

D

y

x

x x

y

z z

y

z z

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The amendment procedure confronts alternatives with each other in pairs so that in each ballot two separate alternatives are compared. Whichever gets the majority of votes proceeds to the next ballot, while the loser is set aside. Figure 2 shows an example of an amendment agenda over three alternatives: x, y, and z. According to the agenda, alternatives x and y are first compared and the winner is faced with z on the second ballot. Both the amendment and successive procedure are very agenda-sensitive systems. In other words, two agendas may produce different outcomes even though the underlying preference rankings of voters and their voting behavior remain the same. Under sincere voting – whereby for all alternatives x and y the voter always votes for x if he prefers x to y and vice versa – Condorcet’s paradox provides an example: of the three alternatives any one can be rendered the winner depending on the agenda. To determine the outcomes – even under sincere voting – of successive procedure requires assumptions regarding voter preferences over subsets of alternatives. Under the assumption that the voters always vote for the subset of alternatives that contains their first-ranked alternative, the successive procedure is also vulnerable to agenda manipulation.

Evaluating Voting Systems The existence of a large number of voting systems suggests that people in different times and places have had somewhat different intuitive notions of how the collective choices should be made. Or they may have wanted to put emphasis on somewhat different aspects of the choice process. The binary systems have, overall, tended to emphasize that the eventual Condorcet winners be elected. An exception to this is the successive procedure which can be regarded as a binary system, albeit one where an alternative is compared with a set of alternatives. Assuming that the voters vote for the set which contains their highest-ranked alternative, it may happen that the Condorcet winner is voted down in the early phases of the process. Also positional voting systems, e.g., plurality voting and the Borda count, may fail to elect a Condorcet winner. A strong version of the Condorcet winner criterion requires that an eventual strong Condorcet winner is elected. A strong Condorcet winner is an alternative that is ranked first by more than half of the electorate. A large majority of the systems considered here satisfies this criterion. The only exceptions are the Borda count and approval voting. This is shown by Table 7 where A is the strong Condorcet winner. However, B’s Borda score is largest. B is also elected by approval voting under Table 7 Borda count and approval voting vs. strong Condorcet winner

7 voters A B C

4 voters B C A

426 Table 8 Fishburn’s example

H. Nurmi

1 voter D E A B C

1 voter E A C B D

1 voter C D E A B

1 voter D E B C A

1 voter E B A D C

the additional assumption that all voters approve of their two topmost-ranked alternatives (or the four-voter group approves B only). Electing the Condorcet winner has often been deemed a desirable property of voting systems. Profile component analysis results by Saari as well as a counterexample of Fishburn have, however, cast doubt on the plausibility of this criterion as a general determinant of choice (Saari 2003; Fishburn 1973). Fishburn’s example is reproduced in Table 8. Here the Borda winner E seems more plausible choice than the Condorcet winner D since the former has equally many first ranks as D, strictly more second and third ranks and no voter ranks it worse than third, whereas D is ranked next to last by one voter and last by one voter. Another criterion associated with Condorcet’s name is the Condorcet loser one. It requires that an eventual Condorcet loser be excluded from the choice set. This criterion is generally accepted as plausible constraint on social choices. These two are but examples of criteria to be found in the literature. Another criterion that many find compelling is monotonicity. It says that additional support should never harm a candidate’s chances of getting elected. To state this requirement more precisely, consider a preference profile P consisting of rankings of n voters over the set X of k candidates. Suppose that voting rule f is applied to this profile and that candidate x is the winner. That is: f ðP, XÞ ¼ x Suppose now that another profile P0 is formed so that x‘s position is improved in at least one individual ranking, but no other changes are made in P. The method f is monotonic if f ðP0 , XÞ ¼ x: While many voting systems – e.g., plurality voting and Borda Count – are monotonic, there are commonly used procedures that are non-monotonic, e.g., plurality runoff and single transferable vote. Their failure on monotonicity is exhibited in Table 9. Here A and B will face each other in the second round, whereupon A wins. Suppose now that A had somewhat more support to start with so that the two rightmost voters had the preference ranking ABC instead of BAC. In this new profile, A confronts C in the second round, where the latter wins. The same result is obtained using Hare’s system since with three alternatives it is equivalent with plurality runoff.

Group Decisions: Choosing a Winner by Voting Table 9 Nonmonotonicity of plurality runoff and STV

6 voters A B C

5 voters C A B

427 4 voters B C A

2 voters B A C

Upon closer inspection monotonicity takes on several different forms. As above it may be related to changes in preference profiles in a fixed electorate, but it may also apply to changes that include varying the electorate by adding new voters or removing some voters in specific ways. Thus we can distinguish between monotonicity in fixed and variable electorates. In variable electorates monotonicity means that a group of identically minded voters never benefits from abstaining rather than voting according to its preferences. In other words, voting never harms a voter. This is known as the principle of participation. Occasions where voting may be harmful – in the sense of leading to a worse outcome – for a group of identically minded voters are known as no-show paradoxes. They take on two “directions.” (i) Abstaining, ceteris paribus, may yield an outcome that is better for the abstainers than the outcome resulting from their voting. This can be called the upward monotonicity failure (Miller 2017). This is what Fishburn and Brams (1983) in their pioneering article call more-is-less paradox. (ii) Another direction pertains to situations where a group of identically minded voters may change the outcome from x to y by abstaining, ceteris paribus, where x is their last-ranked alternative while y is some other alternative that is ranked higher by the group. In other words, by voting according to its preferences, ceteris paribus, the group brings about their worst outcome, while by abstaining something better would have been the outcome. This is called downward monotonicity failure. Fishburn and Brams (1983) call it the no-show paradox.3 Both (i) and (ii) are thus violations of the principle of participation. Pareto criterion is quite commonplace in economics, but it has an important place in the theory of voting as well. In this context it is phrased as follows: if every voter strictly prefers alternative x to alternative y, then y is not the social choice. Most voting systems satisfy this plausible requirement, but notably the agendabased ones do not. Pareto violations of the amendment and approval voting have been shown, e.g., in Nurmi (1987, p. 86–87). An instance of Pareto violation of the successive procedure can be seen by applying the successive agenda of Fig. 1 to the profile of Table 10, where B will be elected even though everyone prefers A to B. Another criterion of considerable intuitive appeal is consistency. It concerns choices made by subsets of voters. Let the voter set N and profile P be partitioned into N1 and N2, with preference profiles P1 and P2, respectively. Let F(X, Pi) denote

3

For further distinctions among monotonicity-related paradoxes, see Felsenthal and Tideman (2013) as well as Felsenthal and Nurmi (2017) and Felsenthal and Nurmi (2019).

428 Table 10 Pareto violation of successive procedure under agenda of Fig. 1

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1 voter A B C D

1 voter1 C A B D

1 voter D A B C

the choice set of Ni with i = 1, 2. Suppose now that some of the winning alternatives in N1 are also winning in N2, that is, F(X, P1) \ F(X, P2) 6¼ 0/. Consistency now requires that F(X, P1) \ F(X, P2) = F(X, P). In words, if the subgroups elect same alternatives, these should be also chosen by the group at large. Despite its intuitive plausibility, consistency is not common among voting systems. Of the systems discussed here, only plurality, Borda count, range voting and approval voting are consistent. Even more rare is the property called Chernoff (a.k.a. property α, heritage, or subset choice condition). It states that, given a profile and a set X of alternatives, if an alternative, say x, is the winner in X, it should be the winner in every proper subset of X it belongs to. This property characterizes only approval voting, range voting and majority judgment. A summary evaluation of the voting systems introduced above is presented in Table 11.4 The evaluation is based on several assumptions: 1. The voters vote according to their preferences, i.e., the profiles dealt with are the reported ones (leaving the question of “true preferences” aside). 2. The amendment and successive procedures are evaluated assuming fixed agenda. 3. In evaluating the approval voting, it is assumed that the acceptability of an alternative remains the same regardless of the availability of other alternatives. 4. In evaluating range voting and majority judgment, it is assumed that any grade assignment consistent with a given preference ranking is possible.

Profile Analysis Techniques The standard starting point in social choice theory is the preference profile, i.e., a set of complete and transitive preference relations – one for each voter – over a set of alternatives. Under certain behavioral assumptions, these profiles together with the voting rule determine the set of chosen alternatives. In the preceding the behavioral assumption has been that the voters vote according to their preferences at each stage of the process. This assumption is not always plausible, but can be justified as benchmark for voting system evaluations. Moreover, it is useful in extending the 4

Y (N, respectively) in the table means that the desideratum represented by the column is satisfied (not satisfied) by the procedure represented by the row. For an evaluation of 20 procedures in terms of a more extensive set of criteria, see Felsenthal and Nurmi (2018).

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Table 11 Summary evaluation of some voting systems Voting system Amendment Successive Copeland Dodgson Max-min Plurality Borda Approval Black Plurality runoff Nanson Hare Coombs Range voting Majority judgment

Criteria a Y N Y Y Y N N N Y N Y N N N N

b Y Y Y N N N Y N Y Y Y Y Y N N

c Y Y Y Y Y Y N N Y Y Y Y Y N N

d Y Y Y N Y Y Y Y Y N N N N Y Y

e N N Y Y Y Y Y N Y Y Y Y Y Y Y

f N N N N N Y Y Y N N N N N Y N

g N N N N N N N Y N N N N N Y Y

a Condorcet winner, b Condorcet loser, c majority winning, d monotonicity, e Pareto, f consistency, and g Chernoff

results to multi-criterion decision-making (MCDM) and/or in applying the MCDM results (see chapter ▶ “Multicriteria Methods for Group Decision Processes: An Overview”). To translate the voting results into MCDM, one simply substitutes “criteria” for “voters.” The assumption that voting takes place according to preferences (or performance rankings in MCDM) is then most natural. Several descriptive techniques have been devised for the analysis of preference profiles. The outranking matrix is one of them. Given a profile of preferences over k alternatives, the outranking matrix is a k  k matrix, where the entry on the ith row and jth column equals the number of voters preferring the ith alternative to the jth one. Ignoring the diagonal entries, the Borda scores of alternatives can now obtained as row sums so that the sum of all non-diagonal entries on the ith row is the Borda score of the ith alternative. From the outranking matrix, one can form the tournament (a.k.a. dominance) one by placing 1 in ith row and jth column if the ith alternative beats the jth one. Otherwise, the entry equals zero. From the tournament matrix one can directly spot an eventual Condorcet winner: it is the alternative that corresponds the row where all non-diagonal entries are 1s. Similarly, the Condorcet loser is the alternative represented by a row in the tournament matrix with all non-diagonal entries equal to zero. In the preceding we have assumed that the voters vote sincerely at each stage of the process. There are, however, contexts in which it is plausible to expect that voters vote strategically in the sense of trying to achieve as good an end result as possible even though that would imply voting in a way that differs from the voter’s preferences. This often happens in plurality or plurality runoff systems if the voters have

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some information about the distribution of the support of various candidates. Voting for a “lesser evil” rather than for one’s favorite may be quite plausible for the supporters of candidates with very slim chances of getting elected. The analysis of strategic or sophisticated voting based on the elimination of dominated voting strategies in binary agendas was started by Dummett and Farquharson (1961, see also Farquharson 1969). The goal was to predict the voting outcomes starting from a preference profile and voting rule under the assumption of strategic voting. The method of eliminating dominated strategies is somewhat cumbersome. For binary voting systems, McKelvey and Niemi (1978) have suggested a backward induction procedure whereby the sophisticated voting strategies can be easily determined, if the preference profile is known to all voters (see also Shepsle and Weingast 1984). Given an agenda of pairwise votes, the procedure starts from the final nodes of the voting tree and replaces them with their strategic equivalents. These are the alternatives that win the last pairwise comparisons. In Fig. 2, we have two final nodes: one that represents the x vs. z comparison and the other representing the y vs. z comparison. Since the profile is known, we can predict what will be the outcome of these final votes as at this stage the voters have no reason not to vote sincerely. We can thus replace the left-hand (right-hand, respectively) final node with x or z (y or z) depending on which one wins this comparison under sincere voting. What we have left, then, is the initial node followed by two possible outcomes. By the same argument as we just presented, we now predict that the voters vote according to their preferences in this initial node whereupon we know the sophisticated voting strategy of each voter. The same backward induction method can be used for successive procedure, i.e., in settings where the agenda (e.g., Fig. 1) and the preference profile are known. The McKelvey-Niemi algorithm is agenda-based. A more general approach to determining the outcomes resulting from strategic voting is to look for the uncovered alternatives (Miller 1980). Given a preference profile, we define the relation of covering as follows: alternative x covers alternative y if the former defeats the latter in pairwise contest and, moreover, x defeats all those alternatives that y defeats. It is clear that a covered alternative cannot be the sophisticated voting winner since no matter what alternative it is confronted with in the final comparison, it will be defeated. Hence, the set of uncovered alternatives includes the set of sophisticated voting winners. Miller (1980) has shown that for any alternative x in X, any alternative y in the uncovered set either defeats x or there is an alternative z which (i) is defeated by y, and (ii) defeats x. This suggests the use of the outranking matrix and its square to identify the uncovered set (Banks 1985): T ¼ U þ U2 where U the tournament matrix. When the number of alternatives is k, this is a k  k matrix of 0s and 1s such that whenever the entry on the ith row and jth column is 1, indicating that the ith alternative beats the jth one, the entry on the jth row and ith

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column is 0, i.e., the jth alternative loses to the ith one. The alternatives represented by rows in T where all non-diagonal entries are non-zero form the uncovered set. The uncovered set contains all sophisticated voting outcomes, but is too inclusive. In other words, there may be uncovered alternatives that are not sophisticated voting outcomes under any conceivable agenda. A precise characterization of the sophisticated voting outcomes has been given by Banks (1985). It is based on Banks chains. Given any alternative x and preference profile, the Banks chain is formed by first finding another alternative, say x1, that defeats x. If no such x1 exists, we are done and the end point of the Banks chain is x. If it does exist, one looks for a third alternative, say x2, that defeats x and x1. Continuing in this manner we eventually reach a stage where no such alternative can be found that defeats all its predecessors. The last alternative found is called a Banks alternative, i.e., it is the end point of a Banks chain beginning from x. The Banks set consists of all Banks alternatives. In other words, the set of all sophisticated voting outcomes can be found by forming all possible Banks chains and considering their end points. In contrast to the uncovered set, there are no efficient algorithms for computing the Banks set.

Some Fundamental Results No account of voting procedures can ignore the many – mostly negative – results achieved in the social choice theory over the last five decades. Voting procedures are, in fact, specific implementation devices of abstract social choice functions. The notoriously negative nature of some of the main theorems stems from the incompatibility of various desiderata demonstrated by them. The results stated in the following are but a small and biased sample. The best-known incompatibility result is Arrow’s impossibility theorem (Arrow 1963). It deals with social welfare functions. These are rules defined for preference profiles over alternatives. For each profile, the rules specify the social preference relation over the alternatives. In other words, a social welfare function is denoted by f : R1  . . .  Rn ! R, where the Ri denotes the set of all possible complete and transitive preference relations of individual i, while R is the set of all complete and transitive social preference relations. The most common version of the theorem is: Theorem 2 (Arrow 1963). The following conditions imposed on f are incompatible: • Universal domain: f is defined for all n-tuples of individual preferences. • Pareto: if all individuals prefer alternative x to alternative y, so does the collectivity, i.e., x will be ranked at least as high as y in the social preference relation. • Independence of irrelevant alternatives: the social preference between x and y depends on the individual preferences between x and y only. • Non-dictatorship: there is no individual whose preference determines the social preference between all pairs of alternatives.

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This result has given rise to a voluminous literature and can be regarded as the starting point of the axiomatic social choice theory (see, e.g., Kelly 1978). Yet, its relevance for voting procedures is limited. One of its conditions is violated by nearly all of them, viz., the independence of irrelevant alternatives.5 So, in practice this condition has not been deemed indispensable. There are systems that violate Pareto as well, e.g., the amendment and successive procedures. Another prima facie dramatic incompatibility result is due to Gibbard (1973) and Satterthwaite (1975). It deals with a special class of social choice functions called social decision functions. While the social choice rules specify a choice set for any profile and any set of alternatives, the social decision functions impose the additional requirement that the choice set be singleton valued. In other words, a single winner is determined for each profile and alternative set. The property focused upon by the Gibbard-Satterthwaite theorem is called manipulability. To define this concept, we need the concept of a situation. It is a pair (X, P) where X is a set of alternatives and P is a preference profile. The social choice function F is manipulable by individual i in situation (X, P) if F(X, P0) is preferred to F(X, P) by individual i and the only difference between P and P0 is i‘s preference relation. Intuitively, if i‘s true preference ranking were the one included in P, he can improve the outcome by acting as if his preference were the one included in P0. A case in point is plurality voting where voters whose favorites have no chance of winning act as if their favorite were one of the “realistic” contestants. The theorem says the following: Theorem 3 (Gibbard 1973; Satterthwaite 1975). All universal and non-trivial social decision functions are either manipulable or dictatorial. A non-trivial choice function is such that for any alternative, a profile can be constructed so that this alternative will be chosen by the function. In other words, no alternative is so strongly discriminated against that it will not be elected under any profile. Universal decision functions are defined for all possible preference profiles. This theorem sounds more dramatic than it is mainly because it pertains to rules that are not common. After all, nearly all voting procedures may result in a tie between two or more alternatives. That means that these procedures are not social decision functions. Nonetheless, all voting procedures discussed in the preceding can be shown to be manipulable. Somewhat less known is the theorem that shows the incompatibility of two commonly mentioned desiderata. One of them is the Condorcet winning criterion discussed above. The other is defined in terms of the no-show paradox (Fishburn and Brams 1983). This paradox occurs whenever a voter or a group of voters with

5

The exceptions are range voting and majority judgment which both are independent of irrelevant alternatives. They are also based on somewhat non-standard voter input, viz., not just rankings, but grade values of alternatives are required.

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identical preference rankings would receive a better outcome by not voting at all than by voting according to their preferences. Theorem 4 (Moulin 1988). All procedures that satisfy the Condorcet winning criterion are vulnerable to the no-show paradox. These three theorems are representatives of a wide class of incompatibility results that have been proven about various desiderata on voting and, more generally, choice methods.

Context Effects One of the common features in the above results is their general nature: the incompatibilities envisaged hold when one imposes no restrictions on the types of preference profiles. That means that in order to establish such an incompatibility between various social choice desiderata, all one needs to find is a single profile where the choices allowed for by the desiderata are incompatible. From the practical viewpoint, this prompts a question of relevance: do those profile types that one expects to encounter in practice exhibit these incompatibilities? In other words, are the group decision contexts typically of the kind that the incompatibility results pertain to? For example, if the results are proven using profiles where cyclic majorities are present, is it likely that the group decision settings of interest typically exhibit cyclic majorities or is it likely that a Condorcet winner exists? This issue was dealt with even before the earliest of the above results, Arrow’s theorem, saw the light of day, viz., Black (1948) introduced the concept of single-peakedness a few years before Arrow’s dissertation. As the name suggests, a profile of preferences over three alternatives is single-peaked if the alternatives can be arranged along a horizontal axis so that the utility curves representing the preferences have one and only one maximum value. Black showed that if an arrangement of alternatives can be found so that all triples of alternatives exhibit simultaneously single-peaked preferences, then the pairwise majority comparison method leads to a complete and transitive collective preference relation. The upshot is then that to the extent we can expect the profiles to satisfy the single-peakedness condition, we can expect the pairwise majority comparison to lead to a stable outcome. Decisions are, however, seldom one-dimensional and the conditions for singlepeakedness are pretty stringent in multiple-dimensional settings. Hence, other profile restrictions are worth examining. One such restriction characterizes the Condorcet domains, i.e., profiles where a Condorcet winner exists. Given the important result of Moulin on the incompatibility of Condorcet consistency and invulnerability to the no-show paradox, it is of interest to find out whether the no-show paradoxes can also occur in Condorcet domains. In other words, are the Condorcet extensions vulnerable to no-show paradoxes also in the domains where the initial profile is apparently stable in the sense of containing a Condorcet winner? This question has been recently approached by Felsenthal and Nurmi (2019). These authors compare the

434 Table 12 Kemeny’s median and the no-show paradox

H. Nurmi

5 voters D B C A

3 voters A D C B

3 voters A D B C

Condorcet extensions – which by definition elect the Condorcet winner in the initial Condorcet domain – with other procedures under the restriction that the initial profile contains a Condorcet winner and this alternative is also elected. The motivation for this analysis is the idea that if one can assume that the profiles typically encountered contain the Condorcet winner and if the Condorcet extensions avoid vulnerability in those domains, then Moulin’s result is less damaging for these procedures. More specifically, if the existence of a Condorcet winner would preclude the possibility of a no-show paradox, then Moulin’s theorem would lose some of its bite for Condorcet extensions. Alas, this is not the case. For most Condorcet extensions, the existence of a Condorcet winner does not rule out the possibility of a no-show paradox (Felsenthal and Nurmi 2017, p. 83). Table 12 illustrates the possibility of the no-show paradox when the procedure examined is Kemeny’s median and the initial profile contains a Condorcet winner which is elected by virtue of the fact that Kemeny’s median is a Condorcet extension (Felsenthal and Nurmi 2017, p. 77–78). In Table 12 A is the Condorcet and, thus, Kemeny’s median winner. Suppose now that a group of four voters with a preference ranking BCAD joins the electorate. In the ensuing 15-voter profile, Kemeny’s median ranking is DBCA. Hence, by joining the electorate, ceteris paribus, the four voters bring about their worst outcome, while by abstaining they would have guaranteed a better outcome.

Methods for Reaching Consensus The existence of a multitude of voting methods for reaching an apparently identical result – singling out the collective preference relation – is puzzling, given the fact that the methods are non-equivalent. The reasons for their invention and adoption are difficult if not impossible to ascertain. It can be argued, however, that there is a common ground underlying the methods, viz., an idea of a consensus state accompanied with a measure that indicates how far any given situation is from the consensus state. Moreover, it is arguable that each method is based on the idea of minimizing the distance – measured in some specific way – between the prevailing preference profile and the postulated consensus state. If this idea of the common ground is accepted, it becomes possible to understand the multitude of the methods by referring to differences of opinions concerning the consensus states as well as measures used in the distance minimization process. In general group decision contexts as opposed to strictly power-related elections, the kind of consensus sought

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for is typically quite important since the degree of disagreement over the outcomes often gives clues regarding the possibilities for future cooperation. Indeed, there is a method which is explicitly based on the above idea of distance minimization: Kemeny’s median rule (Kemeny 1959). Given an observed preference profile, it determines the preference ranking over all alternatives that is closest to the observed one in the sense of requiring the minimum number of pairwise changes in individual opinions to reach that ranking. Thus, the postulated consensus state from which the distance to the observed profile in Kemeny’s system is measured is one of unanimity regarding all positions in the ranking of alternatives, i.e., the voters are in agreement about which alternative is placed first, which second, etc. throughout all positions. The metric used in measuring the distance from the consensus is the inversion metric (Baigent 1987; Meskanen and Nurmi 2006). This procedure was explained above. We now focus upon the Borda count and consider an observed profile P. For a candidate x, we denote by W(x) the set of all profiles where x is first-ranked in every voter’s ranking. Clearly in all these profiles, x gets the maximum Borda points. We consider these as the consensus states for the Borda count (Nitzan 1981). For a candidate x, the number of alternatives above it in any ranking of P equals the number of points deducted from the maximum points. This is also the number of inversions needed to get x in the winning position in every ranking. Thus, using the metric above, wB is the Borda winner if dK ðP, WðwB ÞÞ  dK ðP, WðxÞÞ

8x  X∖wB :

The plurality system is also directed at the same consensus state as the Borda count, but its metric is different. Rather than counting the number of pairwise preference changes needed to make a given alternative unanimously first-ranked, it minimizes the number of individuals having different alternatives ranked first. To represent the plurality system as distance-minimizing, we define a metric dd: dd(R, R0)

=0, if R(1) = R0(1) =1, otherwise.

Here R(1) and R0(1) denote the first-ranked alternative in preference rankings R and R0, respectively. The unanimous consensus state in plurality voting is one where all voters have the same alternative ranked first. With the metric dd we tally, for each alternative, how many voters in the observed profile P do not have this alternative as their first-ranked one. The alternative for which this number is smallest is the plurality winner. The plurality ranking coincides with the order of these numbers. Using this metric we have for the plurality winner wp, d d P, W wp





 dd ðP, WðxÞÞ

8x  X∖wp :

The only difference to the Borda winner is the different metric used.

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Many other systems can be represented as distance-minimizing ones (Meskanen and Nurmi 2006). It seems, then, that the differences between voting procedures can be explained by the differences in the underlying consensus states sought for and the measures used in minimizing the distances between rankings.

The Best Voting System? Voting is one type of group decision process. The multitude of voting systems as well as the large number of criteria used in their assessment suggests that the voting system designers have had different views regarding the choice desiderata. Since no system satisfies all criteria, one is well-advised to fix one’s ideas as to what a system should be able to accomplish. An even more profound issue pertains to voting system inputs: are the voters assumed to be endowed with preference rankings over candidates or something more or less demanding? An example of more demanding input is the individual utility function or “cash value” of candidates. Range voting and majority judgment are examples of procedures using this kind of voter input. With regard to systems based on individual preference rankings, the scholarly community is still roughly divided into those emphasizing success in pairwise comparisons and those of more positional persuasion. This was essentially the dividing line some 200 years ago when Borda and Condorcet debated the voting schemes of their time. Until the mid-1990s, it appeared that the social choice scholars were leaning largely to the side of Condorcet, but with the advent of Saari’s geometrical approach many (including the present writer) began to hesitate. The Borda count had proven to be easily vulnerable to strategic maneuvering and undesirably unstable under changes in the number of alternatives. However, Saari has pointed out that the Condorcet winners are not stable, either. Furthermore, the Borda count seems largely immune to all kinds of monotonicity failures both in fixed and variable electorates, while such failures plague Condorcet extensions, many of them even in restricted domains where the initial profiles contain a Condorcet winner. The strategic weaknesses of the Borda count are evident. So, to make Borda count more immune to strategic voting, one could suggest Nanson’s method which takes advantage of the weak relationship between Borda and Condorcet winners: the latter always receive higher than average Borda scores. As we saw in the preceding, this “synthesis” of two winner intuitions comes with a price: Nanson’s method is nonmonotonic. Thus, one of the fundamental advantages of positional systems, monotonicity, is sacrificed when striving for less vulnerability to strategic preference misrepresentation and compatibility with the Condorcet winning criterion. For many, this is too high a price. The same holds, mutatis mutandis, to Kemeny’s median. For those who stress positional information in group decisions, the Borda count is undoubtedly still one of the best bets. Its several variations have all proven inferior to the basic version (see Nurmi and Salonen 2008). For those inspired by the

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Condorcet criteria – especially the winning one – Copeland’s method would seem most plausible in the light of the criteria discussed above. A caveat is, however, in order: we have discussed but a small subset of existing voting systems and evaluation criteria. With different criterion set one might end up with different conclusions. A final point pertains to the context of voting. The failures of procedures typically occur in circumstances characterized by the number of alternatives and voters as well as the general features of the preference profiles. The more one knows about the circumstances under which the procedures are to be used, the more enlightened choices between procedures is one able to make. While some results on the contextual effects on voting outcomes are already available, it seems that more work is required to determine the relevance of theoretical properties for the choice of a voting procedure.

Cross-References ▶ Group Decisions with Intuitionistic Fuzzy Sets ▶ Group Decisions: Choosing Multiple Winners by Voting ▶ Multicriteria Methods for Group Decision Processes: An Overview ▶ Supporting Community Decisions

References Arrow K (1963) Social choice and individual values, 2nd edn. Yale University Press, New Haven. (1st edn. 1951) Baharad E, Nitzan S (2002) Ameliorating majority decisiveness through expression of preference intensity. Am Polit Sci Rev 96:745–754 Baigent N (1987) Metric rationalization of social choice functions according to principles of social choice. Math Soc Sci 13:59–65 Balinski M, Laraki R (2011) Majority judgement: measuring, ranking, and electing. MIT Press, Cambridge, MA Banks J (1985) Sophisticated voting outcomes and agenda control. Soc Choice Welf 1:295–306 Black D (1948) On the rationale of group decision-making. J Polit Econ 56:23–34 Brams S (2008) Mathematics and democracy. Princeton University Press, Princeton Brams S, Fishburn P (1983) Approval voting. Birkhäuser, Boston De Grazia A (1953) Mathematical derivation of an election system. Isis 44:42–51 Dummett M, Farquharson R (1961) Stability in voting. Econometrica 29:33–42 Farquharson R (1969) Theory of voting. Yale University Press, New Haven Felsenthal DS, Nurmi H (2017) Monotonicity failures afflicting procedures for electing a single candidate. Springer, Cham. https://doi.org/10.1007/978-3-319-51061-3 Felsenthal DS, Nurmi H (2018) Voting procedures for electing a single candidate. Proving their (in) vulnerability to various voting paradoxes. Springer, Cham. https://doi.org/10.1007/978-3-31974033-1 Felsenthal DS, Nurmi H (2019) Voting procedures under a restricted domain. An examination of the (in)vulnerability of 20 voting procedures to five main paradoxes. Springer, Cham Felsenthal DS, Tideman N (2013) Varieties of failure of monotonicity and participation under five voting methods. Theor Decis 75:59–77

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Fishburn P (1973) The theory of social choice. Princeton University Press, Princeton Fishburn P, Brams S (1983) Paradoxes of preferential voting. Math Mag 56:201–214 Gehrlein WV, Lepelley D (2017) Elections, voting rules and paradoxical outcomes. Springer, Cham Gibbard A (1973) Manipulation of voting schemes. Econometrica 41:587–601 Hägele G, Pukelsheim F (2008) The electoral systems of Nicholas of Cusa in the Catholic concordance and beyond. In: Christianson G, Izbicki TM, Bellitto CM (eds) The church, the councils & reform – the legacy of the fifteenth century. Catholic University of America Press, Washington, DC Kelly J (1978) Arrow impossibility theorems. Academic Press, New York Kemeny J (1959) Mathematics without numbers. Daedalus 88:571–591 McKelvey R, Niemi R (1978) A multistage game representation of sophisticated voting for binary procedures. J Econ Theory 18:1–22 McLean I, Urken A (1995) General introduction. In: McLean I, Urken A (eds) Classics of social choice. The University of Michigan Press, Ann Arbor Meskanen T, Nurmi H (2006) Distance from consensus: a theme and variations. In: Simeone B, Pukelsheim F (eds) Mathematics and democracy. Springer Verlag, Berlin-Heidelberg Miller N (1980) A new solution set for tournaments and majority voting. Am J Polit Sci 24:68–96 Miller N (2017) Closeness matters: monotonicity failure in IRV elections with three candidates. Public Choice 173:91–108 Moulin H (1988) Condorcet’s principle implies the no show paradox. J Econ Theory 45:53–64 Nitzan S (1981) Some measures of closeness to unanimity and their implications. Theor Decis 13:129–138 Nurmi H (1987) Comparing voting systems. D. Reidel, Dordrecht Nurmi H (2010) Voting systems for social choice. In: Kilgour DM, Eden C (eds) Handbook of group decision and negotiation. Advances in group decision and negotiation, vol 4. Springer, Dordrecht/Heidelberg/New York. https://doi.org/10.1007/978-90-481-9097-3 Nurmi H, Salonen H (2008) More Borda count variations for project assessment. AUCO Czech Econ Rev 2:109–122 Saari D (1992) Millions of election rankings from a single profile. Soc Choice Welf 9:277–306 Saari D (1995) Basic geometry of voting. Springer, Berlin/Heidelberg Saari D (2003) Capturing ‘The will of the people’. Ethics 113:333–349 Satterthwaite M (1975) Strategyproofness and Arrow’s conditions. J Econ Theory 10:187–217 Shepsle K, Weingast B (1984) Uncovered sets and sophisticated voting outcomes with implications for agenda institutions. Am J Polit Sci 28:49–74 Tangian A (2014) Mathematical theory of democracy. Studies in choice and welfare. Springer, Berlin/Heidelberg

Group Decisions: Choosing Multiple Winners by Voting D. Marc Kilgour

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Excellence Versus Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ballots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordinal Ballots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cardinal Ballots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Approval Ballots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

440 441 445 446 448 449 450 457 458 459 460

Abstract

Voting is a common group decision technique to select one candidate, who might be an individual, option, or project. Voting can also be used when the objective is to select not one candidate, but several. However, new issues arise when the purpose of voting is to choose several candidates; prominent among them is avoidance of “tyranny of the majority,” wherein a voting bloc controls more than its share of the choices. A good voting procedure should strike an appropriate balance between the requirement that each selected candidate has strong support among the voters and the requirement that the set of selected candidates is broadly supported within the set of all voters. Multi-winner voting is often the most efficient way to make group decisions. Single-winner voting procedures can be used for this purpose, but they are generally not recommended because they ignore the issue of individual versus group support. Procedures that have been proposed for group decisions to select a predetermined number of candidates are D. M. Kilgour (*) Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_49

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described and illustrated, and their properties as voting procedures discussed. Multi-winner voting can make it easier for a group to choose a set of candidates, options, or projects, but care must be taken to ensure that the choices are appropriate, fair, and balanced. Keywords

Group decision · Crowd-scale · Voting · Multi-winner · Diversity · Ballot forms

Introduction Voting is often a component of a group decision process. If the group must choose among several fixed alternatives, several features of voting make it useful: • It gives every participant an opportunity for input. • It restricts the input that a participant can provide. • It aggregates all inputs in an even-handed way. Because of these properties, voting reveals information about the diversity of views within the group. In particular, it identifies consensus or near-consensus. Voting may serve at least three distinct purposes for a group making a decision: 1. As the final step in decision-making, a group may conduct a formal vote to confirm that its choice is acceptable to all, or most, of the group. 2. After discussion, a group may use a formal vote to determine its choice from among the alternatives under consideration. 3. Prior to a detailed discussion, a group may vote to gain information about its relative preferences. The outcome may be called a “straw poll” if it is informal or a shortlist if it is formal. The three contexts for making a decision by voting have distinct characteristics. In (1), each voter votes for one of two alternatives, usually framed as Yes and No. In this case, Majority Rule is the best voting procedure, as established by the theorem of May (1952), which shows that Majority Rule is the most decisive voting system that is consistent with a fundamental principle of democracy – more votes can never harm a candidate. Thus, in context (1), there is a best way to vote to make a group decision. This is not true in context (2). In the most common application, the group is faced with m > 2 known alternatives and must choose (exactly) one of them. Of course, the group must discuss the alternatives thoroughly. If differences of opinion or preference remain, voting offers a way to make a choice. Methods of conducting a vote to select one alternative are the subject of the chapter ▶ “Group Decisions: Choosing a Winner by Voting,” by H. Nurmi. There are many good ways to carry out singlewinner voting, but none of them is unquestionably best. The choice of ballots is controversial, let alone the procedure for counting them (Brams and Fishburn 2002;

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Laslier 2012). In particular, it is often impossible to draw conclusions about the “preferences” of the group. In a variant of context (2), the group may wish to select not one of the alternatives before it, but two or more. Single-winner procedures can often be used for this purpose, but they may make the best choices less clear; one subgroup of voters may determine all of the winners. Consequently, the choosers, and therefore the winners, may not “represent” the group. Sometimes diversity of support is not an issue, but often it is, and when it is the use of a single-winner procedure precludes controlling for the level of diversity among the supporters of the winners and therefore among the winners themselves. In context (3), the group aims to identify a subset of alternatives for further discussion. The purpose of such a preliminary vote is to shape the subsequent debate, which is generally more efficient if there are fewer alternatives to discuss, as each alternative increases the cost and effort of discussion. Context (3) is different from context (2) only in that the number of alternatives to be selected may not be fixed in advance. This feature is sometimes appropriate, as illustrated by the familiar Doodle poll. In summary, it is common for a group to want to select two or more alternatives from among m > 2 candidates. In democratic contexts, for instance, citizens sometimes choose a group of representatives. In group decision-making, a retailer must select a number of products to feature in advertising, a Program Committee must decide which contributed papers to accept for a conference, or the Local Arrangements Committee must select menus for the banquet. This chapter begins with a discussion of a major issue in the design of multiwinner voting systems in section “Excellence Versus Diversity.” Then section “Ballots” describes the ballots commonly used in multi-winner voting, and section “Procedures” continues with accounts of the most popular procedures, subdivided according to ballot type. Some of this material is drawn from an earlier survey on this topic (Kilgour 2018). Multi-winner voting is a special case of voting in combinatorial domains; for this broader perspective, see (Lang and Xia 2016). Section “Properties” describes some properties that multi-winner voting procedures may possess, or not. Finally, section “Conclusions” offers a summary and some conclusions.

Excellence Versus Diversity Most single-winner voting procedures calculate a score for every candidate and then select the candidate with the highest score. Such a procedure can be used to select more than one candidate, say k of them, simply by declaring that the k top-scoring candidates are the winners. However, multi-winner procedures derived from singlewinner procedures in this way have a common feature that may be undesirable. It is possible for all winning candidates to be supported by similar sets of voters, so that the winners, as a group, do not represent the voters, as a group. This phenomenon, sometimes called “tyranny of the majority,” is not a problem for some decisions, but for others winners with diverse support are strongly preferred.

442 Table 1 Ratings of candidates A, B, and C by three voters

Table 2 Voting for individual candidates: sum, Borda sum, and product

D. M. Kilgour

Candidate A B C

Candidate A B C

V1 10 9 1

V1 10 9 1

V2 8 5 3

V2 8 5 3

V3 1 2 7

Sum 19* 16* 11

V3 1 2 7

Borda sum 7* 6* 5

Product 80* 90* 21

* ¼ Winner

To illustrate, we use the data in Table 1, which is in the context of a group decision to select two winners from three candidates, A, B, and C. Table 1 shows the scores assigned to each candidate by three independent assessors, V1, V2, and V3. Each assessor’s ratings are interpreted as estimates of the value or worth of the candidates. First, we consider voting systems in which the assessors are asked to vote for individual candidates; the system then declares that the two winners are the two top vote-getters. In Table 2, the three assessors’ ratings are turned into votes in three ways: sum, Borda sum, and product. The sum system simply adds the ratings (treating them as range votes, on a 0–10 scale); the Borda sum system awards 3 points for a first choice, 2 for a second, and 1 for a third and then adds points; the product system multiplies the ratings. In Table 2, the top two scores in each scoring column have been indicated with an asterisk. In all three of these systems, the top two candidates are A and B; i.e., so the winning set is AB. But should the combination of A and B win? If a voting system such as any of the three above (and many others) really measures quality, then it must be accepted that A and B are the best candidates. The objection that can be raised against AB is that selecting both A and B may be very pleasing to voters V1 and V2, but it must be very disappointing to voter V3, who gave both of those candidates a very low rating. According to this line of thought, including C among the selected candidates would be more fair, as the set of winners would then better represent the voters in the sense that for every voter there is a preferred candidate among the winners. For example, consider the group decision of the Program Committee of a conference, which aims to select papers of the highest quality. Suppose that there are three applicants for the last two positions on the program, A, B, and C, and that Table 1 contains ratings of their papers by three independent assessors, V1, V2, and V3. Then it is easy to understand why the Program Committee may wish to choose AB, as those are the highest-quality papers; A has the top rating, and B is highestrated of all papers other than A. Of course, this example is extreme, as we are not considering factors that Program Committees often wish to include, such as the distribution of papers over subfields.

Group Decisions: Choosing Multiple Winners by Voting Table 3 Voting for twocandidate subsets: sum, Borda sum, and product

Candidate AB AC BC

443

Sum 35* 30 27

Borda sum 13* 12 11

Product 7200* 1680 1890

* ¼ Winner

Table 4 Minimax voting for two-candidate subsets

Subset AB AC BC

V1 10 10 9

V2 8 8 5

V3 2 7 7

Minimax 2 7* 5

* ¼ Winner

A contrasting example is provided by the group decision of the Local Arrangements Committee when it decides on banquet menus. Because each attendee is to have only one meal, the fact that B is rated almost as high as A is not relevant, since everyone who likes meal B likes meal A even more. Now choosing AC ensures that each assessor can find a highly rated menu. In this case, after A is selected, the committee’s problem is to find a choice for those who do not favor A. Again, this example is extreme; now we are trying to avoid candidates whose support duplicates the support of others. Of course, in most real-world choices with multiple winners, both dimensions are important – support should be both high and broad. Committee decisions generally pay attention to both, though the relative priorities may vary. This tension will be discussed in more detail below. We have already shown that voting can support a multi-winner group decision made exclusively on the high-support dimension. We now show that voting can also support multi-winner group decisions that depend entirely on breadth of support. But to do so, the voting mechanism must be restructured. We now express the multi-winner vote not as a contest of candidates, but as a contest of the multi-candidate subsets that might be selected. Table 3 shows our example with the individual candidates replaced by combinations: AB, AC, and BC. The principle is that the score of a subset is obtained by combining the scores of the candidates within it. For example, the sum score for subset AB equals the sum score for A plus the sum score for B, both found in Table 2. Similarly, the Borda sum score for a subset is the sum of the Borda sum scores of the individual candidates in Table 2. The product score for subset AB equals the product score for A multiplied by the product score for B, again from Table 2. Note that keeping track of the scores of subsets does not change anything; the asterisks in Table 3 indicate that the winning subsets are exactly the same as in Table 2. Table 4 shows the calculation of a new score for subsets, called the minimax score. It begins with the premise that a voter’s score for a subset is the score the voter assigns to the most preferred candidate in the subset. To understand the entries of

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Table 4, compare it with Table 1; for instance, the score assigned by voter V1 to AB is 10, which is V1’s highest rating for any candidate in AB. V1’s rating for AC is also 10, as that subset also contains V1’s favorite candidate, A. But, for BC, V1’s rating falls to 9, which is V1’s rating of candidate B. The other voters’ scores are calculated similarly. The minimax score of a subset (right-hand column of Table 4) is the minimum of all voters’ scores for the subset. For instance, the minimax score of AB is 2, the minimum of the voters’ scores (10, 8, and 2). (The minimax is the minimum of the maxima.) A higher minimax score is better because it guarantees that every voter has at least one candidate with as high a rating as possible, so the best subset is the one with the highest minimax. To summarize, the minimax score measures the happiness of the unhappiest voter, so it is reasonable to choose a subset that maximizes it. The minimax choice in our example, indicated by the asterisk, is AC. Any other subset has a lower minimax value, meaning that at least one voter would be less happy than the unhappiest voter at AC. One reason to expect a great variety of multi-winner voting procedures is that multi-winner group decisions balance two objectives. We phrase these objectives as follows: • Individual Support: Each candidate in the winning set should be well-supported by the voters, in comparison to other candidates. • Group Support: The winning subset should be well-supported by the voters as a group, in comparison to the groups of voters who support other (similar-sized) subsets. As discussed above, individual support is a measure of excellence, while group support is a measure of diversity. These objectives are often consistent but, sometimes, they are in conflict and must be traded off against each other. Different multi-winner voting procedures take different approaches to this tradeoff, so the choice of voting procedure implies different relative weights for the two objectives. A well-chosen method aims to identify sets of candidates that do well on both group support and individual support. But the possible conflict of these criteria implies that multi-winner voting is a kind of multi-criteria decision problem. (For a view of general principles, see the chapter ▶ “Multicriteria Methods for Group Decision Processes: An Overview,” by Salo et al.) But while standard solutions to MCDA problems can be used in specific instances, they unfortunately do not determine voting rules and so are not directly applicable. But before we consider multi-winner voting procedures, we ask whether they are really necessary. The approach above, voting to choose a combination of candidates directly, worked very well – why not use it instead of a multi-winner procedure where voters vote on individual candidates? The combination approach would enable voters to express any perceived synergies, positive or negative, between or among candidates. In fact, it is always better to use single-winner voting where candidates are slates (or subsets of candidates) – but they are often impractical due to the combinatorial explosion of the number of “candidates.” If the numbers are small,

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for example, if two candidates out of four are to be chosen, there are six subsets to be compared, a task that is reasonable for most voters. But if the problem is to choose 3 candidates out of 8, voters must assess 56 different slates, which is probably too much to ask. And choosing 12 candidates out of 24 is out of the question, as there are over two million alternatives. Often, multi-winner voting is the only practical approach.

Ballots A voter’s ballot is a message from the voter to the voting system about the voter’s preferences over the candidates. The voter must choose one of a finite number of available messages: in the simplest ballot form, the voter indicates only her most favored candidate; in more complex forms, she may give her order of preference over the candidates and even the relative strength of those preferences. When a vote is to produce multiple winners, there is obviously a greater need for information about preferences, as more than one candidate is to be selected. At minimum, ballots should offer the opportunity to support several candidates or to give extra support to one or two candidates. The diversity of ballot forms in common use for multi-winner voting is illustrated in Fig. 1. Ballots that are ordinal rank the candidates; ballots that are cardinal indicate the voter’s score for each candidate. On an approval ballot, a voter either approves, or not, each candidate. The central position of approval ballots reflects that they are both Ranked (with only two levels available) and Graded (with 0 and 1 as the only possible candidate scores). Some additional variations are not indicated in Fig. 1. Ballots may or may not permit ties. Ordinal ballots may be truncated – the voter may choose, or be permitted, Cardinal Ordinal

Ranked

Approval

Graded (Range)

Plurality-at-Large SNT

Block

Cumulative

Fig. 1 Ballot forms for multi-winner voting. (Source: Kilgour 2018)

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to rank only her top few candidates. Graded (or range) ballots require that candidates be scored on some scale, typically 0–10 or 0–100, but sometimes letter scales like A, B, C, D, or F are used. For a vote on the choice of k candidates, a cumulative ballot gives each voter k votes to be distributed over the candidates; a voter may choose to give a candidate more than one vote. In a plurality-at-large vote, each voter may submit up to k approvals; in a block vote, exactly k; and in a single nontransferable vote, exactly 1. (Thus an SNT vote uses the plurality ballot, the simplest available for single-winner voting.) Note that there are some messages about candidate preferences that these standard ballots do not allow because they refer only to individual candidates. No multiwinner ballot has ever been proposed, so a voter cannot express views about synergies between or among sets of candidates, even though these views may well be pertinent to the selection of the winning set. In other words, a fundamental problem of multi-winner voting is that ballots can describe only voters’ views of individual candidates and nothing about which combinations of candidates they find appealing, or not. Effectively, it is assumed that there are no synergies, positive or negative, within any group of two or more candidates. The fact that voters are unable to send messages about nuances of preference is one reason why a vote on a single-winner “slate” is to be preferred to a multi-winner vote. But, as already noted, multi-winner voting is often the only practical procedure. The ability to express preferences on a ballot is only one issue that affects the choice of multiple winners by voting. Another is how the ballots are counted – that is, the procedure by which the messages from the voters are aggregated to determine a subset of the candidates.

Procedures We now discuss common procedures for multi-winner voting. We assume that the set of candidates is fixed and that the voters are to choose a fixed number, k > 1, of them. (Later, we discuss briefly what happens if the number of winners is not fixed in advance.) We have already discussed many possible ballots. Now we concentrate on procedures for counting them, i.e., for determining the winning subset of candidates. For the most part, we postpone a description of the properties that sets of winners might possess to section “Properties.” However, the diversity issue described in section “Excellence Versus Diversity” merits further discussion before specific procedures are described. In a multi-winner vote, the subset of candidates chosen is generally required to display adequate group support, or “diversity” – insofar as reasonably possible, every voter should support some members of the winning subset. To achieve suitable levels of diversity, two “vote design” strategies are common. The first is to impose admissibility rules, which specify in advance which subsets of candidates are permitted to win, defining them so as to achieve the required diversity (Fishburn and Pekeč 2004). Within universities, for example, it is common to find multi-winner elections in which the winning set must include at least one candidate from each

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faculty, school, or department. When the Program Committee of a conference decides in advance which subfields are to be represented in the papers selected for presentation, it is implementing an admissibility requirement. The advantage of the admissibility approach is that it works with practically any vote-counting method. For instance, admissibility permits the repeated use of singlewinner procedures, which as already noted are not by themselves likely to meet any diversity criterion. Of course, there can be problems with this approach: some subfields may attract an unexpected fraction of the best researchers, and that can change over time, as indeed can the definitions of the subfields themselves. Moreover, admissibility becomes unwieldy when there are many criteria: the Program Committee may consider defining admissibility not only in terms of subfield but also using gender, age group, minority status, geographic location, etc. The second strategy to achieve a suitable level of group support is to select a ballot and ballot-counting procedure with the property that subsets with high group support tend to receive higher scores. In the end, of course, candidates who do well are generally those with high levels of individual support, but a well-chosen ballotcounting procedure typically trades off some individual support for increased levels of group support. Of course, group support means only that the chosen candidates broadly represent the voters, which is valuable insofar as the voters themselves are appropriately diverse. Procedures for multi-winner voting that offer some control over the diversity of the candidates selected are more complex than procedures for single-winner voting. Yet this kind of voting is increasingly common, in part because software is readily available; indeed, many group choices are made on the Internet. The first procedural studies, (Kilgour 2010; Kilgour and Marshall 2012), developed later into more extensive approaches (Faliszewski et al. 2017; Lang and Xia 2016; Lackner and Skowron 2020). Of course, procedures for counting ballots – that is, for determining the winning subset of candidates – depend on the kind of ballots used. Moreover, the same set of ballots can be counted by many different procedures, often resulting in different choices. Perhaps this is to be expected, as different procedures emphasize different features, including their tradeoff of individual support versus group support. To illustrate the procedures, we will apply them to an illustrative vote that can be conducted using the different ballots and counted using various counting rules. We begin with each voter’s evaluation of (or utility for) each candidate. In the example of Table 5, there are m ¼ 5 candidates (A, B, C, D, and E) and n ¼ 6 voters (V1, V2, Table 5 Evaluations of five candidates by six voters on 0–10 scale Candidate A B C D E

V1 4 5 10 9 2

V2 5 2 9 7 1

V3 3 4 1 5 6

V4 9 0 10 7 8

V5 7 6 1 5 2

V6 0 2 1 3 10

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D. M. Kilgour

V3, V4, V5, and V6). The multi-winner vote is to choose k ¼ 3 candidates according to the preferences of the voters as expressed on their ballots. As required for any multi-winner procedure, we assume that utilities for subsets of candidates are additive – that is, we make no effort to include any synergies among candidates. We also assume that each voter votes sincerely and selects a “reasonable” ballot that represents her preferences accurately within the restrictions of the ballot. We discuss voting procedures for ordinal ballots in Subsection 4.1, cardinal (range) ballots in 4.2, and approval ballots in 4.3. Each procedure is given a short name that is used in the comparison shown in Table 12.

Ordinal Ballots An ordinal ballot lists the candidates in descending order of the voter’s preference. For the example of Table 5, the ordinal ballots submitted by the voters are as shown in Table 6. Note that a voter’s most preferred candidate is at the top of its column, etc. The best-known procedure for counting ordinal ballots is the Borda procedure, or Borda count: Compare the total scores of candidates when they are awarded 4 points for each first place vote, 3 for each second, 2 for third, and 1 for fourth. For the ballots of Table 6, the Borda scores of the individual candidates are (in order) 11, 10, 13, 15, 11. This is a single-winner procedure, so (in the absence of admissibility conditions) we take as winners the three top-scoring candidates: D, C, and then a tie between A and E. Thus, the multi-winner vote ends in a tie between ACD and CDE. The Borda procedure is a convenient illustration, but it is a single-winner procedure – so we do not recommend it in general, as it takes no account of group support. (In this case, ACD seems to do a better job of representing all voters than CDE.) An alternative procedure for counting ordinal ballots is single transferable vote or STV. Begin by counting the number of first choices for each candidate and comparing them to a threshold called the Droop quota, which equals the smallest integer d such that it is impossible for more than k candidates (for our example, k ¼ 3) to receive at least d first choices each. Here, d ¼ 2. It follows that both C and E are elected on round 1, C with a surplus of 1 and E with a surplus of 0. The next step of STV is to transfer any positive surpluses to next-choice candidates. For E there is no surplus to transfer, so voters V3 and V6 now have an effective weight of 0. But electing C took only 2/3 of the votes of voters V1, V2, and V4, so there is 1/3 remaining. The consequence is that voters V1, V2, and V4 continue to Table 6 Ordinal ballots of six voters Position First Second Third Fourth Fifth

V1 C D B A E

V2 C D A B E

V3 E D B A C

V4 C A E D B

V5 A B D E C

V6 E D B C A

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Table 7 Example: Second round of STV voting procedure Position First Second Third Weight

V1 D B A

V2 D A B

1 3

1 3

V3 D B A 0

V4 A D B 1 3

V5 A B D 1

V6 D B A 0

participate in subsequent rounds, but with a weight of 1/3. In the second round, the only active candidates are A, B, and D; the votes and weights are now as shown in Table 7. In the second round of STV, the candidates’ weighted scores are A, 2/3; B, 0; and D, 4/3. No candidate obtains the Droop quota, so the candidate with the fewest firstchoice votes is dropped: candidate B is now out of the running. Repeating Table 7 without candidate B again fails to produce a candidate with more than the Droop threshold, so again the candidate with fewest first-choice votes – in this case, D – is dropped. The winning committee according to STV is ACE. The STV winners do take account of group preference: every voter’s first-choice candidate is a member of this committee. But the STV procedure is not recommended because it is non-monotonic. To see this, suppose that voter V3 submits an (untruthful) ordinal ballot of (D, E, B, A, C) rather than the truthful ballot, (E, D, B, A, C). It can be verified that the STV result now changes to CDE and that voter V3 in fact prefers this result to ACE, which results from V3’s truthful ballot. Thus V3 has an incentive to regret casting an “honest” ballot. There are many other single-winner procedures based on ordinal ballots, but few that take account of group support and avoid other problems such as non-monotonicity. This is an area for future research.

Cardinal Ballots We now discuss cardinal, or range, ballots (see Fig. 1), in which voters submit a cardinal score for each candidate, within some specified limits. We take the limits to be 0 and 10, so that the candidate evaluations given in Table 5 can be used directly as range scores. The easiest way to count range ballots is by total range score for each candidate: A, 28; B, 19; C, 32; D, 36; and E, 29. It follows that the range winner result is CDE. Of course, range is a single-winner system and, as discussed above, is not recommended for a multi-winner vote. Instead we recommend Reweighted Range Voting (RRV), a more appropriate method for range ballots when multiple winners are to be chosen (Kok and Smith 2017). RRV proceeds round by round, determining one additional winner in each round until the required number has been identified. In round 1, each voter has weight 1. In subsequent rounds, each voter is downweighted according to the support the voter gave to the winners who have already been determined.

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Specifically, suppose that rounds 1, 2, . . ., h are complete and the winners determined in those rounds were C1, C2, . . ., Ch. Then the weight of voter Vi in round h + 1 is whi þ 1 given by whi þ 1 ¼

1 1 þ hM

1 Ph

j¼1 Vi

  Cj

where all scores are within 0–M, and voter Vi’s range vote for candidate Cj is Vi(Cj). The effect of the calculation is to reduce a voter’s weight in accordance with the voter’s support for candidates already chosen. For our example, the RRV procedure elects D in the first round, which is identical to single-winner range voting. On the second round, the voters have new weights 0.526, 0.588, 0.667, 0.588, 0.667, and 0.769, respectively. (Notice that voter V6 gave the least support to D and has the most weight in round 2.) The weighted voting scores in round 2 are A, 17.007; B, 11.244; C, 18.542; and E, 19.372, resulting in the choice of E. Now that both D and E have been chosen in rounds 1 and 2, the reweighting formula gives third-round weights of 0.313, 0.384, 0.313, 0.250, 0.417, and 0.278, respectively. The weighted scores in round 3 are A, 9.278; B, 6.360; and C, 10.093, so C is chosen. Thus RRV produces the choice CDE. (As commented previously, this choice suggests that RRV gives greater priority to individual support than to group support.) Another cardinal ballot form is cumulative voting (CUM). If k candidates are to be chosen (k ¼ 3 for our example), each voter has k votes, which may be distributed over the candidates as the voter sees fit – including possibly giving a candidate more than one vote. If voters follow one reasonable strategy for multi-winner cumulative voting, the outcome in our example is CDE (Kilgour 2018).

Approval Ballots On an approval ballot, a voter indicates whether each candidate is approved or not approved. For a multi-winner vote, there is a kind of symmetry between the votes and the outcome: Each voter names a subset of (approved) candidates, and the vote determines a winning subset of candidates. In general, the voter’s subset can be of any size, even if (as is usual) the number of candidates to be chosen is predetermined. For example, a voter may support only one candidate (called a “bullet vote”), or alternatively may support every candidate but one, effectively giving the nonapproved candidate a “negative vote.” For general information on approval voting and its use in single-winner voting, see (Brams and Fishburn 1983). As Fig. 1 shows, approval ballots are formally both ordinal and cardinal. Therefore all of the procedures already covered can be used on approval votes. However, many of them are not used often, as procedures designed for ordinal or cardinal ballots tend to produce too many ties when the ballots are approval ballots. However, many other procedures that have been proposed specifically for approval ballots will

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be discussed below. Many details and original references can be found in (Kilgour 2010; Kilgour and Marshall 2012). For the data given in Table 5, it is not obvious which candidates each voter would approve. Clearly this is a strategic decision. We assume that voter Vi’s approval set, denoted Ai, consists of exactly those candidates for whom the voter’s utility exceeds the voter’s average utility for all candidates. Under this assumption, the approval sets are shown in Table 8. For example, voter V1’s average utility for all candidates is 6.0, so V1 approves the candidates with evaluation exceeding 6.0, and therefore V1’s approval set is A1 ¼ {C, D}. In Table 8, note that V6’s strategy is to bullet vote for E, while V4 is casts a negative vote for B. The candidates approval vote counts are 3, 2, 3, 5, and 3, respectively. The Simple Approval (AV) procedure selects as winners the top k ¼ 3 vote-getters. Thus the Simple Approval choice is a three-way tie, ACD, ADE, and CDE, which can be expressed as choosing D for certain, plus two of A, C, and E. Of course, Simple Approval is a single-winner procedure, so this choice reflects only individual support (as recorded in approval ballots) and takes no account of group support. The Satisfaction Approval (SAV) procedure is a variation on the Simple Approval procedure that reduces the support a candidate receives from ballots that support many candidates (Brams and Kilgour 2014). Under SAV, a voter’s contribution to the score of a candidate it supports equals the inverse of the size of the voter’s approval set. Thus V6’s support for candidate E counts as 1 for E, whereas V4’s support for E counts as 1/4 for E and V3’s as 1/3. Thus, E’s Satisfaction Approval score is 1 þ 14 þ 13 ¼ 1:583. The Satisfaction Approval scores of the five candidates are 0.917, 0.667, 1.083, 1.75, and 1.583, respectively, so that the winners under Satisfaction Approval are CDE. A variant of SAV, called the Modified Satisfaction Approval (MSAV) procedure, also produces CDE in our example (Kilgour 2018). Sequential procedures are another class of counting procedures for approval ballots. In each round, one winner is identified; then, if another round is required, the voters are reweighted to reflect the number of candidates they supported who have already been elected. The simplest version of this procedure, called Sequential Proportional Approval Voting (SPAV), is exactly Reweighted Range Voting in the context of approval ballots. A voter’s weight remains 1 until that a candidate supported by the voter is elected; after that, it drops to 12 ; should two candidates supported by that voter be elected, it drops in subsequent rounds to 13, etc. The SPA Table 8 Approval votes for five candidates by six voters Candidate A B C D E

V1

V2 X

X X

X X

V3

V4 X

X X X

X X X

V5 X X

V6

X X

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D. M. Kilgour

  procedure, first proposed by Thiele (1895), depends on the sequence 1, 12 , 13 , . . . . For history and modern variants of this procedure, see (Lackner and Skowron 2020). For our example, with the approval ballots given in Table 8, candidate D, with five approval votes, is selected in the first stage. Then the voters are reweighted to 0.5, 0.5, 0.5, 0.5, 0.5, and 1, respectively. The candidates’ second-round weighted votes are A, 1.5; B, 1; C, 1.5; and E, 2, so candidate E is then selected. For the third round, voter weights become 0.5, 0.5, 0.333, 0.333, 0.5, and 0.5, respectively. In the third round, the weighted votes for the three remaining candidates are A, 1.333; B, 0.833; and C, 1.333, so that the third round results in a tie between candidates A and C. Thus the SPAV choice is a tie between ADE and CDE. Noticing that the sequence of fractions defining Sequential Proportional approval, 1, 12 , 13 , . . ., are exactly those of Jefferson (d’Hondt) apportionment, it was suggested that other sequential procedures could be linked to other apportionment methods (Brams et al. 2019). In this sense, SPAV is called Sequential Jefferson; in contrast, the Sequential Webster procedure (SWEB) is based on Webster (Sainte-Laguë) apportionment, with weights 1, 13 , 15 , . . . . Relative to SPAV (Jefferson), SWEB tends to produce winners with greater group support relative to individual support. In our example, however, Sequential Webster produces the same winners as Sequential Jefferson, a tie between ADE and CDE. We now turn to procedures that adopt the approach considered in section “Excellence Versus Diversity” of this chapter: Instead of regarding the multi-winner vote as a competition among candidates with several winners, we regard it as a competition among subsets of candidates, with only one subset to win. Of course, we are using ballots designed for single-winner voting, so voters cannot express synergistic preferences for, or against, particular combinations of candidates. Nonetheless, this approach has the advantage of giving us the opportunity to measure all aspects of a subset, including individual support and group support, so we can select a subset that has both good scores and good balance. Of course, when we select a measure, we select implicitly the criteria that will be applied. Several “yardsticks” have been suggested and will be described below. One additional consideration is that our approach can easily become costly or impractical, because the number of subsets increases much faster than the number of candidates. For our example, in which there are m ¼ 5 candidates and k ¼ 3 are to be chosen,     5 m there are ¼ ¼ 10 possible subsets, each of which must be assessed k 3   m against all others. This comparison may be manageable for most voters, but k rises to 56 when m ¼ 8, k ¼ 3 and to over 2,000,000 when m ¼ 24, k ¼ 12. A Generalized Approval procedure assigns a score to each possible winning subset of candidates. The score for a subset is the sum over all voters of a representation (rep) score that depends only on how many candidates in the subset are supported by the voter. A subset receives a higher score if it represents more voters; the subset with the greatest total score is then selected.

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Subset scores are determined by a sequence (r(0), r(1), r(2), . . .), called a rep sequence, which always satisfies r(0) ¼ 0 and r( j)  r( j  1) for j ¼ 1, 2, 3. . .. For each voter, the rep score of a subset is r(0) if the voter approves no candidates in the subset, r(1) if the voter approves one candidate in the subset, r(2) for two approvals, etc. Thus the total score of a subset equals r(0) times the number of voters who approve no candidates in the subset, plus r(1) times the number of voters who approve exactly one candidate, plus r(2) times the number who approve exactly two, etc. To be formal, if voter Vi’s approval set is Ai, then Vi’s rep score for subset S is r(|Ai \ S|), where \ refers to the set intersection of Ai and S, or the candidates common to those two sets, and the vertical bars j  j count candidates. Note that only the number of candidates in the intersection matters, not their identities. Turning to our example, Table 9 lists the ten possible winning subsets of candidates across the top and the approval sets of the six voters on the left. In the body of the table are the counts of candidates in both the row (approval set of a voter) and the column (possible winning set). Deciding the winning subset of our multi-winner vote means choosing a column. For a Generalized Approval procedure, the rep sequence chosen will determine the column with “best” set of counts. For example, simply adding the counts in a column of Table 9 gives a total score for each subset; in fact, it is the Simple Approval (AV) score – discussed above – which equals the Generalized Approval score based on the rep sequence of (0, 1, 2, 3, . . .). Clearly, this rep sequence considers only individual support; to reflect group support also, the rep scores r(2), r(3), etc. must be smaller. Representation measures were developed in (Fishburn and Pekeč 2004). The simplest, an extreme measure of group support, is embodied in the REP-1 procedure, which was proposed earlier (Chamberlin and Courant 1983). It is based on the rep sequence (0, 1, 1, 1, . . .), which says that the rep score of a subset of candidates, S, for voter Vi is 1 if and only if Vi supports at least one candidate in S; otherwise, the score is 0. Thus, the total REP-1 score for a subset S equals the number of nonzero entries in column S of Table 9. These scores are shown in the REP-1 line of Table 10. The REP-1 choice is the subset that maximizes the number of voters who support at least one member of this subset; in our example, it is a five-way tie between ACE, ADE, BCE, BDE, and CDE (emphasized in Table 10).

Table 9 Counts of approved candidates in possible winning subsets Approval set CD ACD BDE ACDE ABD E

ABC 1 2 1 2 2 0

ABD 1 2 2 2 3 0

ABE 0 1 2 2 2 1

ACD 2 3 1 3 2 0

ACE 1 2 1 3 1 1

ADE 1 2 2 3 2 1

BCD 2 2 2 2 2 0

BCE 1 1 2 2 1 1

BDE 1 1 3 2 2 1

CDE 2 2 2 3 1 1

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Table 10 Generalized Approval procedures for ten subsets Procedure REP-1 REP-2 REP-3 PAV

ABC 5 3 0 6.5

ABD 5 4 1 7.33

ABE 5 3 0 6.5

ACD 5 4 2 7.67

ACE 6 2 1 7.33

ADE 6 4 1 8.33

BCD 5 5 0 7.5

BCE 6 2 0 7.0

BDE 6 3 1 7.83

CDE 6 4 1 8.33

The REP-2 procedure delivers quite different results in our example. Based on the rep sequence (0, 0, 1, 1, 1, . . .), it finds the subset that maximizes the number of voters who approve at least two candidates in the subset. The REP-2 score of a subset equals the number of counts in the corresponding column of Table 9 that equal or exceed 2; the REP-2 selection is BCD. For completeness, Table 10 also shows that the REP-3 winner is ACD, the only subset for which two (or more) voters approve all three members. The apportionment-related procedures, which are characterized by a decreasing sequence of fractions, give rise to Generalized Approval procedures when the decreasing sequence is converted to a rep sequence by adding the terms. For example, the Sequential Proportional procedure, or Sequential Jefferson, defined by the    sequence 1, 12 , 13 , . . . , corresponds to the rep sequence 1, 1 þ 12, 1 þ 12 þ 13 . . . ¼ ð1, 1:5, 1:833, . . .Þ. The latter procedure is better known by the name Proportional Approval Voting (PAV) and is attributed to Thiele (1895). It is applied to our example in Table 10. (To calculate a subset score in Table 10, start with 1 for each nonzero entry in the column of Table 9, add 12 for each entry greater than or equal to 2, and then add 13 for each entry greater than or equal to 3.) As shown in Table 10, the Proportional Approval choice in our example is a tie, ADE and CDE. As noted earlier, this choice could also be called the Simultaneous Jefferson choice. The Sequential Webster procedure corresponds to a Generalized Approval procedure, called Simultaneous Webster (WEB), that is based on the rep  sequence 1, 1 þ 13, 1 þ 13 þ 15, . . . ; for our example (not shown), its results are the same as Simultaneous Jefferson, or PAV. An entirely different class of procedures for multi-winner approval voting, called centralization procedures, are based on distances between subsets (Brams et al. 2005). If A and S are sets of candidates, the Hamming distance between A and S, denoted D(A,S), equals the number of candidates who are in one of A or S, but not both of them. The Minisum Procedure (MSUM) chooses a set of k candidates, S, that minimizes the sum of D(Ai, S) over all voters Vi, in other words, it chooses the set of k candidates at minimum total distance from all other candidates. The Minimax Procedure (MMAX) chooses the set S that minimizes the maximum of D(Ai,S) over all voters Vi, in other words, the set of candidates such that the most distant approval set of any voter is as close as possible. Formally, the Hamming distance between a set Ai and a set S is given by DðAi , SÞ ¼ jAi j þ jSj  jAi \ Sj :

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Table 11 Hamming distances between approval sets and subsets, minisum and minimax Approval set CD ACD BDE ACDE ABD E Sum Maximum

ABC 3 2 4 3 2 4 18 4

ABD 3 2 2 3 0 4 14 4

ABE 5 4 2 3 2 2 18 5

ACD 1 0 4 1 2 4 12 4

ACE 3 2 4 1 4 2 16 4

ADE 3 2 2 1 2 2 12 3

BCD 1 2 2 3 2 4 14 4

BCE 3 4 2 3 4 2 18 4

BDE 3 4 0 3 2 2 14 4

CDE 1 2 2 1 4 2 12 4

In our example, jSj ¼ 3 for all possible winning sets S, so all Hamming distances can be computed using D(Ai, S) ¼ jAij þ 3 jAi \ Sj, using the size of Ai and the size of Ai \ S from Table 9. The result is Table 11. For our example, ACD, ADE, and CDE are tied as minisum choice; their distance sum is 12, which is the minimum, as shown in Table 11. Also shown is the minimax choice, ADE, the only set S for which the maximum distance is 3; for all other sets S, the maximum distance is at least 4. Centralization procedures tend to be very sensitive to outliers, and it is not surprising that variations have been proposed that downweight extreme ballots. In one version (Kilgour et al. 2006), ballots are weighted proportional to their frequency and inversely proportional to the sum of their distances to all other ballots. The resulting procedures are called Weighted Minisum (WMSUM) and Weighted Minimax (WMMAX). For the six ballots in the example, the proposed procedure produces weights proportional to 8.33, 8.33, 8.33, 8.33, 7.14, and 6.25, respectively. The effect is substantial; the Weighted Minisum winner is ADE, while the Weighted Minimax winner is a tie among ABD, ADE, and BCD. Finally, we mention three common variations on approval ballots shown in Fig. 1. Assume k candidates are to be chosen. Using proportional-at-large (PAL) ballots, a voter may approve at most k candidates. Using block ballots, a voter must approve exactly k candidates. In a single nontransferable vote (SNTV), a voter must approve exactly one candidate; in other words, SNT voting uses a plurality ballot. These elections are generally scored using Simple Approval (AV); in our example, referring to Table 5 and assuming that voters never support candidates with below-average utility unless required to do so, the outcomes are, for PAL, a tie of ACD, ADE, and CDE; for block, a tie of ABD, BCD, and BDE; and for SNTV, ACE. The summary Table 12 gives a sense of how procedures affect outcomes. The table also keeps track of the number of winning subsets to indicate how decisive the procedure is for our example. Note that our example is small; if there were more voters and more candidates, there would likely be fewer ties. Nonetheless, it is remarkable that, of the ten possible winning subsets, only one is never selected by any method.

Procedure Borda STV Range RRV CUM AV SAV MSAV SPAV SWEB REP-1 REP-2 REP-3 PAV WEB MSUM MMAX WMSUM WMMAX PAL Block SNTV

ABC

✓

ABD

✓

ABE

Table 12 Procedures and winning subsets: example

✓

✓

✓

✓

ACD ✓

√

√

√

ACE

✓ ✓ ✓ ✓ ✓ ✓ ✓

✓ ✓ ✓

✓

ADE

✓

✓

✓

BCD

✓

BCE

√

✓

BDE

✓

✓ ✓ ✓

✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓

CDE ✓

Count 2 1 1 1 1 3 1 1 2 2 5 1 1 2 2 3 1 1 3 3 3 1

456 D. M. Kilgour

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As noted earlier, in some multi-winner votes, the number of winners is not specified in advance. Examples include voting on honorary status and voting on a shortlist (as a step in assessment of candidates for a position). In these cases, the procedures described here are not directly applicable because they all depend on k, the number of candidates to be chosen. For scoring procedures, including most with approval ballots, one solution is to specify a threshold score; all candidates whose scores exceed the threshold are declared elected. But this threshold is essentially arbitrary, motivating a search for procedures that determine a set of winners intrinsically – that is, directly from the ballots, without any imposed threshold. For details, see (Kilgour 2016).

Properties This chapter has addressed group decision procedures that use voting to select multiple candidates. A glance at the comparable chapter, ▶ “Group Decisions: Choosing a Winner by Voting,” by H. Nurmi, will show a substantial difference in content: In the single-winner context, the discussion focuses not so much on procedures as on their properties. In the multi-winner context, we have procedures – many borrowed and adapted from single-winner procedures – but know much less about the properties they exhibit, or indeed about what properties that they should exhibit. Simply put, properties of multi-winner procedures are a topic of current research. For additional accounts of the properties of singlewinner voting, often phrased in terms of paradoxes, see (Nurmi 1999; Zwicker 2016). The first comprehensive study of the properties of multi-winner voting rules was (Elkind et al. 2017). The most recent review of the state of knowledge is (Lackner and Skowron 2020). Some basic properties are linked to similar properties in the well-studied single-winner context. For instance, all of the procedures discussed above are anonymous, which means that they treat all candidates equally. Also, they are neutral, which means that they treat all candidates equally. Finally, a procedure is resolute if it never results in a tie. All of the procedures discussed here are irresolute, though they can be made resolute if they are combined with some tie-breaking procedure. We have left the issue of ties open, because of our group decision context: If a procedure recommends multiple courses of action, we suggest that the group consider the grounds for its decision carefully, look for new evidence or new points of view, and then repeat its consideration. A multi-winner voting procedure is committee monotonic if, whenever the number of winners is increased from k to k + 1, the winners at size k are included in the winners at size k + 1. (This condition assumes the ballots are identical, and does not account for ties.) AV, SAV, SPAV, and SWEB are committee monotone, but REP-1, REP-2, etc., PAV, and MMX are not. Committee monotonicity is seen as a desirable property if a choice is to reflect excellence, as the best k candidates should be included among the best k + 1 candidates. Thus, failure to satisfy this property would seem to rule out some procedures where excellence is an important criterion.

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Monotonicity is a much-studied property and was referred to in our discussion of the STV procedure. It seems an important property, but unfortunately it is complex. One variant holds only if the set of voters is fixed (i.e., no additional voters can be added). For current knowledge, see Table 1 of (Lackner and Skowron 2020). A property borrowed from single-winner voting is consistency: if the outcome of a vote is the same for two non-overlapping groups of voters, then it should not change if the procedure is applied to a single group that includes all voters. Of the procedures in section “Procedures,” AV, SAV, REP-1, and PAV are consistent; all others are not. There is much interest in a concept of proportionality for multi-winner voting. Proportionality means, roughly, that if a coherent (in some sense) subset of voters is large enough, then some winning candidates should reflect the votes of that subset. In the context of approval ballots, Faliszewski et al. (2017) define a coherent set of voters V to have the property that j\i  VA(i)j  1; the voters in V vote for at least one common candidate. A procedure satisfies justified representation if, for every cohern ent set of voters V that satisfies jVj , the winning set W satisfies jA(i) \ W j  1 for k at least one i  V; the winners include at least one candidate supported by some voter in V. This rather weak property states that a large-enough coherent set cannot be completely “shut out”; at least one elected candidate must be supported by some voter in the subset. The property of extended justified representation goes slightly further. Let l be a positive integer, and define an l-coherent set of voters V by j\i  VA(i)j  l; so the voters in V all vote for at least l common candidates. The property requires that, for n each l, for every l-coherent set of voters V that satisfies jVj l  , the winning set W k satisfies jA(i) \ Wj  l for at least one i  V; in other words, at least one voter V has supported l of the winning candidates. Aziz et al. (2017) proved that PAV satisfies the extended justified representation property, whereas most of the procedures we have discussed do not. But PAV is not the unique procedure with this property, a fact that has motivated some new definitions. Extended justified representation is not the end of the study of proportionality. There are several competing approaches (Lackner and Skowron 2020), and it is not yet possible to identify one that is compelling. Even for the most common case with a fixed number of winners, the analysis of properties of multi-winner voting procedures is really just getting under way.

Conclusions Multi-winner voting is a technique that can be applied by many groups to address a very common decision problem – how to choose not one option, but several. It can be efficient for most groups and most choice problems. But there are limitations that should be understood.

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A major caveat is that, because what is to be chosen is a subset of alternatives, evaluation should focus on subsets rather than on individual alternatives. In part, the concern is that individual decision-makers may have views about candidates’ synergies, positive or negative, but have no way to express them if ballots relate only to individual candidates. There has been little or no research on ways to redesign ballots or otherwise change procedures to prevent the loss of this potentially valuable information. Most single-winner voting procedures are scoring procedures and are therefore easy to adapt to multi-winner voting. However, a new issue arises in the context of multi-winner voting – the relative weight of individual support and group support when candidates are selected. Single-winner procedures measure only individual support, so they risk “tyranny of the majority”; a large-enough group of voters may be able to control more than its share of choices. There are two ways to address this problem, and they can be applied simultaneously. Classifying all sets of candidates as admissible (available to be chosen) or inadmissible (not eligible to be chosen) is one way to ensure a suitably diverse choice. It is easy to adapt the admissibility strategy to scoring rules; the winning subset is the highest-scoring admissible subset. The second strategy is to adopt a counting procedure that rewards candidates for breadth of support. Of the 22 procedures discussed above, at least 17 take some account of diversity of support, though they do so in very different ways. Using a procedure such as PAV or MMAX, perhaps in conjunction with an admissibility structure, seems a good way to address the balance of individual and group support that a group might require in the choice of several candidates. Many voting procedures are in use, and even more have been proposed. Naturally, the question of which procedure to recommend in a particular vote has arisen, but few convincing guidelines have been proposed. The formulation of desirable properties of multi-winner voting procedures is an ongoing project and will perhaps lead to specific recommendations. But if the experience of singlewinner procedures is a guide, there will not likely be any general agreement on which multi-winner procedure is best, or even on which systems are good, and in what circumstances. Nonetheless, this active area of research will no doubt stimulate new ideas toward both the design and assessment of multi-winner voting procedures. And the ubiquity of problems involving the choice of more than one alternative ensures that there will be opportunity to test conclusions against real-world experience.

Cross-References ▶ Group Decisions with Intuitionistic Fuzzy Sets ▶ Group Decisions: Choosing a Winner by Voting ▶ Multicriteria Methods for Group Decision Processes: An Overview ▶ Supporting Community Decisions

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References Aziz H, Brill M, Conitzer V, Elkind E, Freeman R, Walsh T (2017) Justified representation in approval-based committee voting. Soc Choice Welf 48(2):461–485 Brams SJ, Fishburn PC (2002) Voting procedures. In: Arrow KJ, Sen A, Suzumura K (eds) Handbook of social choice and welfare, vol 1. Elsevier, Amsterdam, pp 173–226 Brams SJ, Fishburn PC (1983) Approval Voting. Birkhäuser, Cambridge, MA Brams SJ, Kilgour DM (2014) Satisfaction approval voting. In: Fara RV, Leech D, Salles M (eds) Voting power and procedures: essays in honour of Dan Felsenthal and Moshé Machover. Springer, Cham, pp 323–346 Brams SJ, Kilgour DM, Potthoff RF (2019) Multiwinner approval voting: an apportionment approach. Public Choice 178:67–93 Brams SJ, Kilgour DM, Sanver MR (2005) A minimax procedure for electing committees. Public Choice 132(3–4):401–420 Chamberlin JR, Courant PN (1983) Representative deliberations and representative decisions: proportional representation and the Borda rule. Am Polit Sci Rev 77(3):718–733 Elkind E, Faliszewski P, Skowron P, Slinko A (2017) Properties of multiwinner voting rules. Soc Choice Welf 48:599–632 Faliszewski P, Skowron P, Slinko A, Talmon N (2017) Multiwinner voting: a new challenge for social choice theory. In: Endress U (ed) Trends in computational social choice. AI Access Foundation. 27–47. http://aiaccess.org/ Fishburn PC, Pekeč A (2004) Approval voting for committees: threshold approaches. Technical report. http://archive.dimacs.rutgers.edu/Workshops/DecisionTheory2/PekečFishburn04a.pdf. Accessed 22 July 2020 Kilgour DM (2010) Approval balloting for multi-winner elections. In: Laslier J-F, Sanver MR (eds) Handbook on Approval Voting. Springer, Heidelberg, pp 105–124 Kilgour DM (2016) Approval elections with a variable number of winners. Theor Decis 81:199–211 Kilgour DM (2018) Multi-winner voting. Estudios de Economia Applicada 36:167–180 Kilgour DM, Brams SJ, Sanver MR (2006) How to elect a representative committee using approval balloting. In: Simeone B, Pukelsheim F (eds) Mathematics and democracy: recent advances in voting systems and collective choice. Springer, Heidelberg, pp 83–95 Kilgour DM, Marshall E (2012) Approval balloting for fixed-size committees. In: Machover M, Felsenthal DS (eds) Electoral systems: paradoxes, assumptions, and procedures. Springer, Heidelberg, pp 305–326 Kok J, Smith WD (2017) Reweighted range voting: a proportional representation voting method that feels like range voting. www.rangevoting.org/RRV. Accessed 22 July 2020 Lackner M, Skowron P (2020) Approval-based committee voting: axioms, algorithms, and applications. arXiv:2007.01795. Accessed 20 July 2020 Lang J, Xia L (2016) Voting in combinatorial domains. In: Brandt F, Conitzer V, Endriss U, Lang J, Procaccia AC (eds) Handbook of computational social choice. Cambridge UP, New York, pp 197–222 Laslier J-F c (2012) And the loser is . . . plurality voting. In: Machover M, Felsenthal DS (eds) Electoral systems: paradoxes, assumptions, and procedures. Springer, Heidelberg, pp 327–351 May KO (1952) A set of independent necessary and sufficient conditions for simple majority decisions. Econometrica 20(4):680–684 Nurmi H (1999) Voting paradoxes and how to deal with them. Springer, Heidelberg Thiele TN (1895) Om flerfolds valg. In: Oversigt over det kongelige danske videnskabernes selskabs forhandlinger. pp 415–441 Zwicker WS (2016) Introduction to the theory of voting. In: Brandt F, Conitzer V, Endriss U, Lang J, Procaccia AC (eds) Handbook of computational social choice. Cambridge UP, New York, pp 23–56

Part V Game Theory Developments for Group Decision and Negotiation

Looking Back on Decision-Making Under Conditions of Conflict Liping Fang and Keith W. Hipel

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decision Situations Under Conflict . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . North-Western Electronics as a Single Participant-Multiple Criteria Situation . . . . . . . . . . . . North-Western Electronics as a Multiple Participant-Single Criterion Situation . . . . . . . . . . . North-Western Electronics as a Multiple Participant-Multiple Criteria Situation . . . . . . . . . . Formal Conflict Analysis Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple Participant-Multiple Criteria Decision Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single Participant-Multiple Criteria Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple Participant-Single Criterion Decision Situations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relationships of Conflict Analysis Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decision Support Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

464 465 465 466 466 467 468 468 470 475 478 480 481 481

Abstract

The combined field of group decision and negotiation (GDN) often tackles decision situations involving genuine disagreement – conflicting aims and objectives over specific issues. Decision situations, or problems, that can occur under conditions of conflict can be classified as single participant-multiple criteria, multiple participant-single criterion, or multiple participant-multiple criteria. Here, participants are individuals or groups with common interests, and criteria refer to aims and objectives. A real-world business application is utilized to illustrate the characteristics, similarities, and differences of these three types of L. Fang (*) Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, Canada e-mail: [email protected] K. W. Hipel Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_31

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decision problems. Formal approaches to the modeling and analysis of all three are reviewed, and meaningful connections and relationships among problems and the methodologies that can address them are clearly explained. A flexible decision support system is one that can be applied to a range of specific situations within a type of decision problem, in order to assist researchers and practitioners who want to better understand and resolve actual decision problems under conditions of conflict. Available flexible decision support systems for this purpose are listed and briefly described, and important issues for future research are suggested. A platform which links many chapters of this handbook is furnished. Keywords

Group decision and negotiation · Development from game theory · Graph model · Conflict analysis · Metagame · Drama theory · Multiple participant-multiple criteria · Decision support system

Introduction The domain of group decision and negotiation (GDN) is concerned with multiple participants. When participants interact with one another over issues they care about, conflict is practically inevitable. For example, in a committee in an industrial enterprise charged with developing a strategic plan, members representing different parts of the organization often have different and incompatible objectives. Similar divisions were observed over the last several years as representatives of the USA, Mexico, and Canada crafted the USA–Mexico–Canada Agreement (USMCA), which replaced the North American Free Trade Agreement (NAFTA) on July 1, 2020. Their extended interactions were intense, drawn-out, and sometimes bitter, and illustrated clearly that in group decision and negotiation parties often have conflicting aims and objectives, and that disagreements are genuine. Radford et al. (1994) and Hipel et al. (1993) discussed and compared various decision problems under conditions of conflict that are multiple participant-multiple criteria (MPMC), multiple participant-single criterion (MPSC), and single participantmultiple criteria (SPMC). In those papers and also in this chapter, individuals or groups with common interests are called participants, and aims and objectives are referred to as criteria. Meaningful connections and relationships among these types of decision problems were presented, and a range of decision support systems were discussed. The major objective of this chapter is to provide a retrospective on Radford et al. (1994) as well as the related paper by Hipel et al. (1993) by assessing and recontextualizing these pieces given the many achievements over the decades after their publication. This chapter also helps to link many of the other chapters appearing in this handbook. This chapter is organized as follows. A real-world example is used to demonstrate the three important types of decision situations in section “Decision Situations Under Conflict.” In section “Formal Conflict Analysis Approaches,” various conflict analysis approaches for investigating the three types

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of decision situations are reviewed and relationships among approaches are presented. A survey of decision support systems (DSSs) for studying decision making under conditions of conflict is provided in section “Decision Support Systems.” A summary of the chapter and a discussion of important issues for future research are given in section “Summary and Conclusions.”

Decision Situations Under Conflict In this section, a simple and practical real-world example is given to illustrate the three important types of decision problems, namely single participant-multiple criteria (SPMC), multiple participant-single criterion (MPSC), and multiple participant-multiple criteria (MPMC) (Radford et al. 1994). Because this practical case is based upon consulting work carried out for a client, the name of the organizational entity involved, as well as other identifying information, has been altered. Nonetheless, the actual modeling of the case is the same as one completed for the client. This example was presented in Radford et al. (1994).

North-Western Electronics as a Single Participant-Multiple Criteria Situation North-Western Electronics is a corporation that manufactures electronics components. It is in the process of developing a strategic plan that will lead its activities over the next 5–10 years. The company has developed several criteria against which possible future activities must be assessed. These criteria can be described briefly as follows: • C1: The firm’s return on investment in each alternative activity over a period of 3 years must be at least 11%; • C2: The organization’s activities must be diversified by undertaking new ventures that can be related or unrelated to its present activities; • C3: The firm can accept a high level of risk in any of its activities only if the return from such activities is correspondingly high; • C4: The company wants ease of entry into a new venture; • C5: The company requires ease of exit from an activity if it does not demonstrate to be profitable. The firm has also determined three possible activities that might enhance its future development. These alternative activities are stated briefly as follows: • A1: To acquire an electronics firm that is at a stage of development comparable to its own and that produces products compatible with its own; • A2: To invest in a firm that engages in research related to its current business; • A3: To invest further in parts of the present company that are deemed likely to generate good returns in the years to come.

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Table 1 Assessment of alternative activities in the strategic plan of North-Western Electronics

Criteria C1: Return on Investment (%) C2: Degree of Diversification C3: Degree of Risk C4: Ease of Entry C5: Ease of Exit

Alternative activities A1: Acquire A2: Invest in firm research 11.7 15.6 A BBB B CC+ A-

A3: Invest in current business 10.5 C+ AA B+

Source: Table 1 of Radford et al. (1994)

The firm wishes to assess these possible new activities with respect to its multiple criteria. Therefore, it can be considered as being in an SPMC decision-making situation. A first step in this assessment is to evaluate the performance of various future activities against the aforementioned criteria. The results of this evaluation are displayed in Table 1, where Return on Investment is the only criterion that can be assessed on a numerical scale. Assessment of the remaining criteria has to be carried out in ordinal form by use of letter grades such as: A, very good; B, good; C, average; D, fair; and E, poor. This letter grade scale can be extended by adding a plus or a minus to the letter, as in B+ or C-. The task on hand for the firm is to place the possible alternative activities in an order of preference, considering the information shown in Table 1.

North-Western Electronics as a Multiple Participant-Single Criterion Situation In section “North-Western Electronics as a Single Participant-Multiple Criteria Situation,” the decision problem facing North-Western Electronics has been considered as an SPMC decision situation. Suppose now that the president of the firm decided that the decision situation should be investigated by a panel consisting of the firm’s five vice presidents, who are denoted by VPA, VPB, VPC, VPD, and VPE. At this stage, each vice president has the same single overall objective of ensuring that the firm continues to be successful. However, each vice president has his or her own criterion for assessing the alternative activities. Their differences of opinion are shown in Table 2, which displays the initial preferences of the five vice presidents for the three alternatives. Specifically, for each vice president, the three alternative activities (A1, A2, and A3) are ranked from most preferred on the left to least preferred on the right. Therefore, the North-Western Electronics situation is formulated as an MPSC problem.

North-Western Electronics as a Multiple Participant-Multiple Criteria Situation When this case study was actually conducted, the decision situation was first considered as an SPMC problem, as described in section “North-Western Electronics

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Table 2 Participants’ initial preferences for alternative activities in the North-Western Electronics conflict Participants VPA VPB VPC VPD VPE

Initial preferences of participants (most preferred to least preferred) A1 A3 A2 A1 A2 A3 A3 A2 A1 A3 A1 A2 A2 A3 A1

Source: Table 3 of Radford et al. (1994) Table 3 North-Western Electronics problem: comparision of MPSC and MPMC situations

Participants VPA

MPSC: ordering of alternatives (most preferred on the left) A1 A3 A2

Participants VPA

VPB

A1

A2

A3

VPB

VPC

A3

A2

A1

VPC

VPD

A3

A1

A2

VPD

VPE

A2

A3

A1

VPE

Criteria CA1 CA2 CA3 CB1 CB2 CC1 CC2 CD1 CD2 CD3 CE1 CE2

MPMC: ordering of alternatives (most preferred on the left) A2 A1 A3 A2 A3 A1 A1 A2 A3 A1 A2 A3 A1 A3 A2 A3 A1 A2 A3 A2 A1 A3 A2 A1 A1 A3 A2 A3 A1 A2 A2 A3 A1 A2 A3 A1

Source: Table 5 of Radford et al. (1994)

as a Single Participant-Multiple Criteria Situation.” Then it was seen as an MPSC situation, as in section “North-Western Electronics as a Multiple Participant-Single Criterion Situation.” Later, however, it was recognized that the firm’s five vice presidents in fact wanted to assess the new alternatives in terms of multiple criteria, rather than a single criterion. Moreover, some vice presidents wished to evaluate activities using their own criteria – different from those adopted by their colleagues. The consequences of these evaluations might be the problem shown on the right side of Table 3, which is an MPMC decision situation.

Formal Conflict Analysis Approaches In this section, the ways in which MPMC decision problems described in section “North-Western Electronics as a Multiple Participant-Multiple Criteria Situation” can be investigated are discussed first. Techniques for modeling and analyzing SPMC and MPSC situations, explained in sections “North-Western Electronics as a Single Participant-Multiple Criteria Situation” and “North-Western Electronics as a Multiple Participant-Single Criterion Situation,” are reviewed in sections “Single Participant-

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Multiple Criteria Decision-Making” and “Multiple Participant-Single Criterion Decision Situations,” respectively. Relationships among conflict analysis approaches are presented in section “Relationships of Conflict Analysis Approaches.”

Multiple Participant-Multiple Criteria Decision Situations The North-Western Electronics decision situation formulated as an MPMC decision and shown on the right side of Table 3 is an example of the most general type of decision problem under conditions of conflict. One approach to resolve the MPMC situation facing North-Western Electronics is to convert the situation to an MPSC problem as follows: 1. Refer to the top right of Table 3. Treat VPA to be confronted by an SPMC situation, in which he or she has to determine the ordering of alternative activities on the basis of criteria CA1, CA2, and CA3. The results of this SPMC process are then recorded on the left side of Table 3 as VPA’s preference in the MPSC evaluation. 2. Repeat the process for VPB, VPC, VPD, and VPE. 3. Carry out an MPSC analysis using the information on the left side of Table 3 or as given in Table 2. Another method is to convert the situation to an SPMC structure. For example, five vice presidents constitute a committee. Initially, each vice president assesses the alternatives and envisions the situation as being MPMC. However, by terms of reference, the committee may remodel the problem as an SPMC structure through discussions and debates over a series of meetings, resulting in the ordinal-ranking version of Table 1 (see the left of Table 6). Actually, the process is a type of group decision. As a matter of fact, Hipel et al. (1993) asserted that MPMC decision problems can be converted into MPSC or SPMC problems and that suitable approaches developed to model and analyze the latter two types can be utilized in studying the first. This assertation is summarized in Fig. 1 (Hipel et al. 1993; Radford et al. 1994). In Fig. 1, the arrows represent the directions in which conversions can occur from one decision situation to another. For example, MPMC situations can be converted into MPSC problems, but not vice versa. Converting an MPSC problem to an MPMC situation does not have practical meaning. Similarly, one would not transform an SPMC situation to an MPMC problem. The relationship between SPMC and MPSC situations is explained in section “Relationships of Conflict Analysis Approaches.”

Single Participant-Multiple Criteria Decision-Making The North-Western Electronics problem shown in Table 1 is a typical SPMC decision situation. Because the model in Table 1 only depicts the perspective of a

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Fig. 1 Relationships among decision situations. (Source: Hipel et al. (1993), Fig. 1 and Radford et al. (1994), Fig. 1)

single participant, such as the president of North-Western Electronics, the decisionmaker (DM) is not explicity given in the table. Furthermore, because SPMC decision problems appear so often in practice, significant theoretical and practical research has been reported. It should be noted that SPMC decision-making is often labeled as multiple criteria or multiple objective decision-making (MCDM or MODM) in the literature. Many techniques have been developed for tackling SPMC decision problems (Keeney and Raiffa 1976; Saaty 1980; Roy 1985; Hipel 1992; Keeney 1992; Kilgour et al. 2010; Camilleri and Zaraté, ▶ “A Group Multicriteria Approach”; Corrente, Figueira, Greco, and Słowiński, ▶ “Multiple Criteria Decision Support”; Moreno-Jiménez, Aguarón, Escobar, and Salvador, ▶ “Group Decision Support Using the Analytic Hierarchy Process”). One multiple-criteria decision-making method, the Elimination Method, is founded on the basic principles of linguistic rule-based models (MacCrimmon 1973; Radford 1989). This approach uses a priority-ordered list of evaluation factors and the minimum or maximum level of performance for each factor to rank alternative activities. The decision problem shown in Table 1, above, is utilized to demonstrate the elimination method as follows. Assume that the priority list of factors and levels of performance established by the firm are as shown on the left side of Table 4. For example, it is specified that, for the first factor, the Return on Investment must be greater than 11%. A “Yes” in Table 4 indicates that the minimum performance is met by the alternative against the factor shown, while a “No” means that the level is not met. The most preferred alternative activity can be ascertained using the following process. Begin with the highest-priority evaluation factor (Return on Investment) and eliminate A3. Move down to the second-most-important factor and notice that both A1 and A2 would remain at this stage. Move to the third-most-important factor and notice again that A1 and A2 would remain at this stage. At the fourth-mostimportant factor, A2 is eliminated and A1 remains. Therefore, the analysis process indicates that the alternative activities can be ranked from most to least preferred as A1, A2, and A3.

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Table 4 Performance of alternative activities for North-Western Electronics (“Yes” indicates that the criterion is met; “No,” that it is not) Factors (in order of decreasing importance) C1: Return on Investment must be greater than 11% C2: Degree of Diversification must be C+ or better C3: Degree of Risk must be C+ or better C4: Ease of Entry must be B or better C5: Ease of Exit must be B or better

Alternative activities A1: Acquire A2: Invest in firm research Yes Yes

A3: Invest in current business No

Yes

Yes

Yes

Yes

Yes

Yes

Yes No

No Yes

Yes Yes

Source: Table 2 of Radford et al. (1994)

In the elimination method, a factor in the priority-ordered list of evaluation factors can be criteria linked using conjunctive (and), disjunctive (or), negative (not), conditional (if), biconditional, or if and only if (iff), and brackets (“(“ and”)”) logical connections (Radford 1989). For example, the first factor could be stated as “Return on Investment must be greater than 10% and Ease of Exit must be C+ or better” (Radford 1989). As can be seen from this case study, the elimination method can take into account both quantitative and nonquantitative criteria. The method can produce a ranking of alternative activities that reflects the performance estimates of the DM and that can be useful in practice. The resulting ranking may contain equally preferred alternatives. Ma et al. (2008) and Talukder et al. (2017) use the elimination method to compare transboundary water treaties and to assess agricultural sustainability, respectively.

Multiple Participant-Single Criterion Decision Situations For tackling MPSC decision situations such as the North-Western Electronics problem as modeled in Table 2, various approaches have been developed. Such approaches are rooted in the noncooperative game theory of von Neumann and Morgenstern (1953) and are called conflict analysis methods. A particularly informative method to classify formal game theoretic approaches is in terms of the kinds of preferences, as shown in Fig. 2 (Hipel and Fang 2005; Hipel et al. 2020). In this lineage, game theoretic approaches that require only relative preference information are shown in the left branch, while those reliant on cardinal preferences are shown on the right. As an example of relative preference, a friend might ask you if you would prefer to drink coffee or tea, to which you might reply that you would prefer to drink coffee. When a cardinal number, such as a utility value, is not utilized to represent preference, the preference information is said to be relative or nonquantitative, and the amount by which one prefers one object to another is not required. In the context of relative preference, coffee is either more preferred, equally

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preferred, or less preferred to tea. Moreover, relative preference can be transitive and intransitive. If transitive, a DM who prefers scenario a to scenario b and b to c also prefers a to c. However, under intransitive preferences, c is preferred or equally preferred to a. If cardinal numbers representing utility or monetary values, for instance, are used to denote preferences in a game theoretic model, the preferences are referred to as cardinal or quantitative. Game theoretic approaches, such as normal form, extensive form, and cooperative game theory, on the right-hand branch of Fig. 2, are part of what is called classical game theory, originally developed by von Neumann and Morgenstern (1953). See Chatterjee, ▶ “Non-cooperative Bargaining Theory” for the use of noncooperative game theory in negotiation. In noncooperative game theory which analyzes the actions of fully rational players, Nash equilibrium, based on the concept of rationality, is the basic stability concept. Howard (1971) developed the theory of metagames, stimulating the series of developments given in the left-hand branch of Fig. 2 (Hipel and Fang 2005; Hipel et al. 2020; Bryant, ▶ “From Game Theory to Drama Theory”; Kilgour, Hipel, and Fang, ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions”; Hipel, Kilgour, Xu, Xiao, ▶ “Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives”). To overcome the breakdowns of rationality illustrated by using generic games, Howard (1971), in addition to the Nash stability, introduced two new kinds of stability: general metarationality (GMR) and symmetric metarationality (SMR). As indicated in Fig. 2, metagame analysis requires only relative preferences for DMs. Cardinal preferences are not required. As shown in Fig. 2, metagame analysis was developed in two directions: drama theory (Howard 1994a, b, 1999; Bryant 2016; Bryant, ▶ “From Game Theory to Drama Theory”; Bryant and Bennett, ▶ “Using Drama Theory to Model Negotiation”) and conflict analysis (Fraser and Hipel 1979, 1984). In drama theory, the metaphor of a drama is utilized to model, analyze, and interpret how a conflict may dynamically evolve over time from its inception in act 1, through the build-up,

Fig. 2 Genealogy of formal game theoretic approaches. (Source: Hipel and Fang (2005))

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climax, and resolution to the finale at the end of the performance. As the drama transforms, dilemmas are encountered and resolved. The theory of how a manyperson frame in drama theory is transformed was developed by Howard’s (1994a, b) two papers, which were published in the special issue of Group Decision and Negotiation introduced by Radford et al. (1994). Fraser and Hipel (1979, 1984) expanded and enhanced metagame analysis to form a methodology called conflict analysis for addressing a variety of real-world conflict situations. The techniques developed within conflict analysis include the following (Hipel et al. 2020): • Sequential stability for taking into account credible sanctions; • Simultaneous sanctioning for considering two DMs moving together to a unilaterial improvement; • Tableau form for conveniently carrying out a stability analysis; • Methods for systematically eliminating infeasible states; • Preference tree method for eliciting DMs’ preferences (Fraser and Hipel 1988); • Coalition analysis to ascertain if a DM can do better by cooperating with other DMs by joining a coalition; • Hypergame analysis for modeling and analyzing a conflict in which one or more DMs have misperceptions about the dispute. A decision support system called DecisionMaker was developed for implementing techniques developed within the conflict analysis methodology (Fraser and Hipel 1988, 1989). Through studies of actual conflict situations, it was recognized that significant advances were required in order to tackle a richer range of conflict situations for enhancing both the theory and practice of conflict analysis. That led to the development of a new generation of decision technologies, called the graph model for conflict resolution (GMCR) (Kilgour et al. 1987; Fang et al. 1993; Kilgour, Hipel, and Fang, ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions”; Hipel, Kilgour, Xu, and Xiao, ▶ “Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives”). GMCR is a significant expansion and enhancement of the conflict analysis methodology. Thinking in terms of moves and countermoves by DMs, a conflict is naturally modeled as a directed graph in which the vertices denote states and the arcs indicate movements from one state to another unilaterally controlled by the DMs. Significant research achievements and extensions in many directions, attributable to GMCR, have been made and are summarized in two other chapters of this handbook (Kilgour, Hipel, and Fang, ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions”; Hipel, Kilgour, Xu, and Xiao, ▶ “Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives”). To assess and compare GMCR and drama theory, Obeidi and Hipel (2005) applied both techniques to three different phases of an international controversy over the export of water in bulk quantities from Canada. They found that the two techniques complement one another, and that GMCR is more convenient to apply in practice.

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Two specific techniques – option form and option prioritizing – are discussed here in more detail so that they can be used in section “Relationships of Conflict Analysis Approaches.” Howard (1971) devised the option form to conveniently represent conflicts in metagame analysis. The option form is often used by the methods emanating from metagame analysis: drama theory, conflict analysis, and GMCR. Here, a hypothetical illustrative model of a situation in which the USA and China are negotiating over whether or not to cooperate with one another by significantly reducing greenhouse gas emissions, as given in Table 5, is used to explain the option form (Hipel et al. 2020). In the left column of Table 5, the DMs and the option or options controlled by each of the DMs are listed. For the negotiation conflict, each DM has one option of cooperation. The columns of “Y”s and “N”s denote the four possible states that could arise. For instance, state 3, denoted by s3, is the scenario for which “N” or “no” option 1 is not selected by the USA and “Y” or “yes” option 2 is chosen by China. The ranking of states from most preferred to least preferred for each DM is displayed in the bottom part of Table 5, where s3  s1 in the row for the USA means that the USA strictly prefers state 3 to state 1. A key advantage of the option form is that it can conveniently represent a conflict having any finite number of DMs and options. The decision support systems DecisionMaker, GMCR II, and GMCR+ can generate all mathematically possible states and eliminate infeasible states easily. An important input in any decision model is the values or preferences of a DM or DMs. In the MPSC decision problems, it is necessary to separately ascertain the preferences for each of the DMs. Fraser and Hipel (1988) developed an efficient and effective method, called the preference tree method, for eliciting preferences for each of the DMs in the conflict analysis methodology. For a conflict model represented by the option form, the number of options is much smaller than the number of feasible states. For example, for a conflict model with six options, there are 64 (26) mathematically possible states. Actually, a DM often expresses his or her basic preferences regarding what could take place in a conflict by making preference statements about options (e.g., taking or not taking an option, or a combination of two options) that are hierarchically ordered from most to least important. Based on this fact, Fraser and

Table 5 Climate change negotiations in option form DMs and Options USA 1. Cooperate (CUS) China 2. Cooperate (CCh) State numbers

States Y

Y

N

N

Y 1

N 2

Y 3

N 4

Ranking of states USA: s3  s1  s4  s2 China: s2  s1  s4  s3 Source: Modified from Table 2 of Hipel et al. (2020)

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Hipel (1988) designed the preference tree method for ordinally ranking states in which equally preferred states are allowed. For the climate change negotiation model shown in Table 5, for example, the USA could state that what is most important for the USA is that China chooses option 2 by cooperating. Next, the USA would prefer not to select option 1. These two preference statements for the USA can be expressed in a priority-ordered list of 2, 1, shown horizontally in Fig. 3. The first preference statement of 2 divides the feasible state set into two subsets: {s1, s3} on the left and {s2, s4} on the right, as shown in Fig. 3. The first subset contains the states in which option 2 is selected, indicated by T (True), while the second subset consists of the states in which option 2 is not chosen, signified by F (False). Similarly, the second preference statement of 1 divides the sets {s1, s3} and {s2, s4} into two subsets: {s3} on the left and {s1} on the right, as well as {s4} on the left and {s2} on the right, respectively. The resulting preference for the USA is s3  s1  s4  s2. A scoring method, as shown at the bottom of Fig. 3, can also be used to rank the states, in which a higher overall number indicates a greater preference. The preference tree method has been refined and extended by Fang et al. (2003a, b); this “option prioritizing method” handles preference statements containing logical connectives, such as conjunction (and), disjunction (or), negation (not), conditional (if), biconditional, or if and only if (iff), and brackets (“(“and”)”) (Kilgour, Hipel, and Fang, ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions”).

Fig. 3 Preference tree for the USA. (Source: Fig. 2 of Hipel et al. (2020))

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Relationships of Conflict Analysis Approaches In this subsection, connections among decision situations as shown in Fig. 1 are further explained, and relationships of formal approaches for analyzing MPMC, MPSC, and SPMC problems are discussed. Progress made is summarized. As discussed in section “Multiple Participant-Multiple Criteria Decision Situations,” Hipel et al. (1993) put forward an assertion that MPMC decision situations can be tackled by converting them into MPSC or SPMC problems. To tranform an MPMC situation into an MPSC problem, each participant or decision-maker (DM) is confronted by an SPMC situation. Techniques for handling SPMC situations are often called multiple criteria decision-making (MCDM) in the literature. Hipel et al. (1993) also explained the relationship between SPMC and MPSC decision situations. If the North-Western Electronics situation formulated as an SPMC problem shown in Table 1 is presented in the ordinal ranking version, the resulting formulation is displayed on the left side of Table 6, where alternative activities are ranked with respect to the five criteria. In particular, each number represents an ordinal ranking where a higher number indicates greater preference. For example, according to criterion C2 on the left, alternative A1 is most preferred and A3 is least preferred. The left side of Table 3, when the North-Western Electronics situation is formulated as an MPSC problem, appears at the right side of Table 6, where the preferences of five participants or DMs for the three outcomes or alternatives are displayed. Table 6 demonstrates the similarity of structure between the SPMC and MPSC problems, which indicates that techniques that have been developed to deal with one type of situation can be utilized in the other. Therefore, an SPMC decision situation such as that displayed in Table 1 can be investigated using methods that have been developed for studying an MPSC situation. Similarly, the MPSC situation in Table 2 can be analyzed using approaches developed for SPMC situations. The interchangeability of participants and criteria allows greater flexibility in the analysis of both multiple-participant and multiple-criteria decision situations. In fact, Hipel et al. (1993) asserted that the structures of SPMC and MPSC decision problems are essentially the same. When using this same structure, appropriate techniques for analyzing SPMC situations can be utilized for studying MPSC situations, and vice Table 6 Comparison of SPMC and MPSC problems for North-Western Electronics SPMC Criteria C1 C2 C3 C4 C5

MPSC Activities A1 A2 2 3 3 2 1 2 2 1 1 3

A3 1 1 3 3 2

Participants VPA VPB VPC VPD VPE

Source: Table 4 of Radford et al. (1994)

Preferences for outcomes (most preferred to least preferred) A2 A1 A3 A1 A2 A3 A3 A2 A1 A3 A1 A2 A2 A3 A1

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versa, which are explained in detail in the remainder of this subsection. Another way to make a decision based on preference orderings is voting (Nurmi, ▶ “Group Decisions: Choosing a Winner by Voting”). A number of studies have appeared in the literature using MCDM techniques to elicit preference information for DMs in conflict analysis methods, in particular, the GMCR approach: 1. An analytic hierarchy process (AHP)-based preference-ranking method is incorporated into GMCR to investigate the Canadian west coast port congestion problem (Ke et al. 2012a). 2. An MCDM approach based on the outranking method, ELECTRE III, is utilized to elicit each DM’s ordinal preferences over the possible states within the GMCR framework (Ke et al. 2012b). 3. An operationalized methodology that employes value-focused thinking, AHP, and a variety of methods, such as criteria-satisficing, optimization, prioritization, and weighting, to capture DMs’ ordinal preferences from their value systems is integrated with GMCR (Bristow et al. 2014). Preferences are generated to take into account evolving contextual variables in order to simulate DMs’ responses dynamically. 4. An MCDM approach based on the preference-ranking organization method for enrichment evaluations (PROMETHEE) is used to rank possible states according to four criteria for one DM within the framework of GMCR (Silva et al. 2017a). 5. Probabilistic composition of preferences, an MCDM technique, is used to rank possible states for one of the DMs when analyzing a real-world conflict using GMCR (Silva et al. 2017b). 6. A methodology based on the integration of Dempster-Shafer Theory and AHP to elicit DMs’ preference information from experts is implemented within the GMCR framework (Silva et al. 2019). The elimination method in section “Single Participant-Multiple Criteria DecisionMaking” and the option prioritizing approach in section “Multiple Participant-Single Criterion Decision Situations” are developed separately in the areas of SPMC and MPSC decision-making, respectively. Based on the relationships between SPMC and MPSC presented in Hipel et al. (1993), Fraser (1993) pointed out that the elimination method and the preference tree approach (Fraser and Hipel 1988) are similar. As discussed in section “Multiple Participant-Single Criterion Decision Situations,” the option prioritizing method is developed from the preference tree approach. Therefore, the option prioritizing method of eliciting DMs’ preferences in GMCR and the elimination method for use in ranking alternatives in an SPMC problem are essentially the same. This can be explained as follows. By applying the option prioritizing method, the initial set of states is divided into two subsets that are determined by the truth or falsity of the first-ordered statement in the priority-ordered list of preference statements from a DM. The DM prefers any state in the truth subset to any state in the falsity subset (Fang et al. 2003a, b). The process continues for the second-ordered statement, third-ordered statement, . . ., until all of the statements are applied.

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Similarly, by applying the elimination method, the initial set of alternatives is divided into two subsets that are determined by meeting or not meeting the first factor statement in the priority-ordered list of evaluation factors. The DM prefers any alternative in the subset of meeting the factor statement to any alternative in the subset of not meeting the factor statement. The process continues until all of the factor statements are met (or not). Both preference statements and evaluation factors can contain logical connectives, such as conjunction (and), disjunction (or), negation (not), conditional (if), biconditional, or if and only if (iff), and brackets (“(“and”)”). A committee of members is often charged to evaluate a large number of alternatives based on combinations of alternatives, and to make recommendations. The problem can first be considered as an MPMC situation. Committee members have diverse interests, and each member has his or her own value system. By its mandate, however, the committee is required to make its overall recommendations. Urtiga et al. (2017) developed a methodology to support such committees. Each committee member’s SPMC problem is solved by using techniques developed for MPSC situations to obtain a ranking of alternatives, and a group-decision method – voting – is utilized to attain the committee’s recommendations by aggregating the final individual ranks. Specifically, Urtiga et al. (2017) considered a watershed committee with representatives from the government, water users, and civil society. Based on the original alternatives, possible combinations of alternatives for tackling a problem are systematically produced by using the option form representation discussed in section “Multiple Participant-Single Criterion Decision Situations.” Moreover, the option prioritizing method (also mentioned in section “Multiple Participant-Single Criterion Decision Situations”) is utilized to elicit each member’s ranking of the combinations of alternatives. Two decision support systems, GMCR II (Hipel et al. 1997; Fang et al. 2003a,b; Kilgour, Hipel, and Fang, ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions”) and GMCR+ (Kinsara et al. 2015, 2018; Kilgour, Hipel, and Fang, ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions”), developed for GMCR and described in section “Decision Support Systems” are able to support the generation of possible combinations of alternatives and the elicitation of preferences from committee members. The individual preferences are aggregated by using the weighted voting system based on classification by Quartile (Morais and de Almeida 2012) to obtain the final recommendations of the committee. Portfolio decision analysis focuses on the choice of a portfolio of alternatives rather than a single alternative. To achieve multiple, incommensurate, and often conflicting objectives, a subset of competing alternatives is selected. For example, to consider both the expected rate of return and variance, an investor selects to invest in a portfolio of alternatives rather than in a single alternative. MCDM methods are often utilized in portfolio decision analysis. Ge et al. (2014) developed a portfolio decision analysis approach for capability-based system-of-systems (SoS) architecting using GMCR, an MPSC approach. An SoS is a complex system whose system elements are themselves complex systems. To achieve the defined missions of an SoS, robust capabilities for a wide range of possible scenarios and circumstances as opposed to a specific situation or condition are required.

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Fig. 4 Relationships among conflict analysis approaches

Ge et al. (2014) defined the basic building block of what can or cannot be chosen to support capabilities as a “system option.” Moreover, each capability area and all potential technically feasible system options within the capability area are modeled as a DM and as options under the control of this DM, respectively, with the GMCR methodolgy. In this way, the generation of feasible portfolios, specification of possible portfolio changes, and elicitation of the DMs’ preferences over the feasible portfolios are carried out using techniques developed in GMCR. Thus, an analytical system portfolio selection model is built as a GMCR model with feasible states, allowable state transitions, and preference rankings over states. Subsequently, GMCR analysis procedures are utilized to carry out an extensive analysis of the possible strategic interactions among the DMs (capability areas) in order to predict potential compromise portfolios. A detailed case study that applies the portfolio decision analysis approach developed to architect a notional maritime threat response SoS is reported by Ge et al. (2014). Relationships among confict analysis approaches can be summarized as given in Fig. 4. Figure 4 is drawn from Fig. 1 with relationships among conflict analysis approaches added. Notice that for a general MPMC decision problem, it can be converted to an MPSC situation by using MCDM methods to separately rank states for each DM, or transformed into an SPMC problem via group decision-making processes. An MPSC decision problem can be approached as an SPMC situation by treating each DM as a criterion or by treating all of the DMs as forming a grand coalition. Finally, an SPMC situation can be considered as an MPSC problem by treating each criterion as a DM. Techniques developed for investigating SPMC problems can be suitably modified to study MPSC decision situations, and vice versa.

Decision Support Systems A wide variety of formal approaches for investigating MPMC, MPSC, and SPMC decision situations is reviewed in section “Formal Conflict Analysis Approaches.” In addition to having a sound theoretical basis, decision approaches often require

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implementation algorithms to facilitate their use in practical applications. Furthermore, to allow convenient and expeditious utilization by researchers and practitioners, a given decision technique and its associated algorithms should be implemented as a software system to serve as a decision support system (DSS) (Sage 1991). In this manner, the decision technique is transformed into a realizable decision technology. Table 7 furnishes a list of DSSs that have been developed for investigating MPSC and MPMC decision situations. A universal design of a flexible DSS for GMCR that Table 7 Decision support systems for application to conflict problems Name, author, and references AUTHOR and SCRIPT (Bryant and Bennett, ▶ “Using Drama Theory to Model Negotiation”) Conan (Howard 1990; Bryant and Bennett, ▶ “Using Drama Theory to Model Negotiation“) Confrontation Manager (Idea Sciences 2005; Bryant and Bennett, ▶ “Using Drama Theory to Model Negotiation”)

DecisionMaker (Fraser and Hipel 1984, 1988, 1989) Dilemma Explorer (Young 2017; Bryant and Bennett, ▶ “Using Drama Theory to Model Negotiation”) GMCR I (Fang et al. 1993; Kilgour et al. 1995; Kilgour, Hipel, and Fang, ▶ ”Conflict Resolution Using the Graph Model: Individuals and Coalitions”) GMCR II (Hipel et al. 1997; Fang et al. 2003a, b; Kilgour, Hipel, and Fang, ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions”)

GMCR+ (Kinsara et al. 2015, 2018; Kilgour, Hipel, and Fang, ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions”)

INTERACT (Bennett et al. 1994; Bryant and Bennett, ▶ “Using Drama Theory to Model Negotiation”)

Purposes Enables a user to conduct a drama theory analysis and present the analysis results for immersive briefing Uses the option form of metagame analysis to interactively model and analyze disputes Models a set of nested confrontations utilizing the options’ board notation, similar to the option form; identifies the dilemmas; and furnishes a narrative explanation of the various means in which the dilemmas could be eliminated Utilizes the option form and solution concept of sequential stability to model, analyze, and interpret both small and large disputes Examines confrontations, identifies those drama theory dilemmas that are blocking agreement, and shows the steps that are required to overcome the dilemmas Computes the stability of every state for every DM in two- or n-DM disputes according to a wide variety of models of human behavior using the graph model for conflict resolution (GMCR) Contains a user-friendly input subsystem based on the option form, an analysis engine adapted from GMCR I, and an output subsystem facilitating poststability analysis to investigate conflicts having two or more DMs using GMCR Contains four analysis engines – logical, matrix, inverse, and goal seeker – as well as interfaces to communicate graph models and to visualize postanalysis results to study two- or n-DM conflicts utilizing GMCR Utilizes the option form and graphical displays to investigate situations under the control of several interested DMs

Source: Updated and modified from Table 6 of Radford et al. (1994)

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will incorporate all of the progress made to date and allow easy expansion of the DSS, as new theoretical and practical developments are attained, is presented by Xu et al. (2018, Ch 10). A survey of DSSs that can be utilized for studying SPMC decision problems is beyond the scope of this chapter. Weistroffer and Li (2016) provide a survey of DSSs for MCDM problems.

Summary and Conclusions Group decision and negotiation involve multiple participants, each of whom may have multiple objectives. Therefore, it is fundamentally important to consider each DM’s values and objectives in studying and analyzing group decision and negotiation processes. Sometimes, a negotiation ends when an ingenious way is found to rearrange the issues so that all parties consider that they have won. However, it is much more common to find that “getting to yes” by cleverly slicing and dicing the issues is simply not possible. Any possible outcome involves one side winning and the other (or all others) losing. The best one can hope for is that each party wins on the issues it thinks are most important. Good procedures for making group decision involve DMs acting on their values and objectives to drive the process toward a conclusion that requires minimal concessions from all participants. As demonstrated in the chapter, significant strides have been made in the development and application of techniques in the areas of multiple participant-multiple criteria (MPMC), multiple participant-single criterion (MPSC), and single participant-multiple criteria (SPMC) decision-making, and in the development and implementation of decision support systems (DSSs). Those techniques and associated DSSs can assist in identifying parties or DMs involved in group decisions and negotiations, their values and objectives, and the courses of actions under their control; generating possible scenarios; eliciting each party’s preferences; examining possible strategic interactions among parties as well as possible coalition formations by parties; and carrying out poststability analysis. It is also shown in this chapter that progress has been made in adapting techniques developed in one area of decisionmaking for employment in another area. Although good progress has been made in the design, development, and implementation of useful decision technologies and associated DSSs, much research remains to be done. More work is required for adding to the box of decision tools available for use in the three decision situations shown in Figs. 1 and 4. By further understanding and strengthening the useful connections among these decision situations depicted in Fig. 4, significant work can be accomplished to transfer and adapt appropriately modified decision technologies from one area to another as well as to develop new and more comprehensive techniques. Certainly, a bright future awaits those who can create operational decision technologies for satisfying the research needs in the three decision situations and their connections identified in Fig. 4.

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Cross-References ▶ A Group Multicriteria Approach ▶ Conflict Resolution Using the Graph Model: Individuals and Coalitions ▶ Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives ▶ From Game Theory to Drama Theory ▶ Group Decision Support Using the Analytic Hierarchy Process ▶ Group Decisions: Choosing a Winner by Voting ▶ Group Decisions: Choosing Multiple Winners by Voting ▶ Multicriteria Methods for Group Decision Processes: An Overview ▶ Multiple Criteria Decision Support ▶ Non-cooperative Bargaining Theory ▶ Using Drama Theory to Model Negotiation

References Bennett PG, Tait A, MacDonagh K (1994) INTERACT: developing software for interactive decisions. Group Decis Negot 3(3):351–372 Bristow M, Fang L, Hipel KW (2014) From values to ordinal preferences for strategic governance. IEEE Trans Syst Man Cybern Syst 44(10):1364–1383 Bryant JW (2016) Acting strategically using drama theory. CRC Press, Boca Raton Fang L, Hipel KW, Kilgour DM (1993) Interactive decision making: the graph model for conflict resolution. Wiley, New York Fang L, Hipel KW, Kilgour DM, Peng J (2003a) A decision support system for interactive decision making, part 1: model formulation. IEEE Trans Syst Man Cybern Part C 33(1):42–55 Fang L, Hipel KW, Kilgour DM, Peng J (2003b) A decision support system for interactive decision making, part 2: analysis and output interpretation. IEEE Trans Syst Man Cybern Part C 33(1): 56–66 Fraser NM (1993) Application of preference trees. In: Proceedings of the 1993 IEEE international conference on systems, man and cybernetics. Le Touquet, 17–20 Oct, pp 132–136 Fraser NM, Hipel KW (1979) Solving complex conflicts. IEEE Trans Syst Man Cybern 9(12):805–816 Fraser NM, Hipel KW (1984) Conflict analysis: models and resolutions. North-Holland, New York Fraser NM, Hipel KW (1988) Decision support systems for conflict analysis. In: Singh MG, Salassa D, Hindi KS (eds) Proceedings of the IMACS/IFOR first international colloquium on managerial decision support systems and knowledge-based systems, Manchester, 23–25 Nov 1987. North-Holland, Amsterdam, pp 13–21 Fraser NM, Hipel KW (1989) Decision making using conflict analysis. OR/MS Today 16(5):22–24 Ge B, Hipel KW, Fang L, Yang K, Chen Y (2014) An interactive portfolio decision analysis approach for system-of-systems architecting using the graph model for conflict resolution. IEEE Trans Syst Man Cybern Syst 44(10):1328–1346 Hipel KW (ed) (1992) Multiple objective decision making in water resources. Set of refereed papers published as AWRA Monograph Series No. 18 by the American Water Resources Association and also published in the February issue of Water Resources Bulletin, vol 28, 1992 Hipel KW, Fang L (2005) Multiple participant decision making in societal and technological systems. Systems and human science, for safety, security, and dependability: selected papers of the 1st international symposium SSR2003, Osaka, Nov 2003. Elsevier, Amsterdam, pp 3–31 Hipel KW, Radford KJ, Fang L (1993) Multiple participant-multiple criteria decision making. IEEE Trans Syst Man Cybern 23(4):1184–1189

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Hipel KW, Kilgour DM, Fang L, Peng J (1997) The decision support system GMCR in environmental conflict management. Appl Math Comput 83(2–3):117–152 Hipel KW, Fang L, Kilgour DM (2020) The graph model for conflict resolution: reflections on three decades of development. Group Decis Negot 29(1):11–60 Howard N (1971) Paradoxes of rationality: theory of metagames and political behaviour. MIT Press, Cambridge, MA Howard N (1990) Soft game theory. Inf Decis Technol 16(3):215–227 Howard N (1994a) Drama theory and its relations to game theory. Part 1: dramatic resolution vs. rational solution. Group Decis Negot 3(2):187–206 Howard N (1994b) Drama theory and its relations to game theory. Part 2: formal model of the resolution process. Group Decis Negot 3(2):207–235 Howard N (1999) Confrontation analysis: how to win operations other than war. CCRP publications. Pentagon, Washington, DC Idea Sciences (2005) Confrontation manager user manual. Idea Sciences, Washington, DC Ke GY, Li KW, Hipel KW (2012a) An integrated multiple criteria preference ranking approach to the Canadian west coast port congestion problem. Expert Syst Appl 39(10): 9181–9190 Ke GY, Fu B, De M, Hipel KW (2012b) A hierarchical multiple criteria model for eliciting relative preferences in conflict situations. J Syst Sci Syst Eng 21(1):56–76 Keeney RL (1992) Value-focused thinking: a path to creative decision making. Harvard University Press, Cambridge, MA Keeney RL, Raiffa H (1976) Decision analysis with multiple conflicting objectives. Wiley, New York Kilgour DM, Hipel KW, Fang L (1987) The graph model for conflicts. Automatica 23(1):41–55 Kilgour DM, Fang L, Hipel KW (1995) GMCR in negotiations. Negot J 11(2):151–156 Kilgour DM, Chen Y, Hipel KW (2010) Multiple criteria approaches to group decision and negotiation. In: Ehrgott M, Figueira JR, Greco S (eds) Trends in multiple criteria decision analysis. Springer, New York, pp 317–338 Kinsara RA, Petersons O, Hipel KW, Kilgour DM (2015) Advanced decision support system for the graph model for conflict resolution. J Decis Syst 24, 2, 117–145 Kinsara RA, Kilgour DM, Hipel KW (2018) Communication features in a DSS for conflict resolution based on the graph model. Int J Inf Decis Sci 10(1):39–56 Ma J, Hipel KW, De M, Cai J (2008) Transboundary water policies: assessment, comparison and enhancement. Water Resour Manag 22:1069–1087 MacCrimmon KR (1973) An overview of multi-objective decision making. In: Cochrane RL, Zelany M (eds) Multiple criteria decision making. University of South Carolina Press, Columbia, pp 18–46 Morais DC, de Almeida AT (2012) Group decision making on water resources based on analysis of individual rankings. Omega Int J Manag Sci 40:42–52 Obeidi A, Hipel KW (2005) Strategic and dilemma analyses of a water export conflict. INFOR 43(3):247–270 Radford KJ (1989) Individual and small group decisions. Springer, New York Radford KJ, Hipel KW, Fang L (1994) Decision making under conditions of conflict. Group Decis Negot 3(2):169–185 Roy B (1985) Methodologie Multicritere d’Aide a la Decision. Economica, Paris Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York Sage AP (1991) Decision support systems engineering. Wiley, New York Silva MM, Hipel KW, Kilgour DM, Costa APCS (2017a) Urban planning in Recife, Brazil: evidence from a conflict analysis of the New Recife Project. J Urban Plann Dev 143(3): 05017007-1–05017007-11 Silva MM, Kilgour DM, Hipel KW, Costa APCS (2017b) Probabilistic composition of preferences in the graph model with application to the New Recife Project. J Leg Aff Disput Resolut Eng Constr 9(3):05017004-1–05017004-13

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Silva MM, Hipel KW, Kilgour DM, Costa APCS (2019) Strategic analysis of a regulatory conflict using Dempster-Shafer theory and AHP for preference elicitation. J Syst Sci Syst Eng 28(4): 415–433 Talukder B, Blay-Palmer A, Hipel KW, vanLoom GW (2017) Elimination method of multi-criteria decision analysis (MCDM): a simple methodological approach for assessing agricultural sustainability. Sustainability 9:287. (17 pages) Urtiga MM, Morais DC, Hipel KW, Kilgour DM (2017) Group decision methodology to support watershed committees in choosing among combinations of alternatives. Group Decis Negot 26 (4):729–752 Von Neumann J, Morgenstern O (1953) Theory of games and economic behavior, 3rd edn. Princeton University Press, Princeton Weistroffer HR, Li Y (2016) Multiple criteria decision analysis software. In: Greco S, Ehrgott M, Figueira JR (eds) Multiple criteria decision analysis: state of the art surveys. Springer, New York, pp 1301–1341 Xu H, Hipel KW, Kilgour DM, Fang L (2018) Conflict resolution using the graph model: strategic interactions in competition and cooperation. Springer, Cham Young M (2017) Dilemma explorer. Available at https://www.decisionworkshops.com/dilemmaexplorer/4581290653. Accessed 31 July 2020

From Game Theory to Drama Theory Jim Bryant

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Games and Hypergames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metagames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Analysis of Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Problem of Inducement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emotional Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Concept of Drama Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drama Theory: Early Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Drama theory is an analytical framework that can be used by parties, either in negotiation or in confrontation with others, to inform their strategic decisions. Its conceptual foundation is game theory and so the elements of a situation upon which attention is focused are the parties that it involves, the strategic choices that they have available to them, and their evaluation of the stability and the outcomes of the resulting situations that they could coproduce. However, game theory is centrally preoccupied with the behavior of rational agents, and it has been shown that in many real-life games paradoxes undermine attempts to make objectively rational choices. This recognition led to the development of metagame analysis and its associated facilitated group process, the analysis of options. While the metagame approach overcame the paradoxes in games of coordination and in confrontations typified by “prisoner’s dilemma,” it failed to surmount the difficulties in the game “Chicken” where players are seeking to induce others to act in J. Bryant (*) Sheffield Business School, Sheffield Hallam University, Sheffield, UK e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_14

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certain ways. In these circumstances, emotionally-fueled changes in individual preferences and perceptions drive the development of an interaction. These developments were codified in “soft game theory” which in turn provided a theoretical foundation for the more rounded schema of drama theory. The latter enables a mapping of the hopes and demands of those involved in an interaction and pays due attention to such practically important matters as the credibility of claims, threats, and promises and the emotional tone of an engagement. Keywords

Negotiation · Development from game theory · Drama theory · Metagame · Conflict analysis · Collaboration · Emotion

Introduction This chapter relies heavily upon the published and unpublished work of the late Nigel Howard, the originator of metagame analysis and ‘soft’ game theory and the principal intellectual driving force behind the development of drama theory. Drama Theory provides an analytical framework that a party can use to inform its choices when dealing with others, either in a negotiation or in a confrontation. It offers a ready means of summarizing within a coherent structure the hopes and demands of those involved and pays due attention to such practically important matters as the credibility of claims, threats and promises, and the emotional tone of an engagement. The approach has evolved from its origins in game theory, developing, as it has diverged, a special focus upon the management of the apparently irreconcilable dilemmas that parties inevitably encounter as they attempt to persuade or are persuaded by others. Drama Theory today is the outcome of an intellectual process as convoluted as many of the other pathways that have characterized technological development. And along this track lies the debris of theoretical structures as impressive – even heroic – in their way as those of pre-Copernican astronomy or of phlogiston theory: theories that met a contemporary scientific need but which, in time, had to be overturned or radically refashioned to meet more exacting requirements. This chapter outlines the development of the intellectual structures that stemmed from Nigel Howard’s searching critique of game theory in the late 1960s and led to a family of analytical approaches to negotiation; while its principal focus in the latter is upon drama theory, other techniques covered in the present volume are also encountered. In a self-conscious echo of Marinetti’s Futurist Manifesto, drama theory was launched with a rhetorical flourish in a manifesto (Howard et al. 1992) that suggested a wish to analyze the emotional and political aspects of choice and so embrace “nonrational” aspects of decision-making (e.g., crisis, emotion, self-realization) rather than restrict itself to the rational choice paradigm on which game theory rests. In retrospect, this aspiration can be seen as a natural progression from Howard’s innovation of metagame theory developed while he was working on a project for

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the US Arms Control and Development Agency (ACDA) and so the present narrative must provide the background to that work and track its ramifications through the following half century.

Games and Hypergames Famously, the philosopher David Hume (1888) argued that “reason is, and ought only to be the slave of the passions,” implying that while our motivating aims are established by the passions, it is reason that guides us in achieving these ends. Game theory is the preeminent analytical tool for implementing this doctrine of instrumental rationality. It does so by treating real human interactions as if they were moves by players in the artificial, rule-based world of games, where strategy depends completely upon means-end rationality. Game-theoretic analysis deals with individual choice in situations where the information base of each party is shaped by the declared intentions and choices of every other participant. Typically, it involves a search for ways of achieving outcomes that are best for the individual – “best” is taken in the limited sense of most-preferred, rather than in the wider sense of satisfying Humean passions – and it emphasizes personal rather than collective utility. A flavor of such analysis can be gained from the chapter ▶ “Non-cooperative Bargaining Theory.” While the modern formalization of game theory can be precisely dated to the publication of the Theory of Games and Economic Behaviour by John von Neumann and Oskar Morgenstern in 1944, game theoretic thinking is evident in Classical writers; indeed some problems posed by Classical philosophers are best addressed through game theory. One example of the latter, given by Plato is his elder brother Glaucon’s argument (Bloom 1991) that it is only for instrumental reasons that a system of human justice has emerged. The argument starts from a view that while people might like to take advantage of others and act unjustly, the harm that they would themselves suffer if in return they were treated unjustly cautions them against exploiting others; the consequence is an unwritten agreement neither to do injustice nor to suffer it. A simple, illustrative game theoretic formulation of this situation involving two parties (call them Alf and Bet) assumes each as having the choice between being just or unjust. According to Glaucon, from Alf’s perspective the worst outcome would result from acting justly whilst Bet acts unjustly; the best to be unjust while Bet is just. Mutual justice and mutual injustice are intermediate in worth, with the former being preferred to the latter (Glaucon said that those who cannot choose but have Table 1 Glaucon’s argument: “natural” injustice Cells show assessments by Alf,Bet. Equilibria are shaded. Alf’s choice

Just Unjust

Bet’s choice Just Good, Good Best, Worst

Unjust Worst, Best Bad, Bad

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experienced injustice would prefer to agree that both should be just). Then the encounter can be summarized as a Normal form game as shown in Table 1. It can be seen that in this game whichever option the other player takes, a party is best off being unjust: the equilibrium state – the state from which no player has an incentive to move – is mutual injustice. According to Glaucon, people intuitively recognize these payoffs and so reluctantly resign themselves to conforming to a system of justice since otherwise they will sink with everyone else into the more disagreeable world of mutual injustice: but given half a chance (Glaucon’s example is the ring of Gyges, which confers invisibility on the perpetrator of evil deeds), people would otherwise act unilaterally in their own selfish interests. Among game theorists, this is immediately recognized as an example of the Prisoner’s Dilemma, a classic game to which, to the chagrin of the game theorists themselves, a rational solution does not exist (unless the game is repeated). To demonstrate the exploration of strategy that game theory facilitates, it is worth briefly examining a variation of the assumptions made in the game above. Suppose that (as Plato proposes) a society be created in which justice is a core value: that is, all accept mutual justice as the very best outcome. Then the game transforms to the game shown in Table 2. Note that idealism has not totally triumphed here and if the cultural aim of collective justice were to collapse people are assumed still to seek personal advantage. Mutual justice is a stable outcome from which neither party can improve. However, the malign presence of mutual injustice persists as an alternative, though collectively undesired equilibrium. This game is well-known to game theorists and describes many situations in which parties seek assurance; for instance, it corresponds to Rousseau’s description of the social contract. It also exemplifies the situation of the oligarchs of Ancient Greece (Simonton 2017) who needed to maintain solidarity in the face of potential democratic uprising: at any time one or more oligarchs might break away from the ruling elite and seek to take control with the wider support of the demos (the Four Hundred oligarchs manifestly failed to achieve this solidarity in 411 BC). One condition normally required in game theory is that of Common Knowledge (CK)(Vanderschraaf and Sillari 2014). This goes beyond the notion of complete information (where each player knows the rules of the game and the preferences of the other parties) by requiring that each player is aware that each other player has complete information; and each player is aware that each other is aware; and so on. However, a moment’s reflection shows that it is far from clear that in everyday life people have CK of situations that they share together: indeed, misperceptions are not uncommon. Essentially, players can be attempting to play different games. Table 2 Glaucon’s argument: a just society Cells show assessments by Alf,Bet. Equilibria are shaded. Alf’s choice

Just Unjust

Bet’s choice Just Best, Best Good, Worst

Unjust Worst, Good Bad, Bad

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Table 3 Glaucon’s argument: misperceptions

Col’s Perception

Dee’s choice

Dee’s Perception

Dee’s choice

Cells show assessments by Col,Dee

Just

Unjust

Cells show assessments by Col,Dee

Just

Unjust

Just

Best, Good

Worst, Best

Col’s choice

Just

Good, Best

Worst, Good

Unjust

Good, Worst Bad, Bad

Unjust

Best, Worst Bad, Bad

Col’s choice

To see the mischief that arises from such misperceptions, consider the “justice game” introduced above but this time with two players Col and Dee who perceive different games (Table 3). On the left in Table 3 is shown the game that Col might perceive. Here it is assumed that Col ranks the outcomes as in the “just society” game (Table 2) earlier. However, it is further assumed that Col suspects that Dee is a reluctant adherent to justice (as in Table 1). This gives the game as seen by Col. On the right is shown the game that, for the sake of illustration, Dee perceives. Making the assumption that Dee’s beliefs about Col, mirror those that Col holds about Dee, then Dee’s perceived game is as on the right. Taking these two games together it can be seen that from Col’s perspective (i.e., in Col’s perceived game) acting unjustly would be Dee’s preferred strategy (in that game, for both Col’s choices, Dee does better by acting unjustly); correspondingly, in Dee’s perceived game, Col always does better acting unjustly. The result is a world of mutual injustice that neither wants. Furthermore, by acting in this way, each confirms the other’s suspicions that they would be wrong to place trust in the other. This is just one way – clearly not the only one – in which mutual mistrust can arise from misperceptions. More complex misunderstandings can arise when one party has options that the other does not even see: thereby “strategic surprise” can occur in military confrontations. The theory of hypergames was developed (Bennett 1980a) to extend game theory into such situations where players’ perceptions of the game they are playing may differ. In this framework an n-person game Γ has n associated hypergames Γk (for k = 1 to n), each representing the perception of the corresponding player. In principle, each such hypergame has, in turn, n associated hypergames Γjk (for j, k = 1 to n) representing j’s perception of k’s perception. An infinite tree of hypergames could be envisaged but to date this is only of theoretical interest and the focus in applications has remained on the first-order hypergames. In retrospective applications of hypergame, analysis to actual conflict situations useful insights have been gained into various aspects of the interactions. An early study (Bennett and Dando 1979) of the Fall of France in World War 2 clearly demonstrated the disastrous significance that an Allied perception, bounded by a blinkered theoretical model, had upon the outcome of the Axis offensive. In another case study (Giesen and Bennett 1979), hypergame analysis showed that a decision that was apparently irrational, even stupid, in terms of a conventional game-theoretic

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formulation was arrived at quite rationally once perceptual limitations and information conditions were considered. Other uses of the hypergame framework have included such contrasting examples as an investigation of football hooliganism (Bennett et al. 1980) and a study of nations “bidding” to attract a major investment by multinational organization (Bennett 1980b). This body of work demonstrated how one shortcoming of game theory can be overcome. More specifically, the hypergame approach offered an effective means of systematically exploring and testing alternative hypotheses about perceptions in conflict and often threw unexpected insights upon the motives underlying observed behavior. For obvious reasons, it proved particularly relevant to situations where the parties misperceived each other and consequently helped to explain the importance and value of communicated information; and by implication, the importance and value of sometimes preventing such communication to occur.

Metagames In his ground-breaking book Paradoxes of Rationality: theory of metagames and political behavior, Nigel Howard (1971) used three generic games – “Co-ordination,” “Prisoner’s Dilemma,” and “Chicken” – successively to demonstrate disabling paradoxes that lie in wait for rational agents. In certain games of coordination – for instance the so-called Battle of the Sexes where a couple wish to spend time together but each argue for using this time differently – there is no single equilibrium: it is impossible for both parties to be objectively rational. In “Prisoner’s Dilemma” (illustrated above) there are pressures to act irrationally: superficially a rational choice may offer a better outcome than an irrational one but when taken with the other party’s response, two rational players fare worse than two irrational ones. Finally, in “Chicken” (e.g., the “Cold War” standoff) both parties must be willing to risk annihilation (to act irrationally) if they are to achieve stability: this is explored more fully below. A theoretical discourse, but nevertheless firmly based in the world of practice through the author’s concurrent work on nuclear proliferation, the Vietnam and Arab-Israeli conflicts and issues of social discord (Bain et al. 1971), Howard’s book directly attacked the dominant concept of instrumental rationality. It was no surprise that the text attracted both favorable (Thrall 1974; Lutz 1974) and strongly critical (Harsanyi 1974a) reviews, the latter leading to a heated debate (Harsanyi 1974b, c; Howard 1974a, b) and subtly but steadily to schism from mainstream work in game theory. This breach is only now being healed through a fresh recognition of the complementary roles that drama theory – the lineal successor of Howard’s earliest work – and game theory can play in modelling strategic conflict. The early history is still relevant because it established a position which carries through to present-day work in drama theory; that the making of unreasonable assumptions about human rationality should be avoided. Undaunted by the impossibility of finding a rational solution to such tricky yet commonplace problems as those introduced above, most game theorists persist in the assumption of strict rationality in their analyses and so are forced to contrive

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artificially complex definitions of rationality to account for people’s behavior. Howard resisted this temptation to revise the common-sense view of rationality and instead embraced irrationality by building upon the concepts of majorant and minorant games originally floated by von Neumann and Morgenstern. These are defined as follows. For a game Γ between Player A and Player B, the game ΓA in which A makes his choice before B and B makes his choice in full knowledge of A’s decision is called the minorant game of Γ, and the game ΓB in which B makes his choice before A and A makes his choice in full knowledge of B’s decision is called the majorant game of Γ. Extending these ideas, Howard’s concept of a “metagame” (Howard 1966a, b) is the game that would exist if one player chose his strategy after the others and in knowledge of their choices: an n-person game Γ has n associated metagames Γk (for k = 1 to n). However, each such metagame has, in turn, n associated metagames Γjk (for j, k = 1 to n); and so on, creating an infinite tree of metagames. The assumption is that behavior in Γ can be interpreted as behavior in the infinite tree of metagames, since for a player to attempt to be objectively rational it must take account of others’ subjective games and choose a “metastrategy” – a strategy for selecting a strategy – in the light of the overall metagame tree. Incidentally, this means that players are treated as being as fully aware of the recursive structure as is any game theorist; there is no privileged “higher” view that is not theoretically accessible to the participants. To demonstrate how the metagame concept “solves” games like “Prisoners Dilemma” return to the Glaucon’s original argument (Table 1 above). For clarity of exposition, the labels “Fair” and “Unfair” will be used to signify “Just” and “Unjust” behavior on Bet’s part (acknowledging the linguistic inexactitude introduced if these were to be interpreted literally). Then the corresponding Alf-metagame (Table 4) and Bet-metagame (Table 5) are as shown.

Table 4 Glaucon’s argument: Alf-metagame

Just/Just Unjust/Unjust Just/Unjust Unjust/Just

Alf

Fair Good, Good Best, Worst Good, Good Best, Worst

Bet

Unfair Worst, Best Bad, Bad Bad, Bad Worst, Best

Table 5 Glaucon’s argument: Bet-metagame

Alf

Just

Fair/Fair Good, Good

Bet Unfair/Unfair Worst, Best

Fair/Unfair Good, Good

Unfair/Fair Worst, Best

Unjust

Best, Worst

Bad, Bad

Bad, Bad

Best, Worst

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The row labels in the Alf-metagame are Alf’s policies: before the forward slash what Alf would do if Bet chooses “Fair”; after the forward slash, Alf’s action if Bet chooses “Unfair.” The column headings in the Bet-metagame have a corresponding interpretation. In metagame analysis it is assumed that each player’s choice is based upon what it anticipates the other player will choose: that is, these metagames are simulated “in the heads” of the two players prior to any actual game play. The equilibrium concept used is also built upon this idea: “an outcome . . .. is ‘stable’ precisely when all players do in fact succeed in predicting it.” Stable outcomes of the original game which are yielded by equilibria of a metagame are termed metaequilibria and these are shaded above. Here the two metagames suggest the same outcome as in the original game but this is not invariably the case. As indicated earlier the metagame concept takes strategic reflection to higher levels: after all, would not each player make its choice taking account of the other player’s predictions of the decision it might take? Such second-level responses can be given for the preceding example: the Alf-Bet-metagame is shown in Table 6. The second column lists all 16 possible reaction patterns (counter policies) by Alf to Bet’s possible policies. The metaequilibria are shaded: while one corresponds to the outcome found in the earlier game, there is also one corresponding to the cooperative solution of this original game. A plausible dialogue based on declarations of their policies could be imagined between the two parties, leading to this apparently “irrational” result. Such conversations and results have been observed in experimental situations, thus supporting this unexpected finding. As to whether one or other of these metaequilibria is more important than the others, metagame analysis remains deliberately agnostic: it is not a theory intended to predict behavior. While Table 6 Glaucon’s argument: Alf-Bet-metagame Alf J/J/J/J U/U/U/U U/U/U/J U/U/J/U U/U/J/J U/J/U/U U/J/U/J U/J/J/U U/J/J/J J/U/U/U J/U/U/J J/U/J/U J/U/J/J J/J/U/U J/J/U/J J/J/J/U

Bet Fair/Fair Good, Good Best, Worst Best, Worst Best, Worst Best, Worst Best, Worst Best, Worst Best, Worst Best, Worst Good, Good Good, Good Good, Good Good, Good Good, Good Good, Good Good, Good

Unfair/Unfair Worst, Best Bad, Bad Bad, Bad Bad, Bad Bad, Bad Worst, Best Worst, Best Worst, Best Worst, Best Bad, Bad Bad, Bad Bad, Bad Worst, Best Worst, Best Worst, Best Worst, Best

Fair/Unfair Good, Good Bad, Bad Bad, Bad Good, Good Good, Good Bad, Bad Bad, Bad Good, Good Good, Good Bad, Bad Bad, Bad Good, Good Good, Good Bad, Bad Bad, Bad Good, Good

Unfair/Fair Worst, Best Best, Worst Worst, Best Best, Worst Worst, Best Best, Worst Worst, Best Best, Worst Worst, Best Best, Worst Worst, Best Best, Worst Worst, Best Best, Worst Worst, Best Best, Worst

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many real-life plays of this game of Prisoner’s Dilemma do indeed resolve in Cooperation (Payoffs = Good, Good), sometimes joint Defection (Payoffs = Bad, Bad) comes about through mutual mistrust. Before moving on it is worth observing that there is of course no limit to the level of recursion that may be used in considering a player’s choices (though there are of course practical limits – even the third order metagame contains more than 4000 payoff cells). Luckily Howard proved that all the metaequilibria of a 2-player game are found at the second stage of the process, and that they persist at higher levels. It is useful to introduce here the concept of a metarational outcome (Management Science Center 1968) since it raises issues that foreshadow subsequent developments of metagame analysis. A metarational outcome is defined in the 2-player case as an outcome that can be made attractive for one player by some policy chosen by the other player. That is, such outcomes are outcomes in the normal-form game that also correspond to rational outcomes for a particular player in a metagame. So in the Bet-metagame (Table 5), Bet’s Fair/Unfair policy makes the outcome (Just, Fair) metarational for Alf in this metagame, while in the Alf-Bet-metagame (Table 6), Alf’s Unjust/Unjust/Just/Unjust policy makes Fair/Unfair metarational for Bet. Identifying which outcomes are metarational for a given player in a given metagame shows what conclusions that player can deduce from a process of thought leading to that particular metagame: for example, the considerations that lead Alf to the Betmetagame may lead him to think that (Just, Fair) is his best outcome. Of course, this also depends upon the policy that the player believes the other player is following in that metagame; if an outcome is not metarational for both players, then it is not a metaequilibrium from that metagame. The above discussion has demonstrated the significance that must be attached to the credibility of players’ policies. For the cooperative outcome (Just, Fair) to be an equilibrium Bet must make credible a “Tit-for-tat” policy (i.e., Fair/Unfair) of being cooperative if the Alf is Just, but uncooperative otherwise. If Alf reacts with the counter-policy U/U/J/U (which is perfectly “rational” since it involves choosing his best response to each of Bet’s policies) then (Just, Fair) will be the optimal outcome for both players. This means that the crucial issue is finding a way of making credible appropriate conditional policies. The challenge is underscored by noting that (Unjust, Fair), Bet’s worst outcome is still metarational for Alf in the Alf-Betmetagame of Table 6. Were Alf to believe that Bet’s policy is always to be fair (i. e., Fair/Fair) then (Unjust, Fair) is the best outcome that Alf can obtain: Alf would see unconditional cooperation as being Bet’s de facto policy if he thought that he might covertly prepare unjust measures. The difficulty here is that (Just, Fair) is not rational for either player but is only metarational, so it needs to be bolstered by credible conditional policies to render it stable. Howard asserted that any specific game is better understood through an analysis of its metagame tree and he demonstrated this through its earliest application. This was a study (Management Science Center 1969a) of the “Bay of Pigs” debacle which precipitated the Cuban Missile Crisis of 1961 and led to a heart-stopping standoff between the major nuclear powers. More telling than the actual models used to depict the evolving crisis was the fact that the historical process was represented and tracked

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using the approach: that is, there was a focus on the dynamics of conflict and on the movement from one phase of the narrative to the next. Interestingly, the models also appeared to achieve some predictive ability (although this was not their intention), a property found in subsequent case studies. What was most impressive about this work was the quality of the insights generated despite the parsimonious nature of the models. It suggested that working with the players’ subjective games was a valid approach.

The Analysis of Options Metagame analysis provided the theoretical foundation for a facilitated group process devised by Howard which he called the Analysis of Options (Management Science Center 1969b). This was a structured means of enabling an “audience” of experts with varied knowledge of a conflict domain to build and subsequently analyze their own model of the situation: software support for this process was also developed. The intention was not to “solve” the conflict but to improve decision-making by gaining a better understanding of the strategic structure of the interactions (Howard 1986). Typically the process commences with the surfacing and listing of the major issues involved in a situation: these might be critical actions, strategic balances, or “bones of contention.” The parties “owning” these issues and the choices that they have available to them – their “options” – are next made explicit: such options are expressed in binary form (they might or might not be done). These options provide the elements using which the possible strategies of each individual player can be stated (as sets of “yes”/“no” choices about the taking of its options) and the potential outcomes of the situation can be described (as sets of players’ strategies). Attention then turns to these outcomes, the stability properties of which are examined from the perspective of a specific player (or a coalition of players): this uncovers successively unilateral improvements, sanctions against such improvements and inescapable improvements. These improvements provide an indication of places where leverage upon the situation might be exerted. Howard’s initial experimental analysis was carried out with members of the US ACDA in May 1968 as they explored the possibilities for the Paris peace talks about the Vietnam War. The issues and players chosen for inclusion in the model (Howard 1969) are shown in the leftmost column of the Table 7. Two practically significant outcomes are shown in the second and third columns of the table, headed descriptively “Cease-fire” and “Negotiated Settlement.” Where an option is “taken” by the player concerned this is shown by a tick in the corresponding cell; an option not taken is indicated by a cross. The outcome is the combination of potential actions taken/not-taken by the players in its column. Howard recommended a sequential process of analysis. This is computationally economical and involves establishing the minimum assumptions needed to answer specific questions that might be asked about the game. To show how such a process might commence consider the stability of the “Negotiated Settlement.” This needs to viewed in turn from the perspective of each player: for the sake of illustration, suppose it is first considered it from the perspective of the North Vietnamese (NVN). Initially unilateral improvements for NVN would be considered. Suppose the experts say that

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Table 7 Vietnam War: metagame analysis Negotiated Settlement

Preferred by NVN

Negotiated Settlement

U.S. Cease bombing Withdraw South Vietnam (SVN)

Settle North Vietnam (NVN)

~ Withdraw National Liberation Front (NLF)

Settle

these are as shown in the column headed “Preferred by NVN” which corresponds to a set of two outcomes (N.B. the tilde “~” symbol represents “either/or”): then in the absence of credible sanctions NVN will not keep to the Negotiated Settlement. However, even though the outcome is not rational for NVN, it can still be stable if credible sanctions can be used against NVN to prevent them moving the situation to their preferred outcome(s). The next stage of analysis is therefore to find what sanctions exist against NVN in such circumstances. This multi-step process is too long to include here but might result in the following list of possible sanctions: USA and SVN resume fighting; USA not withdraw and NLF cease-fire; SVN continue fighting and NLF cease-fire. Whether or not each of these sanctions would be credible is a matter for expert judgment. For instance, the first two sanctions would hardly be credible if US troops had already been withdrawn from South Vietnam! In a rounded examination of an issue using metagames, this sequential probing of one outcome, seen from the perspective of one player would be repeated for other players and other outcomes: Howard likened the overall process to examining a large, dark warehouse with a small flashlight! However, in practice the search and assessment would be greatly accelerated and rendered manageable by the domain expertise of the client group. The use of a table to depict multi-player situations as in the Analysis of Options has proven a versatile presentational device and has been more widely adopted in later work. The scale of the analysis that it potentially requires (e.g., in the Vietnam case with nine options there are potentially 29 = 512 possible outcomes) has also encouraged the development of dedicated software tools to support comprehensive

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investigation, and in turn this has led to the possibility of testing for other, more complex, stability properties. For instance, Fraser and Hipel (1980) introduced and investigated sequential stability in their approach to conflict analysis. This was subsequently incorporated in the generalized formulation due to Kilgour et al. (1987), which represented players’ choices, preferences, and sanctions as moves between outcomes within a directed graph (the so-called Graph Model, covered in the chapter ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions”). The historical retrospective provided by Hipel in the chapter ▶ “Looking Back on Decision-Making Under Conditions of Conflict” provides an account of these developments.

The Problem of Inducement Unfortunately, the shortcomings of rational behavior are not fully overcome by the metagame concept. This was acknowledged by Howard (1971) who set out the case for developing what he called a theory of Inducement. Essentially, inducement is involved in situations where a player, knowing other’s preferences and relying upon their propensity to act rationally (in a metagame, if not in the original game), can so act as to achieve an outcome he prefers. What happens then when different players are seeking to induce different outcomes? To take a practical example, suppose that two countries – call them Blue and Red – threaten each other with weapons of mass destruction (WMD) over some geopolitical issue, as summarized in Table 8. This is a game with two equilibria, at each of which one side but not the other “gives in.” The temptation for each player is to be the one to “stick to its guns” and so achieve its favored equilibrium, but if both sides refuse to step down then they will bring about mutual annihilation. In this game neither Blue nor Red have a “sure thing” strategy (a strategy that is best for itself regardless of what the other player decides). Consider now ΓRed one of the two first-order metagames that can be generated from the standoff in the basic game: this metagame is shown in Table 9. Table 9 shows policies rather than simple choices for Red (as Red is deciding what to do after Blue has chosen): there are now three equilibria. Reviewing Red’s choices, it can be seen that the rightmost column represents a sure-thing policy, since only in this column is it the case that irrespective of whether Blue decides to concede or resist, Red’s payoff cannot be improved. However, this sure-thing policy hands Table 8 Geopolitical Conflict: basic game Cells show assessments by Blue, Red. Equilibria are shaded. Blue’s choice

Concede Resist

Red’s choice Withdraw Good, Good Best, Bad

Threaten Bad, Best Worst, Worst

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Table 9 Geopolitical Conflict: Red metagame

Cells show assessments by Blue, Red Equilibria are circled.

Blue’s strategy

Red’s policy Red’s Policy “X/Y” Withdraw/ Threaten/ Withdraw/ means “Do X when Withdraw Threaten Threaten Blue chooses Concede and Do Y when Blue chooses Resist” Concede Good, Bad, Best Good, Good Good Resist Best, Bad Worst, Worst, Worst Worst

Threaten/ Withdraw

Bad, Best Best, Bad

victory to Blue! If ΓBlue were to be constructed and analyzed a corresponding result would be found: a sure-thing strategy for Blue which allows Red to prevail. However, this paradoxical result does not end there. Any metagame has, in turn, n associated higher-order metagames (e.g., second-order ones are Γjk,for j, k = 1 to n) and, for the present example, the finding that a sure-thing policy gives victory to the other side is promulgated throughout the infinite tree of such metagames. In general, metagame analysis arguably solves descriptively (not normatively) the paradoxes of coordination and cooperation (like “Prisoner’s Dilemma”) but fails to handle this third breakdown of rationality: the inducement problem as exemplified by “Chicken” in the confrontation above. This is because while in the basic game, Γ, of “Chicken” neither side has a “sure-thing” strategy (a “sure-thing” strategy is a strategy that is best for a player regardless of what the other player decides) in the metagame ΓA A has a sure-thing strategy that induces victory for B; and in ΓB B has a sure-thing strategy that ensures victory for A; and this pattern is propagated through the metagame tree. Choosing a “sure-thing” guarantees the best outcome for the other side! Being “sure-thing” rational is clearly a bad idea. It seems reasonable to assume that rational behavior by a player in any game actually means behaving rationally in the infinite tree of metagames; since for a player to attempt to be objectively rational it must take account of others’ subjective games and choose a “metastrategy” – a strategy for selecting a strategy – in the light of the overall metagame tree, not just the immediate game. However, as the example above has illustrated, choosing a “sure-thing” may guarantee the best outcome for the other side! A clue to handling this inducement breakdown came from empirical studies of game players facing the sort of impasse often encountered at conflict points. People were seen to become irritated with each other, sometimes verbalizing this through abusive cliches: “I’ll see you in hell first,” “over my dead body,” etc. Such utterances seemed to drive or to justify sudden changes in preference – Howard termed the changes that occur through players’ frustration at a “sticking point” in the interaction,

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“preference deterioration.” The consequence of one or more players changing their preferences is that the game they are playing changes – and, for instance, previously unattractive outcomes may became favored, thus unsettling the other party’s preferred equilibrium. Subsequently Howard elaborated these ideas about preference change, first by making more explicit the role of emotions in decision-making and then by proposing “soft game theory” as a theoretical foundation for the rounded schema of “drama theory” (which is examined shortly below and then in a separate chapter of this volume ▶ “Using Drama Theory to Model Negotiation”).

Emotional Decision-Making Experimental evidence had shown (Management Science Center 1967) that decision-makers are not rational in the narrow sense of the word (e.g., in Prisoner’s Dilemma they often chose to co-operate) and (as noted above) that in the “heat” of a confrontation their preferences may change. Specifically, emotions such as anger and frustration appear to be concomitants of genuine preference change (whereas people are likely to view as dishonest a party which alters its preferences in a coldly calculated manner or which issues apparently “willing” threats and promises). These emotions are hypothesized to “loosen” parties’ beliefs and values in such a way as to allow them to rationalize their redefinition of the interaction. Such redefinition of the “game” is not envisaged in game theory which takes the players’ options and preferences as fixed. Nor was it part of Fraser and Hipel’s modification of metagame analysis which turned its back upon “unwilling” threats and promises (i.e., “irrational” threats and promises which players are tempted to make credible for strategic advantage). In a wide-ranging assessment of progress made in metagame analysis since the publication of Paradoxes of Rationality Howard (1986) highlighted a number of directions for future development. Arguably the most significant of these was what he termed the “theory of loving preference change”: a formulation of the dilemmas of cooperation illustrated by “Chicken” above. Howard proposed that the challenges of cooperation and conflict which parties face create pressures upon them and prompt emotion of two kinds: positive emotion (love, goodwill) to make promises credible, so eliminating dilemmas of agreement; and negative emotion (anger, resentment) to make threats credible, so eliminating dilemmas of disagreement. While the role of such sentiments as a means of solving the commitment problem had been previously acknowledged (e.g., Frank’s work (1988) on altruism), their explicit role in a coherent analytical framework for modelling confrontations was new. The wider role of emotion in group decision and negotiation is explored more fully in the chapter ▶ “Role of Emotion in Group Decision and Negotiation.” Promises are the most mystical of speech acts: that the verbal issuing of a promissory obligation can (like a magical incantation) change what occurs in the physical world is decidedly mysterious. Voluntarily made, once uttered they impose an immediate obligation upon the utterer. Significantly, the mere fact that a person feels it necessary to issue a promise implies that the promised act is one over which

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there is a temptation to renege: like Odysseus tied to the mast, the promise binds the speaker to ensure that this likelihood is minimized. Furthermore for promises to be believed, a person must be trustworthy and so be someone who is known – who has a reputation, from past actions – to carry out such “irrational,” “unwilling” acts. Identical arguments about the credibility of assertions made and about speaker credibility can be made for threats as for promises; and indeed, the two speech acts (Searle 1969) are generally seen as having similar status. Promises and threats therefore provide a conceptual bridge between the worlds of rationality and irrationality. They also have a second, equally important property: promises and threats highlight the common interests of the parties involved. A promise raises the prospect of an outcome that is better for both players; a threat, the prospect of one that is worse. The corollary is that there must be some commonality of interest involved. It is upon an appeal to this joint interest (through the citing of evidence and the use of rational arguments) that credibility is built. From what has been said here there is an important distinction to be made when analyzing strategic interactions between “willing” and “unwilling” threats and promises: appropriate emotions are required to make the latter credible. Correspondingly, when emotional responses are encountered during the course of an interaction they can be interpreted as symptoms of players’ personal struggles with the challenges of making credible assertions. Howard recommended (Howard 1993) the construction of a “strategic map” to help identify promises and threats whose credibility might need enhancing. Such a diagram depicts the improvements that players can make in moving the situation from one outcome (scenario) to another and the sanctions that can be bought to bear to counter such improvements.

The Concept of Drama Theory By 1991 the foundational elements were present for the construction of a new theory of multi-party decision-making based upon the preceding ideas. What was lacking and was supplied at that point in time was a motivating metaphor around which these ideas might cohere: the metaphor was that of drama. Key aspects of what was declared as a new paradigm were: moving beyond game theoretic rationality assumptions; taking the game to be subjective (i.e., it is what the players see); and, assuming that the game is “soft” (i.e., it changes as players communicate about it). The new theory was intended to show how parties who attempt to act rationally within a fixed game are driven by emotion to act irrationally and change the game, consolidating the transformation by appeals to common interests. These parties strive, not for an ideal solution but for self-realization, and it is through this creative search that they achieve emotional and logical closure of the confrontation. The metaphor of drama with its connotations of an open-ended, emotionally-laden process driven forward through crises by dialogue and prompting fresh awareness, represented far better than the rigid, rule-based concept of games the nature of the exchanges that were to be understood. The adoption of this metaphor was very much in sympathy with wider changes. For instance, in the military domain the Cold War

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had ended and attention was shifting from “war-fighting” to “operations other than war.” At the same time, attempts to find technical solutions to complex problems were being supplanted by problem structuring methodologies intended to stimulate and inform debate and decision-making (Howard 1989): “soft game theory” (Howard 1990) was one such emerging approach. “The aim of drama theory is to explain how characters interact to resolve a given set of issues and how in doing so they are transformed” (Howard 1994). In drama theory, this evolution is seen as taking place through successive episodes, each of which requires the parties – now called characters – involved to declare and subsequently make choices that create the starting conditions for following episodes. A “tree” of episodes is conceived; this includes episodes that might occur, but do not, as well as those that are actually realized. The “interactions” that are modelled in drama theory are the dialogic exchanges between parties as opposed to any physical interactions (except insofar as the latter convey messages). The personal transformations concerned include characters’ aspirations, positions, doubts, and perceptions and involve a shift from their first recognition of the disputed issues through their suggestions for solutions to their eventual attempts at resolution. For analytical purposes, this process has been represented as involving a five-phase process: scenesetting, buildup, climax, resolution, and denouement. Drama involves exchanges between the dramatic personae. Correspondingly drama theory represents these exchanges between characters (which may be individuals or groups of individuals, organized or otherwise). Drama theory models frames. A frame holds an analogous role in drama theory to that of a game in game theory: it is a representation of a situation as seen by a particular character at a particular point in time. A character’s framing of a situation includes its understanding of what the other characters might do (their options), the outcomes that could therefore be co-created by the cast, and its own views about these outcomes. Through dialogue, characters share their frames with each other; initial appreciations may thereby be refined or radically modified until a shared appreciation of their collective predicament is reached. This common reference frame (CRF) may reveal agreement (or at least compatibility) or alternatively might show up apparently irreconcilable differences. In the former case, the characters may simply need to reassure each other of their good intentions, but in the latter, frustration at the impasse may prompt them to issue harsh words or else, placably, to moderate their demands. This is the point at which the emotional temperature of the interaction may rise as the characters attempt to convince others of the sincerity of their promises and threats. The pressures at this Moment of truth (MoT) can cause characters to change the CRF (for instance by pointing out new actions) thereby moving the whole cast into another episode: or they might modify their personal frames and so trigger fresh negotiations towards a revised CRF. At some point, however, all pressure to make further transformations of the final CRF is exhausted. The talking has to cease and actions, whether co-operative or conflictual, are determined by each party. It is at this stage, as they independently face the outcome that together they have helped to shape, that the mental assessments of the characters might be modelled by game theory: the game has been “fixed” through the earlier exchanges and each character

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can think rationally about what its best course of action would be. Whether or not it takes the prescriptions suggested by game theory as a guide depends, of course, on other moral and ethical considerations, but this lies outside the scope of the present exposition. Before moving on briefly to describe the development of drama theory, it is apposite to suggest that the reader contrasts the process of dramatic resolution described here with the models of negotiation processes, both cooperative (see the chapters ▶ “Negotiation as a Cooperative Game” and ▶ “Non-cooperative Bargaining Theory”).

Drama Theory: Early Development The early 1990s saw the consolidation of the model of the process of dramatic resolution, depicting the movement within an episode from “scene setting,” in which the CRF is established, through to the denouement, where the practical implications of enacted choices are faced by the characters. A unique feature of this process was the role attributed to emotion (Bennett 1996) in supporting a character’s “unfreezing” from one position and shifting to another. Much as Frank (1988) had argued that emotion offers a means for people to solve problems of “commitment” (handling those unwilling threats and promises which drama theory was explicitly embracing), so the new theory postulated (Bennett and Howard 1996) that emotion accompanies preference change. Importantly, emotion on the part of one character has the strategic function of altering other characters’ views about a situation, as well as its own. The transformation of the frame which was clearly a central issue for drama theorists was first expressed mathematically in unpublished papers as early as 1993, but it was much later (Howard and Murray-Jones 2002) that it was explored in publications. Essentially, this work considered the formal ways in which a frame could expand or contract (through the addition or removal of characters or their options) and how this might occur to shape transformations in the episodic tree. The paradoxes of rationality are, in drama theory, the triggers for emotions. Initially, the three paradoxes of Howard’s original work (Howard 1971) still remained central to understanding the pressures that characters experienced at the “moment of truth” when they realize that they do not share a single position. However, early applications prompted reconsideration that led to a formulation including five (later six) paradoxes (later called dilemmas). These were defined mathematically by Howard (1998) in a paper that used them to specify conditions for a strong resolution of a situation. A simplification that was to prove important for later work was also made: the realization that for the analysis of a situation it was unnecessary to investigate every scenario: rather it was sufficient to focus on a “confrontation” – that set of scenarios representing the “position” of each character together with the “conflict point” (the future that would occur if each character carried out its sanction). Furthermore, it was realized that the corresponding strategic map only needed to include improvements from these scenarios since the sanctions were included in the conflict point itself. Both

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simplifications arose from practical work with client organizations, but were subsequently given theoretical justification in the context of the growing body of theory. They created further distance from other approaches such as the Theory of Moves (Brams 1994) and the Graph Model (Kilgour et al. 1987) also developing at that time. A final conceptual development that was part of this developmental phase of drama theory was the use of “general” positions implying that there could be elements of a frame on which a character might be undecided. This extension was prompted by analysis of confrontations in Bosnia and the need to better represent and understand compatibility between the various scenarios that characters might cocreate (Murray-Jones and Howard 2001) but it has proved to be of far wider value. By the beginning of the twenty-first century therefore, there had been a full decade during which drama theory had evolved from its origins in metagame analysis into a rounder conceptual framework with its own distinct features. While some theoretical development continued, the field entered a period of consolidation in which practical applications came to the fore. Perhaps inevitably, these applications prompted practitioners working in different domains and with clients having different requirements to create “local” versions of the framework and this has led to the situation today where several well-established variants exist. However, despite such differences (some of which are described in chapter ▶ “Using Drama Theory to Model Negotiation”), the core notion remains that it is productive to think of an interaction as a drama that transforms under the internal pressures which characters create by their stated positions, fallbacks, preferences, and doubts.

Cross-References ▶ Conflict Resolution Using the Graph Model: Individuals and Coalitions ▶ Looking Back on Decision-Making Under Conditions of Conflict ▶ Role of Emotion in Group Decision and Negotiation ▶ Using Drama Theory to Model Negotiation

References Bain H, Howard N, Saaty T (1971) Using the analysis of options technique to analyse a community conflict. J Confl Resolut 15:133–144 Bennett PG (1980a) Hypergames: developing a model of conflict. Futures 12:489–507 Bennett PG (1980b) Bidders and dispenser: manipulative hypergames in a multinational context. Eur J Oper Res 4:293–306 Bennett PG (1996) Games and drama: rationality and emotion. Mershon Int Stud Rev 40:171–175 Bennett PG, Dando MR (1979) Complex strategic analysis: a hypergame study of the fall of France. J Oper Res Soc 30:23–32 Bennett P, Howard N (1996) Rationality, emotion and preference change: drama-theoretic models of choice. Eur J Oper Res 92:603–614 Bennett PG, Dando MR, Sharp RG (1980) Using hypergames to model difficult social issues: an approach to the case of soccer hooliganism. J Oper Res Soc 31:621–635 Bloom A (ed and trans) (1991) The republic of Plato, 2nd edn. Basic Books, New York, pp 36–39

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Brams SJ (1994) The theory of moves. Cambridge University Press, Cambridge Frank RH (1988) Passions within reason: the strategic role of the emotions. Norton, New York Fraser NM, Hipel KW (1980) Metagame analysis of the Poplar River conflict. J Oper Res Soc 31:377–385 Giesen MO, Bennett PG (1979) Aristotle’s fallacy: a hypergame in the oil shipping business . . .. Omega 7:309–320 Harsanyi JC (1974a) Review of paradoxes of rationality: theory of metagames and political behaviour by N. Howard. Am Polit Sci Rev 67:599–600 Harsanyi JC (1974b) Communication. Am Polit Sci Rev 68:730–731 Harsanyi JC (1974c) Communication. Am Polit Sci Rev 68:1694–1695 Howard N (1966a) The theory of metagames. Gen Syst XI:167–186 Howard N (1966b) The mathematics of metagames. Gen Syst XI:187–200 Howard N (1969) Metagame analysis of Vietnam policy. In: Isard W (ed) Vietnam: some basic issues and alternatives. Schenkman Publishing Company, Cambridge, MA, pp 126–142 Howard N (1971) Paradoxes of rationality: theory of metagames and political behaviour. MIT Press, Cambridge, MA Howard N (1974a) Communication. Am Polit Sci Rev 68:729–730 Howard N (1974b) Communication. Am Polit Sci Rev 68:1692–1693 Howard N (1986) Usefulness of metagame analysis. J Oper Res Soc 37:430–432 Howard N (1989) The manager as politician and general: the metagame approach to analysing cooperation and conflict, and the CONAN play. In: Rosenhead J (ed) Rational analysis for a problematic world. Wiley, Chichester Howard N (1990) ‘Soft’ game theory. Inf Decis Technol 16(3):215–227 Howard N (1993) The role of emotions in multiorganizational decision-making. J Oper Res Soc 44:613–623 Howard N (1994) Drama theory and its relation to game theory. Part 1: Dramatic resolution vs. rational solution & Part 2: Formal model of the resolution process. Group Decis Negot 3:187–206 & 207–235 Howard N (1998) n-person ‘soft’ games. J Oper Res Soc 49:144–150 Howard N, Murray-Jones P (2002) Transformations at a drama-theoretic ‘moment of truth’. Defence Evaluation & Research Agency, London Howard N, Bennett PG, Bryant JW, Bradley M (1992/1993) Manifesto for a theory of drama and irrational choice. J Oper Res Soc 44:99–103 and Systems Practice 6, 429–434 Hume D (1888) In: Selby-Bigge LA (ed) A treatise on human nature. Clarendon Press, Oxford. Book 2, Part 3, Section 3, p 413 Kilgour DM, Hipel KW, Fang L (1987) The graph model for conflicts. Automatica 23:41–55 Lutz DS (1974) Review of paradoxes of rationality: theory of metagames and political behaviour by N Howard. Technometrics 15:652 Management Science Center, University of Pennsylvania (1967) A model study of the escalation and de-escalation of conflict. Report ACDA ST-94, United States Arms Control & Disarmament Agency, Washington, DC Management Science Center, University of Pennsylvania (1968) Toward a quantitative theory of the dynamics of conflict. Report ACDA ST-127, United States Arms Control & Disarmament Agency, Washington, DC Management Science Center, University of Pennsylvania (1969a) Conflicts and their escalation: metagame analysis. Report ACDA ST-149 part 1, United States Arms Control & Disarmament Agency, Washington, DC Management Science Center, University of Pennsylvania (1969b) Conflicts and their escalation: the analysis of options: a computer aided method for analysing political problems. Report ACDA ST-149 part 2, United States Arms Control & Disarmament Agency, Washington, DC Murray-Jones P, Howard N (2001) Co-ordinated positions in a drama-theoretic confrontation: mathematical foundations for a PO decision support system. Defence Evaluation & Research Agency, London

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Searle JR (1969) Speech acts: an essay in the philosophy of language. Cambridge University Press, Cambridge Simonton S (2017) Classical Greek oligarchy: a political history. Princeton University Press, Princeton The Telegraph (2008) Nigel Howard: scholar who invented ‘drama theory’, advised the military and industry, and wrote a Kung Fu film. https://www.telegraph.co.uk/news/obituaries/1905492/ Nigel-Howard.html Thrall RM (1974) Review of paradoxes of rationality: theory of metagames and political behaviour by N. Howard. Oper Res 22:669–671 Vanderschraaf P, Sillari G (2014) Common knowledge. In: Zalta EN (ed) The Stanford encyclopedia of philosophy, Spring 2014 edn. https://plato.stanford.edu/archives/spr2014/entries/com mon-knowledge/ von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton

Using Drama Theory to Model Negotiation Jim Bryant and Peter Bennett

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dramatic Episodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis of Dilemmas: Confrontation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Options, Positions, and Intentions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preferences and/or Doubts: DT1 and DT2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of Dilemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preferences for Outcomes (DT1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Doubts About Signalled Intentions (DT2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Choice of Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Framework for Modelling Negotiations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Simple Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analyzing Confrontation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation: Immersive Drama . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Software Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Drama theory provides a practical way of analyzing “strategic conflicts”: situations in which the outcome is shaped by two or more autonomous decision makers. Its principal analytical approach is termed dilemma (or confrontation) analysis, reflecting a focus upon the dilemmas that typically face parties attempting to act rationally in a confrontation. These dilemmas provide the J. Bryant (*) Sheffield Business School, Sheffield Hallam University, Sheffield, UK e-mail: [email protected] P. Bennett Department of Health, Health Protection Analytical Team, London, UK e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_58

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intrinsic triggers for emotion and change which drive the transformation of the situation through parties’ consequent communications and actions. This transformation is viewed as an episodic process in dilemma analysis and involves modification of parties’ positions and intentions as well as their preferences or doubts: the latter alternatives reflect the two principal approaches – preferencebased and doubt-based – that have developed in dilemma analysis. In the practical modeling of a specific situation, both approaches would begin from the same options board model of parties’ positions and intentions, but subsequently their alternative conceptual foci would lead to different emphases in the identification and resolution of dilemmas. The choice of approach is therefore an important consideration for the analyst. In support of negotiation processes, where the conditionality of intentions may be especially important, an approach that combines elements of preference-based and doubt-based analysis can be beneficially employed. Traditional analysis is not the only means of using the conceptual framework of drama theory, and no review would be complete without describing its potential in designing immersive role plays that give participants both cognitive and affective experience of their interactions. Keywords

Negotiation · Development from game theory · Drama theory · Conflict analysis · Collaboration · Emotion · Preference change

Introduction Drama theory models a “large world” (Binmore 2006 after Savage 1951) in which autonomous decision-makers engaged in a “strategic conflict” can be taken by surprise by the actions of others or can themselves surprise other parties as they seek to attain their goals. This is in contrast to the “small world” model offered by most game theory approaches: these typically focus upon searching for “stable” outcomes within a fixed game structure. Drama theory therefore complements and extends the contribution of game theory and similar approaches in supporting group decision and negotiation, in particular by allowing for negotiators’ creativity in seeking to resolve contentious issues. The chapter by Bryant ▶ “From Game Theory to Drama Theory” provides a resumé of the development of drama theory, a narrative covered more fully in Bryant (2016). As explained more fully there, drama theory takes the “rational choice” model of game theory in a radically new direction by asserting that the problems of choice – the dilemmas created by participants’ efforts to act rationally (Howard 1971) – generate emotional pressures that cause the “game” itself to change. Drama theory posits that the intrinsic triggers for emotion and changes in view are essentially the dilemmas of rationality (Bennett 1996; Bennett and Howard 1996; Bryant 2007) – the barriers to rational choice within the frame that characters currently see. Expanding on Howard’s earlier work to identify all possible dilemmas led to a

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formulation in which there are six dilemmas that might face any given character (Howard 1998): as will be seen below, alternative formulations of dilemma analysis differ in the number of distinct dilemmas identified. However, these are essentially differences in classification rather than arguments about the underlying theory. All the substantive theory, e.g., on the role of emotion, is common. The metaphor of drama emphasizes the interplay between participants’ decisions, but the defining characteristic is self-realization rather than rationality. Characters seek to come to terms, both intellectually and emotionally, with a situation through its development or their own. The key role attributed to emotion provides a decisive break with more traditional mathematical models of choice (Howard 1994, 1996; Bennett 1995) but provides linkage to other pre-existing strands of thought on the nature of commitment (e.g., Elster 1979, 1983; Farrell 1987; Frank 1988; Dawes 1988; Cialdini 1993).

Dramatic Episodes Treating the fixed game modelled by game theory as just one “frame” in an evolving sequence, drama theory proposes a model in which situations unfold through a series of episodes: just as in a stage drama or TV “soap opera,” characters’ attempts to resolve the challenges of one episode lead to new challenges in further episodes. The episodic model (Fig. 1, based on Bryant and Howard 2007) is sketched in the chapter ▶ “From Game Theory to Drama Theory” in the present text. Briefly, the initial conditions, typically reflecting any previous interactions between the characters, create the setting within which issues are to be settled. While those involved may recognize the possible relevance of other features of the wider environment, to Fig. 1 Model of an episode

Scene-setting closed environment disagreement

Build-up

agreement

common reference frame Confrontation

Collaboration commitment Decision

to a new episode…

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cope with the complexity of the challenges facing them, their primary attention will be limited to interactions with a relatively narrow set of others, and their mental models of what is going on will be correspondingly simple. The modelling approach reflects this, rather than including all the features that those involved “should have” seen. The participants collectively determine who else (singular or plural actors) is significant – the cast list for the episode. Furthermore, any character can itself house a drama in which sub-characters contest lower-level issues, and the outcome of this may determine the character’s stance at the higher level. Nevertheless, both practical and theoretical explorations of an episode require us – at least provisionally – to isolate it and to regard it as informationally closed. In the build-up phase, characters communicate to create the common reference frame (CRF) which enables them to understand each other’s aspirations and proposals and their potential for getting their own way. In particular, each character will have a view about the resolution of whatever is happening and will suggest this solution to the others: this is its position. As well as stating what it will do, a character’s position also expresses what it would have others do. Normally the positions of the cast do not coincide; indeed, it is unlikely that they will even be compatible. But regardless of whether there is nascent agreement, characters must still be ready for any contingency. They will therefore indicate, either explicitly or implicitly, what they are prepared or not prepared to do, their stated intentions (SIs), given everyone’s positions. The build-up phase ends at the moment of truth (MoT) when all characters have managed to communicate their stands to each other. At this point characters typically face dilemmas of belief and credibility. In trying to get their own way, they find that they have to make threats or promises that run contrary to their own wishes. The emotional temperature rises as each seeks to reinforce what it is saying or to disarm others’ intent. At this climax of the episode, emotion may make a character willing to act against its own pre-existing preferences (i.e., to act irrationally) or cause longer-term changes in preference. The “heat of the moment” stimulates creativity and forces characters to reappraise what is going on. More radical transformations of the frame can occur, for instance, by involving fresh characters or by inventing novel options. Such developments cannot be predicted in specific terms, since they involve redefining the boundary of the scene. But drama theory can set out the various types of change liable to be generated. Howard and Murray-Jones (2002) set out the formal ways in which a frame could expand or contract and how this might shape transformations in the episodic tree. Two sorts of climax, conflictual and collaborative, can be distinguished. In the former, characters have incompatible positions. In pressing for different outcomes, the dilemmas they face are in making incredible threats, in dissuading others from implementing sanctions, and in convincingly rejecting others’ proposals. At a collaborative climax, there is already some nascent agreement in the form of a proposed common position, but characters have difficulty in persuading others that they will keep their promises or in believing that others will keep theirs. Both positive and negative emotions (crudely stated, love or hate) are typically used: negative to sustain damaging threats, positive to cement agreement. Nevertheless, the plausibility of these communicated changes is always uncertain.

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Finally, each character must decide whether to actually implement the actions to which the process has brought them. The initial frame may by now have changed substantially, and a character may be staring into an abyss of wasteful destruction: does it really wish to press through with its threats? Another may be ruing the generous promises it made. Characters may be tempted to back down from their intended decisions, maybe trying to reopen conversations with others – thereby reentering the build-up phase. But if implementation does occur, the situation is irreversibly changed, and the characters find themselves in a new episode.

Analysis of Dilemmas: Confrontation Analysis Options, Positions, and Intentions To examine characters’ dilemmas more formally and to explore their possible consequences, drama theory uses a method known as confrontation (or dilemma) analysis. Characters and their positions can be concisely portrayed in the form of an options board. This is similar to that used in the analysis of options (Fraser and Hipel 1984; Fang and Hipel, this volume) but differs in that the only outcomes normally included are the characters’ positions and SIs, rather than all feasible combinations of options. The options being considered by each character each have a row in the board, while the outcomes are summarized by the columns. Each option is formulated in binary terms (action to be taken or not taken). Taking an option may involve simply continuing with one’s present intentions (or behavior) rather than necessarily doing anything novel. We also allow a character to have an undeclared/undecided view about any given option, leading to a “generalized” position (Murray-Jones and Howard 2001) such as “I’m going to do A, continue with B, and promise not to do C: you should do X and Y, but I don’t mind whether or not you do Z.” In the table, taking, not taking, or ambivalence about an action has been variously denoted by 1/ 0/–, by Y/N/–, by ∎/□/▪, or by ✓/✗/~. The last of these conventions is adopted here. A character “accepts” another’s position if their positions are compatible. They need not be identical if one or both are generalized, but there must be no options definitely taken by one and definitely not taken by the other. Otherwise he or she rejects (or “flouts”) that position. To illustrate, consider a situation that many readers may have faced, in one form or another. Suppose Alf and Bet are partners trying to agree on how to spend a particular evening. They have been planning to spend time with each other, but they have different views on where to go. Alf wants to go to the cinema, while Bet wants to go to a show. To raise the stakes a bit, suppose that the choice of venue is not trivial: both really want to go to their preferred venue. But they also care about spending the evening with each other. In game theory this situation is often referred to as “Battle of the Sexes,” though clearly there is nothing gender-specific about it! It is simple in the sense of there being just two people deciding between just two venues. But as we shall see, the ramifications may be far from simple and are also

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relevant to larger-scale interactions. We build a model in stages, using this, to structure discussion. Alf and Bet are the two characters. Each has two possible courses of action: to go to the cinema or the show. If these are really the only two alternatives under consideration (i.e., if “not cinema” implies “show” and vice versa), this constitutes just one binary choice. We need not put both the alternatives explicitly in the table but doing so may make the table easier to appreciate. One way of doing so is to associate the two alternatives with the “positive” and “negative” poles of the option, a notation similar to that used in cognitive mapping (e.g., Eden and Ackermann 1998). We next specify what positions Alf and Bet are communicating – the outcome each character is advocating. Here, Alf’s position is that they should both go to the film; Bet’s that they both go to the show. Clearly these positions are incompatible. They can be represented by the first two columns shown in the options table below (Table 1). Note that in each cell the tick means that the “left pole” of the option – in this case “cinema” – is chosen and the cross means “show” is chosen. We also suppose that the characters communicate about what they will do in the absence of agreement: this is modelled by defining their stated intentions, or more generally – since communication may be nonverbal – signalled intentions. (Henceforth we use the shorthand SI to cover both.) In this case, suppose that Alf and Bet are really at loggerheads: Alf is saying that he will go to the film come what may, while Bet is being equally insistent about going to the show. The result of all characters sticking to their SI is often referred to as the default outcome (or future). If it implies continued disagreement (as here), it’s also known as the threatened future (TF, which explains the labelling of the rightmost column in the table). In this case, Alf and Bet would spend the evening at their preferred venues, but alone. In this example, each character’s SI simply reiterates his or her position. Nevertheless, the two concepts need to be distinguished. Formally, a position is a proposed choice of options (“yes,” “no,” or “unspecified”) for oneself and for each of the other characters: a position cannot contain conditional choices of options. However, many threats – and as we shall see later, promises – rely on expressions of conditionality. For example, if Bet were to say “IF you insist on going to the film without me, THEN you’ll be sleeping alone as well!,” this is clearly not something she is advocating (position) but would form an important part of her SI. Note that all this is about what the characters are trying to communicate to each other. We are not yet considering whether these communications are sincere or credible. It is quite Table 1 An evening out Alf Cinema . . . show Bet Cinema . . . show

A’s Pos’n

B’s Pos’n

TF

✓

✗

✓

✓

✗

✗

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possible for there to be some hidden agenda and for a character not to intend to carry out his or her part of the deal it is proposing. His or her SI may be the purest bluff. But starting with communications, verbal or otherwise, has the immediate advantage that these are likely to be observable.

Preferences and/or Doubts: DT1 and DT2 Having introduced characters, options, and SI, we now need to ask what the characters want and believe. At this point, different versions of the analysis diverge somewhat. Specifically, analysis can be based on considering characters’ preferences for outcomes, doubts about signalled intentions, or some combination of the two. In the existing literature, preference-based and doubt-based analyses are often referred to as drama theory 1 (DT1) and drama theory 2 (DT2), respectively. This reflects the historical order in which they were proposed. However, these are not rival empirical theories but different ways of approaching the analysis, each of which has relative advantages. Consider our example, initially, in “DT1” terms. We introduce preferences – simple rankings of outcomes from best to worst for each character. Suppose that these run as follows for the three outcomes discussed: Alf • He and Bet go to the cinema together (his position) • He and Bet go to the show together (Bet’s position) • He goes to the cinema alone, Bet to the show (threatened future) Bet • She and Alf go to the show together (her position) • She and Alf go to the cinema together (Alf’s position) • She goes to the show alone, Alf to the cinema (threatened future) Note especially the ordering of the second and third outcomes. At least as our story begins, each of the characters would rather sacrifice their choice of venue so as to be with the other. But that does not mean that there is any lack of confrontation! In principle, a fourth outcome is possible that Alf goes to the show and Bet to the cinema. A game-theoretic model would include this as the least-preferred outcome for both sides. We would then look for an equilibrium – an outcome in which each side is doing the best it can given the fixed choice made by the other(s). There are two equilibria here: Alf and Bet go together to the cinema, or they go to the show. Either outcome may thus have some stability if reached. But the game has no single solution. Although omitting one outcome may not seem like a major difference, this impression is due only to the simplicity of the example. In a more complex case, there may be a large number of possible outcomes (in fact 2n if there are n independent options in total). For approaches that follow game theory more closely, specifying all these outcomes and players’ preferences between them becomes

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a major modelling task (e.g., Fraser and Hipel 1984) involving significant combinatorial complexity. By contrast, confrontation analysis starts from simple questions about what the parties say they want to achieve and what would happen if each sticks to its position. Returning to Alf and Bet, the immediate dilemma for each, given the preference assumptions we have made, is that they would rather accept the other’s position than spend the evening alone (the threatened future). Because it makes it difficult to reject the other side’s proposal, this is known as a rejection dilemma. An alternative way of characterizing this dilemma is in terms of doubt rather than preferences. That is, each has reason to doubt the other’s resolve to spend the evening alone if necessary, rather than give in. This is the “DT2” formulation. Note that this doubt attaches to a specific option within each side’s signalled intentions, whereas in “DT1” preferences for outcomes are primary, and doubts about intentions follow. We discuss the relative merits of each approach below. In either definition, characters’ responses to their dilemmas may cause the situation to play out in many different ways. In reality, Alf and Bet would be unique individuals with some past history and longer-term expectations. Nevertheless, one can predict discomfort at having to fight against one’s existing wishes. There are a number of generic ways to resolve the contradiction. • One common response is negative emotion toward the other side – typically anger. Either character or both may become so angry that they come to prefer an evening apart. (“If you’re going to be like that, then just go. . .. . .”). In this sense, emotion can be seen as the heat generated by the friction of preference change. Hardly a happy outcome, but at least the dilemma disappears! • Alternatively, one might try to simulate emotion – to pretend to be angry enough to go off alone if necessary, so as to bolster the credibility of the threat (recall Richard Nixon’s “madman theory” of nuclear deterrence). But it is actually quite difficult to separate appearance from reality in this way – and in any case the tactic risks stimulating genuine anger on the other side. • One all-too-obvious tactic is to tie one’s own hands – demonstrate irrevocable commitment to one’s own position (see Schelling (1960) and many following works, e.g., Elster (1979)). Alf and Bet have already gone some way down this path through their respective SI. They may pursue this further by trying to present the decision as a fait accompli – “Look, I’ve bought the tickets already. They’re non-refundable. Are you coming or not?” This tactic in turn risks being perceived as manipulative and generating a heated emotional response! • Less confrontational attempts to bolster one’s position will typically include reasoned arguments to justify one’s position – “I’ve been wanting to go to this show since it opened, and the run closes next week. And it’s just the sort of thing you normally enjoy.” And although the disagreement can escalate, this is not inevitable: another response to the initial dilemma is to change one’s position. Again, emotions are important. One character may give in out of sheer frustration, and both end up with a smoldering sense of resentment. But genuine preference change in favor of agreement should be accompanied by positive emotion. If he

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agrees – with good humor, even if reluctantly at first – to go to the show, Alf has actually put his feelings for Bet above his own initial wishes. Consciously or not, he is putting greater value on Bet’s wishes, bringing his preferences in line with his choice: his choice is internally “justified” by feeling more positive toward her. In starting with positions, our analysis may appear rather superficial. But to understand the basis of positions, we have to look more deeply at the values that lead to their being taken – a point well made by Fisher and Ury (1982). For Alf and Bet, the argument may be simply about how they spend the evening. But it may also be “about” how they treat each other, whether or not they respect each other’s wishes, whether their tastes are incompatible, whether one of them is tired of “always giving in to” the other, and so on. The more deeply embedded in values the characters’ positions, the greater the emotional consequences of change. A further response to dilemmas can be the creation of new options. This can again act either to intensify the confrontation or to provide a more collaborative way forward. The first would be typically represented by the addition of new threats – as with Bet’s previously noted indication that if Alf goes to the cinema alone, he will end up sleeping alone too! More collaborative possibilities may come about because Alf and Bet have more than one evening potentially spent together. For example, Bet might come up with a new proposal: “OK, I’ll come to the cinema with you. But next time, it will be my choice.” If Alf agrees, the situation has evolved into one in which he and Bet share a common position. However, that is not necessarily the end of the problem. Establishing a common position may be helpful, but can all sides be confident that it will be implemented? Alf has agreed to give Bet her choice of venue “next time.” But once he has had his evening at the cinema, will he be tempted to renege on the deal?

Classification of Dilemmas So far, we have illustrated one particular type of dilemma (“rejection dilemma”) and have noted that others can exist even once a common position has been agreed. By systematically considering the relationships that can exist between characters’ positions and SI, the fallback future and other outcomes, drama theory has established taxonomies of all the dilemmas that can arise when characters attempt to deal rationally with each other. These taxonomies differ, however, according to whether the dilemmas are classified in terms of preferences for outcomes, doubts about SI, or hybrids of both.

Preferences for Outcomes (DT1) An early mathematical finding of DT in this format was that there are six (and only six) types of dilemma (Howard 1998; Bryant 2003). These are characterized as

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follows for two characters, A and B, though the model generalizes to any number of characters: (i) A has a rejection dilemma if A prefers B’s position to the fallback/threatened future. (ii) A has a threat dilemma if A prefers to implement some other outcome rather than the threatened future. (iii) A has a persuasion dilemma if it believes B prefers the threatened future to A’s position. (iv) A has a cooperation dilemma if it would prefer to move to an outcome other than its own position. (v) A has a trust dilemma if it believes that B would prefer to move to an outcome other than B’s own position. (vi) A has a positioning dilemma if it prefers B’s position to its own. Each dilemma is named for the challenge it poses: a rejection dilemma for A makes it difficult for A to reject B’s position convincingly and so on. (Nomenclature can vary; some accounts use “inducement dilemma” and “deterrence dilemma” for (i) and (iii), respectively). All these dilemmas can be shown schematically as in Fig. 2. The coded arrows show each character’s preference between the two outcomes that they link and are labelled by the dilemma that such a preference would introduce. While the cooperation and trust dilemmas both concern the stability of an agreement, they are not the same thing: it is a dilemma for me if I cannot trust you, but your inability to be trustworthy is a dilemma for you! If there is a common position, as here, the two dilemmas are “mirror images” of each other, but either or both can also occur in the absence of a common position. The positioning dilemma may at first sight seem strange (and is not recognized by all authors) but can be observed. For example, suppose a character has recently relinquished a position still held by erstwhile colleagues and accepted a compromise with others that it does not prefer. It may then find itself reluctantly arguing for a “realistic” solution while really preferring an “ideal” position still held by its former allies. Characters will act in ways that serve to eliminate dilemmas – though there may be many potential ways of doing so, and new dilemmas may be created along the way. It can be shown mathematically (Howard 1994) that if all dilemmas are eliminated, the result must be a strict, strong equilibrium, from which there are no incentives for any character (or coalition of characters) to defect – and no remaining “pressure points” for further transformation.

Doubts About Signalled Intentions (DT2) Attention to characters’ preferences carried over quite naturally from game-based analysis. However, preferences are arguably only of use in allowing us to make deductions about the credibility of threats and promises. If, say, a character has a

Using Drama Theory to Model Negotiation Threat Dilemma for A

Co-operation Dilemma for A

515 Threat Dilemma for B

Trust Dilemma for B

Fallback Future

Rejection Dilemma for A

Persuasion Dilemma for A

Rejection Dilemma for B

A’s Position

Persuasion Dilemma for B

Positioning Dilemma for A

B’s Position

Positioning Dilemma for B Trust Dilemma for A

Co-operation Dilemma for B

A’s preference B’s preference

Fig. 2 Dilemmas consequent on preferences

reason not to carry out a threat, then they have a dilemma. Information about preferences tells us why that may be the case, but is not strictly necessary to the analysis. One can equally start by specifying what doubts characters have about each other’s signalled intentions (SI). For example, if A thinks that B’s threat may be a bluff, this belief could be expressed in terms of B preferring to avoid the threatened future. But it could equally be expressed as A having a doubt about B’s SI. This way of thinking led to a reformulation of the theory itself. New proofs of drama theory’s fundamental theorems were provided (Howard 2008), now recast using the concept of a character’s stand – i.e., the expression of its position, SI, and doubts. Such stands are “observable”: their elements would be overheard or spotted by a third party observing the exchange between the characters. Any element of a character’s stand may be a falsehood (it may lie about its position, its SI may be a bluff, and its expressed doubt about another’s intention may be insincere), but the stands themselves are nevertheless a form of common knowledge.

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The suggested transition from DT1 to DT2 was not universally accepted, and some analysts prefer to use the earlier formulation, or a hybrid of the two. We return to this below, after outlining the DT2 formulation more fully. This identifies just three fundamentally distinct dilemmas (though two can be subdivided). For two characters A and B: If A and B have conflicting positions: (i) A has a rejection dilemma if A’s SI is incompatible with B’s position but B doubts A’s intention to flout B’s position. (ii) A has a persuasion dilemma if either B won’t say whether it will support A’s position or B says it won’t do so and A doesn’t doubt this. If A and B have compatible positions: (i) A has a trust dilemma with B if A’s position requires some specific choice by B and A doubts B’s intention to carry this out. Note that the threat dilemma of DT1 is no longer separated but is now subsumed within the rejection dilemma. Nevertheless, this dilemma can usefully be subdivided. If the SI that are doubted by B are part of A’s position, the rejection dilemma is said to be in position mode. If not – i.e., it’s a separate, conditional threat – the dilemma is said to be in threat mode. Similarly for the persuasion dilemma, according to whether A’s problem lies with part of B’s position or with some other element of B’s SI. There is no longer a separate cooperation dilemma (it is unnecessary to introduce this, as it would now always just be the mirror image of the trust dilemma) nor a positioning dilemma. Significantly, the question as to whether a dilemma arises is asked of each separate option, rather than requiring the comparison of more complex outcomes. While this offers greater simplicity, something is arguably lost in this approach, particularly with regard to the persuasion dilemma. We discuss this further below. Introducing models based on doubt may naturally prompt the question how much doubt is needed to create a dilemma? What degree of belief would dispel it sufficiently? For the purposes of DT, the answer is pragmatic: the doubt is sufficient if it is causing a problem for the character. Even a small doubt about something really important might still prompt some dilemma-resolving behavior. Similarly, for “lack of doubt” in the persuasion dilemma, the certainty has to be sufficient to cause the character concern. (A normative theory of choice would involve multiplying degrees of belief about other characters’ intentions by utility scores attaching to outcomes. But we are not proposing such a theory here.)

Choice of Approach Basing analysis on preferences for outcomes or doubts about options inevitably leads to dilemmas being characterized in different ways and to some natural differences in emphasis:

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• The DT2 option-by-option table encourages one to think more about the gradual evolution of an interaction as fresh options are added to the table and old ones possibly settled or discarded (a process formalized in the software developed by Young (2017), discussed below). DT1 puts more emphasis on looking at alternative futures and how these are shaped by all the characters’ choices. • Discussion of doubt naturally raises the topic of evidence. To dispel doubt and so eliminate a dilemma, a person may hunt around for information; this isn’t (directly at least) a natural focus of a preference-driven model. • Consideration of preferences puts us firmly in the domain of practical rationality. To arrive at preferences between potential future states of the world, imaginative judgment is required. We don’t really know in advance how these scenarios would actually turn out. But in the here and now, we must make some choices that could contribute to them happening. • A major challenge in arriving at preferences can be to weigh up the disparate elements that make up the vector of future intentions for each scenario. This may not be so troublesome when there are only a few options, but if the options board is more complex, then balancing out the components is far from straightforward. Nevertheless, some of the key systemic features of conflict and cooperation depend critically on the interplay of different actors’ choices and the outcomes these produce. And characters may well be motivated by their wish to achieve, or avoid, such outcomes. We do not want to overlook this. In any case, the choice between a “preferences for outcomes” and “doubts about options” approach need not be made in an all-or-nothing way. Analysis of specific cases needs to make best use of whatever information is available, starting with the communications actually being made by the characters. These will often be some mixture of expressed doubts and statements of preference – or proxies that can readily be interpreted as such. Indeed, the most readily observable features might be expressions of the pressures that the characters are experiencing because of the dilemmas that they are facing – e.g., anger and frustration. To understand what is happening, we may have to work “backward” from expressed emotions to diagnose the dilemmas of choice from the pressures they create (Bennett 1998). We should therefore be open to characterizing dilemmas in terms of doubts and/or preferences, though as modellers we might start with a default choice.

A Framework for Modelling Negotiations The following approach combines and develops elements of both DT1 and DT2 and is suggested as a suitable framework for analysis of negotiation at least as a default modelling option. To allow a more complete specification of conditionality, in which characters’ signalled intentions may depend on each other, we extend the definition of SI to include two sets of intentions for each character:

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(a) Where positions are incompatible, options to be taken or not if each other character maintains its current position (these are typically threats, though not necessarily presented as such) (b) Options to be taken or not if each other character accepts one’s position (typically promises of one sort or another, with the same proviso) Part (a) is the pre-existing DT2 definition of SI, containing the negative inducements, which can range from a simple “no deal” through to other actions designed to make the lack of agreement more unpleasant. Adding part (b) allows us to deal with threats and promises in a more symmetric way. In a negotiation setting, this can be seen as the “deal” being offered to other characters. It will obviously include one’s position but may also contain considerably more by way of positive inducements conditional on that position being accepted. Taken together, the SI can be seen as the “scaffolding” used by a character to support its position. Characters may communicate doubts attaching to options in either set. Doubts about actions in set (a) bring into question the character’s resolve to carry out its threats, or its ability to do so. Doubts about those in set (b) question the character’s sincerity or trustworthiness, or indeed its ability to deliver on its promises. Doubts of either type may be important prospectively: in particular, A’s doubts about B’s trustworthiness may prevent them from reaching agreement. But if they do arrive at a common position, any such doubts remain highly relevant, whereas any doubts about B’s resolve become much less so. B’s promises have still to be delivered, whereas the threats are now counterfactual: they only applied prior to the common position being agreed. From this starting point, our approach primarily follows DT2 in identifying rejection, persuasion, and trust dilemmas but draws on elements of DT1 as regards the last of these.

A Simple Example The following illustration is hypothetical, though it does share features of various cases recently played out in the UK. Suppose P is a party politician of some national prominence. She has made public remarks that some regard as offensive and certainly don’t reflect party policy. The party leadership – a deliberately vague term at this point – L has threatened to suspend P from the party unless she issues a public apology. This she is reluctant to do: • At least initially, P’s position is that she won’t apologize (this is also her SI) and should not be suspended. • Put at its simplest, L’s position is “P must apologize” (if there are specifics as to what sort of apology would suffice, these would be included in the model). • To support this, L communicates some key signalled intentions. If the aim is to induce an apology, these need to maximize the relative attractiveness of compliance, as compared with defiance. L tries to make it clear to P (a) “You will be suspended if you don’t apologize adequately” and (b) “You won’t if you do.”

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Table 2 The politician’s apology

Politician Apologize Leadership Suspend P

TF

P’s pos’n

L’s pos’n

L’s SI Offer

Fallback

✗

✗

✓

if ✓

if ✗

✓

✗

~

✗

✓

These positions and SI are represented in the options Table 2 below: (Note that in this example, the negatives of each option are simply “not apologize” and “not suspend.”) Here, the explicit emphasis of the communication is on the threat, rather than the promise of not being damaged if one complies. In other cases, the promise may be explicit, as in the parent’s “if you tidy your room, I’ll take you to the funfair.” But in both circumstances, if the “if” is intended as a strict “if and only if” (the logician’s IFF), then both halves of the intention are important. On the other hand, if the commitment is only to a one-sided “if,” with the other alternative being left vague, the model should reflect that. Returning to our example, there are essentially three ways in which L’s efforts can run into problems: 1. P doesn’t think that L would necessarily suspend her if she remains defiant. 2. P isn’t convinced that L won’t suspend her anyway, even if she apologizes. 3. P is determined not to apologize, even at the cost of being suspended. As archetypes of ways in which characters can fail to influence others, these illustrate the three fundamental dilemmas of drama theory. Each could be elaborated in ways that would make a particular scenario more plausible – we could consider the back story of characters’ previous interactions, their longer-term ambitions, and so on. But for present purposes, a “bare bones” model will suffice. In Case (1) we follow DT2 in representing this as a rejection dilemma (here, in threat mode) for L: P doubts that L will implement his threat. This is a more direct characterization than is provided by DT1, where the dilemma would be modelled by introducing an outcome to which (P suspects) L would prefer to move: the result would then be a threat or rejection dilemma, depending on which outcome this is. And doubt also covers a broader range of possibilities, including both willingness to carry out a threat and ability to implement it. For example, P may reason that L cannot simply suspend her but would have to go through due process set out by party rules, with no guarantee of success. If so, we could expand the model by being more specific about who the “Leader” who is threatening P is and how the drama within the wider party might play out. Case (2) represents a trust dilemma for L in both DT1 and DT2. Note that the expanded concept of signalled intentions introduced above allows us to identify this dilemma prospectively, as something that may inhibit the characters reaching a common position. (Otherwise, using DT2 would require a two-stage model, with

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separate tables to represent the situation before and after any putative agreement.) Given this, DT2 again provides the more direct characterization. This time, P doubts L’s promise if she complies. For example, she might feel that L wants her suspended anyway and is using her remarks as a pretext. No apology P could make would be sufficient. Or she may suspect that L is unduly influenced by P’s rivals within the party, or by the media, and will not be able to hold back from a political gesture. Whatever the case, L’s perceived untrustworthiness gives him a problem too. We can either say that L has to respond to P’s trust dilemma if he is to influence her effectively or call this a cooperation dilemma for L (as in DT1). This is just a matter of nomenclature. Case (3) brings us to the persuasion dilemma. Once again, this can be modelled in terms of doubts or preferences. The description so far tells us that P’s defiance is not based on any doubts about L’s signalled intentions. The DT2 formulation is that L has no doubt that P will continue to flout his position (or, perhaps less awkwardly, that he is certain that P will do so). This formulation again covers inability to comply with another’s demands and unwillingness to do so. If the question is one of willingness, the preference-based formulation becomes more attractive. The problem for L may be that P would rather be suspended than apologize. Indeed, she may say so explicitly. Such a claim might be credible enough: maybe she doesn’t believe that suspension would hurt her prospects in the long run, or she may feel bound to stand by her original comments as a matter of principle. Discussing the persuasion dilemma in terms of preferences helps to highlight a fundamental point. If I want you to do something you would otherwise not do, I try to persuade you by making noncompliance less attractive through threats and/or by making compliance more attractive through promises. Clearly dilemmas arise if you doubt some or all of those. But if I can’t create futures in which you prefer to comply – if my threats and promises are insufficient – then I don’t get past first base. To progress, I need to make more generous promises and/or more dreadful threats, either by adding more of any existing options to my SI or by creating new options altogether. Then I may need to work further on credibility. The DT1 preference-for-outcomes formulation thus has merit in describing this situation. We modify its general formulation slightly, given that positions cannot include conditional commitments: • A has a persuasion dilemma if B prefers the threatened future (defiance, with A’s fallback implemented) to the deal A is offering (i.e., compliance, with A’s promises implemented). In the context of negotiation, relative preferences (and perceived preferences) for “no deal” commonly play a critical role. Character A says that it would prefer to walk away rather than accept B’s position. If B sees this as credible, B has a persuasion dilemma. (If B doubts it, A may well have a rejection dilemma.) Some statements about preferences for alternative futures can thus be well worth including in a DT model. In reality, communication about preferences is not uncommon and is observable in the same way as communication about doubts, and introducing preferences

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can help illuminate interesting features. Nevertheless, the approach proposed here requires fewer preference judgements than in DT1 and many fewer than in more traditional game-theoretic models. Returning to the example, suppose P claims she’d rather be suspended than apologize, and L believes her – at least sufficiently to give him pause. L can see that his inducements are not sufficient – a problem quite distinct from one of credibility. To overcome this, he may escalate the threat from suspension to expulsion from the party and so on. Or he might sweeten the prospect of compliance – e.g., by promising to back P publicly on other issues if she apologizes for her comments on this one. Threat, trust, and persuasion dilemmas can all coexist. However, it may also be useful to see how essential the threat and cooperation dilemmas are. In other words, do they actually affect (B’s expectation of) A’s response? It may be that A doubts some of B’s SI, but the ones he doesn’t doubt are still sufficient. To investigate that, we can repeat the analysis with the doubted commitments turned “on” and “off” and see whether any (willingness-based) persuasion dilemma appears or disappears. That would require more preference judgments, but at any given point, we need only to compare two scenarios. In any version of confrontation analysis, the possibilities for a character facing a dilemma involve either modifying one’s position or inducing someone else to modify theirs – potentially creating new dilemmas in the process. While some paths lead to eventual dilemma elimination, there is clearly the potential for characters to cycle through different dilemmas indefinitely (Bryant 2016).

Applications Drama theory has developed through dialectic between practice and theory. Being an account of how people interact to resolve differences, it has wide relevance. Applications fall into two broad areas: • Modelling specific confrontations • The creation of role-playing simulations

Analyzing Confrontation A good example of practical application is given by studies of interorganizational working in the UK health service, which demonstrated the challenges of operating across boundaries (Bryant 2002). Similar issues in the very different setting of military operations in a postwar zone were examined by Howard (1999), based upon “live” analysis conducted with the UN forces in Bosnia during the 1990s. The latter led to the innovative concept of a C2CC system – a system for Command and Control of Confronting and Collaborating. This could be used to coordinate hierarchical organizations’ handling of their diverse relationships with other parties by

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relating nested confrontation models (Stubbs et al. 1999). This idea was extended to the civilian sector in Bryant and Howard (2007). Normally drama theory, like its antecedents, would be used on behalf of one party in a confrontation to support its dealings with others. This sort of intervention is described in Bryant (1997), Howard (1999), Howard (2001), and Bryant and Howard (2007), though presented in an anonymized form because of the sensitivity of the information used and the “political” ramifications of the negotiations. Incidentally, this very confidentiality explains why accounts of the applications of drama theory are relatively scarce. Sometimes drama theory has been used for academic, post hoc analysis of situations involving conflict (Sensarma and Okada 2010) or collaboration (Handayati et al. 2011). This may be illuminating in the context of a research program, though it cannot proceed much beyond the identification of the dilemmas. A more promising mode of practical application is in mediation. While the principle is that a drama-theoretic model cannot be shared between the parties involved (Bryant and Howard 2007), that does not prohibit the use of drama theory for sharpening the mediation process. The principle is that the mediator asks questions of a character, not as to whether its promise/threat is credible but of other parties as to whether they find the character’s promise/threat credible. The burden of conviction is on the doubted party to make their position or intention credible to others. If the incredulity itself is open to question, then of course the onus is upon the character that is doubted to ground the conviction and so on. Informal applications in mediation have been undertaken, but not yet made available in publications. Aside from relationships between formal organizations, drama theory can be applied to interpersonal relationships and indeed to some of the fundamental questions in human psychology. The former has been addressed in studies in the field of human resource management (e.g., about the psychological contract) as well as in discussion with counsellors and others offering support to individuals facing traumatic personal problems. The latter questions about human behavior have been investigated using experimental methods (Murray-Jones et al. 2003), with drama theory providing a predictive framework within which subjects’ choices could be assessed. A general four-stage process for the practical application of drama theory as the basis for a Group Support System is given in Bryant (2003). While an options board usually provides the most precise and telling summary of the interaction, enabling characters’ dilemmas to be readily exposed, some preliminary scoping and structuring of the situation is normally necessary. If there is a complex of interrelated issues engaging an extensive potential cast list, then capturing the broader picture before selecting a focal area is normal practice. In drama theory, this may be done, for instance, through use of specific tools like the PPS diagram (Bennett et al. 1989) or else by generic tools like the power-interest grid commonly used in strategic analysis (Johnson and Scholes 1997). In either case, starting analysis from a broad view helps to expose the relationships between contested arenas and possible trade-offs between them, so the systems approaches described by Richardson and Anderson in their chapter ▶ “Systems Thinking, Mapping, and Group Model Building” might be highly appropriate.

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Once a provisional focus is established, options boards can be used to model what are ideally the mental models of the protagonists in the confrontation. The entire analytical cycle is intended as a learning process with flexible movement in any direction: for example, aspects of one character’s SI may be recognized or revised during analysis of another character’s position. The key principle is that the options set against each character are genuinely choices for action which are available to them. In practice the construction of the options board with a client may be one of the most insightful processes offered by drama theory. The dilemmas facing each character can next be enumerated and assessed. This is greatly simplified by the use of bespoke software tools as described below. The tugof-war diagram (Howard 2004) is one graphic device for illustrating the pressures on each character and could in principle be adapted to cases involving more than two parties. Dependent upon whether characters are at a conflict point or are tentatively collaborating, different pathways for dispersing the dilemmas will be identified. However it is only by breaking out of the straightjacket that the model represents that the characters will achieve resolution. So creative thinking is essential at this stage. No prescriptions can be given for this, but, for example, if analysis is being undertaken for one party to assist it in its interactions with others, then routes that will eliminate its own dilemmas will be sought. Virtuoso analysis that illustrates this principle can be found in the “plays” written by Howard (1989, 1999, and 2001). A “quick fix” approach to analysis for a single character – “Speed Confrontation Management” – has been proposed by Tait (2006). This provides a structured route to producing a coherent argument that the character could use in its strategic conversation with others. Drama theory has also been applied to fictional situations. Much in the way that Brams (2012) has applied game theory to subjects from literature and the humanities and Chwe (2013) has used it to explore the works of Jane Austen, so drama theory has been used to analyze the storyboard of novels, stage plays, and film scripts. Howard (1996), for example, provided a bravura analysis of two films by Quentin Tarantino, explaining the contrasting denouements of “Pulp Fiction” and “Reservoir Dogs.” Reversing this process, the playwright David Edgar used drama theory to structure his play The Prisoner’s Dilemma (2001), and Howard subsequently made use of drama theory as a means of building and sharing the script of the independent film Brighton Wok released in 2008, so that all those involved in its production had a rounded understanding of their roles and of the overall story arc. Such analysis proved to be especially valuable in avoiding “plotholes” (Bryant 2016), i.e., disjunctions in the storyline.

Simulation: Immersive Drama If drama theory can be used to achieve beneficial outcomes in multiparty situations, then the development of simulations to prepare people to put these ideas into practice provides a natural next step. Such involving experiences help individuals to appreciate the challenges that they may face, at an affective as well as at a cognitive level.

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However, many situations require something more open-ended than implementation of “solutions.” This is the need that “immersive drama” has been developed to fill. The approach is to cast people as specific characters in a situation. They are then required to interact in role with others, usually to attain mutually negotiated ends. This has some similarities with group simulation (e.g., Cambridge Foresight 1999), in placing people in a “world” in which they must learn how to operate effectively. However, immersive drama differs from other forms of simulation in a number of ways. In contrast to providing role-players with a descriptive briefing (typically setting down a character’s history, personality, responsibilities, and resources), “immersive briefings” center upon a character’s relationships with others “. . . what it is trying to achieve, and why and how, and what it thinks others are trying to achieve, and why and how” (Howard 1999). This is what gives immersive dramas their authenticity. The “bones of contention” become the main arenas for collaboration and conflict as the drama unfolds. Characters are given an initial stand on each issue, and this provides the base from which they interact with others. Changing stance requires a character to convince or persuade others that it has done so. For resolution, characters have to invent and agree (possibly reluctantly) upon solutions: this may mean modifying positions, retracting intentions, inventing options, or reconfiguring coalitions. Interactions are not prescribed in any way, and role-players work with others as and when it is mutually agreeable. The purpose of immersive drama is to provide insight into complex multiparticipant situations, to develop a practical repertoire of skills and behaviors for coping in them, and to prepare people for the emotional costs of their interactions with others. The enactment encourages divergence and creativity, rather than offering solutions or normative direction. The approach has been used in a number of fields. Two applications in health management illustrate contrasting approaches to the construction of the drama. In one (Bryant and Darwin 2004), there was a “closed” design wherein other characters fully create the context for each roleplayer’s deliberations; in the other (Bryant and Darwin 2003) the design is “open” with role-players also having to cope with the impact of exogenously generated events. Both were used to prepare managers and staff for future demands upon them: in the latter, for example, the intention was to reveal the interorganizational tensions that might arise in a new service delivery structure and to help those who would have to implement it to develop constructive relationships. Immersive drama also provides a way of analyzing confrontations within a single organization. Even a thin veneer of fictionalization suffices to distance role-players from acknowledging that they are really playing through their own conflict in the exercise. In this way intraorganizational problems can be worked out by those directly involved in them. Elsewhere, immersive drama has been employed to create authentic role-plays purely for the purpose of entertainment. Indeed, this use of drama theory was among its earliest applications and enabled a handful of participants to gain the vicarious experience of “being” public figures engaged in contemporary news stories. Training simulations designed to deliver specific learning outcomes to student audiences could well have such an “edutainment” nature.

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The work done by Young in the field of wargaming (Curry and Young 2017) offers a halfway house between pure analysis and simulation. Typically, workshops in this tradition are attended by military personnel, diplomats, operational and intelligence analysts, or academics who have come together to explore specific current issues: these have ranged from the Libyan War to the Greek financial crisis. As more generally in wargaming, participants are given a lot of freedom to explore ways of achieving their goals and complete flexibility in how, in role, they may engage with other parties. Drama-theoretic analysis may be carried out by the roleplayers to inform their moves or alternatively by a game controller who tracks in plenary sessions the dynamics of negotiations between the teams. Such methods would neatly complement the support systems suggested by Horita and Maemura in ▶ “Supporting Community Decisions” for conflict management.

Software Support The analytical demands of drama analysis are not as great as those posed by other approaches to strategic conflicts, such as the analysis of options or the graph model (see the chapters ▶ “Conflict Resolution Using the Graph Model: Individuals and Coalitions” and ▶ “Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives”), but they still present a significant barrier for the use of the approach by novices or by those unused to the logical reasoning involved. For this reason, a succession of software packages has been developed. Historically the earliest was the CONAN software written by Howard, initially to support his version of the analysis of options. One distinctive feature was the facility to work with a strategic map of the situation, showing the improvements and sanctions from specified scenarios. Further functionality permitted the user to input an incomplete specification of the situation, since the program was often able to infer missing information (e.g., about preferences). In its later versions, CONAN began to incorporate information about the emotional underpinning of conflict resolution strategies as well as the advice about actions to include in what it termed an “interaction strategy.” Bennett instigated the creation of a small software tool called INTERACT (Bennett et al. 1994) that specifically related to the analysis of options. This provided a user-friendly means of building and investigating a strategic map. It also pointed the way toward a second generation of software that enabled modelling to become fully interactive. This new approach was strikingly exemplified by Howard’s first “immersive soap” interface. Designed to support role-players in the immersive drama entertainments described in the last section, this clickable interface enabled a user to explore a drama-theoretic summary of the situation facing a character. Howard subsequently used the same format to feed back the results of analysis to consultancy clients: an example is shown in Fig. 3. Each interface screen represents the situation as seen by a specific character, so different characters would have differently worded interfaces. Bryant developed this concept further in a pair of software programs, AUTHOR and SCRIPT, that respectively enabled a user to carry

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Fig. 3 Specimen role-player screen from immersive briefing

out a drama-theoretic analysis and that presented the results of this analysis for immersive briefing. However, none of these products achieved general distribution. This all changed with the production of the Confrontation Manager™ software in 2005 (Idea Sciences 2005). Largely written by Tait in close consultation with Howard, this program was the first enabling a user to model a set of nested confrontations using the options board notation and to use the distinctive dramatheoretic stress upon characters’ positions and intentions rather than a more general mapping of potential outcomes. With a logic engine based on DT1, this software also identified the dilemmas facing characters and provided a narrative statement explaining the various ways in which they could be eliminated. Confrontation Manager was produced with defense applications in mind and has been used most extensively in that sector, but it is highly general in nature. Upon the introduction of DT2 in 2007, there were immediate plans to support such analysis with a new software tool along the lines of Confrontation Manager, but a perceived lack of commercial viability has so far militated against its completion. Instead, individual developers have created bespoke tools for their own local applications and to suit their individual consulting styles. Given the relatively simple logic engine required to identify drama-theoretic dilemmas, this has proved a perfectly practicable proposition. A number of these tools have been based around an options board using standard spreadsheet software: perhaps the most polished is the Dilemma Explorer package created by Young (2017). One interesting by-product of this diversity of development paths is that it has highlighted the different emphases that are possible in drama-theoretic analysis. For instance, the interface of the

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Decision Explorer package stresses the evolving nature of a confrontation as new options are progressively added to the board and others resolved or amended, whereas earlier tools tended to work with a succession of more static pictures.

Conclusion Drama theory has provided a new way of interpreting and supporting collaborative relationships. Much of its evolution has been in response to the practical requirements of interventions in organizations or of applications in complex decisionmaking environments. This chapter has outlined the theory from such a perspective. The mathematical expression of the theory has kept pace with its sometimes rapid development and can be found elsewhere (e.g., Howard 1999, 2008; Murray-Jones and Howard 2001). The most pressing need for the immediate future is for a consolidation of the framework through a more thorough examination of some of its basic concepts. This need has been illustrated above by the discussion of the methodological choice between DT1 and DT2 (and other variants). However more fundamental questions also need attention: How should strength of preference/doubt be handled? To what extent is or can a character’s position be a statement of group intentionality? Should source credibility be explicitly taken account of in managing doubts? What is the relation between drama theory and the theory of speech acts and performative utterances? Many others could be added to this indicative list. In line with the twin traditions of “theorizing practice” and “putting theory into practice,” it would also be desirable for there to be much more extensive application of the ideas across a range of domains, to strengthen confidence in drama theory as a general framework for modelling human interaction. For the ideas to gain wider credibility in some disciplines (e.g., psychology and economics), experimental validation of some of the basic propositions of the theory will be required: this program has as yet barely started (but see Murray-Jones et al. 2003). And a further measure to bring drama theory into the portfolio of accepted approaches is that the relationship with game theory should be enhanced. To date there has been a certain amount of unnecessary mutual suspicion; a wider view, suggested by the large world – small world complementarity introduced at the start of this chapter – would do much to allay these doubts and to provide the foundations for a constructive dialogue.

Cross-References ▶ Conflict Resolution Using the Graph Model: Individuals and Coalitions ▶ Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives ▶ From Game Theory to Drama Theory ▶ Group Decision Support Practice “as it happens” ▶ Looking Back on Decision-Making Under Conditions of Conflict

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References Bennett PG (1995) Modelling decisions in international relations: game theory and beyond. Mershon Rev Int Stud 39:19–52 Bennett PG (1996) Games and drama: rationality and emotion. Mershon Rev Int Stud 40:171–175 Bennett PG (1998) Confrontation analysis as a diagnostic tool. Eur J Oper Res 109:465–482 Bennett P, Howard N (1996) Rationality, emotion and preference change: drama-theoretic models of choice. Eur J Oper Res 92:603–614 Bennett P, Huxham C, Cropper C (1989) Modelling interactive decisions: the hypergame focus. In: Rosenhead J (ed) Rational analysis for a problematic world. Wiley, Chichester, pp 283–314 Bennett PG, Tait A, MacDonagh K (1994) INTERACT: developing software for interactive decisions. Group Decis Negot 3:351–372 Binmore K (2006) Making decisions in large worlds. ADRES conference, Marseille. http://www. carloalberto.org/files/binmore.pdf Brams SJ (2012) Game theory and the humanities. MIT Press, Cambridge, MA Bryant J (1997) The plot thickens: understanding interaction through the metaphor of drama. Omega 25:255–266 Bryant J (2002) Confrontations in health service management: insights from drama theory. Eur J Oper Res 142:610–624 Bryant J (2003) The Six Dilemmas of Collaboration: inter-organisational relationships as drama. Wiley, Chichester, UK Bryant J (2007) Drama theory: dispelling the myths. J Oper Res Soc 58:602–613 Bryant J (2016) Acting strategically using drama theory. CRC Press, Boca Raton Bryant J, Darwin J (2003) Immersive drama: testing health systems. Omega 31:127–136 Bryant J, Darwin J (2004) Exploring inter-organisational relationships in the health service: an immersive drama approach. Eur J Oper Res 152:655–666 Bryant J, Howard N (2007) Achieving strategy coherence. In: O’Brien FA, Dyson RG (eds) Supporting strategy: frameworks, methods and models. Wiley, Chichester Chwe MS-Y (2013) Jane Austen, game theorist. Princeton University Press, Princeton Cialdini R (1993) Influence: science and practice. HarperCollins, New York Curry J, Young M (2017) The confrontation analysis handbook: how to resolve confrontations by eliminating dilemmas. Available through The history of wargaming project. www.wargaming.co. Accessed 8 May 2019 Dawes R (1988) Rational choice in an uncertain world. Harcourt Brace Jovanovich, Orlando Eden C, Ackermann F (1998) Making strategy: the journey of strategic management. Sage, London Edgar D (2001) The Prisoner’s dilemma. Nick Hern Books, London Elster J (1979) Ulysses and the Sirens. Cambridge University Press, Cambridge Elster J (1983) Sour grapes: studies in the subversion of rationality. Cambridge University Press, Cambridge Farrell J (1987) Cheap talk, coordination and entry. RAND J Econ 18(1):34–39 Fisher R, Ury W (1982) Getting to yes: negotiating agreement without giving in. Hutchinson, London Foresight C (1999) Learning through group simulation. Cambridge Foresight, Cambridge, UK Frank RH (1988) Passions within reason: the strategic role of the emotions. Norton, New York Fraser N, Hipel KW (1984) Conflict analysis: models and resolutions. North-Holland, New York Handayati Y, Simatupang TM, Sridharan R (2011) An analysis of collaboration between Coca-Cola and Carrefour using drama theory. Int J Value Chain Manag 5:1 Howard N (1971) Paradoxes of rationality: theory of metagames and political behavior. MIT Press, Cambridge, MA Howard N (1989) The manager as politician and general: the metagame approach to analysing cooperation and conflict, and The CONAN play. In: Rosenhead J (ed) Rational analysis for a problematic world. Wiley, Chichester

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Howard N (1994) Drama theory and its relation to game theory. Part 1: dramatic resolution vs. rational solution & Part 2: formal model of the resolution process. Group Decis Negot 3:187– 206. and 207–235 Howard N (1996) Negotiation as drama: how ‘games’ become dramatic. Int Negot 1:125–152 Howard N (1998) n-person ‘soft’ games. J Oper Res Soc 49:144–150 Howard N (1999) Confrontation analysis: how to win operations other than war. Department of Defense, CCRP Publications, Washington, DC Howard N (2001) The M&A play: using drama theory for mergers and acquisitions. In: Rosenhead J, Mingers J (eds) Rational analysis for a problematic world revisited. Wiley, Chichester Howard N (2004) Resolving conflicts in a tree: drama theory in the extensive form. In: Bryant JW (ed) Analysing conflict and its resolution. Proceedings of a conference of the Institute of Mathematics and its Applications. IMA, Southend-on-Sea Howard N (2008) Drama theory as a theory of pre-game communication and equilibrium selection. Sheffield Hallam University, Sheffield Howard N, Murray-Jones P (2002) Transformations at a drama-theoretic ‘moment of truth’. Defence Evaluation & Research Agency, London Idea Sciences (2005) Confrontation manager user manual. Idea Sciences, Washington, DC Johnson G, Scholes K (1997) Exploring corporate strategy, 4th edn. Prentice-Hall, London Murray-Jones P, Howard N (2001) Co-ordinated positions in a drama-theoretic confrontation: mathematical foundations for a PO decision support system. Defence Evaluation & Research Agency, London Murray-Jones P, Stubbs L, Howard N (2003) Confrontation and collaboration analysis: experimental and mathematical results. CCRTS symposium, Washington, DC. http://www.dodccrp.org Savage L (1951) The foundations of statistics. Wiley, New York Schelling T (1960) Strategy and conflict. Harvard University Press, Cambridge, MA Sensarma S, Okada N (2010) Redefining the game in local water management conflict: a case study. Water Resour Manag 24:4307–4316 Stubbs L, Howard N, Tait A (1999) How to model a confrontation – computer support for drama theory. In: Proceedings of 1999 command and control research and technology symposium, Naval War College, Newport, 29 June – 1 July 1999 Tait A (2006) Speed confrontation management. www.ideasciences.com Young M (2017) Decision Explorer. https://www.decisionworkshops.com/dilemma-explorer/ 4581290653. Accessed 8 May 2019

Non-cooperative Bargaining Theory Kalyan Chatterjee

Contents Introduction: Game Theory and Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Approaches to Modelling Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Non-cooperative Models of Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Non-cooperative Multilateral Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Non-cooperative game theory has contributed several major ideas to the study of negotiation. In the two-person context, the line of research initiated by Chatterjee and Samuelson focused on the strategy of making demands, showing the importance of each side’s perception of the other, and how these perceptions can lead to inefficiency. The Rubinstein Alternating Offers game emphasizes the role of time and establishes a link to the Nash bargaining solution. More recent studies have turned to coalitional bargaining and its relation to the core. Keywords

Negotiation · Game theory · Coalition formation · Non-cooperative · Nash bargaining solution · Nash equilibrium · Pareto-optimal · Subgame perfect equilibrium

K. Chatterjee (*) Department of Economics, The Pennsylvania State University, University Park, PA, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_9

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Introduction: Game Theory and Negotiation Game Theory was first systematised by John von Neumann and Oskar Morgenstern in the book Theory of games and economic behavior (1944). The theory addresses the choices that individuals “rationally” make in situations where their interests are different but not entirely in conflict. It is therefore a natural context for the study of bargaining, where the players may have a common interest – when there is an outcome that all parties prefer to no agreement – but where there are also real conflicts of interest. (Different kinds of bounded rationality have also figured in the recent literature on game theory, but we shall not discuss them in this chapter.) Von Neumann and Morgenstern divided game theory into non-cooperative and cooperative branches; in the latter, agreements can be enforced without cost, whereas in the former enforcement occurs only within the context of the original problem. The first game-theoretic treatments of negotiation fell within cooperative game theory, and cooperative game theory approaches remain an active area of research. But it was later realized that non-cooperative models were essential, as only they could capture the “give and take” that must characterize genuine bargaining. These non-cooperative approaches are the main subject of this chapter.

Approaches to Modelling Negotiation There are two major game-theoretic frameworks for modelling bargaining and negotiation. The first, due to Nash (1950, 1953) and later expanded by Roth (1979), proceeds by first proposing some principles or axioms that are supposed to characterise the negotiations they wish to model. The axioms are usually strong enough to give rise to a “solution” or a prediction of the result of the bargaining. Nash’s first paper, probably the most famous one in bargaining, lays out the following axioms that describe the solution to a two-player negotiation. The first is a requirement that utilities be cardinal (as in von Neumann and Morgenstern), so if the same agreement is described by two different utility functions, the description is equivalent if the utility functions differ only (if at all) in the choice of origin and scale. In effect, the origin is chosen to be a specific utility pair, known as the status quo point. This is supposed to be the utility outcome in the event of disagreement or conflict. (Nash’s second paper determines this in a game, whilst the first assumes this is given exogenously). The set of feasible agreements (in utility terms) is assumed by Nash to be convex (this might call for joint randomisation between feasible agreements), closed and non-empty. Nash’s work depends on a couple of apparently innocuous axioms, first, that if the set of feasible utility pairs is symmetric, given the status quo point as origin, then the solution should give equal utilities to the two players, and second, that the solution should be efficient. (This latter condition means it is not possible to make a player strictly better off without making the other player strictly worse off. It follows that, with a symmetric utility possibility frontier, the solution has to be the intersection of the Pareto frontier with the 45° line from the status quo point.)

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The last axiom is not innocuous. It can be interpreted as saying that the players are behaving in negotiation as if they are jointly maximising some welfare function, though the actual statement, called the Independence of Irrelevant Alternatives by Nash, is weaker. The condition is that if the solution for a utility-possibility set A is in B and B(
)A, then it must also be the solution for a utility possibility set B. There is an important additional requirement, namely that the status quo points of A and B must be the same, so the solution is not independent of this particular alternative. Given these axioms, Nash proved in an elegant theorem that the solution had to be the pair of utilities that maximised the product of utilities measured with the status quo point as origin. A programme of research started thereafter, relaxing and changing the axioms, and a superb description of this work is in Roth’s 1979 book. The beautiful Nash result, however, raised many questions. First, the properties of the negotiation process appeared to impute some collective rationality to the players – they would never reach something inefficient and wasteful and they would, in fact, be behaving as if jointly maximising a particular social welfare function. This idea seems somewhat optimistic, given that real-world bargaining clearly suffers from many inefficiencies, giving rise to impasses, strikes, wars and so on. A second, less fundamental, question was the assumption of symmetry, which seemed to imply all bargainers were equally skilful and had equal “bargaining power,” whatever that was supposed to be. (See Roth’s book for an account of what happens if one relaxes either the efficiency or the symmetry assumptions made by Nash.) A third question, which occurred to Nash himself, was that the axioms were not particularly informative in terms of identifying which kinds of bargaining fell under their rubric and which were excluded. The reason, of course, was that the axiomatic description was free of any description of the actual bargaining procedure. (In an odd twist of fate, this feature is now regarded by some as a virtue of the axiomatic approach.) Nash went on to propose a “demand game,” one of whose Nash equilibrium outcomes coincided with his bargaining solution. The demand game is a one-stage game in which the two players write down their utility demands, simultaneously and independently. If the demands are compatible, that is if the demand pair is feasible, each player gets his or her utility demand (or, to put it in terms of the physical agreement, an agreement is reached in the bargaining that gives each player this utility demand). If the pair is infeasible, the players get their status quo utilities. There is a multiplicity of Nash equilibrium outcomes in this game, including the Nash bargaining solution and the status quo point. Nash proposes a selection criterion, which presages some of the later work in refinements of equilibrium, in order to choose his bargaining solution as the most plausible equilibrium. The important feature of the Nash demand game was that it pioneered the second major approach to theoretical work in bargaining, the non-cooperative approach. It proposes an explicit description of the bargaining procedure, rather than the mysterious implicit description obtained through the axioms, and uses the standard game-theoretic notion of equilibrium as the solution concept. It is interesting that even this early attempt at an explicit description generated inefficient disagreement as an equilibrium outcome, thus establishing a more direct link to real world outcomes.

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Since then, there was a gap of about 25 years before a number of non-cooperative bargaining models appeared in the economics and operations research literature (Unfortunately, there now seems to be an ideological predilection against publishing game-theoretic papers in some of the leading operations research journals; some editors believe that only experiments are worthwhile in game theory. Thus the injunction to young researchers is “Go forth and experiment,” never mind on what, since it needn’t be on evaluating theories against each other – given that theories don’t deserve to be published.). Some of these earlier models will be described in the next section and their relevance to important economic issues examined.

Non-cooperative Models of Bargaining We will discuss two popular models that were formulated and analysed in the late 1970s and early 1980s. The two models both turned out to be related to Nash’s work. One, by Chatterjee and William Samuelson (1979, 1983), considered a form of the Nash demand game, but introduced incomplete information. In the context of a buyer and a seller, the buyer had a reservation price or maximum willingness to pay v2 for a single indivisible item owned by the seller, who had similarly a minimum price she was willing to accept v1 Each player’s reservation price was his or her private information; the reservation prices were independent random variables and the probability distributions were common knowledge. Given this private information, the players simultaneously and independently wrote down price demands – a bid price for the buyer, a2 and an ask price for the seller, a1 If a2  a1, there was trade 1 at a price somewhere in between the two (for concreteness, let us suppose at a2 þa 2  this choice has certain properties to be mentioned later). If a2 < a1 there was no trade and players got their no trade payoffs, assumed to be 0. If the distributions of v1 and v1 are overlapping, so it is not commonly known that gains from trade are possible, one would suspect that strategic behaviour in this game would always lead to too little trade, so that sometimes players would not agree even when agreement would be mutually beneficial. For the distributions being both uniform on [0,1], Chatterjee and Samuelson derived an equilibrium in linear strategies, such that a player’s demand was a positive affine function of his or her 1 reservation price (with slope 23 for the case where the price was set at a2 þa 2 Chatterjee (1982), with some simple mechanisms but including axioms for discrete distributions, and Myerson and Satterthwaite (1983) in a seminal paper in a much more general setup overall (but not considering discrete distributions), showed that it was not possible to design any bargaining procedure that would always have an equilibrium with the efficient amount of trade when gains from trade were not common knowledge. Myerson and Satterthwaite also showed that in the uniform distribution 1 case with the price set at a2 þa 2 , the Chatterjee-Samuelson linear equilibrium of the incomplete information demand game would maximise expected gains from trade among all equilibria of all games in that environment. These results effectively

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settled the argument on the question of whether rational bargainers would always find a mutually beneficial solution when one was available. It also gave a possible explanation of why there was inefficiency in bargaining – namely private information and the absence of common knowledge of gains from trade. Rubinstein (1982) adopted a completely different approach. In the simplest setting in his paper, he considered two players bargaining to divide a prize (“pie”) of a fixed size of 1. The bargaining would take place as follow: First Player 1 would propose a division, x, 1  x. Player 2 would then accept or reject. If Player 2 accepted, the game would end. Otherwise, it would proceed to the following period, when Player 2, the rejector of the previous period’s offer, would make a counter-offer of a division y, 1  y, which Player 1 would accept or reject (with the first quantity, x, y denoting the share of Player 1). If Player 1 were to eccept, the game would end. Otherwise, in period 3, Player 1 would again make an offer and so on. Waiting was costly-an agreement a time Δ after the game began would lead to payoffs discounted by erΔ ¼ δ where r was the discount rate. A player could not withdraw his offer, once it had been made, before the other player responded with an accept or reject. Players alternated between accepting and rejecting. An agreement v, 1  v at time t would therefore give period 1 payoffs of δt  1 (v, 1  v) to the two players. Using the stronger equilibrium notion of Selten (1965), subgame perfectness, Rubinstein showed there was a unique subgame perfect δ 1 equilibrium in which a player always offered his opponent 1þδ , keeping 1þδ for himself, whenever it was his turn to make an offer and always accepted any offer that δ when it was his turn to respond to an offer. The equilibrium is gave him at least 1þδ history independent-players don’t make concessions if the game continues beyond the first period, which it is not supposed to in the equilibrium; no matter how long the bargaining goes on, the offers will always be the same and the expectation will be that the game ends in the immediate aftermath. Binmore, Rubinstein and Wolinsky (1986) also considered the role of outside options or “best alternatives to a negotiated agreement” (Raiffa 1982) in the setting of this model. If a player could choose to leave the game and take his non-deteriorating outside option rather than make a counter-offer, an outside option δ less than or equal to 1þδ would be strategically irrelevant, in that it wouldn’t affect offers or responses. A higher outside option of z would increase the amount offered in equilibrium to z but no more, provided the sum of the outside options was less than the size of the pie (failing which there would be no point bargaining). Alternatively, one could consider an exogenous probability of 1  δ that the game ended after a rejection (rather than discounting future payoffs), in which case the players would be forced to take their outide options. In such a case, the outside option values played the role of conflict payoffs in Nash’s bargaining solution; as δ ! 1 the equilibrium payoffs in the Rubinstein model approached as a limit the payoffs in the Nash bargaining solution. Thus the set of bargaining procedures that would give the Nash bargaining solution as the equilibrium outcome garnered an additional member; one that is nowadays used interchangeably with the Nash bargaining solution in many application papers. (Many applications typically say something like “Assume

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bargaining takes place such that the Nash bargaining solution is the outcome; the Rubinstein model gives a strategic bargaining equivalent.”) The Rubinstein model, as modified in Binmore, Rubinstein and Wolinsky, certainly was the most outstanding success of the so-called Nash programme, more so because the bargaining procedure of offer and counter-offer and time elapsing in bargaining was so close to the natural real-world bargaining processes that we have all experienced. Of course, in some applications, say in billion dollar mergers, one could question whether the offers made were determined by the relative discount factors of the parties, but given the description of the environment, the result was striking and neat. There have been many attempts to combine the two aspects featured in these two papers – incomplete information in one and the sequential offer and counter-offer process in the other. This, as expected, has led to more complex models and made it difficult to obtain clean solutions of the type in Rubinstein’s model and related work. The basic picture, abstracting from issues of choosing among sequential equilibria by specifying plausible beliefs, seems to me to be best addressed in a model that is a first-cousin of a concession game, such as the one in Chatterjee and Larry Samuelson (1987). Such a first-cousin is Chatterjee and L. Samuelson (1988) and perhaps a recent third cousin is the striking paper of Abreu and Gul (2000), though that is based more on a similar idea in Myerson’s textbook (1991) than on the ChatterjeeSamuelson papers. The basic idea in the two Chatterjee-Samuelson papers is: that there is a period of impasse, when the two parties seek to convince each other of their relative strength. The one who folds first reveals her “type” through an appropriate (depending on the state of the game) offer, that starts a game in which there is only one player who has private information. When that player too, after stonewalling for a bit more, reveals his type, there is complete information and the Rubinstein game starts. Beliefs off the equilibrium path determine what offer is chosen to reveal and how unexpected choices of offers are interpreted. Other areas that have been covered in the non-cooperative approach include more descriptive models of the outside option a player has; this presumably arises from search or the threat to go search for an alternative offer and of “inside options,” where a player can stay in the bargaining but take actions that affect the payoffs. Muthoo’s book (2000) is an excellent introduction to many of these models derived from Rubinstein’s paper. A somewhat different take on bargaining and search is in the papers by Lee (1994) and Chatterjee and Lee (1998). Osborne and Rubinstein’s (1990) “Bargaining and Markets” provides a rigorous exposition of both two-person sequential bargaining and models where bilateral bargaining takes place in a stylised market setting. We now briefly describe non-cooperative multilateral bargaining.

Non-cooperative Multilateral Bargaining There are several possible interpretations of the word “multilateral” in the title of this section. Any bargaining problem that explicitly includes the choices of at least three independent players could be considered “multilateral” in some sense. This includes

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markets of many players in which all transactions are bilateral, as in the bargaining and search literature mentioned in the previous section. Unanimity games, in which there are three or more players, all of whom must agree before an agreement is reached, are more properly included in the category of multilateral bargaining, as are coalitional games in which proposals could include more than two parties and the final outcome could have several coalitions forming. The standard starting point for the unanimity game is the multiplicity result mentioned in Binmore (1985), Herrero (1985) and Shaked (1986). This result considers three or more players with a common discount factor who make proposals sequentially on the division of a pie of size 1, as in Rubinstein’s bilateral bargaining model. For concreteness, suppose there are three players and the fixed order of proposals and responses is 1, 2, 3. Player 1 moves first and makes a proposal (x1, x2, 1  x1  x2) to the other players who then sequentially accept or reject. If there is a rejection, the game goes to the next stage and Player 2 makes the proposal. It is possible to show that any allocation of the pie, including the extreme ones, can be sustained as a subgame perfect equilibrium for sufficiently high values of δ. This result has started showing up as a problem in graduate textbooks, but a summary of the reason this is true is given here. The basic idea is that the extreme solutions (1,0,0), (0,1,0), (0,0,1) sustain one another as equilibria. For example, suppose the equilibrium played is (0,1,0) and the equilibrium path is that Player 1 proposes this and Players 2 and 3 accept it. If either 2 or 3 reject the offer they are given, the play proceeds to the next period and Player 2 makes the same offer. In general, a rejection of the equilibrium offer keeps each player in the same “state” where the same proposal is made and accepted (though by different proposers and responders). Thus rejection of an offer cannot be a profitable unilateral deviation. What about making a different proposal? Why doesn’t player 1 offer player 2 δ instead of 1, the usual starting point in the argument that leads to the Rubinstein solution for two-player games? It is true that Player 2 will always accept such an offer but as soon as it is made, the state for each player switches to state 3, where the next period equilibrium offer is (0,0,1) and Player 3 now rejects any offer less than δ. Therefore, for any δ  12, the deviation by the proposer is not profitable. This construction relies on each player’s strategy having three “states” corresponding to the three extreme points, essentially to reward players for rejecting offers and to punish deviators, as well as a state in which the equilibrium offer is made and accepted, if different from one of these three. The language of “states” suggests that one could explicitly model strategies in this game as finite automata and check if, in fact, some notion of reducing the complexity of these automata would give us back something akin to the Rubinstein equal division in the limit. In fact, the unique stationary equilibrium in this case does lead to equal division as δ ! 1. Chatterjee and Sabourian (2000) investigate whether this intuition is, in fact, correct. The fact that a single extensive-form game is being played and one that could end in any finite period, necessitates a new framework to be developed to apply the “Nash equilibrium with complexity” notion of Abreu and Rubinstein

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(1988). It turns out that the main difficulty is finding an appropriate notion of complexity. With this appropriate notion, it is possible to prove that a “subgame perfect equilibrium with complexity” exists and is unique. Moreover, as δ ! 1, this goes to the equal division solution. We do not discuss this in detail, since this paper and its follow-up papers in the area of markets are extensively discussed in (Chatterjee and Sabourian 2009). With this justification for assuming some form of stationarity in strategies as a way of reducing complexity for the same payoffs, it is possible to make some progress in the general study of coalition formation (though chronologically some of the papers we discuss came earlier). The analysis of coalition formation in fact goes back further than Nash, to the founding fathers of game theory, von Neumann and Morgenstern (1944), who invented the notion of “characteristic function” for coalition formation games and also proposed a solution for such games. In the context of zero-sum games, von Neumann and Morgenstern defined the characteristic function for a coalition S, which is a subset of the set of all players N to be the maximum players in S could guarantee themselves by writing a binding agreement on actions, given that players in N\S also acted as a single player to minimise S0s payoffs. This set function was called v(S) For non-zero sum games, there is a distinction between maximin and minimax and therefore two versions of the characteristic function. One could also think of an equilibrium being played between S and N\S in which case the v(S) would depend on equilibrium selection in the presence of multiplicity. It is also not clear that the coalition N\S will always form; the coalition structure, π, usually affects the payoffs in equilibrium. In general, therefore, given a particular selection of an equilibrium in the strategic form game, we have a set function v(S| π) where S  π We will assume that v(S| π) is independent of π and just write v(S) This eliminates the large and important area of games with externalities, which are generally hard to analyse. A very good discussion of these games and multiperson bargaining in general is in Ray (2007). Another survey (Bandyopodhyay and Chatterjee 2006) is focused on games without externalities and serves as the foundation for this section. The basic questions that a model of coalition formation has to answer are: (i) What coalitions form in equilibrium and (ii) how is the surplus from a coalition divided among its members? We shall focus primarily on a sequential offers model, though several alternative approaches exist (see the aforementioned surveys for more details). Most of the sequential offers models we shall consider are natural extensions of Rubinstein’s bilateral bargaining model, and, like Rubinstein, focus on the limiting equilibrium allocation as the discount factor δ ! 1. (This contrasts with the work of the pioneers (Harsanyi 1974; Selten 1981) who both consider models without discounting.) Selten (1981) proposed a sequential offers model of coalitional bargaining in which there is a fixed order of players and the first person in this order makes a proposal, naming a coalition S (of which the proposer is a member) and a payoff division among the players in S. Each named player responds (in sequence) either

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accepting or rejecting. All the members of S have to accept before the coalition forms. As soon as one coalition forms, the game ends. Since no discounting is used, the characteristic function satisfies a rule called zero normalisation (This condition basically says that if we subtract v({i}) from the worth of each coalition of which i is a member, the resulting characteristic function is strategically equivalent. This is not true in the Rubinstein game with outside options, for example. A game with a pie of 1 and two players with outside options of 0.6 and 0 is not strategically equivalent to one where a surplus of 0.4 is split among two players. (In the first, the Rubinstein limiting solution gives (0.6,0.4); in the second (0.8,0.2). This is a consequence of the fact that, with discounting, 0 has the specific meaning of the utility of bargaining forever.) If someone in S rejects, that person makes the offer in the next period. Not surprisingly, Selten was not able to get determinate results without imposing an additional axiomatic structure on the stationary subgame perfect equilibria of this model. A sequential offers model with discounting was proposed by Chatterjee et al. (1993). This model, like Selten’s, has a fixed order of players, the first one of whom makes an offer naming a coalition and an allocation of the coalitional worth among the members of S. Other members of S accept or reject. If everyone accepts, S leaves the game and the initiative passes to the specified first player in N\S without discounting. (Note that this model does not assume that only one coalition forms.) If some member of S rejects, that person makes the next offer in the next period. All players discount the future with the discount factor being δ. (That is, a payoff of x in period t + 1 is equivalent to a payoff of δx in period t.) If a coalition S forms and obtainsP a coalitional worth v(S) in period t, player i in S obtains a payoff δt  1xi where xi ¼ vðSÞ. iS

Two other variants of this model have received some attention and are often more convenient to use than the rejector-proposes protocol. In the first, if an offer is rejected, the rejector does not make the next offer but the next player in the pre-specified order does (as in the Shaked analysis of the unanimity game where all members of N have to agree to a proposal for it to take effect-see Osborne and Rubinstein (1990)). In the second, the next proposer after a rejection is chosen randomly (as in Okada (1996)). Though most of the results are quite similar to the Chatterjee et al. paper, these differ in one important respect-in strictly superadditive games (those with v(S [ T ) > v(S) + v(T ) for S, T disjoint) the stationary equilibria in the rejector-proposes protocol could have equilibrium delay. The sequential offers extensive forms do not take into account competition among different coalitions for some members who are common to both. However, the experiment in Bolton et al. (2003) is suggestive in that the model appears to reflect, partially if not fully, the interplay between competition and equity that one sees in real-life bargaining. The solution concept used in all these papers is that of stationary, subgame perfect equilibrium. “Stationary” in this context means that offers made and response strategies (that is, whether or not to accept an offer (S, x) currently on the table)

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depend only on the set of players in the game and not on the history of past offers and counter-offers (This is not always a natural assumption and has been criticised (see Osborne and Rubinstein (1990)). As mentioned earlier, a formal justification of stationarity as economising on complexity costs was formulated for the unanimity game by Chatterjee and Sabourian (2000).). Turning back to the Chatterjee et al. model, there are two negative findings given by illuminating examples and one positive characterisation result. These examples are briefly discussed here, reproduced from the original 1993 paper. The first is that the grand coalition need not form for a given order of proposers, even with a non-empty core, and therefore that the equilibrium of the game need not be in the core. Example 1. The characteristic function is given by v({1, 2, 3}) ¼ 1, v({1, 2}) ¼ 0.7, v({1, 3}) ¼ v({2, 3}) ¼ 0.2, v(S) ¼ 0 otherwise. As δ ! 1 the limiting stationary subgame perfect equilibrium allocation depends on who proposes. If Player 1 or 2 proposes, each will propose the coalition {1, 2} and the other will accept. Player 3 will get 0 and Players 1 and 2 will each get 0.35 (in the limit). If Player 3 proposes, he proposes the grand coalition and the limiting equilibrium allocation is (0.35,0.35,0.3). Thus, if Player 3 proposes, the equilibrium outcome is in the core; otherwise, it is not even efficient. The same point can be made even more forcefully in the following example, where the equilibrium allocation is inefficient for every order of proposers. Again, we only need a three-player game for this example. Example 2. Suppose v({1, 2, 3}) ¼ 1.2, v({1, 2}) ¼ 1, v({1, 3}) ¼ 0.99, v({2, 3}) ¼ 0.4, v(S) ¼ 0 otherwise. Here the limiting equilibrium allocation will be (0.5,0.5,0) if either Player 1 or Player 2 is the first proposer and (0.5,0,0.49) if Player 3 is the first proposer. Note that the core is non-empty-for example (0.8,0.2,0.2) is in the core of the game. The key feature in both these examples is that the per capita payoff is greater in the two-player coalition than in the efficient, three-player one. In the unanimity game, on the other hand, in which v(N ) ¼ 1, v(S) ¼ 0 otherwise, the per capita payoff is trivially greater in the grand coalition and one would expect equal division to be the limiting (stationary) equilibrium payoff. (It is.) A condition called domination by the grand coalition in Chatterjee et al. guarantees efficient grand coalition formation for all orders of proposers; this condition states that the per capita payoff of the grand coalition must be greater than that of any other coalition. This essentially reduces the relevance of the alternative sub-coalitions and makes the grand coalition attractive to propose and accept. Another interesting example of inefficiency in the sequential offers model arises because of equilibrium delay, even in stationary equilibrium. We do not discuss the example, due to Elaine Bennett and Eric van Damme, but it is extensively examined in the Chatterjee et al. paper. Here we need at least four players. The possibility of equilibrium delay and unacceptable offers creates some difficulties with any characterisation results, and this is not unique to the particular Chatterjee et al. paper. However, they also show that a sufficient condition for no delay is for the game to exhibit a high degree of increasing returns to

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coalition size, namely that it be strictly convex (This means that if S
T, then v (S [ {i}  v(S) < v(T [ {i}  v(T), for all S, T.). We now mention the main positive result for the model; namely that for strictly convex games, for all sufficiently high values of δ, there exists an efficient equilibrium for some order of proposers and the limit of the efficient equilibrium allocation, which depends on δ, as δ ! 1, is the allocation that maximises the product of utilities of players among all allocations in the core. Thus, for games showing sufficiently strong increasing returns, we get a unique limiting allocation in the core, and moreover the “most equal” point in the core. (We can also think of this as a modified Nash bargaining solution, where the Nash product is maximised over all allocations in the core. Binmore (1985) comes to a similar conclusion in a different three-player game.) The Nash bargaining solution and the core, derived on very different grounds make their reappearance here. The paper of Okada (1996) makes the following important point. If the rejector of an offer is not necessarily the next proposer, there is no (stationary, subgame perfect) equilibrium delay. Okada proves his result for strictly superadditive games but this is a sufficient condition. Examples of his major contention can be constructed for games that are not superadditive. Whilst the models with discounting have sought to determine a unique (stationary) equilibrium, which turns out to be in the core under some conditions and to coincide with a specific point in the core, other models have sought to obtain all the points in the core as stationary equilibria rather than one. Examples of this genre are Perry and Reny (1994) and Moldovanu and Winter (1995), who have models without discounting. Evans (1997) has a different approach, which appears to get to the heart of the motivating assumptions behind the core (competition among weaker players to make offers) by considering a game where players compete first for the right to become a proposer. Gul (1989) (see also the correction by Hart and Levy (1999)) has a different model that yields the cooperative game solution concept, the Shapley value, as its limiting stationary equilibrium allocation for strictly convex games. Finally, it is interesting to consider under what circumstances coalitions could form gradually in a model with discounting (Seidmann and Winter 1998). One possibility is to assume that the characteristic function v(S) actually gives a per period payoff to coalition S In this case, it might be optimal for players to form smaller sub-coalitions as “inside options” to increase disagreement payoffs during bargaining on forming the grand coalition. In such a case, it is possible for coalitions to build up gradually over time, which we certainly observe in the real world.

Conclusions Bargaining still remains an active area of research with papers in economics coming out in bilateral and multilateral bargaining. There is also some interest in combining the models discussed here with the emerging work on networks of communication (for which Bolton et al. 2003 provide some experimental findings). Computer scientists modelling negotiation are particularly interested in protocols that

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“simulate” actual bargaining and this has generated some interest among them in models of the kind discussed in this chapter. It might be noted that there seems to be a big gap in the topics covered here – there is no section on multilateral bargaining with incomplete information. This is an area on which there is little work that I know of, but one where much development is yet to be accomplished. There are many insightful papers on extending the definition of core with incomplete information, an example being Forges et al. (2002) but they do not seem to translate directly into the kinds of models discussed in the last section. Okada (2012) has made some progress in a new paper on a model without discounting. We also have not discussed bargaining with boundedly rational players on which some work has been done recently (see, for example, Yildiz 2003 for an account of overoptimistic bargainers). Overall, non-cooperative bargaining remains an exciting area for future research.

Cross-References ▶ Conflict Resolution Using the Graph Model: Individuals and Coalitions ▶ From Game Theory to Drama Theory ▶ Group Decisions: Choosing a Winner by Voting ▶ Negotiation as a Cooperative Game ▶ The Notion of Fair Division in Negotiations

References Abreu D, Gul F (2000) Bargaining and reputation. Econometrica 68:85–117 Abreu D, Rubinstein A (1988) The structure of Nash equilibrium in repeated games with finite automata. Econometrica 56:1259–1282 Bandyopadhyay S, Chatterjee K (2006) Coalition theory and its applications: a survey. Econ J 116(509):F136–F155, 02 Binmore KG (1985) Bargaining and coalitions. In: Roth AE (ed) Game theoretic models of bargaining. Cambridge University Press, New York Binmore KG, Rubinstein A, Wolinsky A (1986) The Nash bargaining solution in economic modelling. Rand J Econ 17:176–188 Bolton GE, Chatterjee K, McGinn KL (2003) How communication links influence coalition bargaining: a laboratory investigation. Manag Sci 49(5):583–598 Chatterjee K (1982) Incentive compatibility in bargaining under uncertainty. Q J Econ 95:717–726 Chatterjee K, Lee CC (1998) Bargaining and search with incomplete information about outside options. Games Econ Behav 22(2):203–237 Chatterjee K, Sabourian H (2000) Multiperson bargaining and strategic complexity. Econometrica 68:1491–1509 Chatterjee K, Sabourian H (2009) Game theory and strategic complexity. In: Meyers R (ed) Springer encyclopaedia of complexity and systems science. Springer, Berlin/New York, pp 4098–4114 Chatterjee K, Samuelson WF (1979) The simple economics of bargaining mimeo. The Pennsylvania State University and Boston University, USA Chatterjee K, Samuelson WF (1983) Bargaining under incomplete information. Oper Res 31(5):835–851

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Chatterjee K, Samuelson L (1987) Bargaining with two-sided incomplete information: an infinite horizon model with alternating offers. Rev Econ Stud 54:175–192 Chatterjee K, Samuelson L (1988) Bargaining under two-sided incomplete information: the unrestricted offers case. Opera Rese 36(4):605–618 Chatterjee K, Dutta B, Ray D, Sengupta K (1993) A non-cooperative theory of coalitional bargaining. Rev Econ Stud 60:463–477 Evans RA (1997) Coalitional bargaining with competition to make offers. Games Econ Behav 19(2):211–220 Forges F, Mertens J-F, Vohra R (2002) The ex ante incentive compatible core in the absence of wealth effects. Econometrica 70(5):1865–1892 Gul F (1989) Bargaining foundations of the Shapley value. Econometrica 57(1):81–95 Harsanyi JC (1974) An equilibrium-point interpretation of stable sets and a proposed alternative definition. Manag Sci 20(11):1422–1495 Hart S, Levy Z (1999) Efficiency does not imply immediate agreement. Econometrica 67(4):909– 912 Herrero M (1985) A strategic bargaining approach to market institutions. Ph.D. Thesis, University of London, London Lee CC (1994) Bargaining and search with recall: a two-period model with complete information. Oper Res 42:1100–1109 Moldovanu B, Winter E (1995) Order independent equilibria. Games Econ Behav 9(1):21–35 Muthoo A (2000) Bargaining theory with applications. Cambridge University Press, Cambridge Myerson R (1991) Game theory: analysis of conflict. Harvard University Press, Cambridge, MA Myerson R, Satterthwaite M (1983) Efficient mechanisms for bilateral trading. J Econ Theory 28:265–281 Nash J (1950) The bargaining problem. Econometrica 18:155–162 Nash J (1953) Two-person cooperative games. Econometrica 21:128–140 Okada A (1996) A non-cooperative coalitional bargaining game with random proposers. Games Econ Behav 16:97–108 Okada A (2012) Non-cooperative bargaining and the incomplete informational core. J Econ Theory 147:1165–1190 Osborne MJ, Rubinstein A (1990) Bargaining and markets. Academic, New York Perry M, Reny PJ (1994) A non-cooperative view of coalition formation and the core. Econometrica 62(4):795–817 Raiffa H (1982) The art and science of negotiation. Harvard University Press, Cambridge, MA Ray D (2007) A game theoretic perspective on coalition formation. Oxford University Press, Oxford Roth AE (1979) Axiomatic models of bargaining. Springer, New York Rubinstein A (1982) Perfect equilibrium in a bargaining model. Econometrica 50:97–109 Seidmann Dl J, Winter E (1998) A theory of gradual coalition formation. Rev Econ Stud 65(4):793– 815 Selten R (1965) Spieltheoretische Behandlung eines Oligopolmodells mit Nachfrageträgheit – Teil I Bestimmung des dynamischen Preisgleichgewichts. Zeitschrift für die gesamte Staatswissenschaft 121:301–24 Selten R (1981) A non-cooperative model of characteristic function bargaining. In: Böhm V, Nachtkamp H (eds) Essays in game theory and mathematical economics. Bibl Institut, Mannheim, pp 131–151. Reprinted in: Selten R (1989) Models of strategic rationality. Kluwer Academic Publishers, Dordrecht Shaked A (1986) The three-player unanimity game, presented at meetings of Operations Research Society of America, Los Angeles, April 1986 von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton Yildiz M (2003) Bargaining without a common prior – an immediate agreement theorem. Econometrica 71(3):793–811

Negotiation as a Cooperative Game Özgür Kıbrıs

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Bargaining Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bargaining Rules and Axioms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Nash Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Kalai-Smorodinsky Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Egalitarian Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Strategic Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ordinal Bargaining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Game theory provides us with a set of important methodologies for the study of group decisions as well as negotiation processes. Cooperative game theory is a subfield of game theory that focuses on interactions in which involved parties have the power to make binding agreements. Many group decision and negotiation processes (such as legal arbitrations) fall into this category, and as such, they have been central in the development of cooperative game theory. Particularly, an area of cooperative game theory, called bargaining theory, focuses on bilateral negotiations as well as negotiation processes where coalition formation is not a

This is a revised version of the chapter “Cooperative Game Theory Approaches to Negotiation” which was published in the first edition of this handbook. Ö. Kıbrıs (*) Faculty of Arts and Social Sciences, Sabanci University, Istanbul, Turkey e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_10

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central concern. The object of study in bargaining theory is a (bargaining) rule, which provides a solution to each bargaining problem (or in other words, negotiation). Studies on bargaining theory employ the axiomatic method to evaluate bargaining rules. This chapter reviews and summarizes several such studies. After a discussion of the bargaining model, we present the important bargaining rules in the literature (including the Nash bargaining rule), as well as the central axioms that characterize them. Next, we discuss strategic issues related to cooperative bargaining, such as the Nash program, implementation of bargaining rules, and games of manipulating bargaining rules. We conclude with a discussion of the recent literature on ordinal bargaining rules. Keywords

Negotiation · Game theory · Cooperative · Nash bargaining solution · Paretooptimal · Bargaining theory · Axiom · Ordinal bargaining

Introduction Negotiation is an important aspect of social, economic, and political life. People negotiate at home, at work, at the marketplace; they observe their team, political party, country negotiating with others; and sometimes, they are asked to arbitrate negotiations among others. Thus, it is no surprise that researchers from a wide range of disciplines have studied negotiation processes. In this chapter, we present an overview of how negotiation and group decision processes are modeled and analyzed in cooperative game theory.1 This area of research, typically referred to as cooperative bargaining theory, originated in a seminal paper by Nash (1950). There, Nash provided a way of modeling negotiation processes and applied an axiomatic methodology to analyze such models. In what follows, we will discuss Nash’s work in detail, particularly in application to the following example. Example 1 (An Accession Negotiation) The European Union, E, and a candidate country, C, are negotiating on the tariff rate that C will impose on its imports from E during C’s accession process to the European Union. In case of disagreement, C will continue to impose the status-quo tariff rate on import goods from E and the accession process will be terminated, that is, C will not be joining the European Union.

1

Cooperative game theory analyzes interactions where agents can make binding agreements and it inquires how cooperative opportunities faced by alternative coalitions of agents shape the final agreement reached. Cooperative games do not specify how the agents interact or the mechanism through which their interaction leads to alternative outcomes of the game (and in this sense, they are different than noncooperative games). Instead, as will be exemplified in this chapter, they present a reduced form representation of all possible agreements that can be reached by some coalition.

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Nash’s (1950) approach to modeling negotiation processes such as Example 1 is as follows. First, the researcher identifies the set of all alternative agreements.2 (Among them, the negotiators must choose by unanimous agreement, that is, each negotiator has the right to reject a proposed agreement.) Second, the researcher determines the implications of disagreement. In our example, disagreement leads to the prevalence of the status-quo tariff rate coupled with the fact that C will not be joining the European Union. Third, the researcher determines how each negotiator values alternative agreements, as well as the disagreement outcome. Formally, for each negotiator, a payoff function that represents its preferences are constructed. In the above example, this amounts to an empirical analysis that evaluates the value of each potential agreement for the European Union and the candidate country. Finally, using the obtained payoff functions, the negotiation is reconstructed in the payoff space. That is, each possible outcome is represented with a payoff profile that the negotiating parties receive from it. The feasible payoff set is the set of all payoff profiles resulting from an agreement (i.e., it is the image of the set of agreements under the players’ payoff functions), and the disagreement point is the payoff profile obtained in case of disagreement. Via this transformation, the researcher reduces the negotiation process into a set of payoff profiles and a payoff vector representing disagreement. It is this object in the payoff space that is called a (cooperative) bargaining problem in cooperative game theory. For a typical bargaining problem, please see Fig. 1. The object of study in cooperative bargaining theory is a (bargaining) rule. It maps each bargaining problem to a payoff profile in the feasible payoff set. For example, the Nash bargaining rule (Nash 1950) chooses, for each bargaining problem, the payoff profile that maximizes the product of the bargainers’ gains with respect to their disagreement payoffs. There are two alternative interpretations of a bargaining rule. According to the first interpretation, which is proposed by Nash (1950), a bargaining rule describes, for each bargaining problem, the outcome that will be obtained as result of the interaction between the bargainers. According to Nash (1950), a rule is thus a positive construct and should be evaluated on the basis of how well a description of real-life negotiations it provides. The second interpretation of a bargaining rule is alternatively normative. According to this interpretation, a bargaining rule produces, for each bargaining problem, a prescription to the bargainers (very much like an arbitrator). It should thus be evaluated on the basis of how useful it is to the negotiators in obtaining desirable agreements. Studies on cooperative bargaining theory employ the axiomatic method to evaluate bargaining rules. (A similar methodology is used for social choice and fair division problems, as discussed in chapter ▶ “The Notion of Fair Division in Negotiations” of this handbook.) An axiom is simply a property of a bargaining rule. For example, one of the best-known axioms, Pareto optimality, requires that the

2

This set contains all agreements that are physically available to the negotiators, including those that are “unreasonable” according to the negotiators’ preferences.

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u2 6

u2 6

I(S, D)

p1 •

p2 •

S

S

d•

d• u1 -

• p3 u1 -

Fig. 1 The horizontal (respectively, vertical) axis represents the payoffs of Agent 1 (Agent 2). On the left: a strictly d-comprehensive bargaining problem. On the right: a weakly d-comprehensive bargaining problem, the individually rational set, the Pareto set (part of the north-east boundary between p2 and p3) and the weak Pareto set (part of the north-east boundary between p1 and p3)

bargaining rule choose a Pareto optimal agreement.3 Researchers analyze implications of axioms that they believe to be “desirable.” According to the positive interpretation of bargaining rules, a “desirable” axiom describes a common property of a relevant class of real-life negotiation processes. For example, Nash (1950) promotes the Pareto optimality axiom on the basis that the negotiators, being rational agents, will try to maximize their payoffs from the negotiation outcome and thus, will not terminate the negotiations at an agreement that is not optimal. According to the normative interpretation of a bargaining rule, an axiom is a normatively appealing property which we as a society would like arbitrations to a relevant class of negotiations to satisfy. Note that the Pareto optimality axiom can also be promoted on this basis. It is important to note that an axiom need not be desirable in every application of the theory to real-life negotiations. Different applications might call for different axioms. A typical study on cooperative bargaining theory considers a set of axioms, motivated by a particular application, and identifies the class of bargaining rules that satisfy them. An example is Nash (1950) which shows that the Nash bargaining rule uniquely satisfies a list of axioms including Pareto optimality. In the section “Bargaining Rules and Axioms,” we discuss several such studies in detail. As will be detailed in the section “The Bargaining Model,” Nash’s (1950) model analyzes situations where the bargainers have access to lotteries on a fixed and publicly known set of alternatives. It is also assumed that the bargainers’ von Neumann-Morgenstern preferences are publicly known. While most of the following literature works on Nash’s standard model, there also are many studies that analyze 3

As will be formally introduced later, an agreement is Pareto optimal if there is no alternative agreement that makes an agent better-off without hurting any other agent.

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the implications of dropping some of these assumptions. For example, in the section “Ordinal Bargaining,” we discuss the recent literature on ordinal bargaining which analyzes cases where the agents do not necessarily have access to lotteries or do not have von Neumann-Morgenstern preferences. It is important to mention that two negotiation processes who happen to have the same feasible payoff set and disagreement point are considered to be the same bargaining problem in Nash’s (1950) model and thus, they have the same solution, independent of which bargaining rule is being used and how distinct the two negotiations are physically. This is sometimes referred to as the welfarism axiom and it has been a point of criticism of cooperative game theory. It should be noted that all the bargaining rules that we review in this chapter satisfy this property. The chapter is organized as follows. In the section “The Bargaining Model,” we present the bargaining model of Nash (1950). In the section “Bargaining Rules and Axioms,” we present the main bargaining rules and axioms in the literature. In the section “Strategic Considerations,” we discuss strategic issues related to cooperative bargaining, such as the Nash program, implementation, and games of manipulating bargaining rules (for more on strategic issues, see chapter ▶ “Non-cooperative Bargaining Theory” of this handbook). Finally, we present the more recent literature on ordinal bargaining in the section “Ordinal Bargaining.” For earlier surveys of cooperative bargaining theory, please see Peters (1992) and Thomson (1994), and the literature cited therein. These studies contain more detailed accounts of the earlier literature which we have summarized in the section “Bargaining Rules and Axioms.” For a more recent treatment of distributive bargaining, see Binmore and Eguia (2017). In the sections “Strategic Considerations” and “Ordinal Bargaining,” we present a selection of the more recent contributions to cooperative bargaining theory, not covered by earlier surveys. Due to space limitations, we left out some important branches of the recent literature. For nonconvex bargaining problems, see Herrero (1989) or Zhou (1997) and the related literature. For bargaining problems with incomplete information, see De Clippel and Minelli (2004), as well as a literature review by Forges and Serrano (2013). For rationalizability of bargaining rules, see Peters and Wakker (1991) and the following literature. For extensions of the Nash model that focus on the implications of disagreement, see Kıbrıs and Tapk (2010, 2011) and the literature cited therein. For “semi-cooperative solutions” to noncooperative games, see Kalai and Kalai (2013) and the related literature. Finally, a more recent literature focuses on the empirical content of the Nash bargaining rule, as well as its applications (e.g., see Chiappori et al. (2012)). Bargaining problems are cooperative games (called nontransferable utility games) where it is assumed that only the grand coalition or individual agents can affect the final agreement. This is without loss of generality for two-agent negotiations which are the most common type. However, for negotiations among three or more agents, the effect of coalitions on the final outcome might also be important. For more on this discussion, please see Bennett (1997) and Kıbrıs (2004b), and the literature cited therein.

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The Bargaining Model Consider a group of negotiators N = {1,...,n}. (While most real-life negotiations are bilateral, that is N = {1,2}, we do not restrict ourselves to this case.) A cooperative bargaining problem for the group N consists of a set, S, of payoff profiles (i.e., payoff vectors) resulting from every possible agreement and a payoff profile, d, resulting from the disagreement outcome. It is therefore defined on the space of all payoff profiles, namely the n-dimensional Euclidian space ℝN. Formally, the feasible payoff set S is a subset of ℝN and the disagreement point d is a vector in ℝN. In what follows, we will refer to each x  S as an alternative (agreement). There is an important asymmetry between an alternative x  S and the disagreement point d. For the negotiations to end at x, unanimous agreement of the bargainers is required. On the other hand, each agent can unilaterally induce d by simply disagreeing with the others. The pair (S, d ) is called a (cooperative bargaining) problem (Fig. 1, left) and is typically assumed to satisfy the following properties4: (i) S is convex, closed, and bounded. (ii) d  S and there is x  S such that x > d. (iii) S is d-comprehensive (i.e., d ≦ y ≦ x and x  S imply y  S). Let B be the set of all cooperative bargaining problems. Convexity of S means that (i) the agents are able to reach agreements that are lotteries on other agreements and (ii) each agent’s preferences on lotteries satisfy the von Neumann-Morgenstern axioms and thus, can be represented by an expected utility function. For example, consider a couple negotiating on whether to go to the park or to the movies on Sunday. The convexity assumption means that they could choose to agree to take a coin toss on the issue (or agree to condition their action on the Sunday weather), and that each agent’s payoff from the coin toss is the average of his payoffs from the park and the movies. Boundedness of S means that the agents’ payoff functions are bounded (i.e., no agreement can give them an infinite payoff). Closedness of S means that the set of physical agreements is closed and the agents’ payoff functions are continuous. In the section “Ordinal Bargaining,” we will extend the basic model to allow situations where the bargainers do not have access to lotteries and they do not necessarily have von Neumann-Morgenstern preferences. The assumption d  S means that the agents are able to agree to disagree and induce the disagreement outcome. Existence of an x  S such that x > d rules out degenerate problems where no agreement can make all agents better-off than the disagreement outcome. Finally, d-comprehensiveness of S means that utility is freely disposable above d.5

We use the following vector inequalities x ≧ y for each i  N, xi ≧ yi; x ≧ y and x 6¼ y; and x > y if for each i  N, xi > yi. 5 A stronger assumption called full comprehensiveness additionally requires utility to be freely disposable below d. 4

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Two concepts play an important role in the analysis of a bargaining problem (S, d). The first is the Pareto optimality of an agreement: it means that the bargainers can not all benefit from switching to an alternative agreement. Formally, the Pareto set of (S, d) is defined as P(S, d ) = {x  S | y  x ) y 2 = S} and the Weak Pareto set of (S, d) is defined as WP(S, d ) = {x  S | y > x ) y 2 = S}. The second concept, individual rationality, is based on the fact that each agent can unilaterally induce disagreement. Thus, it requires that each bargainer prefer an agreement to disagreement. Formally, the individually rational set is I(S, d ) = {x  S| x ≧ d}. Like Pareto optimality, individual rationality is desirable as both a positive and a normative property. On Fig. 1, right, we present the sets of Pareto optimal and individually rational alternatives. We will occasionally consider a subclass B sc of bargaining problems B that satisfy a stronger property than d-comprehensiveness: the problem (S, d ) is strictly dcomprehensive if d ≦ y ≦ x and x  S imply y  S and y 2 = WP (S, d) (please see Fig. 1; the left problem is strictly d-comprehensive while the right one is not). We will next present examples of modeling the accession negotiation of Example 1. Example 2 (Modeling the Accession Negotiation) The set of bargainers is N = {E,C}. Let T = [0,1] be the set of all tariff rates. As noted in the section “Introduction,” the bargainers’ payoffs from alternative agreements (as well as disagreement) need to be determined by an empirical study which (not surprisingly) we will not carry out here. However, we will next present four alternative scenarios for these payoff functions, UC and UE. In each scenario, we assume for simplicity that each bargainer i) receives a zero payoff in case of disagreement and (ii) prefers accession with any tariff rate to disagreement. Due to (ii), the individually rational set coincides with the feasible payoff set of the resulting bargaining problem in each scenario. In the first scenario, both bargainers’ payoffs are linear in the tax rate. (Thus, both are risk-neutral.6) Scenario 1. LetUE(t) = 1  t and UC(t) = t In the second scenario, we change the candidate’s payoff to be a strictly concave function. (Compared to Scenario 1, C is now more risk-averse than E.) 1 Scenario 2. Let UE(t) = 1  t and UC ðtÞ ¼ t 2 In the third scenario, E’s payoff is also changed to be a strictly concave function. (Now, both bargainers have the same level of risk-aversion.) 1

1

Scenario 3. Let UE ðtÞ ¼ ð1  tÞ2 and U C ðtÞ ¼ t 2 In the fourth scenario, both bargainers have linear payoff functions. That is, they are both risk-neutral. But, differently from Scenario 1, now E’s marginal gain from a change in the tariff rate is twice that of C. Scenario 4. Let UE(t) = 2(1  t) and UC(t) = t

6

A decision-maker is risk-neutral if he is indifferent between each lottery and the lottery’s expected (sure) return.

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uC 6 1 •

uC 6 1 •

S1

d1 •

•

1

uE -

d3 •

d2 •

•

uE

-

1

uC 6

uC 6 1 •

S2

S

3

1 •

•

1

uE

-

d4 •

S4

•

1

•

uE

-

2

Fig. 2 The Accession Game: Scenario 1 (top left), Scenario 2 (top right), Scenario 3 (bottom left), and Scenario 4 (bottom right)

The resulting feasible payoff set and the disagreement point for each scenario is constructed in Fig. 2. Since both bargainers prefer accession of C to its rejection from the European Union, the Pareto set under all scenarios corresponds to those payoff profiles that result from accession with probability 1. The feasible payoff set is constructed by taking convex combinations of the Pareto optimal alternatives with the disagreement point. Thus, they represent payoff profiles of lotteries, including those between an accession agreement and disagreement.

Bargaining Rules and Axioms A (bargaining) rule F : B ! ℝ n assigns each bargaining problem ðS, dÞ  B to a feasible payoff profile F(S, d )  S. As discussed in the section “Introduction,” F can be interpreted as either (i) a description of the negotiation process the agents in consideration are involved in (the positive interpretation) or (ii) a prescription to the negotiators as a “good” compromise (the normative interpretation). In this section, we present examples of bargaining rules and discuss the main axioms that they satisfy. We also discuss these rules’ choices for the four scenarios of Example 2.

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u2 6

u2 6

•

S

a(S, d)

•

N (S, d)

S

K(S, d)

•

d•

d•

•

• u1 -

u1 -

Fig. 3 The Nash (left) and the Kalai-Smorodinsky (right) solutions to a typical problem

The Nash Rule The first and the best-known example of a bargaining rule is by Nash (1950). The Nash rule chooses, for each bargaining problem ðS, d Þ  B the individually rational alternative that maximizes the product of the agents’ gains from disagreement (please see Fig. 3, left): N ðS, dÞ ¼ arg

n Y

max x  I ðS,dÞ

ðxi  d i Þ:

i¼1

Let us first check the Nash solutions to the accession negotiations of Example 2. Example 3 (Nash solution to the accession negotiations) For each of the four scenarios discussed in Example 2, the Nash rule proposes the following payoff profiles (the first payoff number is for E and the second is for C). For Scenario 1,     N S1 , d1 ¼ 12 , 12 . This payoff profile is obtained when the bargainers agree on     accession at a tariff rate t1 ¼ 12 : For Scenario 2, N S2 , d2 ¼ 23 , p1ffiffi3 , obtained at     accession and the tariff rate t2 ¼ 13 : For Scenario 3, N S3 , d3 ¼ p1ffiffi2 , p1ffiffi2 ,   obtained at accession and the tariff rate t3 ¼ 12 : For Scenario 4, N S4 , d4 ¼  1 1, 2 , obtained at accession and the tariff rate t4 ¼ 12 : In Example 3, as C becomes more risk averse from Scenario 1 to Scenario 2, the Nash solution changes in a way to benefit E (since the tariff rate decreases from 12 to 13). This is a general feature of the Nash bargaining rule: the Nash bargaining payoff of an agent increases as his opponent becomes more risk-averse (Kihlstrom et al. 1981).

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Nash (1950) proposes four axioms and shows that his rule satisfies them. These axioms later play a central role in the literature. We will introduce them next. The first axiom requires that the rule always choose a Pareto optimal alternative. Formally, a rule F is Pareto optimal if for each problem ðS, d Þ  B, F(S, d )  P (S, d). As discussed in the section “Introduction,” it is commonly agreed in the literature that negotiations result in a Pareto optimal alternative. Thus, most axiomatic analyses focus on Pareto optimal rules. In Example 3, Pareto optimality is satisfied since all four negotiations result in the accession of the candidate to the European Union.7 The second axiom, called anonymity, guarantees that the identity of the bargainers do not affect the outcome of negotiation. It requires that permuting the agents’ payoff information in a bargaining problem should result in the same permutation of the original agreement. To formally introduce this axiom, let Π be the set of all permutations on N, π : N!N. For x  ℝN, let π(x) = (xπ(i))iN and for S  ℝN, let π(S) = {π(x)| x  S}. Then, a rule F is anonymous if for each π  Π, F (π(S), π(d )) = π(F(S, d )). Note that anonymity applies to cases where the bargainers have “equal bargaining power.” It is common practice in the literature to replace anonymity with a weaker axiom which requires that if a problem is symmetric (in the sense that all of its permutations result in the original problem), then its solution should be symmetric as well. Formally, a rule F is symmetric if for each π  Π, π(S) = S and π(d ) = d implies F1(S, d )=...=Fn(S, d). Note that the bargaining problems under Scenarios 1 and 3 are symmetric. Therefore, their Nash solutions are also symmetric. The third axiom is based on the fact that a von Neumann-Morgenstern type preference relation can be represented with infinitely many payoff functions (that are positive affine transformations of each other) and the particular functions chosen to represent the problem should not affect the bargaining outcome. Formally, let Λ be the set of all λ = (λ1, . . ., λn) where each λi : ℝ ! ℝ is a positive affine function.8 Let λ(S) = {λ(x)| x  S}. Then, a rule F is scale invariant if for each ðS, dÞ  B and λ  Λ, F(λ(S), λ(d)) = λ(F(S, d)). Note that in the accession negotiations, Scenario 4 is obtained from Scenario 1 by multiplying UE by 2, which is a positive affine transformation. Thus, the Nash solutions to the two scenarios are related the same way (and the resulting tariff rates are identical). The final axiom of Nash (1950) concerns the following case. Suppose the bargainers facing a bargaining problem (S, d) agree on an alternative x. However, they later realize that the actual feasible set T is smaller than S. Nash requires that if the original agreement is feasible in the smaller feasible set, x  T, then the bargainers should stick with it. Formally, a rule F is contraction independent if for each ðS, d Þ, ðT, dÞ  B such that T  S, F(S, d)  T implies F(T, d) = F(S, d). Nash

7

This is Pareto optimal since both bargainers prefer accession to rejection. What they disagree on is the tariff rate. 8 A function λi : ℝ!ℝ is positive affine if there is a,b  ℝ with a > 0 such that for each x  ℝ, λi(x) = ax+b.

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(1950) and some of the following literature alternatively calls this axiom independence of irrelevant alternatives (IIA). However, the presumed irrelevance of alternatives in the choice of an agreement (as suggested by this name) is a topic of controversy in the literature. In fact, it is this controversy that motivates the bargaining rule of Kalai and Smorodinsky (1975) as will be discussed in the next subsection. Nash (1950) shows that his bargaining rule uniquely satisfies these four axioms. We will next prove this result for two-agent problems. Theorem 4 (Nash 1950) A bargaining rule satisfies Pareto optimality, symmetry, scale invariance, and contraction independence if and only if it is the Nash rule. Proof It is left to the reader to check that the Nash rule satisfies the given axioms. Conversely, let F be a rule that satisfies them. Let ðS, d Þ  B and N(S, d)=x. We would like to show that F(S, d )=x. By scale invariance of both rules, it is without loss of generality to assume that d=(0,0) and x=(1,1).9 Then, by definition of N, the set P(S, d ) has slope 1 at x. Also, by boundedness of S, there is z  ℝN such that for each x  S, x ≧ z. Now let T = {y  ℝN| Nyi ≦ N xi and y ≧ z}. Then, S  T and ðT, dÞ  B is a symmetric problem. Thus, by symmetry and Pareto optimality of F, F(T, d ) = x. This, by contraction independence of F, implies F(S, d) = x, the desired conclusion. ■ It is useful to note that the following class of weighted Nash rules uniquely satisfy all of Nash’s axioms except symmetry. These rules extend the Nash bargaining rule to cases where agents differ in their “bargaining power.” Formally, let p = ( p1,...,pn)  0,1]N satisfy Npi = 1. Each pi is interpreted as the bargaining power of Agent i. Then the p-weighted Nash bargaining rule is defined as N p ðS, d Þ ¼ arg

n Y max

x  I ðS,d Þ

ðx i  d i Þp i :

i¼1

The  symmetric  Nash bargaining rule assigns equal weights to all agents, that is, p ¼ 1n , . . . , 1n . The literature contains several other characterizations of the Nash bargaining rule. For example, see Peters (1986), Dagan et al. (2002), Anbarci and Sun (2011, 2013), and Rachmilevitch (2015).

The Kalai-Smorodinsky Rule The Kalai-Smorodinsky rule (Raiffa 1953; Kalai and Smorodinsky 1975) makes use of each agent’s aspiration payoff, that is, the maximum payoff an agent can get at an

i Any (S, d) can be “normalized” into such a problem by choosing λi ðxi Þ ¼ Ni ðxS,i d dÞd i for each i  N.

9

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individually rational agreement. Formally, given a problem ðS, d Þ  B, the aspiration payoff of Agent i is ai ðS, d Þ ¼ arg max x  IðS,dÞ xi : The vector aðS, dÞ ¼ ðai ðS, d ÞÞni¼1 is called the aspiration point. The Kalai-Smorodinsky rule, K, chooses the maximum individually rational payoff profile at which each agent’s payoff gain from disagreement has the same proportion to his aspiration payoff’s gain from disagreement (please see Fig. 3, right). Formally,  K ðS, dÞ ¼ arg max

x  IðS, dÞ

 xi  d i min : i  f1, ..., ng ai ðS, d Þ  d i

Geometrically, K(S, d) is the intersection of the line segment [d, a(S, d )] and the northeast boundary of S. Example 5 (Kalai-Smorodinsky solution to the accession negotiations) For each of the four scenarios discussed in Example 2, the Kalai-Smorodinsky rule proposes the following payoff profiles (the first payoff number is for E and the second is for C).     For Scenario 1, K S1 , d1 ¼ 12 , 12 : This payoff profile is obtained when the bargainers agree on accession at a tariff rate t1 ¼ 12 : For Scenario 2, K at accession and the tariff rate t2 = 0.38. For (S2, d2) = (0.62,0.62), obtained  3 3  1 1  Scenario 3, K S , d ¼ pffiffi2 , pffiffi2 , obtained at accession and the tariff rate t3 ¼ 12 :     For Scenario 4, K S4 , d4 ¼ 1, 12 , obtained at accession and the tariff rate t4 ¼ 12 : In Example 5, as C becomes more risk averse from Scenario 1 to Scenario 2, the Kalai-Smorodinsky solution changes in a way to benefit E (since the tariff rate decreases from 12 to 0.38). This is a general feature of the Kalai-Smorodinsky bargaining rule: the Kalai-Smorodinsky bargaining payoff of an agent increases as his opponent becomes more risk-averse (Kihlstrom et al. 1981). As can be observed in Example 5, the Kalai-Smorodinsky rule is Pareto optimal for all two-agent problems. With more agents, however, it satisfies a weaker property: a rule F is weakly Pareto optimal if for each problem ðS, d Þ  B, F(S, d )  WP(S, d). Example 5 also demonstrates that the Kalai-Smorodinsky rule is symmetric and scale invariant. Due to weak Pareto optimality and symmetry, the Kalai-Smorodinsky solutions to (S1, d1) and (S3, d3) are equal to the Nash solutions. Due to scale invariance, the two rules also coincide on (S4, d4). For the problem (S2, d2), however, the two rules behave differently: the Kalai-Smorodinsky rule chooses equal payoffs for the agents while the Nash rule favors E. The Kalai-Smorodinsky rule violates Nash’s contraction independence axiom. Kalai and Smorodinsky (1975) criticize this axiom and propose to replace it with a monotonicity notion which requires that an expansion of the feasible payoff set (and thus an increase in the cooperative opportunities) should benefit an agent if it does not affect his opponents’ aspiration payoffs. Formally, a rule F satisfies individual monotonicity if for each ðS, dÞ, ðT, d Þ  B and i  N, if S  T and

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aj(S, d ) = aj(T, d ) for each j 6¼ i, then Fi(S, d ) ≦ Fi(T, d ). The Nash rule violates this axiom. Kalai and Smorodinsky (1975) present the following characterization of the Kalai-Smorodinsky rule. We will next prove this result for two-agent problems. Theorem 6 (Kalai and Smorodinsky 1975) A bargaining rule satisfies Pareto optimality, symmetry, scale invariance, and individual monotonicity if and only if it is the Kalai-Smorodinsky rule. Proof It is left to the reader to check that the Kalai-Smorodinsky rule satisfies the given axioms. Conversely, let F be a rule that satisfies them. Let (S, d)  ℬ and K(S, d ) = x. We would like to show that F(S, d ) = x. By scale invariance of both rules, it is without loss of generality to assume that d= (0,0) and a(S, d) = (1,1).10 Then, by definition of K, x1=x2. Now let T = conv{x, d, (1,0),(0,1)}. Then, T  S and ðT, dÞ  B is a symmetric problem. Thus, by symmetry and Pareto optimality of F, F(T, d) = x. Since T  S, x  P(S, d), and a(S, d) = a(T, d), individual monotonicity implies that F(S, d)=x, the desired conclusion. ■ Roth (1979) notes that the above characterization continues to hold under a weaker monotonicity axiom which only considers expansions of the feasible set at which the problem’s aspiration point remains unchanged. Formally, a rule F satisfies restricted monotonicity if for each (S, d), (T, d)  ℬ and i  N, if S  T and a(S, d) = a(T, d) then F(S, d) ≦ F(T, d).The Nash rule violates this weaker monotonicity axiom as well. The literature contains several other characterizations of the Kalai-Smorodinsky bargaining rule. For example, see Dubra (2001) and Karos et al. (2018).

The Egalitarian Rule The Egalitarian rule, E, (Kalai 1977) chooses for each problem ðS, dÞ  B the maximum individually rational payoff profile that gives each agent an equal gain from his disagreement payoff (please see Fig. 4, left). Formally, for each ðS, dÞ  B,  E ðS, dÞ ¼ arg

max

x  I ðS,dÞ

min

i  f1,...,ng

 ðxi  di Þ :

Geometrically, E(S, d) is the intersection of the boundary of S and the half line that starts at d and passes through d + (1,...,1). Example 7 (Egalitarian solution to the accession negotiations) For each of the four scenarios discussed in Example 2, the Egalitarian rule proposes the following payoff i Any (S, d) can be “normalized” into such a problem by choosing λi ðxi Þ ¼ ai ðxS,i d d Þdi for each i  N.

10

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u2 6

u2 6

• E(S, d) S

S o d • 45

•

U (S, d)

d• u1 -

u1 -

Fig. 4 The Egalitarian (left) and the Utilitarian (right) solutions to a typical problem

profiles (the first payoff number is for E and the second is for C). For Scenario 1,     E S1 , d1 ¼ 12 , 12 : This payoff profile is obtained when the bargainers agree on accession at a tariff rate t1 ¼ 12 : For Scenario 2, E(S2,d2) = (0.62, 0.62), obtained at     accession and the tariff rate t2 = 0.38. For Scenario 3, E S3 , d3 ¼ p1ffiffi2 , p1ffiffi2 ,     obtained at accession and the tariff rate t3 ¼ 12 : For Scenario 4, E S4 , d 4 ¼ 23 , 23 , obtained at accession and the tariff rate t4 ¼ 23 : The Egalitarian rule satisfies Pareto optimality only on the class of strictly dcomprehensive problems B SC . On B, it only satisfies weak Pareto optimality.11 As observed in Example 7, the Egalitarian rule is weakly Pareto optimal and symmetric. Due to these two axioms, the Egalitarian solutions to (S1,d1) and (S3,d3) are equal to the Nash and Kalai-Smorodinsky solutions. Also, since the aspiration point of problem (S2,d2) is symmetric, a(S, d) = (1,1), the Egalitarian and the KalaiSmorodinsky rules pick the same solution. Unlike the Nash and the Kalai-Smorodinsky rules, the Egalitarian rule violates scale invariance. This can be observed in Example 7 by comparing the Egalitarian solutions to (S1,d1) and (S4,d4).12 The Egalitarian rule however satisfies the following weaker axiom: a rule F satisfies translation invariant if for each ðS, dÞ  B and z  ℝN, F(S + {z}, d + z) = F(S, d ) + z.13 11 On problems that are not d-comprehensive, the Egalitarian rule can also violate weak Pareto optimality. 12 For a scale invariant rule, (S1,d1) and (S4,d4) are alternative representations of the same physical problem. (Specifically, E’s payoff function has been multiplied by 2 and thus, still represents the same preferences.) For the Egalitarian rule, however, these two problems (and player E’s) are distinct. Since it seeks to equate absolute payoff gains from disagreement, the Egalitarian rule treats agents’ payoffs to be comparable to each other. As a result, it treats payoff functions as more than mere representations of preferences. 13 This property is weaker than scale invariance because, for an agent i, every translation xi + zi is a positive affine transformation λi(xi) = 1xi + zi.

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On the other hand, the Egalitarian rule satisfies a very strong monotonicity axiom which requires that an agent never loose in result of an expansion of the feasible payoff set. Formally, a rule F satisfies strong monotonicity if for each ðS, d Þ, ðT, dÞ  B, if S  T, then F(S, d) ≦ F(T, d ). This property is violated by the Kalai-Smorodinsky rule since this rule is sensitive to changes in the problem’s aspiration point. The Nash rule violates this property since it violates the weaker individual monotonicity property. The following characterization of the Egalitarian rule follows from Kalai (1977). We present it for two-agent problems. Theorem 8 (Kalai 1977) A bargaining rule satisfies weak Pareto optimality, symmetry, translation invariance, and strong monotonicity if and only if it is the Egalitarian rule. Proof It is left to the reader to check that the Egalitarian rule satisfies the given axioms. Conversely, let F be a rule that satisfies them. Let ðS, dÞ  B and E (S, d ) = x. We would like to show that F(S, d ) = x. By translation invariance of both rules, it is without loss of generality to assume that d = (0,0).14 Then, by definition of E, x1 = x2. Now let T = conv{x, d, (x1, 0), (0, x2)}. Then, T  S and ðT, d Þ  B is a symmetric problem. Thus, by symmetry and weak Pareto optimality of F, F(T, d ) = x. Since T  S, strong monotonicity then implies F(S, d ) ≧ x. Case 1: x  P(S, d ). Then F(S, d )  x implies F(S, d ) 2 = S. Thus, F(S, d ) = x, the desired conclusion. Case 2: x  WP(S, d ). Suppose Fi(S, d ) >  xi forsome i  N. Let δ > 0 be such that xi + δ < Fi(S, d ), let x0 = x + (δ, δ), x00 ¼ d i , x0i and S0 = conv{x0 , x00 , S}. Then E(S0 , d ) = x0  P(S0 , d ) and by Case 1, F(S0 , d) = x0 . Since S  S0 , by strong monotonicity, F(S0 , d ) = x0 ≧ F(S, d ). Particularly, xi + δ ≧ Fi(S, d ), a contradiction. Thus, F(S, d ) = x. ■ The literature contains several other characterizations of the Egalitarian bargaining rule. For example, see Chun and Thomson (1990), Myerson (1981), Peters (1986), Anbarci and Sun (2011, 2013), Rachmilevitch (2011), and Karos et al. (2018).

Other Rules In this section, we will present some of the other well-known rules in the literature. The first is the Utilitarian rule which chooses for each bargaining problem ðS, d Þ  B the alternatives that maximize the sum of the agents’ payoffs (please see Fig. 4, right): Any (S, d ) can be “normalized” into such a problem by choosing λi(xi) = xidi for each i  N.

14

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U ðS, dÞ ¼ arg max xS

n X

xi :

i¼1

The Utilitarian rule is not necessarily single-valued, except when the feasible set is strictly convex. However, it is possible to define single-valued refinements (such as choosing the midpoint of the set of maximizers). Also, the Utilitarian solution to (S, d ) is independent of d. Thus, the Utilitarian rule violates individual rationality. Restricting the choice to be from the individually rational set remedies this problem. Finally, the Utilitarian rule violates scale invariance. However, a variation which maximizes a weighted sum of utilities satisfies the property (e.g., see Dhillon and Mertens 1999). The Utilitarian rule is Pareto optimal, anonymous contraction independent, and translation invariant even though it violates restricted monotonicity. For more on this rule, see Myerson (1981) and Thomson (1981). Blackorby et al. (1994) introduce a class of Generalized Gini rules that are mixtures of the Utilitarian and the Egalitarian rules. The second rule represents extreme cases where one agent has all the “bargaining power.” The Dictatorial rule for Agent i chooses the alternative that maximizes Agent i’s payoff among those at which the remaining agents receive their disagreement payoffs (please see Fig. 5, right): Di ðS, dÞ ¼ arg max xi : x  I ðS, d Þ s:t:xi ¼di

This rule is only weakly Pareto optimal, though on strictly d-comprehensive problems it is Pareto optimal. The following rule does not suffer from this problem: the Serial Dictatorial rule is defined with respect to a fixed order of agents and it first maximizes the payoff of the first ordered agent, then among the maximizers, maximizes the payoff of the second and so on. Both the dictatorial and serial dictatorial rule violate symmetry (and thus anonymity). Otherwise, they are very well-behaved. Both rules are scale invariant. In fact, they satisfy an even stronger property, ordinal invariance, that we introduce and discuss in the section “Ordinal Bargaining.” These rules also satisfy contraction independence and strong monotonicity (and thus, all weaker monotonicity properties). The next class of rules, introduced by Yu (1973), is based on minimizing a measure of the distance between the agreement and the problem’s aspiration point (defined in the subsection “The Kalai-Smorodinsky Rule”). Formally, for p  (1,1), the Yu rule associated with p is

Y ðS, dÞ ¼ arg max p

xS

n X i¼1

!1p p

jai ðS, d Þ  xi j

:

Negotiation as a Cooperative Game u2 6

561 u2 6 D2 (S, d) = x0 •

•

S

A

EA(S, d) S

d• u1 -

d•

1

•x

B

•

x2 = y 2 = P M (S, d)

C

•y

1

D

u1 y 0 = D1 (S, d)

•

Fig. 5 The Equal Area solution to a typical problem equates the two shaded areas (left); the PerlesMaschler solution to a polygonal problem is the limit of the sequences {xk} and {yk} which are constructed in such a way that (i) x0 = D2 (S, d ), y0 = D1(S, d ) are the two Dictatorial solutions and (ii) the areas A, B, C, and D are maximal and they satisfy A = D and B = C

The Yu rules are Pareto optimal, anonymous, and individually monotonic. However, they violate contraction independence, strong monotonicity, and scale invariance. The final two rules are defined for two-agent problems. They both are based on the idea of equalizing some measure of the agents’ sacrifices with respect to their aspiration payoffs. The first, Equal Area rule, EA, chooses the Pareto optimal alternative at which the area of the set of better individually rational alternatives for Agent 1 is equal to that of Agent 2 (please see Fig. 5, left). This rule violates contraction independence but satisfies anonymity, scale invariance, and an “area monotonicity” axiom (e.g., see Calvo and Peters 2000). The second rule is by Perles and Maschler (1981). For problems (S, d) whose Pareto set P(S, d) is polygonal, the Perles-Maschler rule, PM, chooses the limit of the following sequence. (The Perles-Maschler solution to any other problem (S, d) is obtained as the limit of Perles-Maschler solutions to a sequence of polygonal problems that converge to (S, d)). Let x0 = D2(S, d) and y0 = D1(S, d). For each k  ℕ, let xk, yk  P(S, that (i) x k1 ≦yk1 , (ii) [xk1,xk]  P(S, d),  k1d) be ksuch  k1 k1 k , y ]  P(S, d), (iv) x1  x1 x2  xk2 ¼ yk1  yk1 yk1  yk2 , (iii) [y 1 2  k1   xk2 is maximized (please see Fig. 5, right). The Perlesand x1  xk1 xk1 2 Maschler rule is Pareto optimal, anonymous, and scale invariant. It, however, is not contraction independent or restricted monotonic. For extending this rule to more than two agents, see Calvo and Gutiérrez (1994) and the literature cited therein.

Strategic Considerations As noted in the section “Introduction,” Nash (1950) interprets a bargaining rule as a description of a (noncooperative) negotiation process between rational agents. Nash (1953) furthers this interpretation and proposes what is later known as the Nash program: to relate choices made by cooperative bargaining rules to equilibrium outcomes of underlying noncooperative games. Nash argues that “the two

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approaches to the (bargaining) problem, via the (noncooperative) negotiation model or via the axioms, are complementary; each helps to justify and clarify the other.” Nash (1953) presents the first example of the Nash program. Given a bargaining problem (S, d), he proposes a two-agent noncooperative Demand Game in which each player i simultaneously declares a payoff number si. If the declared payoff profile is feasible (i.e., s  S), players receive their demands. Otherwise, the players receive their disagreement payoffs with a probability p and their demands with the remaining probability. Nash shows that, as p converges 1, the equilibrium of the Demand Game converges to the Nash solution to (S, d ). Van Damme (1986) considers a related noncooperative game where, given a bargaining problem (S, d ), each agent simultaneously declares a bargaining rule.15 If the solutions proposed by the two rules conflict, the feasible payoff set is contracted in a way that an agent cannot receive more than the payoff he asks for himself. The two rules are now applied to this contracted problem and if they conflict again, the feasible set is once more contracted. Van Damme (1986) shows that for a large class of rules, the limit of this process is well-defined and the unique Nash equilibrium of this noncooperative game is both agents declaring the Nash bargaining rule. Another well-known contribution to the Nash program is by Binmore et al. (1986) who relate the Nash bargaining rule to equilibrium outcomes of the following game. The Alternating Offers Game (Rubinstein 1982) is an infinite horizon sequential move game to allocate one unit of a perfectly divisible good between two agents. The players alternate in each period to act as “proposer” and “responder.” Each period contains two sequential moves: the proposer proposes an allocation and the responder either accepts or rejects it. The game ends when a proposal is accepted. Rubinstein (1982) shows that the Alternating Offers Game has a unique subgame perfect Nash equilibrium in which the first proposal, determined as a function of the players’ discount factors, is accepted. Binmore et al. (1986) show that, as the players’ discount factors converge to 1 (i.e., as they become more patient), the equilibrium payoff profile converges to the Nash bargaining solution to the associated cooperative bargaining game. For more recent work on the Nash program, see Anbarci and Boyd (2011), Abreu and Pearce (2015), Binmore and Eguia (2017), and Karagözoğlu and Rachmilevitch (2018). Another strategic issue arises from that fact that each negotiator, by misrepresenting his private information (e.g., about his preferences, degree of risk aversion, etc.), might be able to change the bargaining outcome in his favor. Understanding the “real” outcome of a bargaining rule then requires taking this kind of strategic behavior into account. A standard technique for this is to embed the original problem into a noncooperative game (in which agents strategically “distort” their private information) and to analyze its equilibrium outcomes. This is demonstrated in the following example.

15

Thus, as in Nash (1953), each agent demands a payoff. But now, they have to rationalize it as part of a solution proposed by an “acceptable” bargaining rule.

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Example 9 (A noncooperative game of manipulating the Nash rule) Suppose that agents C and E in Example 2 have private information about their true payoff functions and that they play a noncooperative game where they strategically declare this information to an arbitrator who uses thenNash o rule. Using the four scenarios of 1

Example 2, fix the strategy set of C as t, t2 and the strategy set of E as n o 1 1  t, ð1  tÞ2 , 2ð1  tÞ : The resulting tariff rate is determined by the Nash   1 bargaining rule calculated in Example 3 except for the profile t, ð1  tÞ2 . The following table summarizes, for each strategy profile, the resulting tariff rate.

C

\E t 1 t2

1−t 0.5 0.33

1

(1 − t) 2 0.66 0.5

2 (1 − t) 0.5 0.33

Note that this is a competitive game: C is better-off and E is worse-off in response to an increase in the tariff rate t. Also note that, for C, declaring t strictly dominates 1 declaring t2 (that is, he gains from acting less risk-averse). Similarly, for E, declaring 1

(1t) strictly dominates declaring ð1  tÞ2 and, since the Nash bargaining rule is scale invariant, declaring (1t) and 2(1t) are equivalent. The game has two equivalent dominant strategy equilibria: (t,1t) and (t,2(1t)) where both players act to be risk-neutral. In some cases, such as Example 9, it is natural to assume that the agents’ ordinal preferences are publicly known. (In the example, it is common knowledge that C prefers higher tariff rates and E prefers lower tariff rates.) Then, manipulation can only take place through misrepresentation of cardinal utility information (such as the degree of risk-aversion). In two-agent bargaining with the Nash or the KalaiSmorodinsky rules, an agent’s utility increases if his opponent is replaced with another that has the same preferences but a more concave utility function (Kihlstrom et al. 1981). On allocation problems, this result implies that an agent can increase his payoff by declaring a less concave utility function (i.e., acting to be less risk-averse). For the Nash bargaining rule, it is a dominant strategy for each agent to declare the least concave representation of his preferences. For a single good, the equilibrium outcome is equal division. If ordinal preferences are not publicly known, however, their misrepresentation can also be used for manipulation. The resulting game does not have dominant strategy equilibria. Nevertheless, for a large class of two-agent bargaining rules applied to allocation problems, the set of allocations obtained at Nash equilibria in which agents declare linear utilities is equal to the set of “constrained” Walrasian allocations from equal division with respect to the agents’ true utilities (Sobel 1981, 2001; Gómez 2006). Under a mild restriction on preferences, a similar result holds for pure exchange and public good economies with an arbitrary number of agents and for all Pareto optimal and individually rational bargaining rules (Kıbrıs 2002).

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Ordinal Bargaining Nash (1950) and most of the following literature restricts the analysis to bargaining processes that take place on lotteries and assumes that the bargainers’ preferences on lotteries satisfy the von Neumann-Morgenstern assumptions (thus, they are representable by expected utility functions). This assumption has two important consequences. First, in a bargaining problem (S, d), the feasible payoff set S is then convex. Second, the scale invariance axiom of Nash (1950) is sufficient to ensure the invariance of the physical bargaining outcome with respect to the particular utility representation chosen. In this section, we drop these assumptions and analyze bargaining in ordinal environments, where the agents’ complete, transitive, and continuous preferences do not have to be of von Neumann-Morgenstern type. For ordinal environments, (i) the payoff set S is allowed to be nonconvex and (ii) scale invariance needs to be replaced with the following stronger axiom.16 Formally, let Φ be the set of all ϕ = (ϕ1,...,ϕn) where each ϕi : ℝ!ℝ is an increasing function. Let ϕ(S) = {ϕ(x)| x  S}. Then, a rule F is ordinal invariant if for each (S, d)  ℬ and ϕ  Φ, F(ϕ(S), ϕ(d )) = ϕ(F(S, d)). Note that every ordinal invariant rule is also scale invariant but not vice versa. If there are a finite number of alternatives, many ordinal invariant rules exist (e.g., see Kıbrıs and Sertel 2007). With an infinite number of alternatives, however, ordinal invariance is a very demanding property. Shapley (1969) shows that for twoagent problems, only dictatorial bargaining rules and the rule that always chooses disagreement satisfy this property. This result is due to the fact that the Pareto optimal set of every two-agent problem can be mapped to itself via a nontrivial increasing transformation ϕ = (ϕ1,ϕ2). In the following example, we demonstrate the argument for a particular bargaining problem. Example 10 Consider the problem (S1, d1) in Scenario 1 of Example 2 (represented in Fig. 2, upper left). Note that the Pareto set of (S1, d1) satisfies uC 1

1

+ uE = 1. Let ϕC ðuC Þ ¼ u2C and ϕE ðuE Þ ¼ 1  ð1  uE Þ2 and note that ϕC(uC) + ϕE(uE) = 1. Thus, the Pareto set of the transformed problem (ϕ(S1), ϕ(d1)) is the same as (S1, d1). In fact, S1 = ϕ(S1) and d1 = ϕ(d1). To summarize, ϕ maps (S1, d1) to itself via a nontrivial transformation of the agents’ utilities. Now let F be some ordinally invariant bargaining rule. Since the two problems are identical, F(ϕ(S1), ϕ(d1)) = F(S1, d1). Since F is ordinally invariant, however, we also have F(ϕ(S1), ϕ(d1)) = ϕ(F(S1, d1)). For both requirements to be satisfied, we need ϕ(F(S1, d1)) = F(S1, d1). Only three payoff profiles in (S1, d1) satisfy this property: (0,0), (1,0), and (0,1). Note that they are the disagreement point and the two dictatorial solutions, respectively. So, F should coincide with either one of these rules on (S1, d1). 16

This is due to the following fact. Two utility functions represent the same complete and transitive preference relation if and only if one is an increasing transformation of the other.

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u2 6

1

(p21 , p12 , p23 ) (p01 , p12 , p13 )

 

 



•

•

•p

0

•p

1

•

2

(p11 , p22 , p23 )

-

 p0

u1

•

(p11 , p02 , p13 )

6

  u3  



•

•

1

• (p1 , p2 , p3 )

Fig. 6 The Shapley-Shubik solution to (S, d ) is the limit of the sequence {pk}

The construction of Example 10 is not possible for more than two agents (Sprumont 2000). For three agents, Shubik (1982) presents an ordinally invariant and strongly individually rational bargaining rule which we will refer to as the Shapley-Shubik rule.17 The Shapley-Shubik solution to a problem (S, d) is defined as the limit of the following sequence. Let p0 = d and for each k  {1,...}, let pk  ℝ3 be the unique point that satisfies 

  k k1 k   k k k1  k k pk1  PðS, dÞ: 1 , p2 , p3  PðS, d Þ, p1 , p2 , p3  PðS, d Þ, and p1 , p2 , p3

The Shapley-Shubik solution is then ShðS, dÞ¼ lim k!1 pk : The construction of the sequence {pk} is demonstrated in Fig. 6. Kıbrıs (2004a) shows that the Shapley-Shubik rule uniquely satisfies Pareto optimality, symmetry, ordinal invariance, and a weak monotonicity property. Kıbrıs (2012) shows that it is possible to replace monotonicity in this characterization with a weak contraction independence property. Samet and Safra (2005) propose

17 There is no reference on the origin of this rule in Shubik (1982). However, Thomson attributes it to Shapley. Furthermore, Roth (1979) (pp. 72–73) mentions a three-agent ordinal bargaining rule proposed by Shapley and Shubik (1974, Rand Corporation, R-904/4) which, considering the scarcity of ordinal rules in the literature, is most probably the same bargaining rule.

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generalizations of the Shapley-Shubik rule to an arbitrary number of agents. VidalPuga (2015) analyzes a noncooperative game whose subgame perfect Nash equilibrium coincides with the Shapley-Shubik rule. The literature following Shapley (1969) also analyze the implications of weakening the ordinal invariance requirement on two-agent bargaining rules. Myerson (1977) and Roth (1979) show that such weakenings and some basic properties characterize Egalitarian type rules. Calvo and Peters (2005) analyze problems where there are both ordinal and cardinal players. There is also a body of literature which demonstrates that in alternative approaches to modeling bargaining problems, ordinality can be recovered (e.g., see Rubinstein et al. 1992; O’Neill et al 2004; Kıbrıs 2004b). Finally, there is a body of literature that allows nonconvex bargaining problems but does not explicitly focus on ordinality (e.g., see Herrero (1989), Zhou (1997), and the following literature).

Conclusion In the last 60 years, a very large literature on cooperative bargaining formed around the seminal work of Nash (1950). In this chapter, we tried to summarize it, first focusing on some of the early results that helped shape the literature, and then presenting a selection of more recent studies that extend Nash’s original analysis. An overview of these results suggests an abundance of both axioms and rules. We would like to emphasize that this richness comes out of the fact that bargaining theory is relevant for and applicable to a large number and wide variety of real-life situations including, but not limited to, international treaties, corporate deals, labor disputes, pre-trial negotiations in lawsuits, decision-making as a committee, or the everyday bargaining that we go through when buying a car or a house. Each one of these applications bring out new ideas on what the properties of a good solution should be and thus, lead to the creation of new axioms. It is our opinion that there are many more of these ideas to be explored in the future.

Cross-References ▶ Group Decisions: Choosing a Winner by Voting ▶ Group Decisions: Choosing Multiple Winners by Voting ▶ Non-cooperative Bargaining Theory ▶ Sharing Profit and Risk in a Partnership ▶ The Notion of Fair Division in Negotiations

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Anbarci N, Sun C (2011) Distributive justice and the Nash bargaining solution. Soc Choice Welf 37:453–470 Anbarci N, Sun C (2013) Robustness of intermediate agreements and bargaining solutions. Games Econ Behav 77:367–376 Bennett E (1997) Multilateral Bargaining Problems. Games Econ Behav 19:151–179 Binmore K, Eguia JX (2017) Bargaining with outside options. In: Schofield N, Caballero G (eds) State, institutions and democracy. Springer, Cham, pp 3–16 Binmore K, Rubinstein A, Wolinsky A (1986) The Nash bargaining solution in economic modeling. RAND J Econ 17(2):176–189 Blackorby C, Bossert W, Donaldson D (1994) Generalized Ginis and Cooperative Bargaining Solutions. Econometrica 62(5):1161–1178 Calvo E, Gutiérrez E (1994) Extension of the Perles-Maschler solution to N-person bargaining games. Int J Game Theory 23(4):325–346 Calvo E, Peters H (2000) Dynamics and axiomatics of the equal area bargaining solution. Int J Game Theory 29(1):81–92 Calvo E, Peters H (2005) Bargaining with ordinal and cardinal players. Games Econ Behav 52(1): 20–33 Chiappori P-A, Donni O, Komunjer I (2012) Learning from a piece of pie. Rev Econ Stud 79:162–195 Chun Y, Thomson W (1990) Bargaining with uncertain disagreement points. Econometrica 58(4): 951–959 Dagan N, Volij O, Winter E (2002) A characterization of the Nash bargaining solution. Soc Choice Welf 19:811–823 De Clippel G, Minelli E (2004) Two-person bargaining with verifiable information. J Math Econ 40(7):799–813 Dhillon A, Mertens JF (1999) Relative utilitarianism. Econometrica 67(3):471–498 Dubra J (2001) An asymmetric Kalai-Smorodinsky solution. Econ Lett 73(2):131–136 Forges F, Serrano R (2013) Cooperative games with incomplete information: some open problems. Int Game Theory Rev 15(02):134009. (17 pages) Gómez JC (2006) Achieving efficiency with manipulative bargainers. Games Econ Behav 57(2): 254–263 Herrero MJ (1989) The Nash program – non-convex bargaining problems. J Econ Theory 49(2): 266–277 Kalai E (1977) Proportional solutions to bargaining situations: interpersonal utility comparisons. Econometrica 45(7):1623–1630 Kalai A, Kalai E (2013) Cooperation in strategic games revisited. Q J Econ 128(2):917–966 Kalai E, Smorodinsky M (1975) Other solutions to Nash’s bargaining problem. Econometrica 43:513–518 Karagözoğlu E, Rachmilevitch S (2018) Implementing egalitarianism in a class of Nash demand games. Theor Decis 85(3–4):495–508 Karos D, Muto N, Rachmilevitch S (2018) A generalization of the egalitarian and the KalaiSmorodinsky bargaining solutions. Int J Game Theory 47(4):1169–1182 Kıbrıs Ö (2002) Misrepresentation of utilities in bargaining: pure exchange and public good economies. Games Econ Behav 39:91–110 Kıbrıs Ö (2004a) Egalitarianism in ordinal bargaining: the Shapley-Shubik rule. Games Econ Behav 49(1):157–170 Kıbrıs Ö (2004b) Ordinal invariance in multicoalitional bargaining. Games Econ Behav 46(1): 76–87 Kıbrıs Ö (2012) Nash bargaining in ordinal environments. Rev Econ Des 16(4):269–282 Kıbrıs Ö, Sertel MR (2007) Bargaining over a finite set of alternatives. Soc Choice Welf 28:421–437 Kıbrıs Ö, Tapk İG (2010) Bargaining with nonanonymous disagreement: monotonic rules. Games Econ Behav 68(1):233–241 Kıbrıs Ö, Tapk İG (2011) Bargaining with nonanonymous disagreement: decomposable rules. Mathematical Social Sciences 62(3):151–161

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Kihlstrom RE, Roth AE, Schmeidler D (1981) Risk aversion and Nash’s solution to the bargaining problem. In: Moeschlin O, Pallaschke D (eds) Game theory and mathematical economics. North-Holland, Amsterdam Myerson RB (1977) Two-person bargaining problems and comparable utility. Econometrica 45:1631–1637 Myerson RB (1981) Utilitarianism, egalitarianism, and the timing effect in social choice problems. Econometrica 49:883–897 Nash JF (1950) The bargaining problem. Econometrica 18(1):155–162 Nash JF (1953) Two person cooperative games. Econometrica 21:128–140 O’Neill B, Samet D, Wiener Z, Winter E (2004) Bargaining with an agenda. Games Econ Behav 48:139–153 Perles MA, Maschler M (1981) A super-additive solution for the Nash bargaining game. Int J Game Theory 10:163–193 Peters H (1986) Simultaneity of issues and additivity in bargaining. Econometrica 54(1):153–169 Peters H (1992) Axiomatic bargaining game theory. Kluwer Academic, Dordrecht Peters H, Wakker P (1991) Independence of irrelevant alternatives and revealed group preferences. Econometrica 59(6):1787–1801 Rachmilevitch S (2011) Disagreement point axioms and the egalitarian bargaining solution. Int J Game Theory 40:63–85 Rachmilevitch S (2015) Nash bargaining with (almost) no rationality. Math Soc Sci 76:107–109 Raiffa H (1953) Arbitration schemes for generalized two-person games. In: Kuhn HW, Tucker AW (eds) Contributions to the theory of games II. Princeton University Press, Princeton Roth AE (1979) Axiomatic Models of Bargaining. Springer-Verlag Rubinstein A (1982) Perfect equilibrium in a bargaining model. Econometrica 50(1):97–109 Rubinstein A, Safra Z, Thomson W (1992) On the interpretation of the Nash bargaining solution and its extension to nonexpected utility preferences. Econometrica 60(5):1171–1186 Samet D, Safra Z (2005) A family of ordinal solutions to bargaining problems with many players. Games Econ Behav 50(1):89–106 Shapley L (1969) Utility comparison and the theory of games. In: La Décision: Agrégation et Dynamique des Ordres de Préférence. Editions du CNRS, Paris, pp 251–263 Shapley LS, Shubik M (1974) Rand Corporation Report R-904/4. Game Theory in Economics: Chapter 4, Preferences and Utility Shubik M (1982) Game theory in the social sciences. MIT Press, Cambridge, MA Sobel J (1981) Distortion of utilities and the bargaining problem. Econometrica 49:597–619 Sobel J (2001) Manipulation of preferences and relative utilitarianism. Games Econ Behav 37(1): 196–215 Sprumont Y (2000) A note on Ordinally equivalent Pareto surfaces. J Math Econ 34:27–38 Thomson W (1981) Nash’s bargaining solution and utilitarian choice rules. Econometrica 49:535–538 Thomson W (1994) Cooperative models of bargaining. In: Aumann R, Hart S (eds) Handbook of game theory with economic applications. North-Holland, Amsterdam Van Damme E (1986) The Nash bargaining solution is optimal. J Econ Theory 38(1):78–100 Vidal-Puga J (2015) A non-cooperative approach to the ordinal Shapley-Shubik rule. J Math Econ 61:111–118 Yu P (1973) A class of solutions for group decision problems. Manag Sci 19:936–946 Zhou L (1997) The Nash bargaining theory with non-convex problems. Econometrica 65 (3):681–685

Conflict Resolution Using the Graph Model: Individuals and Coalitions D. Marc Kilgour, Keith W. Hipel, and Liping Fang

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Analysis of Strategic Conflicts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Graph Model for Conflict Resolution: Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . What Is a Graph Model? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Graph Model Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decision-Support Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GMCR I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GMCR II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GMCR+ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Follow-Up Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Status Quo Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coalition Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

The graph model for conflict resolution is a methodology for modeling and analysis of strategic conflict. Like related techniques of conflict analysis, it is based on the assumption that the outcome of a conflict depends on the purposive behavior of independent actors. The graph model for conflict resolution stands D. M. Kilgour (*) Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada e-mail: [email protected] K. W. Hipel Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada e-mail: [email protected] L. Fang Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, Canada e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_13

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out among these techniques, both for the flexibility of its models and the breadth of its analysis. The graph model system is prescriptive, aiming to provide a specific decision-maker (DM) with relevant and insightful strategic advice based on their own understanding of the situation and preferences about the outcome. The basics of a graph model – DMs, states, movements (graphs), and preferences – are described, along with the stability definitions that form the foundation of the analysis. Developments that facilitate the application of basic graph models are discussed and illustrated, including the decision-support systems GMCR II and GMCR+. A major extension to the graph model is the notion of coalition, representing a group of DMs who can act to achieve an outcome that is in their common interest. The main definitions of coalition moves and coalition improvements are discussed, illustrated, and applied to basic stability definitions, which are both expanded and altered by the extension to coalitions. The capacity of the graph model to generate useful advice is emphasized throughout, and illustrated using a real-life groundwater contamination dispute. Keywords

Group decision and negotiation · Development from game theory · Graph model · Conflict analysis · Coalition · Decision support system

Introduction Conflict analysis seeks to model and analyze a strategic conflict, or multidecisionmaker policy problem, using models of the purposive behavior of actors. Among these methods, the graph model for conflict resolution combines model flexibility and analysis breadth and depth. A review of its historical development facilitates a brief comparison to noncooperative game theory and to other conflict analysis techniques that it inspired, such as drama theory. The graph model system is prescriptive, aiming to provide a specific decision-maker with relevant and insightful strategic advice. The capacity of the graph model to generate useful advice, which is emphasized throughout, is illustrated using a real-life groundwater contamination dispute. The description of the graph model includes the basic modeling and analysis components of the methodology and the decision-support systems, GMCR II and GMCR+ that are widely used to apply it. The development of various forms of coalition analysis is recounted, the methodologies outlined, and illustrated. This review is an update and expansion of Hipel et al. (2020) and Kilgour and Hipel (2005, 2010).

The Analysis of Strategic Conflicts A strategic conflict is an interaction involving two or more independent decisionmakers (DMs), each of whom makes choices that together determine the final state of the system, and each of whom has preferences over the final state, or outcome. Thus,

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a strategic conflict is a joint, or interactive, decision problem; there are two or more DMs, each DM must make a choice of one out of two or more courses of action, and each DM is concerned about the others’ actions insofar as the outcome depends on all DMs’ choices. More specifically, each individual DM can be better or worse off according to the choices of others. It is clear that strategic conflicts are very common in human interactions in many contexts and levels, including personal, family, business, national, and international. The need for principles and methods to improve conflict decision-making by encouraging positive, rather than destructive, resolutions of conflicts was obvious long ago. Not only would the DMs themselves benefit from a better understanding of strategic conflict, so would mediators, who propose resolutions, and policy-makers, who design structures within which conflicts are played out. There will be a need for conflict analysis methods as long as humans interact. Virtually all methods of conflict analysis are rooted in the noncooperative game theory of von Neumann and Morgenstern (1953). One of the landmark intellectual achievements of the twentieth century, Theory of Games and Economic Behavior had an impact that is difficult to overestimate. It changed the direction of economics, and later other social sciences, toward more formal models emphasizing the interconnections of decisions and the formal analysis of choice. Non-cooperative game theory is normative (it analyzes the choices of fully rational individuals, and the outcomes that would occur), and caused social scientists to focus on rational choice. The famous theorem of Nash (1950) demonstrated that every finite game has at least one Nash equilibrium, which can be interpreted as a state or scenario that meets minimal standards of rationality for all players. Game theory has developed enormously in the ensuing 75 years, and now constitutes a well-developed body of theory that has been influential in many disciplines. However, there are issues with the use of a non-cooperative game model of strategic conflict. For instance, in a game, the order of action of the DMs (called players) must be specified but, in many strategic conflicts such as negotiations, the order of action is not fixed in advance – when to make an offer is almost as important as what to offer. Such indeterminacy can be built into a game model, but it becomes clumsy and hard to analyze. Another requirement of game models is the representation of players’ preferences by real-valued (von Neumann–Morgenstern) utilities, which are crucial to allow for mixed strategies (probabilistic mixtures of actions). This requirement is a serious drawback for two reasons: utilities are notoriously difficult to measure; and mixed strategies are often hard to interpret as “advice.” (Would you really tell your President to toss a coin to decide whether to attack or press for peace?) Yet, the Nash theorem guarantees the existence of a Nash equilibrium only if mixed strategies are available. The need for models that are realistically designed and easier to analyze led to an effort to develop alternatives. For details of the development of game theory-based methods of conflict analysis, see Looking Back on Decision-Making under Conditions of Conflict, this volume. The Graph Model, the subject of this chapter, is indeed one of these methods. Another one which influenced the development of the graph model was Nigel Howard’s metagames (Howard 1971), described in From Game Theory to Drama Theory, this volume.

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Metagame models address some of the drawbacks of classical game theory by permitting DMs to move at any time, in any order, or not at all. The models are easy to create and easy to analyze. Using option form notation, any finite number of DMs and options can be represented. The groundwater contamination conflict which is shown as a graph model in Fig. 2 is easy to express in option form – essentially, it is Fig. 3. Metagames also did not require cardinal preferences, such as utilities; they required only knowledge of each DM’s relative preferences – the analyst must know whether the DM prefers state a to state b, or prefers b to a, or is indifferent between the two. In addition to a stability derived from Nash equilibrium, metagames included two new stability definitions, general metarationality (GMR) and symmetric metarationality (SMR). From states with these forms of stability, a DM might be able to make an improvement, but would be deterred from doing so by the possibility of a sanction by opposing DMs. The graph model for conflict resolution takes ideas from a number of sources including game theory, metagame analysis, and Fraser and Hipel’s conflict analysis (1979, 1984). As indicated in the name, graphs are a key component of the graph model; a DM’s available (one-step) moves are encoded in a directed graph. The graph model uses all of the stability definitions of other approaches, and others as well. Many of them account for DMs with high foresight or other characteristics that strengthen or broaden the analysis. One important step in the development of the graph model was the ability to automate both the modeling and analysis steps. The decision-support system GMCR II was the first to integrate these two stages, and has facilitated many applications of the graph model to real-world conflicts. GMCR II has been joined by GMCR+, a decision-support system based on later developments including matrix methods and the inverse perspective. But GMCR II remains the standard for many forms of stability and post-stability analysis, which give the analyst information about the accessibility and durability of equilibria. Another development was the extension of graph model definitions from individual DMs to coalitions of DMs. A coalition is a group of DMs who may coordinate their actions if the net effect is to benefit every member of the coalition. Note that while the coalition acts only in pursuit of common interests, it is not a “composite” DM (though Wu et al. (2020) studied such DMs); the members remain individuals, each with their own capabilities and preferences. Coalition analysis often provides insights into why actions are taken, or not taken – insights that would not be uncovered if analysis took place only at the level of individual DMs. The remainder of this chapter summarizes the graph model and its capabilities. The next section, The Graph Model for Conflict Resolution: Fundamentals, provides the history and basics of the graph model, including many variants that have been proposed; Decision-Support Systems then describes the decision-support systems, GMCR II and GMCR+, that have been used to automate and strengthen applications of the graph model; and then Follow-Up Analyses describes post-stability analysis – extensions of the graph model to Status Quo Analysis and to coalitions of DMs. Finally, Summary and Conclusions offers a general summary, and sets the contents of this chapter in a more comprehensive context.

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The Graph Model for Conflict Resolution: Fundamentals The graph model for conflict resolution provides a methodology for modeling and analyzing strategic conflicts that is simple, flexible, and requires minimal information. A graph model of a conflict provides a good understanding of why DMs should avoid certain actions and how they should choose what to do; in fact, it encourages them to “think outside the box.” The original formulation of the graph model for conflict resolution appeared in Kilgour et al. (1987) and the first complete presentation is the text of Fang et al. (1993). Since then, the graph model has been used by DMs, analysts, and third parties in a wide range of application areas; examples include environmental management at the local level (Kilgour et al. 2001; Noakes et al. 2003; Hamouda et al. 2004a, b; Li et al. 2004; He et al. 2014; Matbouli et al. 2014) and the international level (Obeidi et al. 2002; Noakes et al. 2005; Hipel et al. 2014); labor-management negotiation (Fang et al. 1993, Sect. 8.5); military and peacekeeping activities (Kilgour et al. 1998); infrastructure conflicts (Silva et al. 2017) and international negotiations on economic issues (Hipel et al. 2001); and arms control (Obeidi et al. 2005). A complete list of publications is maintained on the website https://uwaterloo. ca/conflict-analysis-group/.

What Is a Graph Model? The graph model for conflict resolution, described in full in Fang et al. (1993), is summarized here. A graph model has four components, which constitute answers to four questions: 1. 2. 3. 4.

Who are the DMs? What are the possible states of the conflict? What can each DM do to change the state of the conflict? What are each DM’s preferences over the states (as endpoints of the conflict)?

For example, Fig. 1 shows a very simple graph model, with two DMs, DM 1 and DM 2, and four states, 1, 2, 3, and 4. Note that DM 1’s moves and preferences are on the left and DM 2’s are on the right. Formally, the answers to the four questions are input to the system by specifying the following: 1. N, the set of decision-makers (DMs), where 2
n ¼ |N| < 1. By default, we write N ¼ {1, 2, . . ., n}. 2. S, the set of (distinguishable) states, satisfying 2
m ¼ |S| < 1. One particular state, s0, is usually designated as the status quo state. 3. For each i  N, DM i’s directed graph Gi ¼ (S, Ai). The nodes of every DM’s graph are the states, S. The arc set of DM i’s graph, Ai  S  S, has the property that if (s, t)  Ai, then s 6¼ t; in other words, Gi contains no loops. The entries of Ai are the state transitions controlled by DM i.

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1

1

2

3

s2

s

s

4

s

≻1 3 ≻1 1 ≻1 4

G1 = (S, A1)

2

3

s1

s

≻2 4

≻2

4

s3

s

≻2 2

G2 = (S, A2)

Fig. 1 Example graph model. (Source: Adapted from Kilgour and Hipel (2010))

4. For each i  N, a complete binary relation ≽i on S that specifies DM i’s weak preference over S. If s, t  S, then s ≽i t means that DM i prefers s to t, or is indifferent between s and t. Following well-established conventions, we say that i strictly prefers s to t, written s i t, if and only if s ≽i t but :[t ≽i s] (i.e., it is not the case that t ≽i s). Also, we say that i is indifferent between s and t, written s i t, if and only if s ≽i t and t ≽i s. The arcs in a DM’s graph represent state transitions that the DM controls; specifically, if s, t  S and s 6¼ t, then there is an arc from s to t in DM i’s graph, i.e., (s, t)  Ai, if and only if DM i can (unilaterally) force the conflict to change from state s to state t. In this case, we say that t is reachable for i from s. Because all DMs’ graphs have the same vertex set, S, it is often convenient to describe a relatively small graph model using the integrated graph G ¼ (S, (A1, A2, . . ., An)). The integrated graph is a directed graph (possibly with multiple arcs), in which each arc is labeled with the name of the DM who controls it. The graph model methodology does not insist that preference relations be transitive. (The relation ≽ is transitive if, whenever s ≽ t and t ≽ u, then s ≽ u also). Intransitive preferences are rare in well-thought-out graph models, but nonetheless the system does allow for them. Preferences are always antisymmetric (if s ≽ t and t ≽ s, then s  t), so if a DM’s preference is transitive, it can be used to order the state set S, reflecting that the DM can rank the states in order of preference, possibly with some ties. The assumption of ordinal (i.e., transitive) preferences makes the presentation of a graph model using its integrated graph particularly compact. The decision-support systems GMCR II and GMCR+ assume that all preferences are transitive. Returning to Fig. 1, note that this is a complete graph model, which has n ¼ 2 DMs and m ¼ 4 states; each DM controls three state transitions, and has strict and transitive preferences over the four states as shown. Later, the status quo state will be assumed to be state 1. The graph model of Fig. 1 is a particularly simple one, but

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nonetheless demonstrates that the graph model is a more general representation than other formal models of strategic conflict. (For instance, Fig. 1 could not be expressed as a non-cooperative game.) We use Fig. 1 to illustrate the assumptions that the graph model methodology makes about behavior. The conflict starts in some state, the status quo, which for illustration we take to be state 1. A DM who can move away from the current state of a conflict may choose to do so (with one exception – see below). In this case, only DM 1 can move from state 1; DM 1’s only possible move is to state 2. If DM 1 does not choose to move away from state 1, the model remains there. But to move to state 2 would be an improvement for DM 1 (because DM 1 prefers state 2 to state 1), so DM 1 may well make this move. If DM 1 does so, the model is at state 2, and DM 1 may foresee the possibility that another DM (who, in this case, must be DM 2) will move away from state 2. In fact, DM 2 would do so, as the move from state 2 to state 3 is an improvement for DM 2. Should these moves be made, the game will remain at state 3, because neither player can move away from state 3 – DM 1 cannot, as she has no moves that begin at state 3, and DM 2 cannot, as the graph model methodology forbids consecutive moves by any DM. Thus, in this instance, the conflict can evolve from state 1 to state 2 to state 3, where it must end. We pause for a brief discussion of the no-consecutive-moves rule. In fact, it does not arise very often in practice, since (unlike the graphs of Fig. 1) most DM’s graphs are transitive. Specifically, if a DM has a move from state s to state t and also has a move from state t to state w, then the DM can move directly from state s to state w. But occasionally, a DM’s graph is not transitive: a DM may be able to move from state s to state t, and also from state t to state w, but is forbidden to move directly from state s to state w. To allow for such models, the possibility of consecutive moves by the same DM is not allowed. Otherwise, every graph model would, effectively, contain only transitive graphs. In other words, the no-consecutive-moves rule ensures that a DM’s graph may be intransitive if that is the best representation of DM’s strategic situation. The graph model in Fig. 2, below, is a simple but very useful model of a strategic conflict studied extensively by the authors and their collaborators. In 1991, the citizens and officials of the town of Elmira, Ontario were shocked to learn of the discovery of a carcinogen in the underground aquifer that supplied water to the town. The three DMs in the model are the Ontario Ministry of the Environment (MoE), Uniroyal Chemical Limited (UR), and the Local Governments (LGs). The strategic conflict centers on responsibility for clean-up of the pollution; at the time point of the model, the Ministry has just issued a control order requiring Uniroyal, suspected to be the source of the pollution, to clean it up, but Uniroyal has the right to appeal. This model, called Elmira 1, has nine distinct states. (For more details, see below and Kilgour et al., 2001.) Another way to express a graph model is option form, which sees each DM as controlling one or more options, or Yes–No decision variables. Option form was developed for metagame analysis (Howard 1971) and used later in conflict analysis (Fraser and Hipel 1984) and drama theory (Howard 1999). Option-form specification is very efficient; a subset of a DM’s options is a strategy for the DM (in the sense

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Status Quo 1

MoE

LG

UR

2

3

LG

LG

UR

5

UR

LG UR

6

MoE

4

MoE

UR

UR UR UR

7

UR

8

MoE

UR

UR

9

MoE:

7

3

4

8

5

1

2

6

9

UR:

1

4

8

5

9

3

7

2

6

LG:

7

3

5

1

8

6

4

2

9

Fig. 2 Elmira 1 graph model. (Source: Kilgour et al., 2001, Fig. 3)

that all options in that subset, and no others, are selected); a collection of strategies, one for each DM, is a state, and the state transitions controlled by a DM are generally those that occur when the DM changes strategy (while all other DMs hold firm to their strategies). For example, a simple option-form specification of the Elmira 1 model uses the following options: MoE can Modify the control order to make it more acceptable to UR; UR can Delay the process by appealing, or it can Accept the control order (Accept), or it can Abandon its Elmira facility; and LG can Support the control order. At the status quo, state 1, MoE chooses not to Modify the control order, UR chooses to Delay, and LG chooses not to Support the control order. These options are shown in Fig. 3, below, which was generated by the decision-support system GMCR II. Conditions and contingencies in the choice of options are usually easy to express. There are often restrictions and redundancies among the options (for example, the choice of one option may make another option infeasible) and also among option changes, or state transitions (for example, an option may be reversible or not). For example, in the Elmira 1 model, MoE’s choice to Modify, and any of UR’s choices – to Delay, Accept, or Abandon – are modeled as irreversible. Another phenomenon of option form is state coalescence; the choice of Abandon by UR produces a state that is essentially the same irrespective of the choices of the other DMs. For future reference, note that in the Elmira 1 model (see Fig. 2), Uniroyal most prefers the status quo, which is state 1, whereas both MoE and LG most prefer state 7, where LG

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Fig. 3 Equilibria page of GMCR II analysis of Elmira 1 model. (Source: GMCR II Screenshot)

chooses Support and UR chooses Accept. Note also UR’s choice to Abandon is a powerful threat, as it always produces state 9, the least preferred outcome for both MoE and LG.

Graph Model Stability Analysis The methodology of the graph model for conflict resolution comprises not only the modeling of a strategic conflict, but also the analysis of that model. The fundamental form of analysis is stability analysis, which answers the following question for any DM and any state: If the model is at that state, does the DM choose to move away from it (to some other state)? If the answer is No, then the state is stable for that DM; otherwise, it is unstable. Note that a state is stable for any DM who does not control any transition away from that state. But if the DM can move, will the DM choose to do so? The answer depends on the DM’s analysis of possible moves and their consequences, which is contained in a stability definition. Knowing stability

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information (the Yes or No decisions) can give many insights into the nature of the conflict and the behavior of DMs. Stability analysis is often followed by more advanced forms of analysis (called follow-up analyses), which must take place after stability analysis. This section concentrates on the fundamentals of stability analysis. In the graph model for conflict resolution, a stability definition (also called a solution concept) is a set of rules for calculating whether a DM would prefer to stay at a state or move away from it unilaterally. Thus, a stability definition is a representation of a DM’s strategic approach, and can be thought of as a model of human behavior in strategic conflict. Of course, there are many different stability definitions, and different definitions may be appropriate for different DMs. In graph models with n ¼ 2 DMs, all stability definitions are equivalent to the specification of a state, s, a DM, i, and a two-person finite extensive-form game of perfect information, called a Departure Game, that is constructed using the DMs’ graphs. In this game, the first move must be a choice by DM i to stay at s or to move to some state t 6¼ s such that i has a move from s to t. If i has no moves away from s, or if solving the departure game shows that i’s best choice is to stay at s even though other moves are available, then the Departure Game has outcome s, and s is stable for the DM. Different stability definitions correspond to different departure games. Clearly, DM i’s rational decision to stay at s depends on what alternatives DM i perceives – in other words, on the structure of the departure game. Suppose DM i has the option of moving to some other state, t. Depending on the particular stability definition, subsequent moves by the other DM away from t may be permitted; as well, i may be permitted to make another move. Clearly, DM i’s rational choice at the first move of the departure game must consider all possibilities. If DM i rationally decides to stay at state s, then the state s is stable for DM i under the stability definition used to construct the departure game; otherwise, it is not. Note that stability definitions differ only in the details of the departure games they construct. Note also the consequences of the Departure Game structure. A state is not stable for a DM who has moves from that state – unless the DM anticipates that the actions of the other DM will take the model to a state that the original DM does not prefer to the original state. Such a move by the opponent is called a sanction. In summary, a state is stable for a DM if, and only if, every one of that DM’s unilateral improvement moves from that state is sanctioned. The previous paragraphs apply only to graph models with two DMs. For graph models with n > 2 DMs, stability definitions are generalized in a natural way from the n ¼ 2 case. See Fang et al. (1993) for details. An equilibrium of a graph model under a particular stability definition is a state that is stable according to that definition for every DM. Each equilibrium is a predicted resolution of the strategic conflict modeled by the graph model. In principle, each DM may have a different stability definition, which implies that many kinds of stability calculations may be required to make a prediction based on a model. Moreover, DMs’ stability types may be difficult to determine in practice. A simple approach that addresses this problem in almost all cases has evolved – look

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for states that are equilibria under many definitions. Almost all models contain at least a few of these so-called strong equilibria; they can generally be taken to be the model’s predictions about the patterns of behavior to be expected in the underlying strategic conflict. Here are some definitions that help to distinguish stability definitions. In any general graph model, for any DM i and any state s  S, define DM i’s reachable list from state s by Ri(s) ¼ {t  S : (s, t)  Ai}. Thus, if the model is in state s, then Ri(s) is the set of states that DM i can move to; these moves are called unilateral moves. If t  Ri(s) and t i s, then DM i’s move from s to t is a (unilateral) improvement for i from s. Moreover, DM i’s unilateral improvement list from s is R+i(s) ¼ {t  Ri(s): t i s}. Note also that, if t  Ri(s) is less preferred than s for i, then t is called a (unilateral) disimprovement for i from s. For example, in Fig. 2, beginning at the status quo, state 1, a move by LG to state 5 is a unilateral improvement, whereas a move by UR to state 3 is a unilateral disimprovement. The main stability definitions currently used in graph model analysis include Nash Stability (Nash), general metarationality (GMR), symmetric metarationality (SMR), sequential stability (SEQ), symmetric sequential stability (SSEQ), limited move stability (Lh), and nonmyopic stability (NM). Complete definitions and original references are provided in Fang et al. (1993, Chap. 3) and Rêgo and Vieira (2017). Table 1 describes several important behavioral characteristics embodied in these definitions. Foresight refers to the maximum number of moves foreseen by a DM under a stability definition. Nash stability has foresight one; the conservative definitions (GMR, SMR, SEQ, and SSEQ) have foresight two or three; in Lh-stability, the foresight is equal to h, a parameter of the definition (the parameter h can equal any positive integer); and NM stability is equivalent to SAME AS PREVIOUS LINE Lh–stability for large values of h. Table 1 Main stability definitions used in the graph model

Nash GMR

Foresight 1 2

Knowledge of opponents None Options only

SMR

3

Options only

Sanctions only

SEQ

2

Never

SSEQ

3

Options and preferences Options and preferences

Lh

h1

Strategic

NM

1

Options and preferences Options and preferences

Disimprovements Never Sanctions only

Never

Strategic

How does focal DM (i) anticipate others to respond to i’s unilateral move? No response Sanction i’s improvement at any cost Sanction i’s improvement at any cost; but i can respond to sanction Sanction i’s improvement, but only with improvement Sanction i’s improvement, but only with improvement; and i can respond to sanction Symmetric; i and others move to optimize Symmetric; i and others move to optimize

Based on Table 1 of Kilgour and Hipel (2010), with Rêgo and Vieira (2017)

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Knowledge of opponents refers to how much a DM with a particular stability definition must know about the opponents’ preferences and capabilities. Nash stability requires no knowledge of their choices or preferences; GMR and SMR require knowledge of opponents’ available choices, but not of their preferences; all other definitions require knowledge of opponents’ choices and preferences. Stability definitions also differ with respect to whether disimprovements are permitted: in Nash stability there are none; in GMR and SMR, the focal DM never makes disimprovements, but the opponents might; in SEQ and SSEQ neither the focal DM nor the opponents can choose a disimprovement; and in Lh (h > 1) and NM, disimprovements are permitted provided they are strategic, that is, anticipated to induce other DMs to react in a way that benefits the focal DM. The recommended procedure for predicting the outcome of a graph model relies on the properties elaborated in Table 1. For example, Nash stability can describe the behavior of a DM who lacks knowledge of the opponents’ capabilities, while GMR and SMR describe a cautious DM who understands the opponents’ capabilities but is uncertain about their preferences. As the DM gains this knowledge, SEQ and SSEQ come into play. The limited-move definitions (Lh), including nonmyopic (NM), apply to farsighted, strategic DMs who are confident in their knowledge of opponents’ preferences. This approach brings additional information to the analyst, and encourages better modeling and deeper analysis. Logical relationships among the stability definitions in Table 1 are described in Fang et al. (1993, Chap. 5) and Rêgo and Vieira (2017). For instance, a state that is Nash is also GMR, SMR, SEQ, and SSEQ. Also, a state with any other form of stability must be GMR as well. Graphical depictions of these relationships appear in Fang et al. (1989). Many features of the definitions are suggested in Table 1: for instance, GMR and SMR describe conservative DMs, who expect the opponent(s) to sanction their moves, even if the only available sanctions involve choosing a disimprovement. A DM described by SEQ is willing to take some risk, and expects that the opponents will not choose disimprovements when they sanction – and therefore expects fewer sanctions. By contrast, DMs who follow Lh are calculating and strategic, and see every DM as attempting to optimize – subject to limited foresight, of course. The NM stability definition expresses the ultimate in strategic foresight, but is so demanding that in some models it excludes all states. Using the Elmira 1 model of Fig. 2 as an example, states 5, 8, and 9 are stable for all DMs under the definitions Nash, GMR, SMR, SEQ, SSEQ, Lh for h ¼ 2, 3, . . ., and NM. States 1 and 4 are also stable for all DMs, but for LG they are stable only under the short-sighted, low-knowledge definitions GMR and SMR. Thus, analysis of the Elmira 1 model suggests the conflict is likely to end up at one of state 5 (similar to the status quo, except that LG supports the control order), state 8 (a compromise in which, despite LG’s support, MoE modifies the control order and UR accepts the modification), or state 9 (in which UR abandons the Elmira facility). It should be noted (see Fig. 2) that state 9 must be an equilibrium in this model, because no DM can move away from it. All of this information is contained in Fig. 3, which is the Equilibria page of the decision-support system GMCR II, discussed below.

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We briefly summarize the individual-level analysis of the Elmira 1 model shown in Fig. 2. At the time in question, the status quo was state 1. DM LG quickly indicated its support for the control order, moving the conflict from state 1 to state 5, a unilateral improvement for LG. In the actual event, the conflict remained in this state for some time; the model was considered to have succeeded in predicting the behavior of the DMs. But there were surprises to come – see below.

Decision-Support Systems Three decision-support systems have been developed to apply the graph model to strategic conflicts. The earliest system, GMCR I, is no longer available, but the successors, GMCR II and GMCR+, are now in use around the world. Readers interested in graph model software are asked to contact the authors by email.

GMCR I GMCR I (originally named GMCR) was released in 1990, and distributed as an insert in the book Fang et al. (1993). GMCR I is a program that calculates the stability of every state in a graph model for every DM according to all of the stability definitions listed in Table 1 (except SSEQ, which was not available at the time). It requires input in ASCII code in a specific format, and produces text output. The reliability and comprehensiveness of GMCR I led to a philosophical shift in the analysis of graph models. Instead of assigning a stability type to each DM and then identifying states that are stable for that DM according to the appropriate definition, it was more convenient to identify all states stable for every DM under a range of definitions – the so-called strong equilibria. Strong equilibria are natural predictions of the outcome of the underlying strategic conflict. Of course, when there is some reason to associate a particular stability type with a DM, then states unstable for the DM under that definition must be rejected. But absent any such information, strong equilibria were found to be reliable predictions. The decision-support system GMCR I is no longer in use, but its most valuable component, its analysis capability, was built into the follow-up system GMCR II, which remains in wide use today. The use of GMCR I over three decades is ample evidence of the efficiency of its analysis algorithms. While large models have taken hours to analyze, most simple models of strategic conflicts in the real world are analyzed completely in seconds.

GMCR II The GMCR I software could analyze graph models quickly, completely, and reliably. Its availability increased the number and range of applications of the methodology,

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providing convincing evidence of the utility of the graph model. But actually applying it to a strategic conflict was a slow and error-prone process. The first version of GMCR II became available in 1999 (Hipel et al. 1997; Fang et al. 2003a, b). Its single most important contribution was to eliminate a crucial bottleneck in the use of GMCR I to analyze a strategic conflict: preparation of the input file. GMCR II successfully integrated input preparation into the development of a graph model. Another major advance was GMCR II’s output presentation, which made an enormous difference in usefulness. The output of GMCR I was not organized to facilitate an efficient and in-depth understanding. In contrast, GMCR II provided so much useful information that it came to be a platform for other forms of analysis, the so-called post-stability analysis, designed to be applied after the equilibria have been identified. GMCR II simplified the modeling of a strategic conflict by using option-form entry, which mimics natural language in describing a DM’s options in a conflict, not only allowing convenient entry but also making it easy to adjust existing models. However, significant extensions were required to accommodate the additional flexibility of the graph model. Option-form entry avoids explicit specification of the states of a graph model by identifying a nonempty finite set Oi representing the options, or courses of action, available to DM i. An option can belong to one and only one DM, so O ¼ O1 [ O2 [ . . . [ On represents the set of all options in the model. The default assumption is that a DM can select any subset of its options (including the empty subset); under this assumption, any state is simply a combination of options, in other words, a subset of O. The set of all states is then S ¼ 2°, the set of all subsets of O. GMCR II allows the analyst or modeler to list options without restriction. But it is rare that options are specified so that (1) every option combination is feasible and (2) every option combination is distinct. Therefore, GMCR II follows up with an elicitation process to specify restrictions on choices. For instance, in the original Elmira 1 model (Fig. 2), the domain expert specified three options for Uniroyal: Delay, Accept, and Abandon. But these options are obviously not independent (for example, simultaneous choice of any two of the three is impossible); thus, in the Elmira 1 model, some option combinations are infeasible. Also, UR’s choice of Abandon meant that all other choices were irrelevant; in other words, several different option combinations were, effectively, the same state. In GMCR II, specification of options is immediately followed by removal of infeasible option combinations and coalescing of essentially equivalent combinations of options. The latter procedure was also invoked in the Elmira 1 model; all option combinations that included Uniroyal’s Abandon option were considered to be essentially the same state. In option-form entry, the state transitions controlled by a DM correspond to changes in the DM’s options. By default, any unilateral change of options is allowed. But after the states are determined, GMCR II asks whether any transitions are disallowed. The GMCR II default procedure is simple and usually sufficient in practice, but there is also a series of steps that can disallow any specific state transition. In the Elmira 1 model, the MoE’s choice to Modify and UR’s choices to

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Accept or Abandon were coded as one-way choices, on the grounds that an attempt to reverse any of these moves would imply a substantial change in the underlying model. After the DMs, states, and state transitions are entered, all that remains is to code each DM’s preference. GMCR II provides three methods of preference entry. Direct Entry asks the user to arrange (“drag and drop”) states in decreasing order of the DM’s preference. Direct Entry is flexible in that it can express any transitive preference ordering, but it is often cumbersome. Nonetheless, it is commonly used to make final adjustments to an ordering that is approximately correct; when used for this purpose, the Direct Entry procedure is called Fine Tuning. Another preference-entry procedure, called Option Weighting, relies on the fact that each state corresponds to an exact combination of options. A numerical weight (which may be positive or negative) is assigned to each option to reflect the DM’s attitude to the exercise of that option. Then a “score” for each state is calculated as the sum of the weights of the options that define it. Finally, the DM’s preference ordering is approximated by ranking the states in order of decreasing score. The most sophisticated preference-entry procedure is Option Prioritizing. The user enters, in priority order, a sequence of preference statements, or true-or-false statements about options, which may contain logical connectives such as AND, OR, NOT, IF, and IFF. Typical statements are Option 3 (meaning “option 3 is selected”), NOT Option 4, and Option 3 AND Option 4. For any state s  S, each preference statement is either true or false. GMCR II orders the states so that state s precedes state t if and only if the highest priority preference statement that is true for exactly one of s and t is true for s and false for t. With some practice, users can achieve a plausible ordering quickly with Option Prioritizing, which seems to reflect that priority hierarchies of preference statements mimic the way humans think about preference. Most analysts find that the most efficient way to enter preferences is to use either Option Weighting or Option Prioritizing and then to adjust the resulting ordering using Fine Tuning. The model entry component of GMCR II was successful in that it surpassed what was previously available and added enormously to the usefulness of the graph model methodology. Of course, there are some conflicts that are difficult to enter, but they are rare. Another measure of the success of GMCR II is that it facilitates sensitivity analysis: It is easy to make small changes in a model and reanalyze it, in order to assess how much the changes affect the conclusions. For details regarding GMCR II’s output displays, see Fang et al. (2003b). Typical of these displays is the GMCR II Equilibria property page; for the Elmira 1 model, this page is shown as Fig. 3. Note that Elmira 1 is a very small model; states are described using five options (strictly speaking, only four options are necessary), and only five states have any form of stability for all DMs. A state is expressed as a sequence of Y’s, N’s, and –’s, where “Y” indicates an option selected by the DM controlling it, “N” an option not selected, and “–” means “either Y or N.” Figure 3, the Equilibria page, shows that states 5, 8, and 9 are strongly stable for all DMs (under every stability definition).

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GMCR II also provides an Individual Stability property page, which can be used to find, for each DM, the stability of every state under each of the stability definitions incorporated into the system. For the Elmira 1 model, this page shows that states 1 and 4 are stable for both MoE and UR under all definitions, but are stable for LG only under GMR and SMR. Screens like Fig. 3 provide all of the information that the graph model methodology was designed to provide, which is now referred to as individual-level analysis. The availability of rapid computation and informative displays enabled GMCR II to support the study of many conflicts; it is now used in beta form in over 100 installations worldwide. GMCR II also facilitated the development of several forms of follow-up (or post-stability) analysis, which are discussed below.

GMCR+ GMCR+, a new DSS for the graph model for conflict resolution, was introduced in 2014. The objective of the new system was not so much to address limitations in its predecessors as to expand across new frontiers. It incorporated several advances in the GMCR methodology that supported new technical features; in addition, it simplified computation and improved communication. For example, GMCR+ was designed around a new matrix-based analysis engine that provides for fast computations and supports graph models that include preference uncertainty (Xu et al. 2009a; Kinsara et al. 2015a, b). See chapter ▶ “Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives” for a description of matrix analysis and inverse GMCR, another new feature of GMCR+. The cost, primarily due to the technical properties of matrix computations, is that GMCR+ is limited to only the most basic stability definitions, Nash, GMR, SMR, and SEQ. GMCR+ was a great advance, in part because of its ability to communicate graph models and their analysis. It displays enriched graphs of sections of a graph model to illustrate its analysis, and even narrates the analysis as appropriate. Another design objective of GMCR+ was to enhance communication to and between DMs, analysts, and other third parties, especially in negotiation and conflict management. Every effort was made to take into account cognitive aspects of the communication. For example, it is easy to send graph models and analysis results by e-mail. Another new feature for GMCR+, available in the 2015 release, allows analysts to specify multiple objectives (in terms of options selected or not) and then inquire of GMCR+ whether a state exists that meets these objectives and exhibits some specified stability. If so, the output includes analytics to guide DMs as they strive to achieve their objectives. Scenario building and goal-seeking are new and intuitive functions that appear in post-analysis screens. Rather than reusing components of earlier systems, GMCR+ was developed from the ground up. The result was a framework that is modular and easy to modify; not only does it provide comprehensive support for the analysis and understanding of a graph model, but also it is easy to modify to accommodate new developments and

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approaches. For example, it has already proven easy to integrate some models of preference uncertainty into GMCR+. GMCR+ has four independent analysis engines (solvers), logical, matrix, inverse, and goal-seeker. The first two are used to calculate individual stabilities and determine overall equilibria according to the built-in stability definitions. The inverse solver is devoted to inverse GMCR, which attempts to give the user insights into how a specific resolution might come about (Kinsara et al. 2015b). Finally, the goalseeker solver identifies states that achieve goals specified by the user, determining whether the goal is consistent with specific stability or equilibrium conditions also specified by the user and, if so, providing the details. The output module of GMCR+ provides equilibrium results in various styles, including reporting and narration, graph visualization, and tree diagrams. This module is integrated with the inverse solver and the goal-seeker. Another role of the output module is to enable all model data and results to be exported to Excel. Graphics are an effective communication tool in a wide range of areas, including for graph models and their analysis (Kinsara et al. 2018). In post-analysis, GMCR+ displays stability results using enriched versions of directed graphs. Its visualization feature launches an interactive graph within the results screen. There are two visualization modes. The Tree mode displays a tree-like diagram that captures the graph model starting from an initial (status quo) state that appears at the top of the tree. To trace conflict evolution, click any state other than the status quo to see a new tree diagram with the state clicked as new initial state. Bold lines emphasize the unilateral improvements. The Graph mode of visualization gives an overview of the model that shows the direction of possible moves using arrowheads, associating them with specific DMs using an easily understandable code implemented in colors and line forms (such as dashes). Again, UIs are shown in bold. In both modes, a table listing DMs, options, and states appears when the mouse is pointed to the bottom of the screen. Furthermore, software installation is not required – the visualizer is launched automatically using any web browser. A limitation of many DSSs, including GMCR I and II, is their inability to manipulate data, models, and results unless the actual software is installed. GMCR+ avoids this problem by incorporating features that allow manipulation of model data and results without software. For example, it is sometimes useful to modify data, especially graphs, sent by e-mail. To address this problem, conflict parameters and analysis results can be exported to Excel, or any other spreadsheet supporting comma separated values (CSV). This feature overcomes incompatibilities among systems, making GMCR+ a universal software that can work across platforms (Windows, Mac, and Linux). Results can be displayed on smartphones and tablets. Although the structure of GMCR+ is robust, there are some capacity limitations. As already noted, GMCR+ deals only with the four simplest forms of stability. Moreover, memory can be an issue, as the core of any graph model in GMCR+ is a dense reachability matrix that cannot be shrunk. The full reachability matrix of size m  m (recall that m is the number of states) is created in memory. The observed limit, around 20,000 states using a computer with 4 GB of RAM, reflects the

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Table 2 Comparison of GMCR I, GMCR II, and GMCR+ Year Environment Language Input Output Interface Stabilities Postanalysis Inverse GMCR

GMCR I 1990 Windows C ASCII Text I/O Nash, GMR, SMR, SEQ, Lh, NM None

GMCR II 1999 Windows C++ Query-response Tables GUI Nash, GMR, SMR, SEQ, Lh, NM Coalition (simple)

No

No

GMCR+ 2014 Universal Python, Javascript Query-response Graphs, tables, text GUI Nash, GMR, SMR, SEQ Scenario narration, graph drawing, goal-seeking Included

Source: Modified from Kinsara et al. (2018)

memory requirement for the reachability matrix. The complexity of GMCR+ is discussed in Kinsara (2014). Table 2 compares the features of GMCR+ with those of GMCR I and GMCR II. DSSs for the support of group decision processes, including negotiations, need the flexibility to display and narrate results in multiple ways to convey information correctly and quickly. Most of these problems have been resolved in GMCR+, which can therefore be expected to be the model for future systems implementing the graph model for conflict resolution.

Follow-Up Analyses Stability analysis is the fundamental form of analysis for a graph model. Stability analysis identifies all states that are stable, for each DM, under each of a range of stability definitions; a state is stable for a DM if that DM would not move away from it should it be reached as the conflict evolves. A specific stability definition sets out exactly how the DM evaluates the opportunity to move away from a state provided it is possible to do so. If so, it is to be expected that different definitions sometimes reach different conclusions about the state. States that are stable for every DM are equilibria, and constitute predictions of the outcome of the strategic conflict. Once the equilibria have been identified, follow-up analyses (or post-stability analyses) can be used to answer other questions about stability. Two of them will be discussed here: • An equilibrium is a state that would be stable if it arose – but can it actually arise, starting from the status quo state of the model? Status Quo Analysis is designed to assess how likely the different equilibria are to develop, and takes into account the number of moves required to reach the target state, the nature of those moves (UI or not), etc.

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• An equilibrium is a state that no individual DM is motivated to move away from. But could a group of DMs agree to act together, carrying out a sequence of moves to achieve a final state that benefits everyone in the group? Coalition Analysis is designed to assess whether each equilibrium is vulnerable to a coordinated sequence of individual moves by two or more DMs. It may go on to assess possible responses to the original “group move,” etc.

Status Quo Analysis The main idea of status quo analysis is to look forward in a graph model, identifying which states are attainable, and assessing how easily they can be attained. The starting point of the analysis is the current state, the status quo if the analysis is occurring at the time point of the model. The states that might be attained are usually restricted to known equilibria, as all other states are known to be transient. Thus, there is little point in attempting to carry out status quo analysis before the equilibria are known, so status quo analysis should follow stability analysis. But in a sense, these two forms of graph model analysis are diametrically opposed: Status quo analysis is dynamic and forwardlooking, following the actual choices made by DMs, whereas stability analysis is static and retrospective, identifying states that would be stable if attained. The general idea for status quo analysis was conceived early in the development of the graph model methodology, but the problem was not effectively addressed until the introduction of a consistent set of definitions and algorithms (Li et al. 2004, 2005). The earlier algorithms have been converted to apply to graph models in matrix representation (see chapter ▶ “Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives”). Although it makes provision for status quo analysis, the decision-support system GMCR II did not contain any implementation. The newer system, GMCR+, can provide considerable information relevant to status quo analysis through its goal-seeking function. Several status quo analysis algorithms have been developed and used in practice. One variation is predicated on DMs’ propensity to choose only unilateral improvements – in other words, their tendency to avoid disimprovements. More generally, paths are considered to be more likely the fewer disimprovements they contain. Another more efficient procedure applies only when the graphs Gi ¼ (S, Ai) of all DMs, i, are transitive. The results of a status quo analysis are usually summarized in an Evolution Diagram, which identifies the most likely (usually, the shortest) path – or several competing paths – from the status quo state to a target state. For instance, Fig. 4 shows that the likely evolution of the Elmira 1 model, from the Status Quo, state 1, to the equilibrium at state 5. The other two strong equilibria of the model, state 8 and state 9, are considered unlikely as they would involve at least one disimprovement. Other versions of status quo analysis produce a Status Quo Table such as Table 3 for the Elmira 1 model of Fig. 2. Note that the status quo state, SQ, is state 1. The states reachable from SQ (in this case, all states) are listed on the top row of the table. Rows of the table correspond to numbers of moves from the status quo, h ¼ 0, 1, 2, 3,

588 Fig. 4 Evolution of the Elmira 1 model from status quo state 1. (Source: Li et al. (2005))

D. M. Kilgour et al. Status Quo

Final Transitional Equilibrium Equilibrium

DM

Option

MoE

1. Modify

N

N

Y

UR

2. Delay

Y

Y

N

3. Accept

N

N

Y

4. Abandon

N

N

N

5. Insist

N

Y

Y

1

5

8

LG State

4, . . . . If there is no entry in the cell corresponding to state s and row h, then state s cannot be reached from SQ in exactly h moves. If the name of a DM appears in this cell, then state s can be reached from the status quo in h or fewer moves, and the named DM must make the last move (the move by which the process arrives at state s ). Finally, the symbol √ in column s and row h indicates that state s can be reached from SQ in at most h moves, and that at least two different DMs can make the last move. It is important to keep track of last movers in a Status Quo Table because of the no-consecutive-moves rule: Within a graph model, no DM may move twice in succession. For example, state 3 can be reached from state 1 ¼ SQ in 1 move; in the sequence (SQ, 3), the last mover must be UR. Because only UR can move from state 3 to state 9, it follows that the sequence (SQ, 3, 9) is impossible, as UR’s moves from SQ to 3 and then 3 to 9 would violate the no-consecutive-moves rule (Nonetheless, state 9 is attainable directly from SQ, as all DMs’ graphs are transitive in this model; the one-move sequence (SQ, 9) is available, and involves a move by UR). A Status Quo Table such as Table 3 is built up one row at a time, and ends as soon as a duplicate row is attained. As shown by Xu et al. (2009b), status quo analysis is equally implementable for graph models expressed in matrix form. To summarize, the intent of status quo analysis is to identify the “basin of attraction” of an equilibrium, the set of states from which the conflict is likely to evolve to that equilibrium. Of course, sometimes an initial state might evolve toward two or more equilibria, meaning that the basins overlap. The issue of assessing the likelihood of a particular evolution remains the subject of current research.

Coalition Analysis Structurally, the graph model methodology assumes that actions are taken by individuals acting alone, in their own interests. The possibility of actions by groups of DMs coordinating their actions – i.e., acting as a coalition – was recognized, but

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Table 3 Status quo table for Elmira 1 model, SQ ¼ s1 Moves 0 1 2 3 4

SQ ¼ 1 √ √ √ √ √

2

3

9

5

4

6

7

8

MoE MoE √ √

UR UR √ √

UR UR UR UR

LG LG LG LG

√ √ √

√ √ √

√ √ √

√ √

Source: Li et al. (2005)

early attempts to consider its implications ran into an immediate problem – if the “DM” is a coalition, what are its preferences? A group of DMs may agree on many state comparisons, but almost never on all of them. If some members of a coalition find state s preferable to state t, and some find t preferable to s, does the coalition prefer s to t, or t to s, or is it indifferent? (The graph model does not allow states to be incomparable.) Given a proposed coalition, Kuhn et al. (1983) suggested a state-based metric for measuring the similarity of preferences among its members as a measure of the likelihood that this coalition forms; Hipel and Meister (1994) provided an optionbased metric for the same purpose. The idea was that DMs with similar preferences are more likely to form a coalition; when coalition members disagreed, the coalition was assumed to be indifferent. But this idea was not developed, in part because predictions were weak due to the amount of indifference; as well, no compelling examples of the utility of this approach were discovered. The development of coalition analysis depended on the key observation that the preferences of a coalition are meaningful only insofar as the members have a common interest that they can achieve by coordination starting at their current position. Moreover, the possibility of a coalition depends on the specific circumstances, and coalitions are generally temporary arrangements to take advantage of an opportunity. These views, first elaborated by Kilgour et al. (2001), followed from developments in the real-world strategic conflict represented by the Elmira 1 graph model. Recall (see Fig. 3) that there are two strong equilibria (states 5 and 8) in which Uniroyal does not abandon its Elmira facility. Stability analysis provides no distinction between these equilibria – they are both highly stable for all DMs. In fact, the state 5 equilibrium was reached quickly, as shown in Fig. 4, and remained in place for several months. Then, in a dramatic turn of events, MoE and Uniroyal announced an agreement that effectively shifted the equilibrium to state 8. LG was not part of the agreement, and was in fact harmed by it. What happened? Coalition analysis offers an answer: The equilibrium at state 5 is (by definition) stable against moves by individual DMs but not, as it turns out, against moves by the coalition of MoE and UR. As Fig. 2 shows, MoE and UR together can move from state 5 to state 8. In fact, there are two ways to do so; both include at least one disimprovement, so individual DMs would be unlikely to choose such a path. But state 8 is preferred to state 5 by both MoE and UR and, beginning from state 5, they can achieve it if they act together.

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Formally, an equilibrium is coalitionally stable if and only if no coalition (i.e., no subset of N containing two or more DMs) can execute a sequence of moves (no two consecutive, of course) so as to achieve another equilibrium that all members of the coalition prefer to the original equilibrium. Since the initial state is an equilibrium, the move to the target equilibrium must require at least two moves, by at least two DMs. Moreover, the target state must be an equilibrium; otherwise, the members of the coalition could not be assured of any stability at a state they all prefer to the original equilibrium. When GMCR II was developed, coalition analysis was recognized as a form of post-stability analysis; it classifies equilibria according to coalitional stability. Coalition analysis (invoked by a check box on the Equilibria property page of GMCR II – see Fig. 3) shows that the Elmira 1 model contains a coalitionally unstable equilibrium, namely state 5. In fact, it reports that MoE and UR can jointly move the conflict from state 5 to state 8, and that both prefer state 8 to state 5. The coalition analysis algorithm implemented in GMCR II was influential even though it was quite primitive. In particular, it left unanswered the question of what might follow a coalition move: If a coalition moves away from equilibrium, can a counter-coalition respond? The next step was the development by Inohara and Hipel (2008) of a definition of coalitional stability that was based on coalitional moves. In this definition, the coalition analysis of GMCR II became coalitional Nash stability, and the new definitions offered include coalitional versions of GMR, SMR and SEQ stability. Interrelationships among these stability definitions were also determined, at least in some special cases. Later, Xu et al. (2010) expanded coalition stability to include uncertain preference using matrix representation of a graph model. Other definitions of coalitional equilibria were proposed by Xu et al. (2018, Chap. 8). In a more general approach to coalitions, Zhu et al. (2020) pointed out that the fundamental concept underlying all coalitional stabilities is coalition improvement. All of the approaches above depend upon classical coalition improvements. A broader view of when a coalition might form and act might be appropriate: the minimum condition for a coalition could be that it have the opportunity to benefit at least one member of the coalition and without harming any member. Such a move is called a Pareto coalition improvement. To understand the meaning of coalitional improvement, it is necessary to return to the definition of unilateral improvement for an individual DM. Recall that, for any DM, a unilateral move from a given state is a transition controlled by the DM to another state; a unilateral move is called a unilateral improvement if the DM prefers the resulting state to the original. Coalition moves arose in the graph model even before coalitions were considered. In a graph model with more than two DMs, the opponents of a specific DM, say DM i, are denoted N  i, where |N  i|  2. To sanction a unilateral improvement by DM i, the members of N  i execute a sequence of moves, and therefore act like the members of a coalition, even though each move is made by an individual DM. Thus, the nature of coalition moves in a graph model should be consistent with the rules for sanctions in a multiparty model.

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Let H  N represent a coalition of DMs in a graph model. The coalition H is nonempty if |H| > 0, trivial if |H| ¼ 1, and nontrivial if |H| > 1. We now define unilateral moves and unilateral improvements for a coalition. Let s  S and H  N, where H is a nonempty coalition. Then the reachable list of coalition H from s is RH(s) ¼ {t  S: there exists
s0, s1, s2, , sk  S such that s0 ¼ s, sk ¼ t, and, for ( j ¼ 1, 2, , k, sj  Rij sj1 , where ij  H and, for j > 1, ij 6¼ ij1}. In words, there is a unilateral move for coalition H from s0 ¼ s to sk ¼ t if the graph model can evolve from s to t via a sequence of unilateral moves by members of the coalition H, with only one additional condition – each move after the first is made by a member of H who did not make the previous move. The second kind of coalitional move is unilateral improvement. It is identical to a unilateral move except that each individual move in the evolutionary sequence must be a unilateral improvement for the DM who makes it. The unilateral improvement þ list of a coalition H from state s is denoted by Rþ H ðsÞ. Note that RH ðsÞ  RH ðsÞ. To þ summarize, RH ðsÞ is the set of states that can be attained by any legal sequence of unilateral improvements, by some or all of the DMs in coalition H, starting at state s. These definitions can be applied in the definitions of Nash stability, general metarationality, symmetric metarationality, sequential stability, and symmetric sequential stability for an individual DM in a graph model with three or more DMs. They can also be used to define the same forms of stability for coalitions in any graph model. More recent research has concentrated on refining the stability definitions for coalitions and studying their interrelationships. Zhu et al. (2020) identified 12 varieties of stability and set out their relationships, similar to what the very influential paper of Fang et al. (1989) did for individual stability in the graph model. Another line of research defines coalitional stabilities for a focal coalition, even if the sanctioning coalitions are unknown to the focal coalition and may include any combination of opponents (Zhao et al. 2019).

Summary and Conclusions It is appropriate to end this review of basicgraph model methodology with a perspective on the future. The authors, and their many colleagues and collaborators, are confident that the graph model methodology offers a valuable and flexible tool for the study and understanding of strategic conflict. We believe that strategic conflict is best understood as a process of negotiation – often informal or implicit, and sometimes even ill-structured. We find support for our point of view in the voluminous literature on negotiation, which includes many calls for systems to analyze the strategic problems of negotiators, and some indications of success. Game theory, many have lamented, is not the natural tool to analyze strategic problems that it “should be,” for various reasons including its insistence on fixed rules of play and its strong assumptions about shared knowledge. In fact, many who study negotiation, such as Raiffa (1982, p. 6), have dismissed game theory as “theoretical acrobatics,” later explaining that “for a long

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time I have found the assumptions made in standard game theory too restrictive for it to have wide applicability [to negotiation]” (Raiffa et al. 2002, p. 12). To summarize, our view is that a negotiation or a group decision is a strategic conflict. Moreover, we believe that graph models provide an effective, efficient vehicle for the analysis and understanding of strategic conflicts. The methodology of the graph model for conflict resolution borrows from game theory but uses a unique and simple structure to capture the key characteristics of a strategic conflict. Moreover, the graph model continues to be amenable for further development – initiatives not covered here (see ▶ “Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives”) for lack of space include hierarchical graph models (He et al. 2014), perceptual graph models (Obeidi et al. 2009), policy equilibrium (Zeng et al. 2007), and levels of preference (Hamouda et al. 2004b; Xu et al. 2009c), as well as links to other methodologies (Kuang et al. 2015; Silva et al. 2019). Using the graph model methodology and the decision-support systems that have been developed to support it, strategic issues can be better understood and decisionmakers better informed (Kilgour and Hipel 2005, 2010; Hipel et al. 2020). The many benefits of the graph model methodology are listed below. It can • Put a strategic conflict into perspective • Furnish a systematic structure for describing, comparing, and elaborating a strategic conflict • Facilitate a better understanding of strategic decisions • Permit convenient and unambiguous communication • Point out relevant information that is missing • Allow for a timely understanding of the strategic implications of a strategic conflict – before it is resolved or progresses to another phase • Identify stable compromises • Provide strategic insights and advice • Perform sensitivity analyses expeditiously, so that analysts can see which model characteristics are crucial to the analysis • Suggest optimal decision paths to a specific DM • Identify opportunities or threats for coalitions to form and intervene. The decision-support systems GMCR II and GMCR+ support the above uses of the graph model methodology, and in addition • Support conflict participants and consultants in the analysis of a strategic conflict • Support consultants in the simulation of a strategic conflict, for example, facilitating role-playing exercises to encourage participants to think like their competitors • Provide an analysis and communication tool to mediators • Provide timely analysis for mediators, especially between negotiation sessions, to guide the parties toward a stable win/win resolution and avoid unstable outcomes • Suggest, to a mediator or third party, opportunities for side payments or other adjustments that would change preferences and thereby stabilize desirable outcomes

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• Support a third party of regulator interested in affecting the outcome of a strategic conflict or framing the rules under which the conflict will be played out. Besides these capabilities, the graph model and its decision-support systems can be employed in conjunction with other procedures for negotiation and conflict resolution. We anticipate that future generations of decision support will integrate many approaches, and suggest that the graph model methodology is an appropriate platform to support or adapt solutions from other systems. The graph model for conflict resolution models strategic conflicts in a way that helps analysts, and through them participants, to understand what issues are fundamental. Its strength is its simplicity and flexibility, both in the modeling and the analysis phases. Using the graph model, the analyst can select from among several assumptions about knowledge and rationality, ensuring that multi-DM problems are represented appropriately. Another advantage is that the methodology has been implemented efficiently in decision-support systems, which have proven crucial in a long list of applications (Table 1.8 of Xu et al. 2018). With experience in application came expertise. The most studied instance is no doubt the Elmira groundwater conflict, described above as the basis of the Elmira 1 model – see Figs. 2, 3, and 4, and Table 3. In summer, 1991, the three authors of this chapter met regularly with a domain expert, Dr. Murray Haight. Together, we developed, analyzed, and interpreted the Elmira 1 model. (For more details, see Xu et al. 2018, pp. 6–22.) Not only was the application successful, it strengthened the graph model methodology, and showed us how best to apply it. Moreover, the dramatic turn of events described above, in Coalition Analysis, inspired our initial work on coalition analysis within the GMCR framework. Originated in the 1980s, the graph model is a continuing project that has built up considerable momentum. Despite all that has been accomplished, we are convinced that there remains a great scope for its development and look forward to its future.

Cross-References ▶ Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives ▶ From Game Theory to Drama Theory

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Li KW, Kilgour DM, Hipel KW (2005) Status quo analysis in the graph model for conflict resolution. J Oper Res Soc 56:699–707 Matbouli YT, Hipel KW, Kilgour DM (2014) Strategic analysis of the Great Canadian Hydroelectric Power Conflict. Energ Strat Rev 4:43–51 Nash J (1950) Equilibrium points in n-person games. Proc Natl Acad Sci 36:48–49 Noakes DJ, Fang L, Hipel KW, Kilgour DM (2003) An examination of the salmon aquaculture conflict in British Columbia using the graph model for conflict resolution. Fish Manag Ecol 10(3):1–15 Noakes DJ, Fang L, Hipel KW, Kilgour DM (2005) The Pacific Salmon Treaty: a century of debate and an uncertain future. Group Decis Negot 14(6):501–522 Obeidi A, Hipel KW, Kilgour DM (2002) Canadian bulk water exports: analyzing the Sun Belt conflict using the graph model for conflict resolution. Knowl Technol Policy 14(4):145–163 Obeidi A, Hipel KW, Kilgour DM (2005) The role of emotions in envisioning outcomes in conflict analysis. Group Decis Negot 14(6):481–500 Obeidi A, Kilgour DM, Hipel KW (2009) Perceptual stability analysis of a graph model system. IEEE Trans Syst Man Cybern Part A Syst Hum 39(5):993–1006 Raiffa H (1982) The art and science of negotiation. Harvard University Press, Cambridge, MA Raiffa H, Richardson J, Metcalfe D (2002) Negotiation analysis: the science and art of collaborative decision making. Harvard University Press, Cambridge, MA Rêgo LC, Vieira GIA (2017) Symmetric sequential stability in the graph model for conflict resolution with multiple decision makers. Group Decis Negot 26(4):775–792 Silva MM, Hipel KW, Kilgour DM, Seixas Costa APC (2017) Urban planning in Recife, Brazil: evidence from a conflict analysis on the “New Recife” project. J Urban Plann Dev 143(3):1–11 Silva MM, Hipel KW, Kilgour DM, Seixas Costa APC (2019) Strategic analysis of a regulatory conflict using Dempster-Shafer theory and AHP for preference elicitation. J Syst Sci Syst Eng 28:415–433 von Neumann J, Morgenstern O (1953) Theory of games and economic behavior, 3rd edn. Princeton University Press, Princeton Wu N, Xu Y, Kilgour DM, Fang L (2020) Composite decision makers in the graph model for conflict resolution: hesitant fuzzy preference modeling. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2020.2992272 Xu H, Hipel KW, Kilgour DM (2009a) Matrix representation of solution concepts in multiple decision maker graph models. IEEE Trans Syst Man Cybern Part A Syst Hum 39(1):96–108 Xu H, Li KW, Hipel KW, Kilgour DM (2009b) A matrix approach to status quo analysis in the graph model for conflict resolution. Appl Math Comput 212(2):470–480 Xu H, Hipel KW, Kilgour DM (2009c) Multiple levels of preference in interactive strategic decisions. Discret Appl Math 57:3300–3313 Xu H, Kilgour DM, Hipel KW (2010) Matrix representation and extension of coalition analysis in group decision support. Comput Math Appl 60(5):1164–1176 Xu H, Hipel KW, Kilgour DM, Fang L (2018) Conflict resolution using the graph model: strategic interactions in competition and cooperation. Springer, Cham Zeng DZ, Fang L, Hipel KW, Kilgour DM (2007) Policy equilibrium and generalized metarationalities for multiple decision-maker conflicts. IEEE Trans Syst Man Cybern Part A Syst Hum 37(4):456–463 Zhao S, Xu H, Hipel KW, Fang L (2019) Mixed coalitional stabilities with full participation of sanctioning opponents within the graph model for conflict resolution. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2019.2950673 Zhu Z, Kilgour DM, Hipel KW (2020) A new approach to coalition analysis within the graph model. IEEE Trans Syst Man Cybern Syst 50(6):2231–2241

Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives Keith W. Hipel, D. Marc Kilgour, Haiyan Xu, and Yi Xiao

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basics of the Graph Model for Conflict Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview of Advances in the Graph Model for Conflict Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . Matrix Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preference Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two Scenarios of Uncertainty with Crisp Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fuzzy Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Three System Perspectives of the Graph Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Forward GMCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Behavioral GMCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inverse GMCR Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Major extensions of the Graph Model for Conflict Resolution (GMCR) are delineated and illustrated. The matrix formulation allows stability calculations to be carried out more efficiently and provides a solid foundation for constructing K. W. Hipel (*) · Y. Xiao Department of Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada e-mail: [email protected] D. M. Kilgour Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada e-mail: [email protected] H. Xu College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_45

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theoretical advances. Simple (crisp) preferences can be extended for handling not only unknown preferences, but also other kinds of uncertain preferences, such as fuzzy, gray, and probabilistic. In this chapter, the focus is on fuzzy preferences and how they can be analyzed using the matrix method. Another recent extension of the graph model is to frame it within two systems perspectives, especially the inverse perspective, in which desirable outcomes and stability types are inputs whereas preferences to achieve them are outputs. These extensions increase the capability of the graph model to generate useful strategic advice and insights. A real-world water export conflict is used to illustrate these ideas. Keywords

Group decision and negotiation · Development from game theory · Graph model · Conflict analysis · Matrix representation · Fuzzy preference · Systems perspectives

Introduction The Graph Model for Conflict Resolution (GMCR) has been significantly expanded during the past three decades (Hipel et al. 2019). In this chapter, an overview of the expansions is provided and then some key advances are explained in detail and illustrated with examples. Most of these expansions are motivated by new challenges arising from real-world conflicts, such as the uncertainty that is observed in many decision situations. To handle these challenges, a variety of new techniques in GMCR, such as fuzzy, grey, and probabilistic preference structures, have been proposed. These new techniques significantly expand the capability of GMCR to realistically model more key characteristics of real-life conflicts and provide new strategic insights. The basic design and expansions of GMCR in meaningful directions are based on what is observed happening in actual conflict as well as ideas from psychology and sociology. The underlying mathematics used to capture key characteristics in conflict comes from set theory, logic, and graph theory. Founded on systems ideas coming from the modeling and analysis of physical systems, GMCR is viewed from what is called an inverse engineering perspective and also from an engine or systems identification viewpoint. Prior to the illustration of three major expansions of the GMCR methodology, the very basics of GMCR are first reviewed in section “Basics of the Graph Model for Conflict Resolution”, and then an overview of the advances of GMCR in section “Overview of Advances in the Graph Model for Conflict Resolution” is given. Next, matrix formulation (section “Matrix Formulation”), preference uncertainty (section “Preference Uncertainty”), and inverse GMCR analysis (section “Three System Perspectives of the Graph Model”) are explained in detail. To help readers fully appreciate the power of these new expansions, representative calculations in matrix form are carried out to demonstrate how these expansions can be readily utilized to resolve real conflicts.

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Basics of the Graph Model for Conflict Resolution The Graph Model for Conflict Resolution (GMCR) constitutes a comprehensive and flexible formal approach for systematically investigating real-world conflicts. Founded on a solid mathematical design, it provides a set of powerful techniques to realistically model the key characteristics of a conflict and furnish valuable strategic insights by carrying out extensive stability analyses. In this section, the basics of GMCR are briefly introduced and illustrated by calibrating a conflict model of dispute arising over the proposed controversial export of water in bulk quantities. Definition 1 Graph Model: A graph model is a framework for conflict analysis, which consists of four key components (Fang et al. 1993; Xu et al. 2018): • A nonempty finite set of decision makers (DMs), denoted by N • A nonempty finite set containing the feasible states according to the selection of options controlled by each DM, denoted by S • A set of oriented arcs describing the one-step movements controlled by each DM i  N, denoted by Ai
S  S, for which the symbol  stands for the Cartesian product • A set of preference relationships (i, ~i) on pairs of states (s, q) for each DM i  N, where siq means DM i prefers state s to q, and s ~i q indicates that DM i equally prefers states s and q

It should be mentioned that the movement and preference information can be stored and represented in different forms, such as in graph form and matrix form. Graph form is easy for humans to visualize and understand, while matrix form is convenient for storing information contained in a graph and is computationally efficient. Either of the two forms can be easily transformed into the other. Example Consider a dispute among a firm, government, and environmentalists over the proposed bulk export of water from Lake Gisborne located in the Canadian province of Newfoundland and Labrador (Fang et al. 2002). In June 1995, a water export project was proposed by Canada Wet Incorporated to transport large quantities of fresh water from Lake Gisborne to foreign markets. At the time of this proposal, there was no existing policy on bulk water export in Canada. The proposal was approved by the provincial government of Newfoundland and Labrador in December 1996, due to its potential for bringing huge economic benefits to the province. However, a large group of environmentalists opposed this project arguing that it could open a floodgate for the commercialization of water and thus threaten local ecosystems. In February 1999, the Federal government of Canada announced its water export policy, which prohibited bulk water exports from major drainage basins in Canada. Under pressure from both the environmentalists and the Federal government, the provincial government introduced a new bill in November 1999 to ban water export activities, including the Lake Gisborne project. However, in March

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2001, the new Premier of Newfoundland and Labrador announced a review of the Gisborne project in the face of poor provincial finances and obtained support from several groups. At this point in time, the provincial government can choose to be economically oriented or environmentally oriented. Utilizing this conflict, the aforementioned four key components of GMCR are described next. Decision Makers (DMs): The main DMs are identified in this conflict, as listed in the left column in Table 1. A DM can be an organization or an individual. Each DM controls one option, as displayed in the second column in Table 1, although in general a DM could have any finite number of options at its disposal. The meaning of each option in this real-life conflict under the control of each DM is explained in the right column in Table 1. Feasible States: Each DM can choose whether or not to act according to its available options. Mathematically, there are a total of 23 = 8 states in this conflict because there are a total of three options. All states are feasible, and are listed in Table 2, in which Ys and Ns indicate that the corresponding option on the left side is selected or not chosen, respectively, by the DM controlling it. For instance, state 1 (NNN) means that the Federal government does not choose to continue a nationalwide accord, the Provincial government does not lift the ban, and the support groups do not appeal. Movements: One DM can unilaterally change its selection of options to cause a conflict move from one state to another state, when the other DMs’ choices are fixed. The movement in one step by a DM is referred to as a unilateral move (UM). A UM is defined as a unilateral improvement (UI) when this move is beneficial to the focal DM. For example, assume that the status quo of the conflict is at state 1 (NNN). If the

Table 1 DMs and options of the Gisborne conflict DMs Federal government of Canada

Options 1. Continue

Provincial government of Newfoundland and Labrador Support groups

2. Lift

Explanation Continue a Canada-wide accord on the prohibition of bulk water exports Lift the ban on bulk water export

3. Appeal

Appeal for continuation of the project

Table 2 Feasible states of the Gisborne conflict Federal 1. Continue Provincial 2. Lift Support 3. Appeal State number

N

Y

N

Y

N

Y

N

Y

N

N

Y

Y

N

N

Y

Y

N 1

N 2

N 3

N 4

Y 5

Y 6

Y 7

Y 8

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Federal government decides to continue a nation-wide accord, its choice changes from N to Y, and the conflict thereby moves from state 1 (NNN) to state 2 (YNN). Therefore, this move is called a UM by the Federal government, as indicated by a bidirectional line connecting states 1 and 2 in Fig. 1. Similarly, one can find all UMs taken by each DM, as shown in Fig. 1, in which DMs’ names are labeled to distinguish UMs by different DMs. Preference: One DM would favor certain specific states based on its value systems. A number of techniques are developed to elicit the preference ranking of each DM over the feasible states (Fraser and Hipel 1988; Hipel et al. 1997; Peng et al. 1997). Pairwise comparison technique is a simple but powerful method for preference elicitation. For instance, between states 1 (NNN) and 2 (YNN), the Federal government prefers to continue a nation-wide accord, which leads to state 2 being more preferred to state 1 (2 > 1) by the Federal government. By utilizing this pairwise comparison technique, one can determine the rankings between any pair of states and aggregate them into one complete preference ranking for each DM, as illustrated in Table 3. This ranking will be utilized for stability analysis in the following sections. Once the above input information is obtained, it is possible to calculate the stability and equilibrium results by utilizing a conflict analysis engine, which contains a number of solution concepts, describing how DMs could behave under conflict. For instance, Nash stability (Nash 1950, 1951) describes a situation in which one cannot move to a better state from the current one. Sequential stability

Fig. 1 Integrated graph model for the Gisborne conflict Table 3 Preference ranking of each DM and an economically oriented provincial government DMs Federal Provincial Support

Preference ranking 2>6>4>8>1>5>3>7 3>7>4>8>1>5>2>6 3>4>7>8>5>6>1>2

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(Fraser and Hipel 1979) captures the key characteristics of a situation in which all of a focal DM’s UIs are blocked by UIs of the sanctioning DMs.

Overview of Advances in the Graph Model for Conflict Resolution A significant number of expansions beyond the basic model (individual stability and coalition stability) have been made over the past three decades to enable GMCR to handle more complex situations, as listed in Table 4. Two major expansions, matrix formulation (third point in Table 4) and preference uncertainty (first point in Table 4), are explained in detail with examples in the following sections of this chapter. Moreover, the recently proposed system perspectives for analyzing a conflict, comprising forward GMCR, inverse GMCR (11th point in Table 4 List of advances in the GMCR Advances 1. Preference uncertaintya

2. Degrees of preferences 3. Matrix formulationa 4. Coalition analysis 5. Hypergame analysis 6. Attitude analysis 7. Emotions 8. Evolution of a conflict 9. Hierarchical conflict 10. Power asymmetry 11. Inverse GMCRa

12. Behavioral GMCR 13. Decision support systems a

Explanation When part or all of the preference information is unknown (Li et al. 2004), fuzzy (Bashar et al. 2012), grey (Kuang et al. 2015), probabilistic (Rêgo and dos Santos 2015), and any combination of the above kinds of preference uncertainty DMs may strongly prefer one state over another (Hamouda et al. 2004, 2006) Matrices are utilized to store movement and preference information and to facilitate stability calculations (Xu et al. 2009, 2018) A set of DMs work together to benefit members of the group (Kilgour et al. 2001; Inohara and Hipel 2008a, b; Zhu et al. 2018) Misperceptions exist among DMs (Wang et al. 1988, 1989; Aljefri et al. 2018) DMs’ preferences are modeled by positive, neutral, negative attitudes toward one another (Inohara et al. 2007; Bernath Walker et al. 2009) How emotions can affect the stability of outcomes (Obeidi et al. 2005) How a conflict can evolve over time (Li et al. 2005) Conflicts may have multiple levels (He et al. 2017) DMs may have a leader-follower relationship (Yu et al. 2015) Determine what preference information is required to make a specific outcome stable (Hipel et al. 2015; Kinsara et al. 2015a; Garcia and Hipel 2017; Wang et al. 2018) When input and output are known, it is possible to determine DMs’ behavior (Wang et al. 2017) A set of computer programs to facilitate the decision-making process using GMCR (Hipel et al. 1997, 2008; Fang et al. 2003a, b; Kinsara et al. 2015b)

Addressed in this chapter

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Table 4), and behavioral GMCR, constitute important opportunities for future innovation.

Matrix Formulation As mentioned in section “Basics of the Graph Model for Conflict Resolution”, movement and preference information can be stored and represented in matrices. In this section, it is explained how to mathematically define key components of GMCR in matrix form and how to use matrix form to facilitate the calculation process. In fact, the matrix formulation constitutes one of the most significant enhancements to the GMCR approach. Definition 2 Movement matrices: In a graph model, let Ji and J þ i denote m  m 0–1 matrices representing the unilateral moves and unilateral improvements of DM i, respectively, as follows: ( J i ðs, qÞ ¼ ( Jþ i ðs, qÞ

¼

1, 0,

if ðs, qÞ  Ai otherwise,

1,

if J i ðs, qÞ ¼ 1 and qi s

0,

otherwise:

,¼  ¼ Definition 3 Preference matrices: In a graph model, let Pþ be the i , Pi , Pi and Pi four m  m preference matrices for DM i whose entry (s, q) for which s, q  S is defined as follows:

( Pþ i ðs, qÞ

¼

1, 0,

( P i ðs, qÞ ¼

1,

if si q

0,

otherwise,

1,

if qi s and q 6¼ s otherwise,

( P¼ i ðs, qÞ ¼

0, (

 ,¼ Pi ðs,qÞ

¼

if qi s otherwise,

1  Pþ i ðs,qÞ, 0,

For the above definitions, it ,¼  ¼ Pþ ð s, s Þ ¼ P ð s, s Þ ¼ P ð s, s Þ ¼ P ð s, s Þ ¼ 0. i i i i

if q 6¼ s otherwise:

is

assumed

that

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Definition 4 Joint improvement matrix: In a graph model, the unilateral improvement matrix for a coalition H is the m  m matrix with (s, q) entries: ( Mþ H ðs, qÞ

¼

1,

if q  Rþ H ðsÞ

0,

otherwise:

where Rþ H ðsÞ is the set of unilateral improvements by H. Note that when there exists þ only one DM in H, say DM k, then Mþ H ¼ Jk . For the Gisborne conflict, each DM’s preference matrices are given below. For example, Pþ Fed ð1, 2Þ ¼ 1 indicates that the Federal government prefers state 2 to 1, as explained in section “Basics of the Graph Model for Conflict Resolution” and indicated in Table 3. 2

Pþ Fed

6 60 6 6 61 6 6 60 6 ¼6 61 6 6 60 6 6 61 4 2

Pþ Sup

0

1 0

1

0

1 0

0 0

0

0

0 0

1 0

1

1

1 0

1 0

0

0

1 0

1 0

1

0

1 0

1 0

0

0

0 0

1 1

1

1

1 0

0 1 0 1 0 1 0 0 0 1 1 1 1 1

6 61 6 6 60 6 6 60 6 ¼6 60 6 6 60 6 6 60 4 0

0

1

1 1

1

1

0

0

0 0

0

0

0

1

0 0

0

0

0

1

1 0

0

1

0

1

1 1

0

1

0

1

1 0

0

0

0

1

1 0

0

1

1

3

2

0

7 6 61 07 7 6 7 6 7 60 17 6 7 6 60 07 7 þ 6 7, PPro ¼ 6 7 61 17 6 7 6 7 61 07 6 7 6 7 60 15 4 0 0 3 1 7 17 7 7 07 7 7 07 7 7: 17 7 7 17 7 7 07 5 0

1 1

3

0

1 1

0

0

0

1 1

1

0

0

0 0

0

0

0

1 0

0

0

0

1 1

0

0

1

1 1

1

0

0

1 0

0

0

7 1 17 7 7 0 07 7 7 1 07 7 7, 1 17 7 7 1 17 7 7 0 07 5

0

1 1

0

0

1 0

Each DM’s UM and UI matrices are given below. Consider states 1 and 2, as explained in section “Basics of the Graph Model for Conflict Resolution”, move from states 1 to 2 is a UM for the Federal government, therefore JFed(1, 2) = 1. Because state 2 is more preferred to state 1, this move is also a UI, therefore Jþ Fed ð1, 2Þ ¼ 1.

Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and. . .

0 61 6 6 60 6 60 6 ¼6 60 6 60 6 6 40

1 0

0 0

0 0 0 0

0 0

0 0

0 0

0 1

1 0 0 0

0 0

0 0

0

0

0 0

1

0

0 0

0 0

0 1 0 0

0 0

0 0

3 2 0 0 7 6 07 60 7 6 60 07 7 6 7 60 07 þ 6 7, J Fed ¼ 6 60 07 7 6 7 60 07 6 7 6 40 15

0

0

0

0 0

0

1

0

0

0

1

0 0

0

0

0

0 0

0 0

1 0 0 0

0 0

0 0

1 0

0 0

0 0 0 0

0 0

0 1

0

0

0 0

0

0

0 0

0 0

0 1 0 0

0 1

0 0

0 0

0 0

0 0

1 0

0 0 1 0

0 0

0 0

0 0

0 0

0 1 0 0

0

0

0

0

0 0

1 0

0 1

0 0

0 0

0 0 0 0

3 2 0 0 7 6 07 60 7 6 60 07 7 6 7 60 17 þ 6 7, J Sup ¼ 6 60 07 7 6 7 60 07 6 7 6 40 05

0 0

0

1

0

0 0

0

2

J Fed

2

J Pro

60 6 6 61 6 60 6 ¼6 60 6 60 6 6 40 0 2

J Sup

0 60 6 6 60 6 60 6 ¼6 61 6 60 6 6 40

3

2

605

1 0

0 0

0 0

0 0 0 0

0 0

0 0

0 0

1 0

0 0 0 0

0 0

0

0

0

0 1

0

0 0

0 0

0 0

0 0 0 0

0 0

3 0 07 7 7 07 7 07 7 7 07 7 07 7 7 15

0

0

0

0

0 0

0

0

0

0

1

0

0 0

0

0

0 0

0 0

1 0

0 0 0 0

0 0

0 0

0 0

0 0

0 0 0 0

0 1

0

0

0

0 0

0

0 0

0 0

0 0

0 0 0 0

0 0

0 0

0 0 0 0

1 0

0 1

0 0

0 0 0 0

0 0

0 0

0

0 0

0

0

0 0

0 0 1 0

0 0

0 0

3 0 0 0 07 7 7 0 07 7 0 07 7 7 0 07 7 0 07 7 7 0 05

0

0 1

0

0

0 0

60 07 7 6 7 6 7 60 0 7 6 7 60 07 þ 6 7, J Pro ¼ 6 60 07 7 6 7 60 17 6 7 6 5 40 0 0 0

0

3

07 7 7 07 7 07 7 7 07 7 17 7 7 05 0

Detailed stability analyses with illustrative examples will be given in the next section when preference uncertainty is considered.

Preference Uncertainty Preference uncertainty, which is commonly observed in many real-world conflicts, can be modeled in different ways, such as fuzzy, grey, and probabilistic preference structures. In this chapter, two ways for modeling preference uncertainty are provided. One way is to model it by scenario analysis with crisp preferences, and the other way is to introduce fuzzy set techniques (Zadeh 1965) into GMCR.

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Two Scenarios of Uncertainty with Crisp Preferences Two different scenarios are considered to model preference uncertainty with crisp preference. In one scenario, the Provincial government is assumed to be economically oriented, which implies that the Provincial government prefers to have economic returns rather than to preserve the environment by prohibiting bulk water exports. In the other scenario, the Provincial government is assumed to be environmentally oriented, which indicates that it prefers to prohibit bulk water exports. The preferences of the Provincial government differ under two different assumptions. Stability results are determined and compared in these two scenarios. In the economically oriented scenario, the preferences of the Provincial government are the same as listed in Table 3: 3 > 7 > 4 > 8 > 1 > 5 > 2 > 6, while its preferences in the environmentally oriented scenario are: 2 > 6 > 1 > 5 > 4 > 8 > 3 > 7. Theorem 1 Nash stability: Define MNash ¼ Jþ i i  E, where E denotes the m  m matrix with each entry equal to 1. State s  S is Nash stable for DM i iff MNash ðs, sÞ ¼ 0. i 2

MNash Pro

0 0 1 0 0 0 0 0

6 60 6 6 60 6 6 60 6 þ ¼ J Pro  E ¼ 6 60 6 6 60 6 6 60 4 0 2 1 61 6 6 60 6 60 6 ¼6 61 6 61 6 6 40 0

3 2

1 1 1 1 1 1 1 1

7 6 6 0 0 1 0 0 0 07 7 61 7 6 6 0 0 0 0 0 0 07 7 61 7 6 6 0 0 0 0 0 0 07 7 61 76 6 0 0 0 0 0 1 07 7 61 7 6 6 0 0 0 0 0 0 17 7 61 7 6 6 0 0 0 0 0 0 07 5 41 1 0 0 0 0 0 0 0 3 1 1 1 1 1 1 1 1 1 1 1 1 1 17 7 7 0 0 0 0 0 0 07 7 0 0 0 0 0 0 07 7 7 1 1 1 1 1 1 17 7 1 1 1 1 1 1 17 7 7 0 0 0 0 0 0 05 0

0

0

0 0

0

0

3

7 1 1 1 1 1 1 17 7 7 1 1 1 1 1 1 17 7 7 1 1 1 1 1 1 17 7 7 1 1 1 1 1 1 17 7 7 1 1 1 1 1 1 17 7 7 1 1 1 1 1 1 17 5 1 1 1 1 1 1 1

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Nash Nash Nash Since MNash Pro ð3, 3Þ ¼ MPro ð4, 4Þ ¼ MPro ð7, 7Þ ¼ MPro ð8, 8Þ ¼ 0, states 3, 4, 7, and 8 are Nash stable for the Provincial government.

Theorem 2 Sequential stability: Define h   ,¼ T i þ þ ¼ J  E  sign M  Pi MSEQ , i i Nfig where Mþ Nfig is the joint improvement matrix for the set of DMs N{i}, and sign() is the sign function for which the value of the function equals 1 when the entry is positive, 0 when the entry is zero, and 1 when the entry is negative. State s  S is SEQ for DM i, denoted by s  SSEQ , iff MSEQ ðs, sÞ ¼ 0. i i h    ,¼ T i þ þ MSEQ Pro ¼ J Pro  E  sign MNfProg  PPro 2

0 0 1 0 0 0 0 0

3 02

1 1 1 1 1 1 1 1

B6 0 0 1 0 0 0 07 7 B6 1 1 7 B6 0 0 0 0 0 0 0 7 B6 1 1 7 B6 B6 0 0 0 0 0 0 07 7 B6 1 1 7  B6 61 1 0 0 0 0 0 1 07 B 7 B6 B 7 0 0 0 0 0 0 1 7 B6 61 1 7 B6 0 0 0 0 0 0 0 5 @4 1 1 1 1 0 0 0 0 0 0 0 02 3 2 0 0 1 0 0 1 1 0 0 B6 60 B6 0 0 0 0 0 1 0 0 7 7 6 B6 6 B6 0 0 0 1 0 0 0 0 7 7 61 B6 7 6 B6 6 B6 0 0 0 0 0 0 0 0 7 7 61   signB 7 6 B6 0 0 0 0 0 1 0 0 7 6 6 B6 7 60 B6 7 B6 0 0 0 0 0 0 0 0 7 6 60 B6 6 B4 0 0 1 1 0 0 0 1 7 5 41 @ 0 0 0 1 0 0 0 0 1 3 2 1 1 0 1 1 1 0 1 61 1 1 1 1 1 1 17 7 6 7 6 60 0 0 0 0 0 0 07 7 6 60 0 0 0 0 0 0 07 7 6 ¼6 7 61 1 0 0 1 1 0 17 7 6 61 1 0 1 1 1 0 17 7 6 7 6 40 0 0 0 0 0 0 05 60 6 6 60 6 60 6 ¼6 60 6 60 6 6 40 0

0

0

0 0

0

0

0 0

3

1 1 1 1 1 17 7 7 1 1 1 1 1 17 7 1 1 1 1 1 17 7 7 1 1 1 1 1 17 7 1 1 1 1 1 17 7 7 1 1 1 1 1 15 1 1 1 1 1 1

3T 11 CC C 07 7 C C 7 C C 1 7 CC 7 CC C C 17 7 C C 7 CC 7 0 CC 7 CC C C 07 7 C C 7 C C 1 5 AC A 0

1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0

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SEQ SEQ SEQ Note that since MSEQ Pro ð3, 3Þ ¼ MPro ð4, 4Þ ¼ MPro ð7, 7Þ ¼ MPro ð8, 8Þ ¼ 0, states 3, 4, 7, and 8 are SEQ stable for the Provincial government. Table 5 shows the Nash and SEQ stability and equilibria results under the two scenarios, for which the stabilities for the Provincial government are different. More specifically, under the scenario with an economically oriented Provincial government, states 3, 4, 7, 8 are stable for the Provincial government. While states 1, 2, 5, 6 are stable for an environmentally oriented Provincial government. Accordingly, the equilibrium under the economically oriented scenario is state 4, while under the environmentally oriented scenario, state 6 is the final equilibrium.

Fuzzy Preferences Definition 5 Fuzzy Relative Certainty of Preference Matrix Let s, q  S and i  N, ri(s, q) refers to the preference degree of state q over s for DM i. Then, a m  m matrix that represents the Fuzzy Relative Certainty of Preference Matrix (FRCPM) for DM i in which the element in sth row and qth column is defined as: αi ðs, qÞ ¼ r i ðs, qÞ  r i ðq, sÞ Table 5 Stability and equilibria results of the two scenarios Economically oriented scenario

Environmentally oriented scenario

States 1 2 3 4 5 6 7 8 States 1 2 3 4 5 6 7 8

Nash Fed Pro

Sup

Eq

√ √

√ √ √ √

√

Sup

√ Nash Fed Pro √ √ √ √ √ √

Sup

√

√ √

√ √ √ √

√

√ √

√

Pro

Eq

√ √ √

√

√

SEQ Fed

Eq

√ SEQ Fed √

√ √ √ √

√ √ Pro √ √

√ √

√ √

√

√ √

Sup

√ √ √ √ √ √

Eq

√

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609

Definition 6 Fuzzy Preference Matrices: In a graph model with fuzzy preferences,  ¼ let γ i be a Fuzzy Satisficing Threshold (FST) (0 < γ i  1). Let Pþ i , Pi , Pi be three m  m 0–1 preference matrices for DM i whose entry (s, q) for which s, q  S is defined as follows: ( Pþ i ðs, qÞ

¼ (

P i ðs, qÞ ¼

P¼ i ðs, qÞ ¼

1, 0,

if αi ðs, qÞ > γ i otherwise,

1,

if αi ðs, qÞ < γ i

0, ( 1, 0,

otherwise, if αi ðs, qÞ ¼ γ i otherwise:

Definition 7 Fuzzy Unilateral Improvement Matrix: Let s, q  S and i  N. Then, a m  m 0–1 matrices that represent an FUI matrix of DM i are defined as: ( FJ þ i ðs, qÞ ¼

1, 0,

if ðs, qÞ  Ai and αi ðs, qÞ γ i otherwise:

Definition 8 Fuzzy Nash Stability: Define MFNash ¼ FJ þ i  E, where E denotes the i m  m matrix with each entry being set to 1. State s  S is Fuzzy Nash stable (or FNash) for DM i iff MFNash ðs, sÞ ¼ 0. i Definition 9 Fuzzy Sequential Stability: Define M FSEQ ¼ FJ þ i i h   i   T þ þ  E  sign M Nfig  Pi , where MNfig is the joint improvement matrix for the set of DMs N{i}, and sign() is the sign function for which the value of the function equals 1 when the entry is positive, 0 when the entry is zero, and 1 when the entry is negative. State s  S is fuzzy sequential stable (or FSEQ) for DM i, , iff MFSEQ ðs, sÞ ¼ 0. denoted by s  SSEQ i i Example For the Gisborne conflict, the stability analyses with fuzzy preferences are given below. First of all, the preference information of the Federal government and Support groups are assumed to be crisp, while the Provincial government’s preferences are fuzzy. The preference degree matrices for Federal government and Support groups are:

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rFed

states 1 2 3 ¼ 4 5 6 7 8

2 1 0:5 6 0 6 6 1 6 6 0 6 6 1 6 6 0 6 4 1 0

2 1 0:5 1 1 1 1 1 1

3 0 0 0:5 0 0 0 1 0

rSup

states 1 2 3 ¼ 4 5 6 7 8

21 0:5 6 1 6 6 0 6 6 0 6 6 0 6 6 0 6 4 0 0

2 0 0:5 0 0 0 0 0 0

3 4 1 1 1 1 0:5 0 1 0:5 1 1 1 1 1 1 1 1

4 1 0 1 0:5 1 0 1 1

6 1 0 1 1 1 0:5 1 1

7 8 3 0 1 0 0 7 7 0 1 7 7 0 0 7 7 0 1 7 7 0 0 7 7 0:5 1 5 0 0:5

5 6 1 1 1 1 0 0 0 0 0:5 0 1 0:5 0 0 0 0

7 83 1 1 1 1 7 7 0 0 7 7 0 0 7 7 1 1 7 7 1 1 7 7 0:5 0 5 1 0:5

5 0 0 1 0 0:5 0 1 0

The Provincial government’s preference degrees of one state over another state are obtained from utilizing a fuzzy option prioritization technique proposed by Bashar et al. (2014). Table 6 shows a set of preference statements from most preferred on the top to least preferred at the bottom. Specifically, the Provincial government most prefers to lift the ban, next prefers that the Federal government not continue its national-wide accord, and then does not prefer to see an appeal from the Support groups. Based on these three preference statements, a series of fuzzy truth values can be assigned to each statement at a given state, as listed in Table 7. For example, starting from state 1, the first digit of 0.8 indicates that the truth degree of the first statement for the Provincial government is 0.8, and the second and third digits of 1 imply that the second and third statements are 100% true for the Provincial government. Likewise, a digit of 0 means a statement is false for a DM at a particular state. Generally, a higher fuzzy truth value indicates that a DM is more certain about a statement. Based on the fuzzy truth values given in Table 7, the preference degree matrix (rPro) and the fuzzy relative certainty of preference matrix (αPro) for the Provincial government can be calculated according to Definition 5: Table 6 Preference statements of the Provincial government from most to least importance Preference statements 2 1 3

Interpretation Provincial government most prefers to lift the ban Provincial government would like Federal government not to continue a national-wide prohibition accord Provincial government prefers not to see appeals from support group

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Table 7 Fuzzy truth values of preference statements of Provincial government States 1 2 3 4 5 6 7 8

Fuzzy truth values of preference statements of Provincial government at each state (0.8, 1, 1) (0.5, 0.5, 1) (1, 1, 1) (0.8, 0.5, 1) (0, 0, 0) (0.25, 0.25, 0) (0.5, 0.2, 0) (0.8, 0.5, 0)

rPro

states 1 2 3 ¼ 4 5 6 7 8

2 1 0:5 6 1 6 6 0 6 6 0:78 6 6 1 6 6 1 6 4 1 1 2

αPro

states 1 2 3 ¼ 4 5 6 7 8

2 3 0 1 0:5 1 0 0:5 0:27 1 1 1 0:98 1 0:78 1 0:46 1

1 2 0 1 6 1 0 6 6 1 1 6 6 0:56 0:46 6 6 1 1 6 6 1 0:96 6 4 1 0:56 1 0:08

4 0:22 0:73 0 0:5 1 1 1 0:72

3 4 1 0:56 1 0:46 0 1 1 0 1 1 1 1 1 1 1 0:44

5 0 0 0 0 0:5 0 0 0

6 0 0:02 0 0 1 0:5 0:32 0

5 1 1 1 1 0 1 1 1

7 0 0:22 0 0 1 0:68 0:5 0:13

8 3 0 0:54 7 7 0 7 7 0:28 7 7 1 7 7 1 7 7 0:87 5 0:5

6 7 1 1 0:96 0:56 1 1 1 1 1 1 0 0:36 0:36 0 1 0:74

8 3 1 0:08 7 7 1 7 7 0:44 7 7 1 7 7 1 7 7 0:74 5 0

According to Definition 7, when γ Pro=0.3, αPro(1, 3) = 1, which is greater than 0.3, FJ þ Pro ð1, 3Þ ¼ 1: Similarly, one can calculate the complete fuzzy unilateral improvement matrix for the Provincial government as:

FJ þ Pro

states 1 2 3 ¼ 4 5 6 7 8

21 0 60 6 60 6 60 6 60 6 60 6 40 0

2 0 0 0 0 0 0 0 0

3 1 0 0 0 0 0 0 0

4 0 1 0 0 0 0 0 0

5 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0

7 0 0 0 0 1 0 0 0

83 0 07 7 07 7 07 7 07 7 17 7 05 0

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Based on Definition 8, Fuzzy Nash stability for the Provincial government is: ¼ FJ þ MFNash Pro Pro  E 2 0 0 1 60 0 0 6 6 60 0 0 6 60 0 0 6 ¼6 60 0 0 6 60 0 0 6 6 40 0 0

2

0 1

0 0 0 0

0 0

0 0

0 0 0 0

0 0

0

0 0

1

0 0

0 0 0 0

0 0

3 2 1 0 61 07 7 6 7 6 07 61 7 6 6 07 7 61 76 07 61 7 6 6 17 7 61 7 6 05 41

0 0

0

0 1

0 0

0

0

1

1

1

1 1

1

1

1 0

1 0

1 1 0 0

1 0

1 0

0 1

0 1

0 0 1 1

0 1

0 1

1

1

1 1

1

1

0 0

0 0

0 0 0 0

0 0

0 0

61 6 6 60 6 60 6 ¼6 61 6 61 6 6 40 0

1

1 1

1 1

1 1

1 1 1 1

1 1

1 1

1 1

1 1

1 1 1 1

1 1

1

1

1

1 1

1

1 1

1 1

1 1

1 1 1 1

1 1

3 1 17 7 7 17 7 17 7 7 17 7 17 7 7 15

1

1

1

1 1

1

1

3

17 7 7 07 7 07 7 7 17 7 17 7 7 05 0

FNash FNash FNash Since MFNash Pro ð3, 3Þ ¼ MPro ð4, 4Þ ¼ MPro ð7, 7Þ ¼ MPro ð8, 8Þ ¼ 0, states 3, 4, 7, and 8 are Fuzzy Nash stable for the Provincial government. When γ Pro=0.8, the fuzzy unilateral improvement matrix of the Provincial government according to Definition 7:

FJ þ Pro

states 1 2 3 ¼ 4 5 6 7 8

21 0 60 6 60 6 60 6 60 6 60 6 40 0

2 0 0 0 0 0 0 0 0

3 1 0 0 0 0 0 0 0

4 0 0 0 0 0 0 0 0

5 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0

7 0 0 0 0 1 0 0 0

83 0 07 7 07 7 07 7 07 7 17 7 05 0

Then the Fuzzy Nash stability for the Provincial government is:

Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and. . .

MFNash ¼ FJ þ Pro Pro  E 2 0 0 1 60 0 0 6 6 60 0 0 6 60 0 0 6 ¼6 60 0 0 6 60 0 0 6 6 40 0 0

2

0 0

0 0 0 0

0 0

0

0 0

0

0 0

0 0 0 0

0 1

0 0

0 0 0 0

0 0

3 2 1 0 61 07 7 6 7 6 07 61 7 6 6 07 7 61 76 07 61 7 6 6 17 7 61 7 6 05 41

0 0

0

0 1

0 0

0

0

1

1

1

1 1

1

1

0 0

0 0

0 0 0 0

0 0

0 0

0

0

0 0

0

0

1 1

1 1

1 1 1 1

1 1

1 1

0 0

0 0

0 0 0 0

0 0

0 0

60 6 6 60 6 60 6 ¼6 61 6 61 6 6 40 0

1

613

1 1

1 1

1 1

1 1 1 1

1 1

1

1

1

1 1

1

1 1

1 1

1 1

1 1 1 1

1 1

1 1

1 1

1 1

1 1 1 1

1 1

3 1 17 7 7 17 7 17 7 7 17 7 17 7 7 15

1

1

1

1 1

1

1

3

07 7 7 07 7 07 7 7 17 7 17 7 7 05 0

FNash FNash FNash FNash Since M FNash Pro ð2,2Þ ¼ M Pro ð3,3Þ ¼ M Pro ð4,4Þ ¼ M Pro ð7,7Þ ¼ M Pro ð8,8Þ ¼ 0, states 2, 3, 4, 7, and 8 are Fuzzy Nash stable for the Provincial government. It can be seen that state 2 is an additional stability for the Provincial government when the fuzzy satisficing threshold increases from 0.3 to 0.8. In other words, the change of threshold may result in different stability outcomes. Similarly, one can calculate the SEQ stability based on the aforementioned definitions. Specifically, the joint improvement matrix (Definition 4) and fuzzy unilateral improvement matrix (Definition 7) for the Provincial government are:

FJ þ Pro

states 1 2 3 ¼ 4 5 6 7 8

21 0 60 6 60 6 60 6 60 6 60 6 40 0

2 0 0 0 0 0 0 0 0

3 1 0 0 0 0 0 0 0

4 0 1 0 0 0 0 0 0

5 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0

7 0 0 0 0 1 0 0 0

83 0 07 7 07 7 07 7 07 7 17 7 05 0

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Mþ N fProg

states 1 2 3 ¼ 4 5 6 7 8

21 0 60 6 60 6 60 6 60 6 60 6 40 0

2 1 0 0 0 0 0 0 0

states 2 1 2 0 1 1 60 0 2 6 61 1 3 6 60 1 4 By Definition 5, P ¼ Pro 6 60 0 5 6 60 0 6 6 40 0 7 0 1 8 When γPro=0.3, based on Definition 9, government can be calculated as follows:

3 0 0 0 0 0 0 1 0

4 0 0 1 0 0 0 1 1

5 1 0 0 0 0 0 0 0

3 0 0 0 0 0 0 0 0 the

4 5 1 1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 SEQ

6 1 1 0 0 1 0 0 0

7 0 0 0 0 0 0 0 0

6 7 1 1 1 1 1 1 1 1 0 0 0 0 1 0 1 1 stability

83 0 07 7 07 7 07 7 07 7 07 7 15 0 83 1 17 7 17 7 17 7 07 7 07 7 05 0 for the Provincial

   T  þ þ  ¼ FJ  E  sign M  P MFSEQ Pro Pro pro NfProg 2

0 60 6 6 60 6 60 6 ¼6 60 6 60 6 6 40

3 02 1 0 1 0 0 0 0 0 B 6 7 0 0 1 0 0 0 0 7 B6 1 7 B6 0 0 0 0 0 0 0 7 B6 1 7 B6 B6 0 0 0 0 0 0 07 7 B6 1 7  B6 61 0 0 0 0 0 1 07 B 7 B6 B 7 0 0 0 0 0 0 1 7 B6 61 7 B6 0 0 0 0 0 0 0 5 @4 1

0 0 0 0 0 0 0 0 02 0 1 0 0 1 1 0 B6 B6 0 0 0 0 0 1 0 B6 B6 0 0 0 1 0 0 0 B6 B6 B6 0 0 0 0 0 0 0  signB B6 0 0 0 0 0 1 0 B6 B6 B6 0 0 0 0 0 0 0 B6 B6 4 @ 0 0 1 1 0 0 0 0 0 0 1 0 0 0

3 1 1 1 1 1 1 1 1 1 1 1 1 1 17 7 7 1 1 1 1 1 1 17 7 1 1 1 1 1 1 17 7 7 1 1 1 1 1 1 17 7 1 1 1 1 1 1 17 7 7 1 1 1 1 1 1 15

1 1 3 2 0 0 7 6 07 60 7 6 07 61 7 6 6 07 7 60 76 6 07 7 60 7 07 6 60 7 6 15 40 0

1 1 1 1 1 1

3T 1 1 CC C 17 7 C 7 CC C 17 C C 7 C CC 7 1 7 CC C 7 C CC 07 C 7 CC C C 07 7 C C 7 CC 0 5 AC A 0

1 0 1 1 1 1 1 0 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0

0 0 0 1 1 0 0 1 0 0 1 1 1

Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and. . .

0 61 6 6 60 6 60 6 ¼6 60 6 60 6 6 40

1 1

0 1 1 1

1 1

1 1

0

0 0

0

0

0 0

0 0 0 0

0 1

0 1

1 0

0 1 0 0

1 0

1 0

3 1 1 1 17 7 7 0 07 7 0 07 7 7 1 17 7 1 17 7 7 0 05

0

0

0 0

0

0

0 0

2

615

FSEQ FSEQ FSEQ FSEQ Since M FSEQ Pro ð1,1Þ ¼ M Pro ð3,3Þ ¼ M Pro ð4,4Þ ¼ M Pro ð7,7Þ ¼ M Pro ð8,8Þ ¼ 0, states 1, 3, 4, 7, and 8 are Fuzzy SEQ stable for the Provincial government. In comparison to the Fuzzy Nash stability with the same fuzzy satisficing threshold, state 1 is an additional stability for the Provincial government. When γPro=0.8, the steps for calculating SEQ stability for the Provincial government are:

FJ þ Pro

states 1 2 3 ¼ 4 5 6 7 8

21 0 60 6 60 6 60 6 60 6 60 6 40 0

2 0 0 0 0 0 0 0 0

3 1 0 0 0 0 0 0 0

4 0 0 0 0 0 0 0 0

5 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0

7 0 0 0 0 1 0 0 0

83 0 07 7 07 7 07 7 07 7 17 7 05 0

Mþ N fProg

states 1 2 3 ¼ 4 5 6 7 8

21 0 60 6 60 6 60 6 60 6 60 6 40 0

2 1 0 0 0 0 0 0 0

3 0 0 0 0 0 0 1 0

4 0 0 1 0 0 0 1 1

5 1 0 0 0 0 0 0 0

6 1 1 0 0 1 0 0 0

7 0 0 0 0 0 0 0 0

83 0 07 7 07 7 07 7 07 7 07 7 15 0

By Definition 5, P Pro

states 1 2 3 ¼ 4 5 6 7 8

21 0 60 6 61 6 61 6 60 6 60 6 40 0

2 1 0 1 1 0 0 1 1

3 0 0 0 0 0 0 0 0

4 1 1 1 0 0 0 0 1

5 1 1 1 1 0 1 1 1

6 1 1 1 1 0 0 1 1

7 1 1 1 1 0 1 0 1

83 1 17 7 17 7 17 7 07 7 07 7 15 0

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MFSEQ Pro

¼

FJ þ Pro 2



  T  þ   E  sign MNfProg  Ppro

0 0 1 0 0 0 0 0

60 0 6 6 60 0 6 60 0 6 ¼6 60 0 6 60 0 6 6 40 0 0 0 02 0 B6 B6 0 B6 B6 0 B6 B6 B6 0  signB B6 0 B6 B6 B6 0 B6 B6 @4 0

3 02

B6 0 0 0 0 0 07 7 B6 1 1 7 B6 0 0 0 0 0 0 7 B6 1 1 7 B6 B6 0 0 0 0 0 07 7 B6 1 1 7  B6 B6 0 0 0 0 1 07 7 B6 1 1 6 7 0 0 0 0 0 17 B B6 1 1 7 B6 0 0 0 0 0 0 5 @4 1 1 1 1 0 0 0 0 0 0 3 2 0 1 0 0 1 1 0 0 60 0 0 0 0 1 0 07 7 6 7 6 0 0 1 0 0 0 07 61 7 6 6 0 0 0 0 0 0 07 7 61 76 0 0 0 0 1 0 07 60 7 6 6 0 0 0 0 0 0 07 7 60 7 6 0 1 1 0 0 0 15 40

0 0 0 1 0 0 0 0 0 60 6 6 60 6 60 6 ¼6 60 6 60 6 6 40

0 0 0 0

1 0

1 0

1 1 0 0

0 0

0

0

0 0

0 0 0 0

0 0

0 1

0 0 1 0

0 0 0 0

1 0

1 0

1 1 0 0

3 0 07 7 7 07 7 07 7 7 07 7 07 7 7 05

0

0 0

0

0

0 0

0

2

1 1 1 1 1 1 1 1

3

1 1 1 1 1 17 7 7 1 1 1 1 1 17 7 1 1 1 1 1 17 7 7 1 1 1 1 1 17 7 1 1 1 1 1 17 7 7 1 1 1 1 1 15 1 1 1 1 1 1

3 11 1 0 1 1 1 1 1 T CC C 0 0 1 1 1 1 17 7 C C 7 C C 1 0 1 1 1 1 1 7 CC 7 CC C C 1 0 0 1 1 1 17 7 C C 7 CC 7 0 0 0 0 0 0 0 CC 7 CC C C 0 0 0 1 0 1 07 7 C C 7 C C 1 0 0 1 1 0 1 5 AC A 0 1 0 1 1 1 1 0

FSEQ FSEQ FSEQ FSEQ Since M FSEQ Pro ð1,1Þ ¼ M Pro ð2,2Þ ¼ M Pro ð3,3Þ ¼ M Pro ð4,4Þ ¼ M Pro ð7,7Þ ¼ M FSEQ Pro ð8,8Þ ¼ 0 , states 1, 2, 3, 4, 7, and 8 are Fuzzy SEQ stable for the Provincial government. Therefore, when the fuzzy satisficing threshold increases from 0.3 to 0.8, state 2 is an additional SEQ stability for the Provincial government.

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Three System Perspectives of the Graph Model In a conflict analysis, one may not only wish to determine what could happen based on existing information but also would like to know what measures have to be taken in order to achieve a desired outcome. New system perspectives for analyzing a conflict within the GMCR framework have been put forward to handle these scenarios, as displayed in Fig. 2, where the question marks in the boxes of Fig. 2 indicate the information to be determined. The three perspectives on the graph model, consisting of forward GMCR, inverse GMCR, and behavioral GMCR, are explained respectively in the following subsections, with an illustrative example of the inverse GMCR analysis.

Forward GMCR From a forward perspective, one first collects the required input information for a graph model, such as DMs, options, and preferences, then calculates the stability and equilibrium results based on a variety of stability definitions, as shown at the top of Fig. 2. In fact, most of the existing graph model research, including the analysis furnished in sections “Matrix Formulation” and “Preference Uncertainty” of this chapter, falls within the range of forward GMCR. More details about the forward GMCR were discussed in a previous chapter entitled ▶ “Conflict Resolution Using the

Fig. 2 System perspectives of the graph model

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Graph Model: Individuals and Coalitions”. It should be mentioned that three decision support systems (DSSs) are developed to facilitate the computational process: GMCR I, GMCR II (Fang et al. 2003a, b), and GMCR+ (Kinsara et al. 2015b).

Behavioral GMCR When both the input and output can be observed, one can apply behavioral GMCR to obtain the behavioral pattern followed by DMs in a conflict model, as indicated at the bottom of Fig. 2. Behavioral analysis provides a better understanding of how decisions are made by DMs, thereby enabling an analyst to accurately predict potential outcomes from interactions among these DMs in other conflicts. Wang et al. (2017) provide a basic analytical approach for carrying out behavioral analysis. However, this area is ripe for further development, including a new generation of decision support systems (DSS) to facilitate the calculations and furnish strategic insights.

Inverse GMCR Analysis From a backward perspective, one can ascertain the necessary input required in order to reach a desirable or specified equilibrium within a graph model. These procedures are called inverse GMCR, as portrayed in the middle portion of Fig. 2. Inverse GMCR analysis is especially useful when a facilitator is trying to bring about a win/ win outcome to a conflict in a so-called third party intervention. To better illustrate how the inverse GMCR analysis is carried out, the aforementioned water export conflict is utilized as an example. Assume that only part of the preference information of the Provincial government is known. Specifically, the Provincial government does not like to see the support group appealing its decisions. Therefore, the following preference information can be determined: 1 > Pro 5, 2 > Pro 6, 3 > Pro 7, 4 > Pro 8. In the matrix formulation, this means þ þ þ Pþ Pro ð1, 5Þ ¼ PPro ð2, 6Þ ¼ PPro ð3, 7Þ ¼ PPro ð4, 8Þ ¼ 0. The inequality for calculating preferences within inverse GMCR for the case of sequential stability (SEQ) is: Mþ Nfig 



P,¼ i

T

      T  es J Ti  es ∘ Pþ  es i

where Mþ Nfig is a joint improvement matrix for the set of DMs, N{i}, and the symbol ∘ indicates the Hadamard product of two matrices. The term es stands for an m-dimensional column vector in which the sth element is 1 and all other entries are 0, where there are m feasible states. If state 3 (NYN) is a desirable state under SEQ for the Provincial government where the Federal government does not continue its national prohibition accord, the Provincial government lifts the ban, and the Support groups do not appeal. To determine the remaining preference information of the Provincial government, the following matrices are substituted into the inequality:

Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and. . .

2

Mþ N fProg

Mþ Nfig  2

0 60 6 60 6 60 ¼6 60 6 60 6 40 0 

0

60 6 6 60 6 60 6 6 60 6 60 6 6 40

P,¼ i

1 0 0 0 0 0 0 0 T

0 0 0 0 0 0 1 0

0 0 1 0 0 0 1 1

1 0 0 0 0 0 0 0

1 1 0 0 1 0 0 0

0 0 0 0 0 0 0 0

3 2 0 0 0 1 60 0 0 07 7 6 61 0 0 07 7 6 6 07 7, J Pro ¼ 6 0 1 0 60 0 0 07 7 6 60 0 0 07 7 6 40 0 0 15 0 0 0 0

0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 1

0 0 0 0 1 0 0 0

3 0 07 7 07 7 07 7 07 7 17 7 05 0

2 31 0 B 7 7C 6 07 B 6 0 7C 7 B 6 7C 6 1 7C 07 B 7 B 6 7C B 7 7C 0 7 B ,¼ T 6 6 0 7C 7  B PPro  6 7C 6 0 7C 07 B 7 B 6 7C B 7 6 0 7C 07 B 6 7C 7 B 6 7C 4 0 5A 15 @ 3 0

0 0

1

1

0 0

0

0 0

0

1

0

0 0

0 1 0 0

0 0

0 0

0 0

0 0

0 0 0 0

0 0

1 0

0 0

0

1 1

0

0

0

1

0

0

0 0

0 0

1 0

0 0 1 0

0 0

0 0

0

0

0 0

0

0

1 0

0 0

0 0 0 0

0 0

0 1

0 0

0 0

0 0 0 1

0 0

0 0

0

0

0 0

1

0

0 0 02 0 B6 B6 0 B6 B6 1 B6 B6 B6 0 B B6 0 B6 B6 B6 0 B6 B6 4 @ 0 0

0 1 0 0 0 0 0 0

      T  es J Ti  es ∘ Pþ  es i

1

0

619

0 3T 2 31 0 0 0 C B 7 6 07 607 B 7C 7 6 7C B C 7 B 7 6 0 1 7 6 7C C B 7 7 6 T 0 7 6 0 7C B B ∘B P þ 7  6 7C Pro C 0 7 6 0 7C B 7 6 7C B 6 7 B 17 7 6 0 7C B 7 6 7C B 0 5 4 0 5C A @ 0 0

2 31 0 6 0 7C 6 7C 6 7C 6 1 7C 6 7C 6 0 7C 6 7C  6 7C 6 0 7C 6 7C 6 0 7C 6 7C 6 7C 4 0 5A 0

0 60 6 6 60 6 60 6 6 60 6 60 6 6 40

1 0

0 0 0 0

1 0

1 1

0 0

0 1 0 0

0 0

0 0

0

0 0

0

1

0 0

0 0 1 1

0 0

0 0

3 2 ,¼ 3 3 2 3 2 þ PPro ð3, 1Þ 0 0 1 PPro ð3, 1Þ 7 7 6 7 6 þ 6 ,¼ 0 07 7 6 PPro ð3, 2Þ 7 6 0 7 6 PPro ð3, 2Þ 7 7 6 ,¼ 7 7 6 7 6 þ 0 0 7 6 PPro ð3, 3Þ 7 6 0 7 6 PPro ð3, 3Þ 7 7 6 7 7 6 7 6 7 7 6 7 6 þ 6 ,¼ 0 07 7 6 PPro ð3, 4Þ 7 6 0 7 6 PPro ð3, 4Þ 7 7  6 ,¼ 7 7 6 7 ∘6 þ 0 0 7 6 PPro ð3, 5Þ 7 6 0 7 6 PPro ð3, 5Þ 7 7 6 7 7 6 7 6 7 7 6 7 6 þ 6 ,¼ 0 07 7 6 PPro ð3, 6Þ 7 6 0 7 6 PPro ð3, 6Þ 7 7 6 ,¼ 7 7 6 7 6 þ 0 1 5 4 PPro ð3, 7Þ 5 4 0 5 4 PPro ð3, 7Þ 5

0

0

0 1

0

0

0 0

2

P,¼ Pro ð3, 8Þ

0

Pþ Pro ð3, 8Þ

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3 3 2 þ ,¼ ,¼ P,¼ PPro ð3, 1Þ Pro ð3, 2Þ þ PPro ð3, 5Þ þ PPro ð3, 6Þ 7 7 6 6 P,¼ 0 7 7 6 6 Pro ð3, 6Þ 7 7 6 6 ,¼ 7 7 6 6 PPro ð3, 4Þ 0 7 7 6 6 7 7 6 6 0 0 7 7 6 6 7 7 6 6 7 7 6 6 P,¼ ð 3, 6 Þ 0 Pro 7 7 6 6 7 7 6 6 0 0 7 7 6 6 7 7 6 6 ,¼ ,¼ ,¼ 5 4 PPro ð3, 3Þ þ PPro ð3, 4Þ þ PPro ð3, 8Þ 5 4 0 2

P,¼ Pro ð3, 4Þ

0

,¼ ,¼ þ P,¼ Pro ð3, 2Þ þ PPro ð3, 5Þ þ PPro ð3, 6Þ PPro ð3, 1Þ

P,¼ Pro ð3, 6Þ 0 P,¼ Pro ð3, 4Þ 0 ,¼ ,¼ P,¼ Pro ð3, 3Þ þ PPro ð3, 4Þ þ PPro ð3, 8Þ 0

Based on the known preference information, state 3 is more preferred than 7, ,¼ which means Pþ Pro ð7, 3Þ ¼ 1. Therefore, by Definition 1 one has: PPro ðs, qÞ ¼ 1  ,¼ þ PPro ðs, qÞ when s 6¼ q, and PPro ðs, sÞ ¼ 0. The above inequalities can be simplified to: þ þ þ 1  Pþ Pro ð3, 2Þ þ 1  PPro ð3, 5Þ þ 1  PPro ð3, 6Þ PPro ð3, 1Þ

1  Pþ Pro ð3, 6Þ 0 1  Pþ Pro ð3, 4Þ 0 þ 1  Pþ Pro ð3, 4Þ þ 1  PPro ð3, 8Þ 0

The above inequalities can be further reduced to: þ þ þ Pþ Pro ð3, 1Þ þ PPro ð3, 2Þ þ PPro ð3, 5Þ þ PPro ð3, 6Þ  3,

which means that state 3 cannot be SEQ-stable if states 1, 2, 5, 6 are all more preferred than state 3. Specifically, if state 1 is more preferred to state 3, then the move from states 3 to 1 is an UI for the Provincial government, and it will definitely make this move. Then the opponents can make two possible sanctioning moves starting from state 1. One way is to move to state 2 first by the Federal government and then to state 6 by the Support groups, while the other way is to move to state 5 first by the Support groups and then to state 6 by the Federal government. If states 2, 5, 6 are all more preferred to the original state 3, then the Provincial government would be glad to see any state of states 2, 5, and 6 as a final state, which makes the original state 3 unstable.

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Summary In this chapter, three major expansions of GMCR, namely matrix formulation, preference uncertainty, and inverse GMCR, are explained in detail and clearly illustrated using a real-world water export conflict. Preference uncertainty is analyzed in two different ways: discrete scenario analysis and fuzzy preferences. Matrix formulations are used in stability calculations throughout the chapter, including the Inverse GMCR analysis. These expansions enable GMCR to investigate more complicated conflicts and garner meaningful insights on how to solve them. The aforementioned expansions are simply the tip of the iceberg for the advances of GMCR listed in Table 4 over the past 30 years. As the world becomes even more interconnected and complicated, conflicts are expected to intensify. The need for formal decision technologies to effectively handle even more challenging conflicts is bound to increase. Further opportunities for meaningfully expanding GMCR will most certainly be revealed as the future unfolds.

Cross-References ▶ Conflict Resolution Using the Graph Model: Individuals and Coalitions ▶ Group Decisions with Linguistic Information: A Survey ▶ Looking Back on Decision-Making Under Conditions of Conflict

References Aljefri YM, Hipel KW, Fang L (2018) General hypergame analysis within the graph model for conflict resolution. Int J Syst Sci Oper Logist. https://doi.org/10.1080/23302674.2018.1476604 Bashar MA, Kilgour DM, Hipel KW (2012) Fuzzy preferences in the graph model for conflict resolution. IEEE T Fuzzy Syst 20(4):760–770 Bashar MA, Kilgour DM, Hipel KW (2014) Fuzzy option prioritization for the graph model for conflict resolution. Fuzzy Sets Syst 26:34–48 Bernath Walker SG, Hipel KW, Inohara T (2009) Strategic decision making for improved environmental security: coalitions and attitudes in the graph model for conflict resolution. J Syst Sci Syst Eng 18(4):461–476 Fang L, Hipel KW, Kilgour DM (1993) Interactive decision making: the graph model for conflict resolution. Wiley, New York Fang L, Hipel KW, Wang L (2002) Gisborne water export conflict study. In: Schmitz GH (ed) Proceedings of 3rd International conference on water resources and environment research (ICWRER), vol 1, Dresden, pp 432–436 Fang L, Hipel KW, Kilgour DM, Peng X (2003a) A decision support system for interactive decision making, part 1: model formulation. IEEE Trans Syst Man Cybern Part C-Appl Rev 33(1):42–55 Fang L, Hipel KW, Kilgour DM, Peng X (2003b) A decision support system for interactive decision making, part 2: analysis and output interpretation. IEEE T Syst Man Cybern Part C-Appl Rev 33 (1):56–66 Fraser NM, Hipel KW (1979) Solving complex conflicts. IEEE T Syst Man Cybern 9(12):805–816

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Fraser NM, Hipel KW (1988) Decision support systems for conflict analysis. In: Proceedings of the IMACS/IFOR first international colloquium on managerial decision support systems and knowledge-based systems, Amsterdam, pp 13–21 Garcia A, Hipel KW (2017) Inverse engineering preferences in simple games. Appl Math Comput 311:184–194 Hamouda L, Kilgour DM, Hipel KW (2004) Strength of preference in the graph model for conflict resolution. Group Decis Negot 13:449–462 Hamouda L, Kilgour DM, Hipel KW (2006) Strength of preference in graph models for multiple decision-maker conflicts. Appl Math Comput 179(1):314–327 He S, Kilgour DM, Hipel KW (2017) A general hierarchical graph model for conflict resolution with application to greenhouse gas emission disputes between USA and China. Eur J Oper Res 257(3):919–932 Hipel KW, Kilgour DM, Fang L, Peng X (1997) The decision support system GMCR in environmental conflict management. Appl Math Comput 83(2–3):117–152 Hipel KW, Fang L, Kilgour DM (2008) Decision support systems in water resources and environmental management. J Hydrol Eng 13(9):761–770 Hipel KW, Sakamoto M, Hagihara Y (2015) Third party intervention in conflict resolution: dispute between Bangladesh and India over control of the Ganges river. In: Hagihara K, Asahi C (eds) Coping with regional vulnerability: preventing and mitigating damages from environmental disasters. Springer, Tokyo, pp 329–355 Hipel KW, Fang L, Kilgour DM (2019) The graph model for conflict resolution: reflections on three decades of development. Group Decis Negot: https://doi.org/10.1007/s10726-019-09648-z Inohara T, Hipel KW, Bernath Walker SG (2007) Conflict analysis approaches for investigating attitudes and misperceptions in the war of 1812. J Syst Sci Syst Eng 16(2):181–201 Inohara T, Hipel KW (2008a) Coalition analysis in the graph model for conflict resolution. Syst Eng 11(4):343–359 Inohara T, Hipel KW (2008b) Interrelationships among noncooperative and coalition stability concepts. J Syst Sci Syst Eng 17(1):1–29 Kilgour DM, Hipel KW, Fang L, Peng X (2001) Coalition analysis in group decision support. Group Decis Negot 10(2):159–175 Kinsara RA, Kilgour DM, Hipel KW (2015a) Inverse approach to the graph model for conflict resolution. IEEE Trans Syst Man Cybern-Syst 45(5):734–742 Kinsara RA, Petersons O, Hipel KW, Kilgour DM (2015b) Advanced decision support system for the graph model for conflict resolution. J Decis Syst 24(2):117–145 Kuang H, Bashar MA, Hipel KW, Kilgour DM (2015) Grey-based preference in a graph model for conflict resolution with multiple decision makers. IEEE Trans Syst Man Cybern-Syst 45 (9):1254–1267 Li KW, Hipel KW, Kilgour DM, Fang L (2004) Preference uncertainty in the graph model for conflict resolution. IEEE Trans Syst Man Cybern Part A-Syst Hum 34(4):507–520 Li KW, Kilgour DM, Hipel KW (2005) Status quo analysis in the graph model for conflict resolution. J Oper Res Soc 56:699–707 Nash JF (1950) Equilibrium points in n-person games. Proc Natl Acad Sci 36(1):48–49 Nash JF (1951) Non-cooperative games. Ann Math 54(2):286–295 Obeidi A, Hipel KW, Kilgour DM (2005) The role of emotions in envisioning outcomes in conflict analysis. Group Decis Negot 14(6):481–500 Peng X, Hipel KW, Kilgour DM, Fang L (1997) Representing ordinal preferences in the decision support system GMCR II. In: Proceedings of 1997 IEEE international conference syst man and cybernetics, Florida, pp 809–814 Rêgo LC, dos Santos AM (2015) Probabilistic preferences in the graph model for conflict resolution. IEEE Trans Syst Man Cybern-Syst 45(4):595–608 Wang M, Hipel KW, Fraser NM (1988) Modelling misperceptions in games. Behav Sci 33(3):207–223

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Wang M, Hipel KW, Fraser NM (1989) Solution concepts in hypergames. Appl Math Comput 34(3):147–171 Wang J, Hipel KW, Fang L, Xu H, Kilgour DM (2017) Behavioural analysis in the graph model for conflict resolution. IEEE Trans Syst Man Cybern-Systems 49:904. https://doi.org/10.1109/ TSMC.2017.2689004 Wang J, Hipel KW, Fang L, Dang Y (2018) Matrix representations of the inverse problem in the graph model for conflict resolution. Eur J Oper Res 270(1):282–293 Xu H, Hipel KW, Kilgour DM (2009) Matrix representation of solution concepts in multiple decision maker graph models. IEEE Trans Syst Man Cybern Part A-Syst Hum 39(1):96–108 Xu H, Hipel KW, Kilgour DM, Fang L (2018) Conflict resolution using the graph model: strategic interactions in competition and cooperation. Springer, Cham Yu J, Kilgour DM, Hipel KW, Zhao M (2015) Power asymmetry in conflict resolution with application to a water pollution dispute in China. Water Resour Res 51(10):8627–8645 Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353 Zhu Z, Kilgour DM, Hipel KW (2018) A new approach to coalition analysis within the graph model. IEEE Trans Syst Man Cybern Syst. https://doi.org/10.1109/TSMC.2018.2811402

Part VI Group Support Systems

Group Support Systems: Past, Present, and Future Fran Ackermann

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Defining Group Support Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Early Beginnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mechanisms for Supporting Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Building Communities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evolution of Five Group Support Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ThinkLets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Explorer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Meeting Works and Decision Conferencing: Multi-criteria Decision-Making Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dialogue Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reflections and Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modelling Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technologies Adopted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Application Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reflections on the Past, Present, and Future of GSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

628 628 629 631 632 633 634 635 636 637 639 640 640 640 642 644 644 645 645

Abstract

Group support systems (GSSs) (and group decision support systems (GDSS)) first emerged as a promising field of research in the late 1980s – three decades ago – and the field has benefited from considerable development since these preliminary research endeavors. Initially focusing on harnessing technology to increase meeting F. Ackermann (*) School of Management, Faculty of Business and Law, Curtin Business School, Curtin University, Perth, WA, Australia e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_47

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effectiveness and efficiency through the provision of features such as anonymity, simultaneity, and data structuring through models, the field has expanded its profile and remit. This has been achieved through taking cognizance of theories and concepts from a range of different disciplines (e.g., information systems, operational research, engineering, negotiation, and management, to name a few) along with developments in technology and is illustrated through exploring the genesis and evolution of five specific GSSs. Given an increasing appetite from decision makers to find approaches for managing complex problems in an inclusive and sustainable manner, there is clear scope for further development in the GSS field through extending the problem types addressed, widening application arenas, incorporating new modeling approaches, and further capitalizing on new technologies. Keywords

Group decision · Group support systems · Group behavior · Modeling · Communication · Decision-making · Group support

Introduction Defining Group Support Systems Group Support Systems research began in the 1980s stimulated in part by the advances in technology, e.g., personal computers, enhanced graphics, etc., along with a recognition that while meetings encompassed a considerable amount of managerial time, and were an important component in the work environment, in many situations those attending experienced productivity losses due to factors such as conformity pressures, evaluation apprehension, and cognitive overload to name a few. And yet meetings are ubiquitous and here to stay. As noted by Peter Keen “the lonely decision maker striding down the hall at high noon to make a decision – is true only in rare cases” (based on remarks at a closing plenary session of Decision Support Systems quoted in Gray 1987, p 233). Thus, better support for meetings enabling better group decision-making was an important remit. As with many fields of research, initial work took place in a piecemeal fashion oftentimes with groups working on GSS aspects not being fully aware of work being undertaken by others. This diversity of endeavor is seen in early books on the subject, for example, Jessup and Valacich’s Group Support Systems (1993) and Bostrom, Kinney, and Watson’s Computer Augmented Teamwork (Bostrom et al. 1992). These books provide a compendium of the work being undertaken in the 1980s/1990s and illustrate different foci, systems, and research lenses. A quick review of the material reveals that there is relatively little cross-referencing between the work being presented – a phenomena that is not untypical in new research endeavors. Connected with this diversity of exploration was the variety of names given to the systems being developed, for example, Meeting Support Systems,

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Computer-Supported Cooperative Work Systems, Group Support Systems, and Group Decision Support Systems to note a few. An early definition of a Group Decision Support System is that it is “a set of software, hardware and language components and procedures that support a group of people in a decision related meeting” (Huber 1984, p. 195). Elaborating on this DeSanctis and Gallupe (1987 p 589) noted that “A GSS aims to improve the process of group decision making by removing common communication barriers, providing techniques for structuring decisions and systemically directing pattern, timing and content of the discussion.” Both these definitions highlight the value added that could be gained from harnessing technology in a manner that supported decision-makers in their interactions, communications, and management of information. This potential support to groups reflected a focus on attending to an early definition by Shaw (1976) who argued that actual (meeting) effectiveness equalled potential effectiveness (the skills and knowledge of participants) minus process losses (conformity pressures, etc.) and added to by process gains (creativity, ownership). Thus, an initial (and enduring) aim was to enhance the quality of meetings both in terms of the processes and the outcomes. In essence this meant attending to both procedural justice (Kim and Mauborgne 1995) and procedural rationality (Simon 1976) so as to increase the likelihood of effective meetings with satisfactory outcomes (Briggs et al. 2006).

Early Beginnings Early research in Group Support Systems predominantly took place in two countries (the USA and the UK). Research endeavors in the field in the USA saw a strong focus on technology and information systems – emerging from a background in Data Processing and Management Information Systems before seeing research efforts move on to work in the space of decision support systems (Keen and Morton 1978) and subsequently Group Decision Support Systems (Huber 1984; DeSanctis and Gallupe 1987; Nunamaker et al. 1991). However, while research within the USA was mainly predicated on a focus on technology, nevertheless there were a range of different emphases/research angles. For example, there were researchers focusing on exploring the benefits technology could bring to collaboration (both within and more tentatively across organizations) spawning the field of Computer-Supported Cooperative Work (CSCW) (Grudin 1994; Greif 1988) and Groupware (Johanson 1988; Bate and Travell 1994). Reflecting the fluidity of foci and system definition, CSCW has been seen, by some, as a synonym for Groupware (Johanson 1988) with researchers arguing that “CSCW is a generic term, which combines the understanding of the way people work in groups with the enabling technologies of computer networking and associated hardware, software, services and techniques” (Wilson 1991, p. 1). CSCW has sought to include considerations of social, organizational and psychological theories into the study. These theories and considerations have resonance with those researching in the area of groupware and reveal a range of theories and concepts being integrated in novel fashions to support groups working collaboratively even at the early stage.

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Alongside, and complementary to the work on collaborative system support, others focused on group decision support and developed systems such as Electronic Meeting Systems (Nunamaker et al. 1991; Valacich et al. 1991; Dennis et al. 1988) which subsequently morphed into Group Systems. As with the collaborative work, those working on group support systems adopted a diverse mix of theories and concepts to underpin their research and emergent frameworks. For example, Sanctis and Poole along with Dickson based their research effort on framing the SAMM system on Adaptive Structuration Theory (Giddens 1984; DeSanctis and Poole 1994) and thus were interested in taking a socio-technical angle, and Mantei and colleagues in Michigan spent considerable efforts focusing on room design (Mantei 1988) as did Xerox Park with Colab (Foster and Stefik 1986). Initially many of these systems were relatively simple in the forms of support provided, aiding the capture and to some degree structuring of participant views – dictated in part by the limitations of the technology. Alongside meeting process support, a number of university research efforts were channelled toward building special-purpose rooms to house the group decision support technology – drawing on fields such as ergonomics. This direction was driven by the fact that the group support systems comprised networked computers and public viewing screens, and so researchers envisaged enhancing physical designs to manage social practices and incorporate features such as ensuring participants could easily view one another during the meeting so as to retain necessary social cues. This was achieved through practices such as using computers recessed into desks, placing large public screen(s) in locations (often more than one) enabling all to easily see the captured material and explore and develop it, and hiding the networks enabling easy transmission of data from participants to the server/public screen and back again so as to provide participants with a more familiar environment. Interestingly enough the notion of a specialpurpose room to assist in decision-making is not new. William Churchill had his war rooms (Holmes 2009). Alongside this work in the USA was a growing body of research taking place in the UK. This was gaining traction under the banner of Problem Structuring Methods (Rosenhead 1996) and emerged from the Operational Research world. Originally the Problem Structuring Methods were manual methods (and some have remained that way such as Soft systems Methodology (Checkland 1981)); however over time a number, such as Strategic Choice (Friend and Hickling 1987) and SODA (Eden and Ackermann 1989; Ackermann and Eden 2001a), leveraged the benefits of technology. In contrast to the work in the USA, the focus of these methods was to assist decision-makers with messy, complex, wicked (Rittel and Webber 1973) problems, paying particular attention to sociopolitical considerations, and as such, used different modelling techniques (systems engineering, causal mapping) to manage the attendant complex information surrounding such problems. This attention to social processes dominated the design of the methods, rather than a focus on technology (which came later). The underlying theories included organizational behavior, psychology, systems thinking, sociology, regional and urban planning, and organizational dynamics.

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Regardless of whether the research was being conducted in the UK or the USA, much of the Group Decision Support System development was driven by the aspiration of supporting groups, particularly in helping them avoid the problematic consequences of conformity pressures, evaluation apprehension, information overload, management of complexity (rather than simple reduction), etc. The systems also sought to attend to Simon’s (1976) proposition that decision-making should encompass four phases of decision-making, i.e., intelligence, design, choice, and review, rather than rushing into evaluation. The process was encouraging the avoidance of making decisions too early (Nutt 2002). As such, they comprised features allowing for the generation (intelligence), modelling (design) evaluation (choice), and allocation of responsibilities (review). Of particular concern to researchers were dysfunctional outcomes such as group think (Janis 1972) and the Abilene paradox (Harvey 1974) as these caused groups to make suboptimal decisions. Also of concern was the potential for “social loafing” (Latané et al. 1979), which is where an individual put less energy into a group activity than they would working alone assuming that their individual effort won’t matter to a group. The systems sought to attend to the comprehensive list of challenging meeting behaviors (see Mosvick and Nelson (1987)) such as risky shift (Stoner 1968).

Mechanisms for Supporting Groups Not long after the initial foray into the area, from both the US and UK research endeavors, there started to emerge two subfields/subsystems – those systems focusing on Group Support Systems alongside those that were supporting Group Decision Support Meetings – reflecting the fact that not all of the meetings managers held were decision-making and that support for brainstorming and other such activities was also appropriate. This more general view of meeting support, to a degree, reflected the views of those working in Computer-Supported Cooperative Work (CSCW). As a result of the focus on increasing meeting effectiveness through reducing conformity pressures and increasing creativity, achieved through facilities such as brainstorming, all of the developing systems began to develop a common set of features/modules. These were firstly the ability for participants to enter their contributions directly into the system, enabling simultaneous entry and making meetings more productive, as not only could the time spent on idea generation be reduced but also a greater range of input was possible. Hitherto those who were the most socially or politically able dominated the airtime, freezing out the views of others. This aspect of the system ensured that the views were captured in the manner those expressing them wished them to be captured, rather than being later “edited” or paraphrased by another participant or a facilitator. This feature of a GSS, it was believed, would ensure greater ownership for outcomes as well as increase diversity and thus potential for creativity. In addition to the simultaneous entry feature was the facility to provide anonymity. This feature aimed to reduce, to a considerable extent, conformity pressures as

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participants were unable to be sure that they knew who was saying what. The impact of anonymity on user satisfaction was identified as significant (Valacich et al. 1992a, b; Jessup and Tansik 1991); however care was also needed to avoid negative consequences such as “flaming” (where disinhibition occurs resulting in offensive postings (Kiesler and Sproull 1992)) and social loafing (Stoner 1968). Finally there was the ability to store and organize the range of contributions, providing an organizational memory and providing the means of prioritization through the ability to express preferences/votes and/or ratings. Expressing anonymised preferences could be used as an end point, clarifying the decisions made, or as a dialectic to see the degree (or not) of consensus. Alongside research into testing the usefulness and effectiveness of anonymity and simultaneity, there was also research on the role of facilitators when using a GSS – exploring their contribution to the system’s ability to enable groups to meet more effectively. For example, research explored how facilitators assisted in the design of the meeting in terms of assisting with the selection, ordering, and operation of the tools, as well as managing the actual meeting itself, i.e., supporting those using the technology, assisting with social problems, and determining timing (Eden and Ackermann 1998, p 372–381). Where the system provided a clear and easy-to-use interface with a limited number of features, there was, for some, the belief that the GSS could be run by the group members themselves. However with a growing inclusion of formal models into the system, and taking into account the difficulties of both participating and facilitating, having a chauffeur1 or facilitator became increasingly an important factor. Research by Dickson and colleagues (Dickson et al. 1989) into the benefits and roles of chauffeurs versus user-driven versus facilitation, and work by Bostrom and colleagues (1993), Whiteley and Garcia (1996), Ngwenyama et al. (1996), and Ackermann (1996) in using Group Support Systems, provided a wealth of knowledge as to the roles, contribution, and skills associated with facilitation. Insights from these studies along with those exploring the benefits of simultaneity and anonymity were augmented by studies considering user satisfaction, meeting outcomes, etc.

Building Communities As the field of group support systems emerged, a number of “communities of practice” also emerged. In 1992 a journal dedicated to Group Decision and Negotiation (GDN) appeared, and in the mid-1990s a European Working Group on GDSS was established (as part of the network of working groups exploring dimensions of Operational Research). The GDN journal and its attendant community were linked with INFORMS, the US body of Operations Research and Management Science, and after an inaugural conference on Group Decision and Negotiation in the UK in

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A chauffeur is a technical facilitator focused solely on operating the GSS.

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2000, the two communities sought to collaborate to facilitate cross-pollination of ideas and share research contributions. Overtime Group Decision and Negotiation was established as the premier journal in the field, and the special interest GDSS EURO merged with the INFORMS group, strengthening the vibrant community. Alongside this community, a stream at the Hawaii International Conference on System Sciences (HICSS) focusing on Group Support Systems emerged (and is now over 25 years old) as well as the development of streams at the International Conference in Information Systems (ICIS), the Pacific Asia Conference on Information Systems (PACIS), and the European Conference on Information Systems (ECIS). These two strands (Group Decision and Negotiation and the Information Systems conferences) to some extent reflect the two different origins of the field; nevertheless there are researchers that move between the two strands allowing for dissemination of research and offering potential for collaboration. There are also conferences and journals associated with the CSCW work. Since the early 1980s Group Support Systems and Group Decision Support Systems have evolved in many different dimensions. These dimensions include widening the arenas of application, the models incorporated within them, and the types of problems addressed. Clearly these three dimensions are not mutually exclusive, that is, in seeking to address a particular type of problem, new modelling capabilities may be required, and as different industries seek support, new applications and new problems emerge. Thus, opportunities, in the form of different problems, gave rise to new developments of the systems, which in turn got noticed by decision-makers looking for means of managing different problems – a reinforcing feedback cycle emerged. Initial developments also led to further research questions, drawing in research from many different, but allied, disciplines, such as psychology, decision science, collaboration engineering, etc.

Evolution of Five Group Support Systems Not surprisingly, over the course of the last three decades there have been a number of Group Support Systems/Group Decision Support Systems developed. Some of these have stood the test of time; others have faded either due to resourcing constraints, researchers moving into other areas, or other developments overtaking them. This section of the chapter focuses on five systems, including three that emerged early in the development of the field and two that are more recent developments. They straddle the USA and the UK/Europe where the majority of this research has been based and illustrate different modelling bases and aspirations. This section of this chapter thus aims to provide a quick overview of these five GSSs from initial inception to current practice, so as to illustrate different trajectories, vulnerabilities, and developments. It is not intended to be comprehensive and all-encompassing but illustrative of the different stimuli, objectives, and structures.

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Each system is explored by looking at a number of parameters including the different problem types addressed; the concepts, theories, and models used; and the industry adoption. Additionally comments regarding their presence within the extant literature are also provided.

Group Systems Group Systems is probably the best known and most successful of the Group Support System family. The system emerged from research undertaken in the University of Arizona in Tucson, USA. Nunamaker and colleagues (Vogel, Dennis, Jessup, Konsynski, George, Briggs, etc.) were interested in extending work being carried out in information systems design and optimization and sought to develop a system to support decision-making tasks such as information system design. It could be argued that Group Systems has its origins in work conducted in 1965 with the first version of the GSS being called Plexsys. The intention of Plexsys was to help users determine information system requirements. A set of tools were developed including electronic brainstorming, “issue analyzer,” and “voting.” Over the course of the system’s development, the researchers incorporated ideas from cognitive science, and 16 tools were added to the software acquiring the Group Systems name. For a good discussion on the genesis of Group Systems, see Nunmaker et al. (1992). The development of Group Systems was aided by managers in IBM becoming interested in the system and providing funding but also, possibly more significantly, an opportunity for the researchers to explore and understand how managers in businesses used and benefited from the system (Grohowski et al. 1990). Overtime more and more organizations were interested in the system, including the military (Briggs et al. 1998), education (de Vreede et al. 1999), collaboration (Briggs and De Vreede 1997), and software development (Boehm et al. 2001). During this period, the software became professionally developed and commercialized through the Ventana Corporation and was renamed ThinkTank. It has been developed to enable it to be run in a distributed fashion, support stakeholder management, and assist with the selection and management of enterprise software systems. See www. groupsystems.com. It has also been the foundation for work into collaboration systems (Buttler et al. 2011; Nunamaker et al. 2015; Briggs et al. 2015). Group Systems (and its variants) have contributed to a steady rise in the number of papers produced in the field. This is partly due to the strength of the research team (not always co-located) which emerged through the University of Arizona at Tucson’s PhD program. Group Systems also benefitted from a number of these researchers setting up and running a stream at a well-attended conference, the Hawaiian Conference on Information Systems Sciences (HICSS), which provided a fertile breeding ground for ideas, research collaboration, etc. On average, around 20 papers exploring Group Systems have been published each year, and this is increasing over time demonstrating a healthy active research community.

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Group Systems success, in terms of publication, stems from the system being applied in many different settings. A review of the literature2 provides a remarkable spread with a dominance of its use in health arenas. There are many papers appearing in journals relating cardiology/heart (Douglas et al. 2016; Aziz et al. 2018), cancer (Apolo et al. 2015; Korde et al. 2015), emergency management (Chung et al. 2018), and preventative medicine (Zingg et al. 2019). In addition to health there are also papers in industries such as public affairs (Fink-Hafner and Thomas 2019), communications (Mebane 2005), law/criminology (Jaffe et al. 2013; Salem 2019), group decision-making (Kolfschoten et al. 2010b), business ethics (Hemphill 2004), and drug safety (Platt et al. 2008).

ThinkLets As noted in the above discussion on Group Systems, the system and its research designers have continually extended and augmented the system, reflecting the ongoing exploration into support for decision-makers. Alongside and complementing the development in collaboration systems, Group Systems gave rise to ThinkLets, which is based on collaborative engineering concepts (Kolfschoten et al. 2010a; De Vreede and Briggs 2019) augmented with concepts underpinning the Technology Transition Model (TTM) (Briggs et al. 2001a). ThinkLets was initially developed by De Vreede and Briggs. The emerging field of Collaboration Engineering aims to formulate an approach for designing high-value recurring collaboration processes that capture the best practices of master facilitators and packaging the processes in a fashion that can be transferred to practitioners to execute for themselves without the ongoing intervention of professional facilitators (De Vreede et al. 2006, p140). ThinkLets therefore seeks to provide assistance to organizations wishing to benefit from the support provided by Group Support Systems without the need for either hiring in trained facilitators or developing their own in-house facilitators – both activities acting as a barrier for adoption. As such ThinkLets are short tools/scripts which enable groups to undertake tasks in a standard consistent fashion (Briggs et al. 2001b) and comprise seven basic patterns of thinking: Diverge, Converge, Organize, Elaborate, Abstract, Evaluate, and Build Consensus. The various scripts are able to be combined in different permutations according to the particular organizational requirement and can be instantiated at design time in such a way that a practitioner can use them to recreate a predictable pattern of collaboration. Some training can be provided to assist in the development of blueprint (Briggs et al. 2003). See the chapter ▶ “Collaboration Engineering for Group Decision and Negotiation.” 2

The literature review was conducted using Scopus and Google Scholar databases. Search terms included the name of the group support system, related synonyms, and common authors associated with that system. Inclusion criteria for the literature review were documents in the form of books, edited books, peer-reviewed journal articles, and conferences written in English after 1990. Documents included must have had at least one of the search terms in its abstract to be read further.

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ThinkLets, although relatively recent, has been used in a number of organizational settings including software projects (Piirainen et al. 2012), risk assessment (Kolfschoten et al. 2015), and multi-organizational strategy development (Bragge et al. 2006). The papers appearing show a steady progression in terms of application within the collaborative research field as well as adaptions to the design seeing new developments into leadership and AI (De Vreede et al. 2020).

Group Explorer Group Explorer had its genesis in the UK (initially at the University of Bath and latterly at Strathclyde University). The system emerged from research work into problem structuring methods (Mingers and Rosenhead 2001) as a part of the soft or qualitative Operational Research field. Initial work focused on the use of cause mapping (Eden 1988) for supporting complex messy problems. This early work was informed by theories from psychology, e.g., Personal Construct Theory (Kelly 1955), as well as social construction of reality (Berger and Luckmann 1966). From these theories, along with ideas from organizational behavior, the Strategic Options Development and Analysis (SODA) method (Eden and Ackermann 1989; Ackermann and Eden 2001a) was founded and used to support groups. As technology advanced software was designed to support the modelling process. The first version of the software in the 1980s, COPE, allowed for construction of causal maps and their analysis; however, as computing continued to improve and better graphics appeared, the software was further developed to be able to support decision-makers in real time in workshops and was relabelled as Decision Explorer. Informing these developments in the software, the SODA method was also being extended from supporting messy problems into areas such as strategy making (Eden and Ackermann 2001; Ackermann and Eden 2011), information systems design (Ackermann and Eden 2005a), policy analysis (Eden and Ackermann 2004), and supporting litigation on complex projects (Ackermann and Eden 2005b). Later applications saw its use in areas such as mapping aerospace meteorology in Brazil (Caruzzo et al. 2015), commercialization of knowledge-based companies in Iran (Zahedi et al. 2018), adoption in defense (Ackermann et al. 2019), and public consultation in energy generation in Spain (Upham and Pérez 2015). In each case the method was employed by groups seeking better ways of working together. Capitalizing on further advances in technology and developments in group support system research in the USA, the SODA methodology also saw a move from “single-user group support” of COPE and Decision Explorer to “multiuser group support” – direct entry (Ackermann and Eden 2001b). This shifted the method from either (a) capturing the views as cognitive maps through one-to-one interviews and subsequently weaving the maps together to form a group cause map able to support the group’s exploration and decision-making or (b) using manual techniques such as oval mapping. The developing “multiuser” approach included features allowing for direct entry of views and causal links and assessing preferences for

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action. This adoption of the benefits of multiuser direct entry was informed and influenced by work in negotiation (Fisher and Ury 1982) and provided a means for supporting groups seeking to develop strategy (Bryson et al. 2004), undertake research (Shaw 2006) and to do so in a negotiative manner (Ackermann and Eden 2011), work collaboratively across organizations (Ackermann and Eden 2005b; see Group Support Systems – concepts to practice; Procedural justice in Group Decision Support), and support groups working in conflictual environments (Ackermann et al. 2016). More recently the approach has been developed to leverage the capabilities of server-based anywhere/anytime opportunities: strategyfinder (see www.strategyfinder.pro). Group Explorer has a smaller research following than Group Systems, and as such this is reflected in the volume of papers being produced reflecting its application and development. Nevertheless it has been used in areas such as complex project management and risk (Ackermann et al. 2014) and city resilience (Pyrko et al. 2019) as well as strategy making and negotiation (Franco and Greiffenhagen 2018; Hindle and Franco 2009; Paroutis et al. 2015). Many of the publications appear in Operational Research journals reflecting the early development and/or group decision and negotiation outlets.

Meeting Works and Decision Conferencing: Multi-criteria DecisionMaking Models The two previous systems focused on either incorporating a combination of brainstorming (Osborne 1963; Gallupe et al. 1992), prioritization, and rating tools or adopting modelling methods such as cause mapping to support group working. Another modelling method that was used to provide a basis for group support was multi-criteria analysis (MCA) or multiple-criteria decision analysis (MCDA). This modelling approach also had its genesis in operational research. MCDM has been widely adopted in the GSS field. For example, its use in group decision-making/ Group Support Systems is seen in packages such as Meeting Works (Lewis 2010), VISA (Belton and Stewart 2002; Hodgkin et al. 2005), Promethee (Behzadian et al. 2013), and Decision conferencing (Phillips and e Costa 2007; McCartt and Rohrbaugh 1989; Barcus and Montibeller 2008) along with many others including GRUS (a Group Decision Support System for multiple-criteria decisions). Multicriteria modelling is typically a two-stage process. The first stage encompasses the identification of criteria which could be goals or objectives along with a range of alternatives/options. The second stage then asks the decision-maker(s) to weight the criteria and score the alternatives arriving at the “best” option accordingly. In essence it might be seen as a form of cost-benefit analysis. While some of the research on MCDM work is individually focused, that is, supporting a single manager in choosing between alternatives, there have been systems developed that have actively encouraged group use and have this as a deliberate focus. Two of these are Meeting Works (Lewis 1987, 2010) and Decision conferencing.

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Meeting Works emerged from a PhD study (Lewis 1982, 1984, 1987) initially encompassing support for Nominal Group Technique (Van de Ven and Delbecq 1974) with, as the system developed, further modules such as the ability to undertake cross impact analysis being added (very much in the same manner as Group Systems). Initially research was undertaken within universities and with student groups, but as the software gained more robustness and demonstrated clear benefit to decision-makers, it made the transition to a commercial product. The system was configured to be able to fit the modules together in a manner that best supported the group and task. The mature Meeting Works comprises a number of modules including an agenda setting tool, idea generation facilities, and organizing and evaluating modules. The agenda setting tool helps the facilitator in managing the meeting both in the planning stage and also in the meeting itself. As with many systems, there is a chauffeur module to either support the facilitator or act as a technical assistant. For a more detailed explanation of Meeting Works, see Lewis (2010). Meeting Works, while gaining some popularity early on, has seen less application and has received less publication than other GSSs. In reviewing the literature, over the last 15 years, there have been less than 10 publications with those publications appearing in journals such as Group Decision and Negotiation (Lewis and Shakun 1996; Antunes and Ho 2001), Journal of Technology in Human Services (Lewis et al. 2002), and the Institute of Electrical and Electronics Engineers (Lewis and Spich 1996; Bajwa and Lewis 2002; Chambless et al. 2005). It has predominantly been used in the USA although applications have also appeared in Australia (Klass and Whitely 1996 ). Decision conferencing is another form of multi-criteria decision-making focusing on group support. Initially emerging from the work of Trist and Emery (Emery and Trist 1960), which takes a socio-technical focus (the social aspect drawing heavily on the literature on group decision processes). Decision conferencing research has shown that in many instances, groups don’t outperform their most knowledgeable members unless interaction is ameliorated through the intervention of a facilitator and with the assistance of software. Cam Peterson and Larry Phillips are seen as the original developer and have collaborated with a number of researchers developing group support systems (Phillips 1989, 2007). The two best known group support systems include Hi-View developed by Larry Phillips and colleagues (Phillips 2007; Phillips and e Costa 2007) in the UK and Decision conferencing in the USA (McCartt and Rohrbaugh 1989; Reagan-Cirincione and Rohrbaugh 1992; ReaganCirincione 1994). Decision conferencing has been used in a wide array of studies. A review of the literature shows a fairly even spread across journals ranging from Operations Research-oriented journals (Interfaces, Omega, Military Operational Research, and Annals of Operational Research) to Environmental journals (Environment International) and Information Management journals (Information Systems). This even spread is reflected in applications where papers note the use of Decision conferencing in fields such as Energy (Elghali et al. 2007; Mustajoki et al. 2007),

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Defense (Kitchen et al. 2013), Urban Planning (Quaddus et al. 1992; Moss et al. 1996), Environment (Cowell et al. 2006), and Management (Phillips and e Costa 2007) and has been used in Portugal (Rodrigues 2014), the UK (Elghali et al. 2007), and the USA (Schuman and Rohrbaugh 1991).

Dialogue Mapping Building on work undertaken by Noble and Rittel in the late 1980s (Rittel and Noble 1989), Conklin adapted the Issue-Based Information System (IBIS) method so that it could assist groups in decision-making particularly in the area of messy, wicked problems (Conklin and Begeman 1988, 1989). His work led to the formulation of two processes. The first, “issue mapping,” is a visualization technique which is closely related to argument mapping and which allows the issues facing decisionmakers to be captured and structured assisting with the process of critical thinking. It is a graphical process with the issues, solutions, alternatives, etc. captured and modelled using a set of formalisms. Through teasing out and structuring participants’ points of view, it provides decision-makers with the means of taking a holistic and systemic appreciation of the situation and thus arrive at better decisions. The process comprises three components, namely, questions, ideas, and arguments. The questions focus on determining the criteria for success, the rationale, context, and options. The ideas are structured taking into account argumentation (hence the close link to argument mapping) and can be used for many different problems particularly those that are complex and contentious. Augmenting issue mapping is dialogue mapping (Conklin 2006) which focuses on facilitating groups in the use of issue mapping. As such, the process typically involves a facilitator who captures the views of participants and uses the underlying elements of the dialogue mapping grammar (namely, IBIS – Issue-Based Information System). The map acts as a dialectic prompting further elaboration and allows a hypertext-like display enabling participants to control the material being considered, i.e., take a broad overarching consideration or drill down to seeing the detail. The system is predominantly used within the USA and sees applications in information systems development (Burgess Yakemovic and Conklin 1990) and knowledge engineering (Aurisicchio et al. 2016), with some application in policy (Conklin 2008) and project management (Hällgren et al. 2012). There is relatively little material in the academic literature. As noted above, Group Explorer also capitalizes on building a visualization of the problematic situation – in Group Explorer’s case, the technique is cognitive or cause mapping rather than issue or visual mapping. Nevertheless both Group Explorer and Dialog mapping have much in common in terms of the management of qualitative data, an interest in managing complexity and the use of graphical models with links assuming causality, and a resultant network that can be analyzed. Both aim to support exploration through models as transitional objects (Winnicott 1953; De Geus 1988; Group Support Systems – concepts to practice).

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Reflections and Future Directions As can be seen through the brief review of the five group support systems, GSSs have developed in terms of the technology adopted (capitalizing on new developments), the forms of modelling incorporated, the range of problems and challenges addressed, and the application arenas. As such the initial differences between systems developed in the UK and the USA have virtually disappeared with both the UK and US research incorporating sophisticated modelling approaches alongside adoption of advanced technology. As can be seen from the below diagram (Fig. 1), this amoebic-like growth sees the field touching on many others and as such becomes diffuse and widespread. This final section of the chapter will provide a glimpse of the work being undertaken in the four dimensions in terms of emerging developments before offering up some reflections and comments on the future.

Modelling Approaches When reviewing modelling approaches, GSS have encompassed approaches such as cause mapping, brainstorming, multi-criteria analysis, and collaboration engineering. There are those systems, for example, Group Systems, ThinkLets, and Decision Conferencing/Meeting Works, which take a brainstorming and prioritization focus and other GSSs, for example, Dialogue Mapping and Group Explorer, taking a more graphical mapping format. However GSSs have extended their adoption of modelling approaches to include methods such as analytical hierarchy processes (AHP) Saaty (1988) for procurement in groups (Kar and Pani 2014) and the use of fuzzy logic and numbers in supporting groups (Kar 2015; Hashemian et al. 2014; Wang et al. 2016; Group decisions with intuitionistic Fuzzy Sets). There is also research looking into the use of neural nets to support users of GSSs, as well as agent-based modelling, and the use of knowledge management modelling approaches to support performance evaluation (Alyoubi 2015). Undoubtedly more and more modelling techniques will be incorporated into GSSs particularly as new technologies facilitate their incorporation. These modelling approaches support decision-makers through being able to manage complexity rather than resort to reducing it and do this through structuring, synthesizing, and analyzing large amounts of qualitative data. Alongside, and the complementary to the inclusion of a range of modelling approache’s has been the acknowledgement and inclusion of research into cognition (Winograd and Flores 1986; Carneiro et al. 2018). This interest in cognition has been stimulated through the wealth of insight to draw upon when managing complexity – a characteristic associated with modelling approaches.

Technologies Adopted Developments in technology have given rise to new forms of support – both directly and through enabling new modelling approaches to be adopted. For example, the use

Fig. 1 Illustrative exploration of the infusion of ideas into the GSS realm along with avenues for GSS diffusion into research arenas

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of agent-based modelling can assist group decision-making and is made possible through the advent of technologies. GSS are now used to support users through delegating to agent preferences where the agent argues with other agents to obtain the best alternative for the whole group. As such the system simulates arguments made by real users (Recio-García et al. 2013) allowing more options to be explored and greater efficiencies. There is also research in microworlds and avatars to assist with decision-making. Another avenue of technology development is the advent of cloud- and webbased modes of operating (Carneiro et al. 2018; López et al. 2017; Same-time Different-place Group Support). For example, research is emerging in areas of the exploratory evaluation of user interaction in the context of web-based GDSS (Swobodzinski et al. 2015; Palomares et al. 2013). Alongside this research is work investigating the use of multi-criteria GDSS solving ranking problems collaboratively in different time/different place environments (Leyva Lo’pez 2017l), both instances using cloud/server technologies along with ideas from early work in the area, e.g., groupware. In addition, alongside the two above extensions are the continual developments in the field of video conferencing – which is now offered easily and cheaply through mediums such as Skype, Zoom, and WebEx. These platforms facilitate those working in virtual teams and additionally tap into developments in social media and potentially crowdsourcing (crowd-scale deliberation for group decision-making). As organizations become more global, as well as cost-conscious, there is a growing need to support groups who are distributed widely. By enabling those in different countries to work together effectively, organizations are able to capitalize on the knowledge resources within them. This move to supporting virtual teams builds off a strong base – leveraging work done in the space of computer-supported cooperative work (CSCW) which sought to help groups work together and reflects the growing remit noted by Johanson-Letz and Johanson-Letz (1991) regarding supporting groups operating not only at the same time and place but also at different times and places and the two other associated modes. The development of strategyfinder reflects this move.

Problem Types Starting from an early focus on improving the identification of requirements of information systems, Group Support Systems now address many types of problem. Interestingly, as with modelling approaches, certain GSSs get associated with particular problem types. For example, Group Explorer has been used extensively in strategy making, and ThinkLets is used for collaboration engineering. Many of the systems have been used to support negotiation linking the developments in GSS with those in Negotiation Support Systems. Negotiation Support Systems are “a special class of Group Decision Support Systems which emphasize computerized assistance for situation in which there is strong disagreement on factual or value judgements

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amount group members” (Jelassi and Foroughi 1989, p167). This has provided a strong rationale for the Group Decision and Negotiation journal, annual conference, and this handbook. As part of the focus on negotiation, research work on consensus reaching processes in group decision-making problems is underway. Some of this seeks to develop systems to assist in the reaching of mutual agreement between decisionmakers. There are also research noted in this Handbook, for example, ▶ “Negotiation Process Modelling: From Soft and Tacit to Deliberate” which reflect this ongoing interest in negotiation support. Negotiation and collaboration are closely aligned, and as such research in CSCW and Groupware provides valuable insights to the research in negotiation. That support is needed for groups collaborating is clear – research has shown that collaborations are challenging environments due to a wide range of factors including different objectives, different perspectives and skills sets, and different personalities. Moreover, there is a growing interest in collaborative working, particularly in the public sector, and therefore harnessing the advantages of GSS to help navigate this landscape through features such as anonymity, productivity, gains, etc. appears to be an obvious route and one that has already shown some promise (Ackermann et al. 2005). Effective collaboration needs creativity to assist in arriving at new options. The creation of new solutions is illustrated through work such as the development of an integrated framework for designing group creativity support systems (Voigt and Bergener 2013). Finally, negotiation is allied to conflict management, and here again GSSs can play an important role as illustrated in the works of Ackermann et al. (2016) and Bose (2015), Kilgour, and colleagues (Looking back at decision-making under decisions in conflict; conflict resolution using the Graph Models: individuals and coalitions; Kilgour et al. 1987) and online dispute resolution. The role of emotion in group decision-making is another arena that is attracting research attention. While not a problem type in itself, it affects all problem types as gaining both cognitive and emotional commitment to outcomes increases the likelihood of successful implementation. Managing emotion is particularly important in conflict management and negotiation. The work of Martinovski provides a good example of this work (as illustrated through Martinovski 2009; Martinovski and Mao 2009, Role of emotion in group decision and negotiation). GSSs can help manage emotion through the anonymous mode of entry, through providing participants with sufficient time to move beyond from a physiological response to a more cognitive one and from separating the contribution from the proponent. Finally, in relation to group and negotiation support, the work being undertaken in the Behavioral Operational Research and Micro-processes field (Ackermann et al. 2018; Group support practice: decision support ‘as it happens’; Franco and Hamalainen 2015) provides valuable insights. This work in behavior OR seeks to develop a better understanding, at a detailed level, of group interactions where participants are seeking to agree how to act and move forward in a consensual manner, so as to provide more nuanced and effective support.

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Application Areas As has been intimated through the discussion of the five systems, there is a very wide spread of GSS application from initial work in information systems to areas such as health (Engelgau et al. 2017; Pinheiro et al. 2018; Pinheiro et al. 2008), energy (Cowell et al. 2006; Mustajoki et al. 2007), defense (Kitchen et al. 2013), law (Mayer 2018; Salem 2019), environment (Elghali et al. 2007), organizational behavior (Schulz-Hardt et al. 2002), and strategy. GSSs have been used across the globe – not just in the UK and the USA. Examples include work being done in the UK (Moss et al. 1996; Himmelweit 2005), Portugal (Rodrigues 2014), Brazil (e Costa et al. 2014), Denmark (Weitze 2015), China (Tao et al. 2016), and the USA (Tournès 2018) to note just a few. GSS provide value for a wide range of users. They have been used with board of directors, with top management teams and with middle managers, and with those operating on the shop floor. They have been used with the public sector, the private sector, and the nonprofit organizations. Their application is wide reaching and continues to grow.

Reflections on the Past, Present, and Future of GSS As is reflected in this chapter, and in this Handbook, there has been considerable progress in the field of group support systems. This is evident by reviewing the journals within which researchers in GSS have published. For example, there are GSS-based articles spread across a very wide spectrum from computer science to medicine, from policy to negotiation, and from engineering to urban planning, suggesting a wide take-up of the processes. However, this progress has resulted in the work becoming quite diffuse. Complementary to this breadth of journal articles is also a breadth of systems. For example, there are systems that allow voters to cast their preferences online (e.g., Simply Voting simplyvoting.com) and social media programs on web pages asking for opinion. What is, and isn’t, a GSS becomes more difficult to determine. We see more organizations use video conferencing (e.g., the ubiquitous use of Skype/Zoom/WebEx) and share documents (with sophisticated version control), thus supporting distributed group working. Furthermore, the advent of machine learning and autonomous agents will no doubt make a big difference in the years to come. This is the first challenge – managing to retain a critical mass and focus while having impact and engagement. Another challenge, which to some extent contradicts the first, is that it has been noted that there are adoption challenges. As has been noted by various researchers, Group Support Systems are not widely adopted (Bajwa et al. 2005; Tully et al. 2018). This is partly due to lack of awareness (which raises questions regarding the publications – particularly the type of publications). As with many fields, the contributions of GSS to decision-makers are tied up in academic journals and are therefore not necessarily accessible to those in industry. The lack of adoption may be also due to inertia – organizations not willing to adopt new methods or wary that the systems might alter existing power bases (through direct entry, anonymity, etc.).

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There may be financial concerns (although the need for expensive tailor-made rooms has given way to cloud-/server-based systems reducing some of this worry) requiring business cases to be constructed – challenging in their own right given these take time. A further impediment for adoption is one that has been already touched on in this chapter, that of having experienced facilitators – an investment in itself. That said, the development of GSS such as ThinkLets and the advent of scripts for the design of GSS workshops (Richardson and Andersen; Ackermann et al. 2011) may help alleviate this concern. There is also the possibility that lack of adoption is due to unfamiliarity with technology and/or modelling approaches (some can be quite mathematical and difficult to master). To conclude, despite the advent of many forms of group support, there are still many groups working on challenging problems who do not use any form of support leading to a potential avenue for research. The need is clearly there: as succinctly articulated by Duncan Cummings when writing in the Guardian Newspaper, there is a very real need for “New dynamic tools [to] enable us to think previously unthinkable thoughts and allow us to see and interact with complex systems: to see inside, see across time, and see across possibilities.” Cummings goes on to note the need for “Model-driven material [that] can be used as grounds for an informed debate about assumptions and trade-offs” in decision-making so as to arrive at robust, intelligent, and most importantly sustainable outcomes (Cummings 2019).

Cross-References ▶ Group Support Systems: Concepts to Practice ▶ Group Support Systems: Experiments with an Online System and Implications for Same-Time/Different-Places Working ▶ Looking Back on a Framework for Thinking About Group Support Systems ▶ Multicriteria Methods for Group Decision Processes: An Overview ▶ Systems Thinking, Mapping, and Group Model Building ▶ Time, Technology, and Teams: From GSS to Collective Action

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Time, Technology, and Teams: From GSS to Collective Action Laku Chidambaram, Jama D. Summers, Shaila M. Miranda, Amber G. Young, and Robert P. Bostrom

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . From Small Group Behavior to Collective Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . From GSS to Digital Platforms and Technology Structure to Affordance . . . . . . . . . . . . . . . . . . . . . Chidambaram and Bostrom Revisited in the Era of Collective Action . . . . . . . . . . . . . . . . . . . . . . . . Affordances Across Time in the Context of Crowdfunding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Early Impacts (Pre-proposal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Early and Late Impacts (Early and Late Funding) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Affordances Across Time in the Context of Digital Activism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Early Impacts (Framing) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Midway Impacts (Mobilization) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Late Impacts (Protest Actions) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Toward a Better Understanding of Time in Digitally Enabled Collective Action . . . . . . . . . . . . . The Midway Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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L. Chidambaram (*) Michael F. Price College of Business, University of Oklahoma, Norman, OK, USA e-mail: [email protected] J. D. Summers University of Tennessee, Knoxville, TN, USA e-mail: [email protected] S. M. Miranda University of Oklahoma, Norman, OK, USA e-mail: [email protected] A. G. Young University of Arkansas, Fayetteville, AR, USA e-mail: [email protected] R. P. Bostrom University of Georgia, Athens, GA, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_28

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Entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jolts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Early work in group support systems synthesized decades of research on group development and examined their relevance for what was then an emerging technology. Over the past two decades, technologies associated with group development have continued to emerge, and the original conceptualizations of technology, teams, and time have evolved. Digital technology is ubiquitous, accessible through mobile devices, and includes a growing list of capabilities. These capabilities represent different technological affordances that can be invoked by users at their discretion and represent a broader and more flexible array of choices compared to the relatively immutable structures embedded in group support systems. Moreover, the teams using these affordances often transcend organizational boundaries where membership is fluid with members entering and exiting at will. Finally, notions of time have also evolved from chrontic (clock time) to kairotic (experienced time). Two areas that exemplify these changes in technology, teams, and time are crowdfunding and digital activism. An examination of the relevant literature and synthesis of key findings illustrates that collective action is a broader, more fluid, and inclusive phenomenon compared to group support systems, and new approaches that embrace these changes are needed to study them. Keywords

Group decision and negotiation · Group support systems · Group behavior · Crowdfunding · Digital activism · Collective action

Introduction Through the 1990s, information systems scholars designed and evaluated a cadre of information systems, i.e., group support systems (GSS), oriented toward facilitating group processes (Applegate et al. 1986). This line of research indicated mixed outcomes from GSS use. For example, GSS were associated with improved idea generation (Nunamaker Jr et al. 1987), reduced process losses such as production blocking and free riding (Reinig and Shin 2002), enhanced participation (Zigurs et al. 1988) and information sharing breadth (Miranda and Saunders 2003), more egalitarian group processes, higher group cohesiveness and more productive conflict management (Chidambaram et al. 1990), lower susceptibility to normative pressures (Clapper et al. 1991), and the gender divide in teamwork (Gopal et al. 1997). But GSS use has also resulted in stifling issue-based conflict (Miranda and Bostrom 1993), incomplete information processing (Dennis 1996; Miranda and Saunders 2003), and flaming (Alonzo and Aiken 2004).

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Other research revealed more nuanced effects of GSS use, especially when considering time. For example, impacts of GSS on relational development in teams were found to improve over time (Chidambaram 1996). Rather than the anticipated media differences in experienced social presence and communication effectiveness, Burke et al. (1999) reported differences between co-located and remote portions of work teams over time, with co-located and remote teams especially diverging at the midpoint. Such research built on earlier understandings of temporal factors in group work. For example, McGrath and colleagues (e.g., Kelly and McGrath 1985; McGrath et al. 1984) highlighted the phenomenon of entrainment, i.e., the tendency for teamwork to be paced by cycles beyond team boundaries such as the work week or the rhythms and performance on prior tasks. Gersick (1988) found that teams underwent what she termed a “punctuated equilibrium” in their engagements with their task and one another. In other words, they experienced an initial period of inertia, followed by a ramping up of efforts as the task deadline loomed. While subsequent research has attended to “midpoint” transitions in teamwork, GSS researchers have paid less attention to the role of external cycles. Synthesizing extant knowledge about the temporal patterning of GSS effects, Chidambaram and Bostrom (1997a, b) offered models of group development in such digitally supported collectives. They reviewed how groups develop over time in the context of, what was then, an emerging technology. Their review focused both on analyzing the differences across various models of group development and then synthesizing them to find common themes. Their work highlighted the two areas of focus that had dominated group development research for nearly a century, group processes and outcomes. Initially, unitary models of group development were very popular, that is, the notion that all groups go through a certain series of predefined stages. This deterministic view eventually gave way to a contingency perspective which recognized the uniqueness of each group and consequently rejected the idea of a single, predetermined series of stages. In this chapter, we begin by contrasting collective action, which transcends organizational boundaries, from the focus of GSS on small group behavior typically bounded by organizational parameters. In so doing, we explain how notions of teams, time, and technology have evolved. We then focus on how specific GSS technologies have given rise to ubiquitous digital platforms and how regulated structures embedded in these technologies have given rise to flexible affordances that can be invoked at will. Next we revisit Chidambaram and Bostrom (1997a, b) in the era of collective action and technology affordances, specifically in the context of crowdfunding and digital activism. We conclude with some observations that may help future research on these phenomena.

From Small Group Behavior to Collective Action Since the publication of Chidambaram and Bostrom (1997a, b), digital support has exploded in scale and scope. Dwindling costs and increasing miniaturization have combined to put powerful computing devices into most hands. Widespread diffusion

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of cellular service enables connectivity across those devices. Consequently, the communication technology underlying the erstwhile GSS is now almost ubiquitous. As technological capabilities have expanded, so too have the opportunities for collective action, which no longer is limited to a proximate few or even a handful of collaborators separated in time and space (Turoff et al. 1993). This modern era of ubiquitous connectivity has blown apart our notions of digital support for teams in two ways. First, it has blown apart our understanding of team membership. Even researchers investigating the dynamic and impromptu teams of the 1990s (e.g., Meyerson et al. 1996) could not have anticipated the nature of membership in the modern era. This fluidity of modern interactions belies the term “team.” We therefore resort to the term “collective action” instead. Second, the modern era has heightened a distinction introduced by Orlikowski and Yates (2002) – the distinction between chronos or clock time and kairos or experienced time – in digitally supported collective action. Previously, this distinction appeared academic, at best, when considering GSS. This is because the range of tasks supported by extant digital environments was strongly bounded by clock time – by the work day, the work week, or perhaps the month. In such temporally finite environments, the predominant temporal experience was clock time. Today, however, as collectives have pushed outside of organizational boundaries, temporal regulation of collective action is far more complex and often has little to do with clocks and calendars. In this era, kairos, rather than chronos, defines the pace of collective action. Figure 1 represents the space of collective action as it has evolved from GSS, including electronic meeting management and distributed/virtual teams to global digital platforms that enable forms of collective action such as crowdfunding and social activism. Figure 1 depicts the variety of phenomena related to collective action in relation to the dimensions of team membership and time. In such environments of fluid membership, completely adrift from the structuring effects of organizational boundaries or interpersonal familiarity, and of freedom from conventional temporal regulation, how do we apply and augment the lessons synthesized by Chidambaram and Bostrom (1997a, b)? The first task, we posit, is the need to recast the user from team to collective and the work supported from teamwork to collective action. Below, we summarize the key challenges posed by this required transition: 1. How we think of teams/collectives • Teams are no longer as well defined as they were in the GSS era. Both in crowdfunding and with digital activism, the membership of a collective is large and diffused, with members frequently entering and exiting the collective. • Group size is much larger when examining collective action compared to GSS research (see chapters on ▶ “Crowd-Scale Deliberation for Group DecisionMaking” and ▶ “Discussion and Negotiation Support for Crowd-Scale Consensus” in this handbook).

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Fig. 1 Evolution of technology, time, and teams

• Membership is more fluid, with members joining and leaving the group on a regular basis. • Membership is often voluntary and based upon attraction to the group or task rather than assigned by an organization. • It is often difficult to discern who is a member of the group. Membership is less clearly defined, and there may be multiple interpretations regarding what it means to be a member. 2. How we think of time • Notions of time are different when examining the development of groups using GSS technologies compared to those using digital platforms to achieve group goals. • Phases tend to be longer, ill-defined and depending on the context, and circular at times. • External events serve as “jolts” to initiate and accelerate – or even stop – activist activities. 3. How we think of technology Technology to support collectives has evolved to become more ubiquitous and encompasses all prior structures. In the GSS era, researchers (Chidambaram et al. 1990; Miranda and Saunders 2003; Zigurs et al. 1988) focused on structures since they represented distinct capabilities enabled by different GSS implementations (see also chapters on ▶ “Looking Back on a Framework for Thinking About

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Group Support Systems” and ▶ “Group Support Systems: Past, Present, and Future” in this handbook). In the current environment, technological capabilities are ubiquitous and pervasive requiring a focus on specific affordances activated by users. Hence, we focus on these affordances and map them to the GSS structures from Chidambaram and Bostrom (1997a, b).

From GSS to Digital Platforms and Technology Structure to Affordance The modern digital era ushered a transition from stand-alone technologies such as GroupSystems and VisionQuest to digital platforms. These include general purpose platforms such as Facebook and Twitter, as well as special purpose platforms such as crowdfunding site Kickstarter, and petition site Change.org. A digital platform is a “sociotechnical assemblage encompassing the technical elements (of software and hardware) and associated organizational processes and standards” (de Reuver et al. 2018, p. 126). Unlike stand-alone technologies of the 1990s, digital platforms are generative – meaning they enable the creation of new tools. These emergent tools can be devices such as badges, whereby investors honor projects on a crowdfunding platform or protest memes used to mobilize activism. The sociotechnical assemblages that constitute digital platforms include a vast range of functionalities. No longer is it relevant to consider technology structures and their introduction and appropriation to aid in group development. Technology structures were defined as the “rules and resources provided by technologies and institutions as the basis for human activity” (DeSanctis and Poole 1994, p. 125). Today, technological resources are ubiquitous and the rules governing their use in a constant state of flux. Our technical lexicon accordingly also has evolved from technology structures to technology affordances. The term “affordance” came into use in the digital technology literature to capture the potentially infinite flexibility or malleability of such technology. An affordance is defined as “the possibilities for goal-oriented action afforded to specific user groups by technical objects” (Markus and Silver 2008, p. 620). Whereas early group work was primarily motivated by an assigned task or performance goals, today’s group work encompasses voluntary participation and accommodates a range of personal motivations. Group development, then, depends on the activation of affordances that address both situational and psychological needs of the group. These affordances often employ several, if not all, of the traditional GSS structures at once (Fig. 2). For example, most of the affordances rely on the equal and open access to communication channels provided by simultaneity. Applied to the affordance for interactivity, simultaneity allows multiple users to interact with one another and the virtual environment in real time, such as picking up an object set down by another user in a virtual world. Used in affordances for competition, simultaneity allows users’ equal opportunity to participate. The use of GSS structures also varies depending on how an affordance is invoked. Structures for process structuring are less prevalent across affordances, suggesting that such structures may

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Fig. 2 From GSS structures to technology affordances

be dominantly used for affordances associated with situational needs such as collaboration or group management. Yet, affordances for content sharing are frequently invoked for both situational and psychological needs of a group. For example, a social media platform may allow for simultaneous contribution by many users with little regulation as to who, when, and how content can be contributed. In other cases, as in many online forums, the process is more regulated and structured with rules for who can share and when and what content can be shared. The list of technology affordances in Fig. 2 notwithstanding the range of affordances is evolving with the available technological platforms. Early work on social media affordances, for example, named only four: visibility, persistence, editability, and association (Treem and Leonardi 2012). Platform generativity, however, has seen the evolution of social media platforms such that Facebook users are able to create and manage groups (Moreau 2019), i.e., giving rise to the group management affordance, and run birthday fundraisers (Buxton 2018), i.e., sourcing funds, Twitter users are able to portray a “verified” self (Kanalley 2013), i.e., honing the affordance for self-presentation, and third-party providers such as Hootsuite enable automated, pre-scheduled content sharing. The next major task, we posit, therefore is the need to recast the technological environment from stand-alone technology to digital platform and digital functionality from structure to affordance. Below, we summarize the key challenges posed by this required transition: • In lieu of costly, stand-alone group support technologies, collectives today have access to platforms that offer an array of technological capabilities. • The pool of functionalities available no longer is finite but evolves as users avail of platform generativity to meet their immediate needs and others. • These capabilities are ubiquitous and pervasive, shifting the arena of collective action out from well-heeled organizations to even the most economically marginalized citizen. Given our focus on affordances in the context of collective action, including digital activism and crowdfunding, and detailed descriptions of affordances

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elsewhere (e.g., Karahanna et al. 2018), we refrain from providing generic definitions of each affordance. Below we examine specific affordances across time in each context.

Chidambaram and Bostrom Revisited in the Era of Collective Action Chidambaram and Bostrom (1997a, b) examined the critical question of why group development differed across groups and identified five key factors – the groups examined differed across studies; how development was operationalized also differed across studies; the tasks performed by groups varied in scope and difficulty; the length of time groups existed differed; and the methodologies used to study groups differed. We reexamine these factors in the context of two emergent areas of study related to, yet different from, GSS – crowdfunding and digital activism – referred to as collective action. In particular, we examine how notions of time and teams are different in these contexts and how those differences could impact processes and outcomes.

Affordances Across Time in the Context of Crowdfunding Here we note the differences in notions of time between GSS and crowdfunding: • Time is quite linear and somewhat longer (weeks, months) than in GSS research. • There is a sequence of activities, quite well paced, and outcomes are clearly denoted and visible, with nonperformance being costly. • Of the key temporal milestones, the start and finish are well-marked. Like in GSS research, the start seems to have a significant impact on processes and outcomes. Time in crowdfunding projects typically can be categorized as across-project, within-project, and some combination of across and within-project influences on funding success. An exception to this trend is Burtch et al. (2013) who investigated post-funding consequences of within-project contribution patterns. Across-project studies focus on some form of relationship formation or status production that a project founder receives from past participation. Within-project studies focus on dynamic changes over the life of the funding period, typically either founderinvestor interactions or visibility of investor actions, and the influence those changes have on total funding.

Early Impacts (Pre-proposal) Key affordances invoked in the pre-proposal phase of a crowdfunding project that have shown to impact its outcomes are self-presentation, relationship forming, and content sharing.

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• Self-presentation can be an important affordance at this early phase that affects discrimination (Younkin and Kuppaswamy 2017), although these biases are mitigated by previous project successes. • Relationship forming affordances help leverage internal social capital development within the crowdfunding platform and its strength over the course of multiple crowdfunding projects (Butticè et al. 2017). Thus, having such capital from previous projects can over time impact the current project. • Content sharing affordances invoked in the pre-proposal period are of particular concern with equity crowdfunding. These affordances can have a positive impact over time; however, this effect reaches a threshold and thereafter reduces an entrepreneur’s incentive to exert effort; hence, it can reduce expected profit after this point is reached (Bade and Krezdorn 2018). Similar effects are reported for investor cohesion in that it provides a trade-off in staged investment where the greater number of investors encourages investment through greater likelihood of profit-sharing and encourages project success, yet the same threshold effect can limit project funding.

Early and Late Impacts (Early and Late Funding) Time within-project studies is largely considered fluid between the start and end dates of the funding period, with affordances invoked dynamically over time. However, there is indication that some affordances may be more impactful on outcomes when invoked early rather than later in the funding period. • Self-presentation affordances enable entrepreneurs and investors to reveal information about who is involved with a crowdfunding project. This affordance can be a double-edged sword. Whereas self-presentation by early investors can be positively associated with later contributions (Burtch et al. 2016; Vismara 2016), demographic cues such as gender or race can lead to discrimination that negatively affects project outcomes (Colombo et al. 2015; Mohammadi and Shafi 2018; Younkin and Kuppuswamy 2017). • Content sharing affordances are used by entrepreneurs to provide investors with enhanced information processing about the crowdfunding project. These affordances are invoked over time as both static and dynamic content. Static content sharing at the start of funding can provide cues as to the level of development of the project (Skirnevskiy et al. 2017) or set expectations regarding success measures (Kuppuswamy and Bayus 2017). Other content is more dynamic, with entrepreneurs providing updated content as the funding period progresses (Burtch et al. 2018). • Affordances for browsing other’s content are a dominant aspect of crowdfunding process and outcomes. Investors are heavily influenced by the actions of other investors in terms of contribution amount (Burtch et al. 2016), number of backers (Thies et al. 2016), and total funding progress (Niemeyer et al. 2018). Often, these affordances influence outcomes to a stronger extent than other affordances invoked at the same time (Colombo et al. 2015; Wessel et al. 2019; Xiao and

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Yue 2018). The distinction between early and late funding phases is also strongly evident, where early investment attracts later investment (Bade and Krezdorn 2018) and funding progress is critical when the funding deadline is close (Burtch et al. 2018). • Metavoicing affordances enable investors to actively attract other investors to the crowdfunding project. Invoking these affordances, investors serve as referral agents, often by sharing information about the project on social media (Kuppuswamy and Bayus 2017; Thies et al. 2016). • Competition affordances allow investors to identify and compare alternatives to the crowdfunding project. As with content sharing affordances in the pre-proposal period, affordances for competition are primarily invoked in equity crowdfunding projects. The influence of competition on equity crowdfunding outcomes is mixed (Kuppuswamy and Bayus 2017; Vismara 2016); however, the relationship may be particularly susceptible to changes in time, with differences in the relationship across a single day or over the course of a week (Block et al. 2018). • Affordances for sourcing enable investors to verify information provided by entrepreneurs from external sources. “Staff picks” from the crowdfunding platform or external endorsements such as certificates (Mohammadi and Shafi 2018) or patents (Vismara 2016) are particularly important in attracting investment in the early funding phase. Below, in Table 1, we present a summary of previous research on crowdfunding as it relates to technology affordances and time.

Affordances Across Time in the Context of Digital Activism Here we discuss the second area of focus in this chapter, digital activism. As seen in Fig. 1, notions of time and team membership in the context of digital activism evince the following characteristics: • Time is less linear and much longer (months, even years) when examining collective action. • There is a sequence of activities, but they are halting at times, rushed at times, and backtracking at times, representing sequences seldom seen in GSS group development research. Moreover, outcomes are more difficult to discern although when they occur, they could be significant in terms of magnitude. • None of the key temporal milestones – start, middle, or finish – are well-marked. Within the context of digital activism, there is great variance across affordances in how they interact with time. We focus on synthesizing their impacts loosely

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Table 1 Technology affordances and time in crowdfunding Affordances Selfpresentation

Content sharing

Time Pre-proposal BCW17: founder previous success enhances funding; mediated by previous social capital SBB17: track record of creator is positively associated with early backers

BK18: entrepreneurial effort pre-campaign influences investment early funding HM17: pre-valuation influences willingness to pay for cash flow rights

Early funding Late funding CFR15: projects with male founders are less likely to success BGW16: concealment of investor identity reduces later contributions (likelihood and amount) HM17: geographical distance reduces premium KJT17: advocate geographical distance enhances later funding KJT17: advocate social capital enhances later funding KJT17: gender of entrepreneur is not significant MS18: female investors more likely to invest in projects with greater male investment SKD17: static cues about founder enhance ability to detect fraud YK16: removing founder race enhances funding V16: investors with a public profile increase early investors BCW17: visuals enhance likelihood of funding BCW17: higher targets reduce likelihood of funding BHM18: there is a time delay of the positive effect of updates CFR15: visuals and external information don’t significantly affect likelihood of success HM17: funding goal influences willingness to pay for cash flow rights KB17: updates are positively associated with later support KJT17: higher targets are positively associated with funding amounts KJT17: visuals do not significantly impact funding amounts MS18: female less likely to invest in younger/high tech firms SKD16: static cues (target, number of reward levels) about project enhance ability to detect fraud TWB16: updates decrease number of backers XY18: project description length is positively associated with investor amount XY18: number of updates is positively associated with investor timing WAB18: phantom reward options are associated with backers choosing equivalent but undiscounted rewards (continued)

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Table 1 (continued) Affordances

Interactivity Presence signaling Relationship formation

Group management Browsing others’ content

Time Pre-proposal

Early funding BCW17: external information enhances likelihood of funding early in campaign BHM18: founder updates enhance funding but lose significant the greater the number over time SBB17: external information enhances number of backers and funds raised early in the campaign

Late funding KB17: amount of funding close to the goal will be higher for projects with large vs small goals

BCW17: founder social capital from previous campaigns enhances funding BCW17: longer time between last successful campaign and the current project makes social capital weaker CFR15: founder social capital has positive effect on number of backers and funding early in the campaign SBB17: founder social capital means a higher contribution by “loyal backers” early in the campaign

BGW16: investors are influenced by previous investors’ actions; both in contribution and in selfpresentation/content sharing decision norms BGW16: concealment of investor amount of contribution reduces later contributions (likelihood and amount) BGW13: greater number of views enhances contributions (continued)

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Table 1 (continued) Affordances

Time Pre-proposal

Early funding

Late funding

BHL18: prior contribution is positively associated with investment BHM18: progress in funding and herding positively number of investments within a day and a week BHM18: number of investors negatively associated with amount of investment within a day but not a week HKM17: providing information regarding previous investments enhances funding; particularly when targeted toward those who contribute less than average HM17: number of investors positively associated with willingness to pay for cash flow rights MS18: number of prior investors is positively associated with female investment NTHW18: funding progress enhances investment, arousal in investors TWB16: number of backers positively influences later backers TWB16: number of backers has more immediate effect on funding than Facebook shares XY18: peer investors have stronger influence than fundraisers’ efforts BK18: early funding BHL18: provision positively associated points and time to with later funding deadline moderate (greater chance of influence of prior profit) and negatively contributions on future associated with later investment where it entrepreneurial effort matters more closer to (likelihood of sharing the deadline profit) HM17: sniping at the CFR15: early backers/ end of the auction has capital mediate no significant effect on between founder social willingness to pay for capital and funding cash flow rights KB17: lack of early support enhances the amount of the additional support that happens near the target goal SBB17: early backers mediate effect of creators’ track records on funding (continued)

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Table 1 (continued) Affordances

Metavoicing

Communication

Collaboration Competition

Sourcing

Time Pre-proposal

SBB17: referrals in third-party networks during prior campaigns enhance success of later campaigns

Early funding

Late funding

V16: early investors attract late investors WAB18: number of backers who chose the early bird option weakens the relationship between discount and the phantom effect of soldout rewards BCW17: rewards for “community belonging and sharing” do not significantly affect likelihood of success BHL18: Investors finding project via referral links reduces significance of relationship between browsing and funding CFR15: rewards for “ego boosting” and “community belonging and sharing” enhance likelihood of funding success KB17: number of tweets enhances added backers KJT17: advocate referrals enhance funding amount TWB16: Facebook shares have longer impact on funding than does previous backers SKD17: dynamic discussion content and linguistic cues enhance ability to detect fraud TWB16: number of comments enhances later backers BHM18: competing “blockbuster” projects are positively associated with investment and amount within the same day but not over a week HM17: premium increases with stock market volatility KB17: number of competing projects is not significantly associated with number of added backers V16: competing offerings negatively affect early and late investment BHM18: updates about external certification negatively influence investment amount KB17: “popular” projects list positively associated with added backers MS18: external certificate enhances investment TWB16: Indiegogo tweeting about a project increases backers YK16: third-party endorsements reduce (moderates) bias against black founders (continued)

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Table 1 (continued) Affordances

Time Pre-proposal

Early funding BCW17: “staff picks” enhance likelihood of funding early in campaign SBB17: being a “staff pick” enhances number of backers and funds raised early in the campaign V16: patents positively impact early but not late investment

Late funding

Note: Italics represents equity crowdfunding studies; BK18: (Bade and Krezdorn 2018), BHM18: (Block et al. 2018), BGW13: (Burtch et al. 2013), BGW16: (Burtch et al. 2016), BHL18: (Burtch et al. 2018), BCW17: (Butticè et al. 2017), CFR15: (Colombo et al. 2015), HKM17: (Hashim et al. 2017), HN17: (Hornuf and Neuenkirch 2017), KJT17: (Kang et al. 2017), KB17: (Kuppuswamy and Bayus 2017), MS18: (Mohammadi and Shafi 2018), NTHW18: (Niemeyer et al. 2018), SBB17: (Skirnevskiy et al. 2017), TWB16: (Thies et al. 2016), V16: (Vismara 2016), WAB19: (Wessel et al. 2019), XY18: (Xiao and Yue 2018), YK17: (Younkin and Kuppuswamy 2017)

following an early-middle-late framework so they are consistent with our synthesis of crowdfunding and comparable to the original work of Chidambaram and Bostrom (1997a, b).

Early Impacts (Framing) While many affordances may invoked the early stages of digital activism, referred to as framing, four stand out – self-presentation, content sharing, metavoicing, and communication. • Self-presentation affordances enable users to frame meanings of who they are as individuals or organizations during early stages of online social movements (Young 2018). Such frames may be communicated verbally, graphically, or experientially depending on which technology features are available to users (Yetgin et al. 2012). Self-presentation affordances allow activists and organizations to frame and negotiate identity boundaries early on through digital media (Ortiz et al. 2019). • Content sharing affordances allow diffusion of information about triggering events such as a social injustice, which can spark collective action and social movements (Sandoval-Almazan and Gil-Garcia 2013a) depending on the framing of the information early on. Content sharing affordances allow users to enhance the appeal and memorability of information diffused online (Yetgin et al. 2012).

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• Metavoicing affordances allow users to like, share, comment, and repost content, which may elevate the visibility and impact of frames depending on the user’s clout (George and Leidner 2019). • Communication affordances in online social movements resemble content sharing affordances as much of the communication is broadcast rather than interpersonal communication. Communication affordances can be used for framing during the early stages of a social movement (Zheng and Yu 2016).

Midway Impacts (Mobilization) In addition to the four affordances discussed earlier, mobilization – the middle phase of digital activism – appears to rely on the affordances of relationship formation and group management. These are summarized below: • Affordances for self-presentation allow social movement organizations to rally support around their missions and interests through digital media (Zheng and Yu 2016). As framing gives way to mobilization. • In online social movements, content sharing allows users to sponsor interpretive packages which frame meanings and create social movement culture, which then mobilizes users by focusing attention and effort toward a common goal (Miranda et al. 2016). These affordances also enable recruitment (Zuckerman 2014). • Relationship forming affordances have been used to forge relationships in earthquake responses (Nan and Lu 2014a), provide support during the Gulf oil spill (Vaast et al. 2017), and enroll kids for the Chinese free lunch program (Zheng and Yu 2016). • Group management affordances have been used for a variety of purposes from connecting with fellow Syrian activists (Seo 2019) to identifying people supporting a common cause using hashtags (Sandoval-Almazan and Gil-Garcia 2013b) and from connecting activists (Selander and Jarvenpaa 2016) to helping self-organizing groups (Tye et al. 2018). • Metavoicing is sometimes the product of activist bots inflating protests for the monetary or political gain of the bots’ programmers after they have started (Salge and Karahanna 2018). • While communication affordances can be used for framing during the early stages of a social movement, they can also be used for mobilization through agenda setting (Zheng and Yu 2016).

Late Impacts (Protest Actions) Later in the lifecycle of an online social movement, several affordances appear to impact digital activism by enabling action. • Content sharing affordances have enabled the enactment of solutions (Young 2018) through protest (Miranda et al. 2016; Yetgin et al. 2012), helped coordinate

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safe participation in student marches (Sandoval-Almazan and Gil-Garcia 2013b), replicated information sources on organizing rallies (Tye et al. 2018), and enabled the sharing of online petitions for water rights (Young 2018). • While metavoicing may bring attention to social movement frames or contribute to recruitment and mobilization, the low cost of metavoicing has also been associated with “clicktivism” and “slacktivism” wherein users substitute low-effort metavoicing for meaningful protest actions. • Collaboration affordances enable the emergence of organized collaboration among loose ties. These affordances are harnessed by social movement organizations to recruit and organize activists globally with reduced cooperative costs (Selander and Jarvenpaa 2016). Thus, affordances for collaboration are most salient during the later stages of an online social movement. • Sourcing affordances enable users to find and verify information from multiple sources. These affordances are especially useful in contexts where the press may be censored by the government (Ortiz et al. 2019), religious officials (Stewart and Schultze 2019), or monopolizing corporate interests (Miranda et al. 2016; Yetgin et al. 2012). Sourcing affordances, while useful in the early stages, may also be used later in an online social movement to identify productive protest tools, e.g., code for engaging in hacktivism or developing experiential frames (Yetgin et al. 2012). Distinguishing between real and fake information online is one of the major challenges facing online social movements. Below, in Table 2, we present a summary of previous research on digital activism as it relates to technology affordances and time.

Toward a Better Understanding of Time in Digitally Enabled Collective Action As we discussed in this chapter, conceptualizations of all three elements that Chidambaram and Bostrom (1997a, b) focused on – teams, time, and technology – have dramatically changed over the past two decades. While changes in teams and technology have received scholarly attention, the role of time has largely been ignored, even in the two exemplars of collective action that we examined – crowdfunding and digital activism. Below we highlight some fruitful areas of inquiry for future research.

The Midway Transition Gersick’s (1988) work provides some of the best insight to examining the role of time in emerging research on digital collective action. In Gersick’s work, the chronological midpoint was significant because it represented a change of focus to task completion and a quickening of the pace. While a chronologically identifiable midpoint was not evident in studies of crowdfunding or digital activism, the idea of a transition at a kairotically relevant point was evident in many studies. Early funding

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Table 2 Technology affordances and time in digital activism Affordances Selfpresentation

Content sharing

Time Early (framing) GC15: not showing protesters’ faces in videos of protests in Iran’s green revolution SG13: countering identity challenges with videos documenting their student status in the Mexican “I’m Number 132” movement SJ16: taking selfies to show commitment to Amnesty International campaign SS17: verifying identities of hijab opponents via Facebook profiles Y18: sharing personal accounts of history and identity from tribal elders ZY16: verifying identity of advocates for a free lunch for kids program in China GC15: sharing videos of post-election crisis S19: exposing actions of the Assad regime to the international community SG13: students uploading videos from cell phones to YouTube documenting Pena Nieto evading their efforts to engage OAR13: sharing content about triggering events such as the Mumbai terrorist attacks, Toyota recall, and Seattle café shootings YYM12: sharing a censorship frame to compete with the

Mid (mobilization) MYY16: enable unconstrained emotion sharing ZY16: signaling celebrity participants in China free lunch for kids program via digital “hall of fame”

Late (protest actions) Y18: using ICT tactic tools to challenge dominant narratives of the Klamath Tribes’ organizational identity

MYY16: recruiting participants with catchy “signature elements” illustrating movement frames SJ16: develop action repertoires to mobilize resources for Amnesty International causes Z14: recruiting movement participants with “cute cat” posts YYM12: representing frames verbally, graphically, and experientially Y18: disseminating information on registering to vote and politicians’ stance on issues

S19: sharing tactics and coordinating with other revolutionaries within and outside Syria SG13: coordinating a student march and sharing tactics for safe participation TLTTK18: replicating informational resources and sharing instructions on organizing rallies overseas YYM12: sharing digital resources for participating in online SOPA strike, implementing online protest activities Y18: sharing online (continued)

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Table 2 (continued) Affordances

Time Early (framing)

Mid (mobilization)

proposed piracy frame for the SOPA legislation MYY16: enabled one-sided framing dominate public discourse TLTTK18: enabling the Malaysian diaspora to contribute to political discourse VSLN17: enable advocacy Y18: sharing cultural frames of meaning about who the Tribe is as an organization ZY16: agenda setting and framing

petitions for water rights and environmental causes

Interactivity

YYM12: blacking out digital public resources such as Wikipedia, thereby “closing” them to the public on SOPA strike day SJ16: participating virtually in demonstrations by posting images of themselves outside their embassies

Presence signaling

Relationship formation

Late (protest actions)

MMY16: unconstrained message authorship in SOPA discourse allowed activists to network and diffuse unique frames

G&L19: digital activism participants connect using a variety of ICTs MYY16: unconstrained citation and social influence NL14: forging relationships in earthquake response OAR13: relating via directed tweets VSLN17: providing support during Gulf oil spill ZY16: mobilizing resources and enrolling participants (continued)

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Table 2 (continued) Affordances

Time Early (framing)

Group management

Browsing others’ content

Metavoicing

MYY16: viral sharing of only popular frames leads to dominance of either pro- or antimovement frames

Mid (mobilization) for the Chinese free lunch for kids program NL14: indicating support for crisis response proposals by “ding”ing S19: connecting with Syrian diaspora activists via Facebook groups SG13: using hashtags to identify people with a common issue SJ16: connecting Amnesty International with activists via Facebook group SS17: connecting hijab opponents via a Facebook group TLTTK18: connecting the Malaysian diaspora via self-organizing Facebook and Twitter groups GC15: documenting history via videos of Iran’s post-election crisis OER15: signaling via hashtags in the Egypt revolution NL14: ongoing conversation in aftermath of earthquake GL19: supporting a digital petition GC15: signaling support for a cause by subscribing to, viewing, and/or commenting on YouTube channels and videos SJ16: supporting Amnesty International causes by following them on Facebook and

Late (protest actions)

YYM12: notification of strikes and other protest activities

G&L19: metavoicing may be low cost and low-impact way to protest YYM12: metavoicing as protest can have real political impacts

(continued)

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Table 2 (continued) Affordances

Communication

Collaboration

Time Early (framing)

Z&Y16: framing and agenda setting for the Chinese free lunch for kids program SS17: translating captions for photos of women protesting the hijab Y18: broadcasting desired organizational identity frames NL14: developing and prioritizing proposals for disaster relief

Mid (mobilization)

Late (protest actions)

liking their posts NL14: supporting each other in earthquake aftermath by gathering and conversing online OER15: signaling sympathy with an issue via hashtag use OTRV12: signaling revolution support via retweets SK18: signaling support via automated retweets by bots SS17: signaling support for going hijab-less via likes for a Facebook photo VSLN17: supporting and amplifying retweets of posts regarding the Gulf oil spill OAR13: directed tweets in aftermath of crises

GLH18: guaranteeing a response once a certain number of digital signatures to a petition are obtained NL14: verifying ground truths in aftermath of natural disaster MYY16: evolution of signature elements ZY16: distributed collaboration in implementing the

YYM12: evolution of digital protest resources, hacktivism GL19: data activism, information exposure, hacktivism

(continued)

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Table 2 (continued) Affordances

Time Early (framing)

Mid (mobilization)

Late (protest actions)

Chinese free lunch for kids program Competition

Sourcing

MYY16: competing piracy/censorship frames of the antiSOPA movement SJ16: competing prostitution/trafficking frames GL19: supporting movements via online philanthropy and product sales YYM12: crowdsourcing protest toolkits, sharing ProPublica/SOPA Opera resources

YYM12: crowdsourcing protest memes

Note: Italics represents emergency management studies; GC15: (Ghobadi and Clegg 2015), GLA18: (George and Leidner 2018b), GLH18: (George and Leidner 2018a), MYY16: (Miranda et al. 2016), NL14: (Nan and Lu 2014b), OAR13: (Oh et al. 2013), OER15: (Oh et al. 2015), OTRV12: (Oh et al. 2012), S19: (Seo 2019), SG13: (Sandoval-Almazan and Gil-Garcia 2013a), SJ16: (Selander and Jarvenpaa 2016), SK18: (Salge and Karahanna 2018), SS17: (Stewart and Schultze 2017), TLTTK18: (Tye et al. 2018), VSLN17: (Vaast et al. 2017), YYM12: (Yetgin et al. 2012), Y18: (Young 2018), Z14: (Zuckerman 2014), ZY16: (Zheng and Yu 2016)

in crowdfunding and mobilization in digital activism represented these transitions. What happened before these phases appeared to have a significant impact on what happened after these phases. These ideas need to be studied systematically in future research.

Entrainment Another fruitful area of inquiry about the role of time in digitally enabled collective action is related to entrainment. Entrainment is “the synchronization of the tempo and/or phase of two or more activities” (Pérez-Nordtvedt et al. 2008, p. 785). Extant research suggests crowdfunding may entrain to cycles in the physical environment. For example, Mohammadi and Shafi (2018) reported that contributions to equity projects on the European crowdfunding platform, Companisto, entrained by 10–15% to weather changes, operationalized as changes in cloud cover. Social movements, in contrast, have been found to entrain to social cycles. For example, Earl (2007) reported the digital movement leadership entrained to presidential election cycles. Scholars such as Hensby (2017) and Melgaço and Monaghan (2018) have noted the role of social media in amplifying the entrainment of cross-national cycles of

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contention. Thus, examining what factors affect entrainment patterns in different genres of collective action will offer important insights about the role of time.

Jolts Finally, the relevance of events outside the control of the collective, regardless of when they occur, could have an outsize impact on the stakeholders. Meyer (1982, p. 5) first noted the salience of exogenous jolts, i.e., of “a sudden and unprecedented event,” on the workings of organized groups. On the role of environmental jolts, the crowdfunding literature appears largely silent. The social movement literature points more strongly to the role of environmental jolts than to entrainment. For example, Sine and Lee (2009) pointed to the role of the energy crisis in mobilizing the environmental movement. Like with other temporal phenomena, the timing of the jolt may also be key to understanding its impact. Thus, any study of collective action – especially those prone to exogenous events such as social movements – must incorporate the role of jolts and their interaction with time to better understand outcomes.

Cross-References ▶ Crowd-Scale Deliberation for Group Decision-Making ▶ Discussion and Negotiation Support for Crowd-Scale Consensus ▶ Group Support Systems: Past, Present, and Future ▶ Looking Back on a Framework for Thinking About Group Support Systems

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Group Support Systems: Experiments with an Online System and Implications for Same-Time/Different-Places Working Mike Yearworth and Leroy White

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Implementation of an “Online Mode” for Group Explorer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Time- and Place-Based Typology of Workshop Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Conventional Mode”: Same Time, Same Place . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Phased Mode”: Different Times, Same Place . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Online Mode”: Same Time, Different Places . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Autonomous Mode”: Different Times, Different Places . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temporal Sequencing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scaffolding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Facilitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Animating Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Social Media Platforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prospects: Crowdsourcing and GDN-Like Behaviors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix A: Setting Up and Running Group Explorer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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An analysis of the Group Explorer Group Support System (GSS) is presented from the perspective of its implementation as technology that can support sametime/different-places group workshops. Experiences with using a same-time/ M. Yearworth (*) Business School, University of Exeter, Exeter, UK e-mail: [email protected] L. White Warwick Business School, University of Warwick, Coventry, UK © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_48

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different places GSS are reported and issues that arise from these experiences are discussed with regard to future prospects. The current state of GSS and how they support the use of distributed problem structuring methods (PSMs) in both single organization and multi-organization settings is reviewed. The configuration and use of a cloud-based online version of the GSS is presented that highlights some of the key technological, organizational, and facilitation issues involved in supporting distributed PSM workshops. The future development of such online GSS is discussed with a particular focus on two emerging research questions; the future role of the facilitator in online GSS, and the commonalities between online GSS and social media platforms as different-times/different-places group working, such as crowdsourcing, become prevalent in the context of increasing globalization and the ongoing decentralization of work environments. Keywords

Group decision · Group support systems · Online · Facilitation · Problem structuring methods · Boundary object · Group support

Introduction We believe more needs to be done to improve our understanding of distributed Problem Structuring Methods (PSMs), especially the role of facilitation and the possibility of overlap and synergies with social media platforms. We ground our research in the use of the Group Explorer GSS that supports the Strategic Options Development and Analysis (SODA)/Journey Making methodology (Ackermann and Eden 2001; Eden and Ackermann 2001), which has been designed for use in complex problem contexts and can be considered as a member of the class of PSMs. Our empirical setting is the experimentation undertaken in the process of moving the software components of the Group Explorer GSS to a cloud-based computing environment to support problem structuring workshops, where the participants were based in different locations and represented different organizations. Distributed GSSs have long been a subject for study (Hiltz et al. 1996; Mittleman et al. 2000; Paul et al. 2004; Romano et al. 1999; Tung and Turban 1998; Turoff et al. 1993), but it is only recently that the global availability of lowcost cloud-based computing services has suggested novel ways in which distributed GSS can be deployed. The process of experimentation has suggested new research questions about the nature of facilitation and the role of social media platforms in relation to distributed GSS. The original motivation for our work emerged from the requirement to develop a GSS capability to support problem structuring workshops within an organization that had a globally distributed team and was inspired by the work of Morton et al. (2007). The process of moving the Group Explorer GSS software components to this new online environment prompted a re-engagement with questions about coordination, nonlinear agendas, and asynchronous behaviors (Hiltz et al. 1996). The

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requirement to support an organization with same-time/different-places problem structuring workshops led to a version of the Group Explorer GSS that was just as accessible for participants within a distributed organization (i.e., virtual teams Mittleman et al. 2000; Paul et al. 2004) as participants from different organizations. This prompted further experimentation during the development to support multiorganization group workshops (Ackermann et al. 2005; Franco 2008) as part of an EU-funded Smart Cities project.1 This was a consequence of an emerging requirement to provide a low-cost means of continuing with problem structuring workshops with multi-organization groups in Smart Cities planning. Furthermore, the near ubiquity of social media platforms and their undoubted role in supporting unstructured decision-making2 suggest that there could be a future cross-fertilization of features and use-cases between distributed GSS and social media platforms, especially crowdsourcing, as we discuss in the section “Prospects: Crowdsourcing and GDN-Like Behaviours.” We explore these questions first through a review of the literature concerning distributed GSS and problem structuring collaborative work. We then proceed to further elaborate the four-mode typology of same-time/same-place workshops (Johansen 1991; Lewis 2010). We then discuss our questions based on the experiments conducted using this system.

Review Early work assessing the general capabilities of GSS was conducted by Fjermestad and Hiltz (1998) and Nunamaker et al. (1996). Experiments with distributed GSS were conducted by Hiltz et al. (1996). The SODA methodology (Ackermann and Eden 2001; Eden and Ackermann 2001) was originally implemented using the “classic” tools of the facilitated face-to-face workshop – i.e., Post-it notes/ovals and flipcharts – and was eventually supported by the development of the Group Explorer GSS software. This led to an increase in the productivity of the workshops as well as affording benefits such as enabling anonymity of contribution (Ackermann and Eden 2010b). Causal mapping (Ackermann and Eden 2005) is central to the SODA methodology. Its use as a PSM in a Group Explorer GSS setting is well established (e.g., Ackermann et al. 2014; Franco 2014), and it has been further developed as the strategy making methodology, Journey Making (Eden and Ackermann 2018). Problem structuring methods can be used in problem contexts that involve participants from multiple organizations (e.g., Franco 2008) although this is less common and not without difficulties. For example, Freeman and Yearworth (2017) used a PSM with a multi-organizational group for low-carbon urban 1

The H2020 Smart Cities and Communities (SCC) Lighthouse Project REPLICATE (REnaissance of Places with Innovative Citizenship and TEchnology) (H2020-SCC-2015 691,735) 2 Or non-codified decision-making from a methodological perspective

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energy master planning and encountered a problem with a mismatch of power and interest of the participants taking part in the workshops. This led to lack of clarity about problem ownership and inadequate buy-in to the process, a situation unlikely to have occurred within a single organization. However, there is nothing inherent in the properties of the Group Explorer GSS that limit workshops to participants from a single organization. For example, the Group Explorer GSS supported a case study presented by Ackermann et al. (2005) which involves a certain amount of multi-organization working (see also chapter ▶ “Group Support Systems: Concepts to Practice” by Ackermann and Eden). Moving the Group Explorer GSS into an online setting opens up the possibility for more effectively supporting multi-organizational problem structuring without the need for face-to-face workshops. Such distributed problem structuring interaction is considered by Morton et al. (2007). They make the point that while distributed GSSs have been well studied (Hiltz et al. 1996; Kim et al. 2002; Paul et al. 2004; Tung and Turban 1998; Turoff et al. 1993), there is a “distinctively PSM view on the decision-making process” shared by other PSM writers that sets it apart from the GSS literature (Morton et al. 2007). Inspired somewhat by the policy delphi process (Turoff 1975) for reaching a group consensus view, Morton et al. describe a distributed variant of the SODA methodology, whereby a “group map” was built up from rounds of participant questionnaires that were conducted over a period of time and relied on asynchronous communication, e.g., email. The questionnaires typically contained a section of a group map and associated questions to either develop it further or ascertain some degree of prioritization of the concepts (i.e., preferencing and rating, as discussed later). Their research questions were focussed on comparing the effectiveness of the workshop-less process to a face-to-face workshop using an evaluation approach based on facilitation frameworks (Ackermann 1996) and when it would be appropriate to use such a distributed modality. They were not specifically looking at the distributed mode from the point of view of the performance of a GSS, and their findings talk more to the properties of the SODA methodology that mean that it can be implemented in this distributed modality. However, their conclusions do point to the fact that this enables different groupings of participants in the problem structuring process, particularly in terms of widening participation and suggesting the possibility of “large group interventions” (White 2002), a context we return to later. We see Morton et al. (2007) as setting the scene for the migration of the Group Explorer GSS to supporting distributed problem structuring engagements with stakeholders.

Implementation of an “Online Mode” for Group Explorer A certain amount of technical implementation detail behind the Group Explorer GSS is described here as this is pertinent to the discussion when we look at questions of facilitator-less instantiations of the GSS and its relation to social media platforms. The two main technology components that make up the Group Explorer GSS that supports the SODA/Journey Making methodology are (i) the causal mapping

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Fig. 1 Schematic representation of the components that make up a conventional Group Explorer GSS. Although two facilitators are shown here, it is possible for a single facilitator to combine both roles

software Decision Explorer3 and the (ii) Group Explorer, a software system that enables multiple users to interact directly with the causal map via their own user interface provided by the Chauffeur component and as controlled by the facilitator. In combination, we refer to the overall system as the Group Explorer GSS following usage of Franco (2014) and Yearworth and White (2017). A schematic diagram of the conventional Group Explorer GSS configuration is shown in Fig. 1. We will go on to argue that the mapping component is essential to the methodology and must always exist in a recognizable form but that the Group Explorer system is amenable to automation. The Chauffeur component is a server on the private local network. The actual user interface to the Chauffeur runs on the local participant consoles, which can be laptops or tablets. The user interface changes according to the stage of the meeting. In the “start-up” stage, the user interface is configured to register participants joining the system. In the “gathering” stage, the user interface enables participants to contribute to the causal mapping by entering statements and later linking them. In “preferencing,” participants are allocated colored tokens that can be assigned to label statements in the causal map according to criteria set by the facilitator. Finally, “rating” enables participants to vote on statements in the causal map. Between these stages the user interface is set to a waiting state. The causal map is made visible to the workshop participants by projecting the Public display. In addition to facilitating the workshop participants through the methodology addressing the problem structuring task at hand, the facilitator must configure and sequence the operation of the Chauffeur between the different stages of the meeting and also control the layout of the causal map. The complexity of these tasks sometimes

3

Decision Explorer is a causal mapping software available from https://banxia.com.

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requires two facilitators (as is shown in Fig. 1). An additional component on the Public server provides a summary display of information collected during the preferencing and rating stages of the meeting.

A Time- and Place-Based Typology of Workshop Modes The classification of workshop mode according to same or different time and place of group working is shown in Fig. 2 (Johansen 1991; Lewis 2010). The four modes each have their own distinct set of characteristics but all derive from the same underlying configuration of the Group Explorer GSS components. Their individual properties are described in the following sections. In addition to considering the time and place of workshops, our analysis of modes considers the following issues: 1. Facilitation: What is the division of focus between facilitation of the methodology and managing the operation of the GSS (Franco and Montibeller 2010; Yearworth and White 2017)?

Fig. 2 Four modes of Group Explorer workshops defined by same or different time and place of group working. Based on original figures by Johansen (1991, p. 221) and Lewis (2010, p. 265)

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2. Location: Is the workshop (i) room-based, (ii) online (i.e., distributed across the Internet), or (iii) mixed (Morton et al. 2007; Yearworth and White 2017)? 3. Time boundary: How time-bounded are the participants in the workshop? A roombased workshop, or sequence of them, is fixed to specific times and durations for obvious reasons, whereas online workshops are clearly more flexible. 4. Sequencing: Are the changes in the stage of the meeting, and their associated configurations, under the control of the facilitator, or could they in principle be devolved to the participants’ control? 5. Anonymity: To what degree is anonymity affected by the mode? One of the strengths afforded to participants by most GSSs is the anonymous labelling of contributions (Ackermann and Eden 2010b, p. 183). The four modes seem to provide a more nuanced perspective on anonymity. 6. Additional components: What additional technical components are needed for the GSS to work? In the conventional mode of same-time/same-place, no further technology is required apart from a data projector, laptops or tablets to host the participant user interface, and a wireless router. However, in the online mode, an additional third-party system is required to carry voice, screen sharing, and participant-to-facilitator “chat” messages4 so that participants can see the causal map as it develops on the Public display component.5 7. Data collection: What facilities are there in the GSS that support detailed data collection? Workshops that use GSS are an active focus for research in the Group Decision and Negotiation (GDN), Behavioral Operational Research (BOR), and Problem Structuring Methods (PSMs) research communities. In addition to the data log produced by the Group Explorer GSS and saved versions of the causal map, researchers also use data collection techniques relevant to ethnomethodology (Garfinkel 1996), such as video capture of the meeting room (see, e.g., Franco and Greiffenhagen 2018; Franco and Nielsen 2018), to study the microprocesses of group decision-making (Ackermann et al. 2018). This is practically impossible in the online mode, but the use of the conferencing system affords the capability of producing a combined voice recording and video of the causal map as it is developed on the Public display component (Yearworth and White 2017).

“Conventional Mode”: Same Time, Same Place This mode of using the Group Explorer GSS is not discussed in depth, its configuration is as described in the previous section. Examples of research using the GSS this way are described in, e.g., Ackermann and Eden (2010a), Franco (2014), Franco and Greiffenhagen (2018), and Franco and Nielsen (2018). There have also been

Although not strictly necessary, they do provide a silent “back channel” for the facilitator to provide additional help to participants experiencing problems in using the GSS in this online mode. 5 In the experiments reported here, the Citrix GoToMeeting conferencing system was used (https:// www.gotomeeting.com). 4

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developments in using GSS to support Group Model Building based on System Dynamics (SD) (Richardson and Andersen 2010) (see ▶ “Systems Thinking, Mapping, and Group Model Building”) (e.g., Herrera et al. 2016; Rouwette et al. 2011; Rouwette et al. 2000).

“Phased Mode”: Different Times, Same Place We do not consider this mode as particularly meaningful but is included here for completeness. It is more or less identical to the conventional mode but with potentially improved anonymity as different stakeholder groups could in theory be present in the room at different times between sessions.

“Online Mode”: Same Time, Different Places The porting of the standard Group Explorer GSS installation to the MS-Azure cloud environment is described in detail by Yearworth and White (2017) and is shown in Fig. 3. They discuss the effect on participants and the implications for the facilitator of moving to an online distributed GSS for supporting problem structuring workshops. The assumption behind the configuration of this mode is that the participants would be joining the meeting from many different locations, representing different organizations, and using a range of computers to connect to the GSS, i.e., there would be no controlling or supporting IT services to manage the configuration for the participants and ensure its correct operation.

Fig. 3 A schematic representation of the components that make up an online Group Explorer GSS. Here the servers that host the chauffeur and public components have been moved into the MSAzure cloud environment indicated by the MS-Windows logo. The conferencing system is represented by the Citrix GoToMeeting logo

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Yearworth and White (2017) describe a workshop focussed on making the Group Explorer GSS useable as a distributed GSS and used the online GSS itself to host the meeting. The map from this workshop is presented in Fig. 4. One of the main implications of this move online was that it revealed to the participants a considerable amount of the internal workings of the Group Explorer GSS that would normally be hidden in the conventional setting, where the initial setup and configuration of the system would be carried out before the participants entered the meeting. The facilitator is not co-located with the participants and therefore not able to easily sort out connection problems and help the participant with managing the use of two different user interfaces, to the Chauffeur and to the conferencing system that shares the Public screen showing the model. Considerable amounts of time are required instructing the participants in how to use the system and dealing with issues with audio quality arising from the interplay between the conferencing system and participants’ ICT. It is clear that the technical complexity of the online mode setup presents a real barrier to participants that needs to be overcome before the workshop proper can start (Yearworth and White 2017). As a consequence, detailed briefing notes have been produced to help participants prepare for their first online workshop. An example can be seen in Appendix A. However, once these barriers have been overcome, the “de-centring” of facilitation (Yearworth and White 2017), indicated by the facilitator appearing in the schema shown in Fig. 3 in a position identical to that of a participant, provides an excellent empirical setting for its further investigation.

“Autonomous Mode”: Different Times, Different Places In this mode, as shown in Fig. 5, the facilitator has been removed from the schema. The conferencing system has been downgraded to simply displaying the Public screen, and automation in the form of a “script” has been introduced (as suggested by the cogs) to sequence the Chauffeur component through the different stages of the meeting. The Group Explorer GSS in this configuration needs to be capable of operating unattended over long periods of time without facilitator intervention and starts to look more like an online platform than a GSS. The rules of how it should be used would have to be explained beforehand for it to make any sense as a GSS to the participants. In this mode it starts to make more sense to think of participants less as members of a workshop and more as users of a platform. An experiment has been conducted with this mode of operation in the gathering stage of a meeting (Yearworth and White 2017), and some of the issues are captured in Fig. 4. These are concerned with participants maintaining an understanding of what the map means between engagements with the GSS, especially as other participants will be adding statements to the map when there is no facilitator to modify the layout in Decision Explorer should it be required. However, there was no particular technical issue with remote participants interacting with the causal map, while there was no active facilitation to manage the Decision Explorer component.

Fig. 4 Making the Group Explorer GSS usable in the online mode

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Fig. 5 A schematic representation of the components that make up an autonomous mode of using the Group Explorer GSS. Here the use of the conferencing system is reduced to sharing the causal map. The cogs indicate that a certain degree of automation via scripts is required to control the components

Temporal Sequencing A typical engagement with a client is likely to entail more than one workshop. In the case of the conventional mode, we can just think of this as a sequence of instantiations of the GSS Conventional Mode1 ! Conventional Mode2 ! Conventional Mode3 ! . . . until the group work with the GSS is complete. The expectation is that between instantiations of the conventional mode, the Group Explorer GSS would be shut down to its passive state and thus not incur resource charges in the cloud environment. This is somewhat different from the imagined situation of the phased mode, where there would not be a sequence of instantiations as such but rather a sequence of groups using the same instance of the GSS.6 Results from experiments using the online mode have led us to the conclusion that more can be achieved with workshop participants in the online sessions if the participants already have some familiarity with the GSS and its methodology in the conventional mode, i.e., the sequence

6

Or conceivably, the same stakeholder group reconvening in the workshop space some time later. Between workshops, the Group Explorer GSS would remain active and running the same meeting on the Chauffeur. This mode of operation is somewhat contrived here as an imagined scenario but is entirely consistent with the same-place/different-times scenario using the MeetingWorks system as described by Lewis (2010, p. 265).

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ConventionalMode1 ! OnlineMode1 ! OnlineMode2 ! . . . would be a better way of achieving proficiency with the online mode. The use of the online mode to support multi-organization groups is an emerging need, e.g., in the case of the REPLICATE project. Project meetings, which are expensive and timeconsuming, would provide the opportunity for a conventional mode workshop to take place as a familiarization exercise for interacting with the Group Explorer GSS. Further, if the online mode infrastructure is used to host this face-to-face workshop, then it would provide the opportunity for a facilitator to “debug” the technical issues discussed in the section “Online Mode”: Same Time, Different Places.” The availability of the online mode then enables a subsequent sequence of low-cost workshops. The autonomous mode is envisaged as a continuous single instantiation of the GSS that persists for as long as required by the users.

Scaffolding The review of the four different modes of using the GSS and the temporal sequencing of these operational modes demonstrates that the problem structuring methodology can be thought of as consisting of three parts: (i) the technology of the modelling approach implemented by the software components, (ii) the rules of how these components can be used and when, and (iii) the actual process of using the GSS to support a methodology for achieving the purpose of the engagement. Yearworth and White (2017) have explored the question of how much of the first and second parts can be automated to become a scaffold7 for the methodology. This then leads to our core questions for discussion – What will be the future role of the facilitator as online and autonomous GSS become possible, and what are the commonalities between online GSS and social media platforms that mean that the latter could subsume some of the functionality of the GSS? Work by Yearworth and White (2017, 2018) has surfaced some of the issues behind these questions, which we now discuss.

Discussion To support our discussion, we make use of the behavioral classification schema devised by Yearworth and White (2018, p. 814) to establish the relationship between online platforms and Operational Research (OR) practices, specifically Community OR, an area of OR addressing problem contexts arising from community needs (Midgley et al. 2018; Midgley and Ochoa-Arias 2004). Their purpose was to establish the existence of OR-like behaviors through the patterns of interactions between participants on social media platforms not specifically designed to support OR practices. The behaviors of interest were those considered as matching the 7

Literally a supporting framework implemented in ICT that automates some of the tasks normally carried out by the facilitator in implementing the methodology

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Generic Constitutive Definition (GCD) for PSMs (Yearworth and White 2014). It was realized that the Group Explorer GSS in its online mode occupied a specific position in this schema and thus suggested a way of linking the analysis of problem structuring behaviors on social media platforms with the properties of an online GSS. The classification schema thus affords some analytical utility and we make use of it here. The classification schema shown in Fig. 6 is a development of the original Yearworth and White schema and was devised to help with classifying GSS in the context of group decision and negotiation and with a similar view to identifying GDN-like behaviors in the patterns of interactions between participants mediated by a GSS. The schema concerns behaviors of members of a group who perceive a problem exists and that action is required to resolve the situation. All behaviors of group members using a tool/technique/method that would be recognized by the GDN academic community as GDN-like are considered to be a subset. Here the existence of non-codified problem structuring behaviors is assumed to intersect with the set of behaviors that we have called GDN-like. We draw attention to this because of the argument established by Yearworth and White (2018) that there is a non-zero possibility of observing non-codified problem structuring behaviors mediated by social media platforms. From this it is reasonable to assume by a similar

Fig. 6 Classification of online mode Group Explorer GSS to support GDN based on the original schema devised by Yearworth and White (2018, p. 814)

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argument that we would be able to observe GDN-like behaviors taking place via social media. We make use of this assumption later. The behaviors associated with interactions mediated by the use of the Group Explorer GSS in online mode are classified as GDN-like behaviors. These are problem structuring methods that are also mediated by a digital platform but are not visible publicly.8 We can thus restate our questions as follows: Is there any evidence for behaviors on social media platforms that look like behaviors in the autonomous mode of using the Group Explorer GSS, i.e., do social media platforms enable behaviors that are GDN-like? If there is, then the GDN community might want to collect social media data to study GDN-like behaviors “in the wild” (Callon and Rabeharisoa 2003).

Facilitation We would also want to understand what has happened to the role of facilitation in this scenario. Is facilitation really necessary when working same-time/differentplaces? Can groups self-facilitate once the mechanistic aspects of a GSS, the scaffolding, have been tidied away by the development of better, more automated GSS software? Yearworth and White (2017) discussed this question using the lens of translation, a core concept in Actor Network Theory (ANT) (Callon 1986; Latour 1987). Translation captures the idea that in the evolution of a network of actors, such as formed by the interconnection of participants, facilitator, and the GSS, there are well-defined moments or phases when the way in which the actors interrelate changes. These phases signal that a transition has occurred in the way in which the overall actor network behaves. The moments of problematization and interessement, the binding together of the actors into a network through their interests in resolving the issue, (Callon 1986; White 2009) are likely to be precursors to workshops and thus independent of the use of a GSS. The existence of any mode of using the Group Explorer GSS assumes that the need to use it has already been established. It therefore becomes a tool that is used to bridge between the original moments of problematization/interessement and the group of participants collectively agreeing about what action to take. Certainly, in the case of the conventional mode of using the Group Explorer GSS, it is the facilitator that is instrumental in chaining these translations together. Furthermore, Yearworth and White (2018) observed a situation where spontaneous moments of problematization and interessement mediated by social media were taking place in the event of the severe floods in a city in the northwest of the UK in 2015. In addition, Yearworth and White (2017, p. 79) have observed translation taking place in an online workshop where the expertise of the facilitator, in methodology and the operation of the GSS in online mode, was suspended and replaced by the domain expertise of the participants coming to the fore and engaging in the

8

In set notation, the position occupied by the online mode of Group Explorer GSS is defined by the relationship GE  G \ P \ D  \ N \ ~O between the sets identified in Fig. 6.

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modelling process without prompting from the facilitator. Both these observations lead to the conclusion that in certain situations the conditions are right for GDN-like behaviors to be taking place on platforms without the intervention of the facilitator, at least for short periods of time.

Animating Methodology The translation observed by Yearworth and White (2017) highlighted the moment in a workshop when the entanglement between (i) the expertise of the facilitator in methodology and in the mechanics of operating the GSS, (ii) the GSS as a platform, and (iii) the domain expertise of the workshop participants became momentarily visible as individual threads of sociomaterial activity (Burger et al. 2019; Orlikowski and Scott 2008). Clearly, the purpose of the GSS and the role of the facilitator is to bring the third thread to the fore, but the complexity of the methodology and its implementation through the GSS means there is a trade-off in the amount of time in a workshop that is spent in the facilitator-led phases of the entanglement to enable productive time in the participant-dominant phases. Continuing with empirical work into the nature of this entanglement through the detailed observation of microprocesses in group decision and negotiation (Ackermann et al. 2018; Franco and Nielsen 2018) will likely contribute to further demystification of the role of the facilitator (Yearworth and White 2017) and lead to a better understanding of the animation of methodology (Hiltz et al. 1996). As an alternative approach, specific experiments could be conducted to investigate the effects of automation on specific aspects of the operation of a GSS. Limayem (2006) constructed an experimental setting for investigating the difference in performance between a conventional facilitated GSS and one where the facilitation was automated and incorporated into the GSS. Using a multicriteria decision model for a resource allocation task with a large sample of student participants, Limayen found no appreciable statistical difference in effectiveness between the two approaches. Wong and Aiken (2003) likewise found that automated facilitation was as good as expert human facilitation and actually performed better than novice facilitators, for an idea generation and ranking task. These and other studies reported on by Wong and Aiken (2003) focussed on post-meeting consensus, process satisfaction, and decision quality as key variables to assess the experimental findings from their work. They do point out the limitations of extrapolating from their findings to more complex tasks; therefore they may not apply to the sort of messy problem contexts that the SODA/Journey Making methodology would be used. However, they do suggest that there is a case for automating some of the aspects of the Group Explorer GSS. Some speculation about the feasibility of this is presented in Appendix A.

Social Media Platforms Yearworth and White (2018) argued convincingly for the existence of Community OR behaviors mediated by social media platforms. Their observation opens up the

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realm of academic study in group decision and negotiation away from the narrow world of workshops and corporate environments to the open and unconstrained world of decision-making mediated by social media platforms. While we believe that it is worth the effort to investigate social media for evidence of GDN-like behaviors, we might discover from a preliminary search that they do not exist.9 However, this immediately suggests that we should investigate the questions of what social media platforms might gain from acquiring some of the formal capabilities of a GSS and how these capabilities might be added? We would expect that such a development might improve the quality of debate, if not decision-making, over that taking place on social media today. This is certainly a question that deserves further investigation by scholars. Here we look at how one such online development, that of crowdsourcing, might show the way forward for further work.

Prospects: Crowdsourcing and GDN-Like Behaviors There is an increased interest in processes and methods that can represent the interests of the widest possible range of individuals in an organization or organizations (Bryson and Anderson 2000; White 2002). However, despite the progress in recent years, there is still much to learn about working with the largest group possible; indeed, the approaches to do this are stymied by attempts to get the “whole system in the room” (Weisbord and Janoff 2010). Today, there is a growing interest in more distributed decision-making. With the rapid rise of technology as an efficient means for the coordination of human activity, crowdsourcing is emerging as potentially a new form of problem-solving and group decision-making. Crowdsourcing represents an innovative approach that allows organizations to engage a diverse network of people over the Internet and use their collective creativity, expertise, or workforce for tackling complex problems (Brabham 2013; Brabham et al. 2014). It can be best conceptualized as a learning process with highly distributed participants (Heylighen 2013), where most of the physical constraints that used to govern space, time, matter, energy, and information are removed (Heylighen 2013). Crowdsourcing transforms distributed decision-making into local decision-making, thereby enabling individuals to enjoy the many benefits of distributed collaboration without having to endure many of its costs (Brabham et al. 2014). Examples of crowdsourcing cases include Wikipedia, Galaxy Zoo, and Yahoo! Answers, which rely on undefined crowds and can be distinguished by their logic of process, collaboration, collection, and competition (Zhao and Zhu 2014). In the context of crowdsourcing, a central concept is the “wisdom of the crowd” which describes processes, whereby people (in a crowd) solve problems and provide new insights and ideas leading to product, process, or service innovations (Brabham 9

Although we believe that the review of crowdsourcing in the following section provides sufficient evidence that the assertion is very unlikely to be false

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2013). The capacity to coordinate and network is created by connective and collaborative Web 2.0 environments that enable individuals to engage in virtual social learning, communication, and collaboration (Zhao and Zhu 2014). However, there is little understanding of this for a GDN setting. More research is thus needed on boundary conditions for crowdsourcing, which can be seen as indicative of the need to better understand the underlying processes of social learning and the relationship between distributed decision-making and organizational learning in particular. In other words, further research is needed to gain insight into technology-mediated coordination and how collaboration in large groups can be understood (Engel et al. 2015; Lykourentzou et al. 2013). Specifically, research would need to address the question of how crowdsourcing activity is related to distributed group decisionmaking, the quality of the ideas, and the creation of trust (Jain 2010). It is the type of task that allows group members to combine different abilities, skills, knowledge, or other physical and cognitive resources in a collective product that is more than any group member could produce alone (Laughlin 2011). As such, it can be argued that shared intentionality, i.e., the ability to participate with others in collaborative activities with shared goals and intentions, should be considered in seeking to understanding how crowdsourcing becomes effective (Tomasello and Rakoczy 2003). This review of crowdsourcing suggests compelling evidence of GDN-like behaviors that are mediated by platforms that have grown from the same Web 2.0 technology base as the social media platforms. This suggests that there should be synergies between the capabilities offered by GSS such as Group Explorer and these publicly available platforms. Setting up meetings and the preferencing and voting on options would seem to exist already, i.e., the Chauffeur component already has analogues. However, the cognitive mapping expressed as causal maps and the group elicitation of such maps still seem to be the preserve of the specialist, closed GSS. Ideally future work would focus on questions that concern the more widespread use of cognitive mapping tools and whether there would be uptake on public platforms. Some recent developments in this area such as kialo,10 which focusses on issue-based argumentation, and kumu,11 which supports issue mapping, are worth tracking.

Summary and Conclusions The process of implementing the Group Explorer GSS in an online mode has caused a re-engagement with research questions concerning the operation of same-time/different-places group workshops (Hiltz et al. 1996). The use of cloud-based computer resources to implement the GSS and ease with which 10

https://kialo.com https://kumu.io

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multi-organization group working has been enabled injects a new perspective on the behaviors of participants. The classification schema introduced in the “Discussion” section leads us to the observation that there is a relationship between the use of a distributed GSS to support problem structuring workshops and the presence of GDN-like behaviors taking place on open online platforms, especially those designed to support crowdsourcing. We characterize their relationship as representing two distinct streams of development. The distributed GSS stream is essentially concerned with methodological issues and reflects its emergence from the academic concern of developing problem structuring methods grounded in appropriate theories. In the case of SODA/Journey Making, this would be causal mapping, but we can also see similar threads in the case of the Strategic Choice Approach (SCA) and its concern with risk and uncertainty in planning (Friend and Hickling 1987, 1997, 2005), Causal Loop Diagrams (CLDs) and System Dynamics (SD) focussed on behaviors arising from feedback loops (Sterman 2000), or systems thinking in the case of Soft Systems Methodology (SSM) (Checkland 1981; Checkland 1999; Checkland and Scholes 1999). Eden (1995) has specifically reviewed the role of such decision models in wider group decision-making processes. The use of PSMs and GSS has largely been within organizations and communication about them restricted to academic and teaching texts. On the other hand, crowdsourcing platforms are open and have grown on the basis of meeting the functional requirements of their users. Development and communication have relied largely on Web 2.0 technologies and open source ideals and tools. Whether these two streams are ever likely to cross-share ideas is debatable. To a certain extent, the scaffolding provided by the Chauffeur is recognizable in other forms on other platforms, perhaps more as an implicit way of using them than anything that is provided by way of automation. However, the one thing that does set the two streams apart is the use of formal modelling approaches. As can be seen from the complexity of using Decision Explorer, it is extremely unlikely that formal causal mapping12 capabilities will find their way into open platforms in the future.13 However, the ubiquity of open platforms means that there is potentially a ready audience for better ways of making decisions, if only a way could be found for making these more formal techniques more approachable and easier to use. As an area of further work, we suggest that heuristics could be captured from the detailed analysis of how facilitators use these modelling approaches and then used to produce highly automated versions suitable for integration into open platforms. Unless researchers find a way of breaking out from the confines of purely academic interests in the development of GSS and PSMs, then their work will likely have little impact on the development of platforms that will be used by the majority

12

Or CLDs, SD models, Purposeful Activity System (PAS) models (ex SSM), STRAD (“STRategic ADvisor” ex SCA), or anything else complex and formal 13 Although as noted earlier, developments such as kumu are worth noting.

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of people in the future, even in business. Furthermore, until they find a “way in” to influencing these platforms, it is possible that the quality of debate and decisionmaking on them is always going to be less than that achievable with a well-designed GSS underpinned by an appropriate and well-theorized methodology. Perhaps the way of looking at the participant-developed decision models that underpin methodologies such as SODA, SCA, SSM, and System Dynamics is that in functioning as boundary objects (Franco 2013), they also provide a degree of inertia to the decision-making process, providing some degree of memory to the participants as to the direction of travel and acting to resist sudden changes in group direction. Finding a way of injecting inertia into these public platforms could well be a good thing.

Cross-References ▶ Behavioral Considerations in Group Support ▶ Group Decision Support Practice “as it happens” ▶ Group Support Systems: Concepts to Practice ▶ Introduction to the Handbook of Group Decision and Negotiation Acknowledgments We would like to thank the many colleagues and collaborators in the STEEP and REPLICATE projects who contributed feedback on the development of the MS-Azure cloudbased implementation of the Group Explorer GSS and its use in the online mode. This work was supported in part by (i) the EPSRC-funded Industrial Doctorate Centre in Systems (Grant EP/ G037353/1); (ii) the Innovate UK/NERC project Healthy Resilient Cities: Building a Business Case for Adaptation (Grant NE/N007360/1); (iii) the EU FP7-ENERGY-SMARTCITIES-2012 (314277) project STEEP (Systems Thinking for Comprehensive City Efficient Energy Planning); and (iv) the EU H2020-SCC-2015 (691735) project REPLICATE (REnaissance of Places with Innovative Citizenship and TEchnology).

Appendix A: Setting Up and Running Group Explorer The (nonstandard) installation of the Group Explorer GSS in the MS-Azure cloud environment is described by Yearworth and White (2017, pp. 80–82). Some of the practicalities of starting up and shutting down the GSS are described here to illustrate the actions that would need to be automated in order to achieve an autonomous++ mode of using the Group Explorer GSS, i.e., unlike the simple autonomous mode, where the facilitator merely leaves the GSS running unattended in one its meeting stages, the autonomous++ mode would not require a facilitator to control the GSS at all. The documents shown in Fig. 7 are currently an essential stage in briefing participants in how to use the online mode of the Group Explorer GSS and would also need to be made known to participants for the autonomous mode. The use of a system for audio

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a

b

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Fig. 7 (continued)

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c

Fig. 7 (a, b, c) Instructions to participants for the online mode of using the Group Explorer GSS

conferencing and screen sharing, such as Citrix GoToMeeting, in the online mode is not described here. Microsoft PowerShell “cmdlets” are used to start up and shut down the Group Explorer hosts Public and Chauffeur with their correct IP addresses in the MS-Azure cloud environment. These simplify management and can be “wrapped up” as Applications on the computer used to manage the system. The operation of these cmdlets as Applications is shown in Fig. 8. Once an instance of the Group Explorer GSS has been established in the MSAzure cloud environment using these simple scripting tools, further manual intervention is required to start the Chauffeur and Public components of the GSS. Once these are running, then the methodology requires both manual intervention to move the Chauffeur through the various stages of the meeting and the not inconsiderable task of managing the use of the Decision Explorer component. Automation of the Chauffeur component seems a tractable proposition, and certain workshop participants (e.g., the sponsor or “owner” of the problem) might be identified as “superusers” and given control via a simplified interface similar to the Applications used to start and stop the servers. However, the control of the Decision Explorer component for the collective benefit of the workshop participants requires a considerable skill on the part of the facilitator as can be seen from the complexity of the user guide described by Ackermann and Eden (2011,

Fig. 8 Simple Applications executing scripts written using Microsoft PowerShell “cmdlets” to (i) show the Group Explorer GSS status in the stopped and deallocated (passive) state and (ii) start up the Group Explorer GSS hosts Public and Chauffeur with their correct IP addresses in the MS-Azure cloud environment. The script to shut down the hosts is similar

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pp. 315–330). Some automation to achieve an autonomous++ mode might be achievable through the capture of heuristics from skilled facilitators that could be coded into rules that control the behavior of the GSS and also by ceding some limited control to the same superusers. Developments are underway to achieve some of these capabilities.

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Group Support Systems: Concepts to Practice Fran Ackermann and Colin Eden

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Support Systems: Concepts and Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anonymity and Higher Group Productivity from a GSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GSS as a Means to Create New Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The GSS as a Means to Attend to Procedural Justice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The GSS as a “Transitional and Boundary Object” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Explorer: A Group Support System for Soft Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Support Systems: In Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using a GSS to Facilitate “Soft” Negotiation: Negotiating a Way of Working Between a Nuclear Power Station Owner and the Regulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emergent Implications from Case Study Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Postscript . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Group support systems have been in existence for 40 years and have been applied widely since their inception. One particular realm is using group support systems (GSSs) for assisting managers who must negotiate the resolution of messy, complex, and/or strategic problems in order to achieve an agreed outcome. F. Ackermann (*) School of Management, Faculty of Business and Law, Curtin Business School, Curtin University, Perth, WA, Australia e-mail: [email protected] C. Eden Strathclyde Business School, University of Strathclyde, Glasgow, UK e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_59

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Taking cognizance of concepts such as procedural justice and boundary objects, as well as the underlying features of GSS, an intervention involving social and psychological negotiation is presented and examined. The case intervention deals with two organizations needing to move from adversarial modus operandi to a more productive and collaborative mode in order for both to operate more effectively. The intervention is presented in a chronological manner allowing particular phases to be explored, considered alongside research into the nature of failed decisions, group behaviors, and social and psychological negotiation, and a number of salient elements and their implications for facilitators are provided. Keywords

Group decision and negotiation · Group support systems · Collaboration · Procedural justice · Causal mapping · Negotiation process · Cognition · Boundary objects · Problem structuring

Introduction Group support systems (GSS) have been in existence for the past 30 plus years. They have been used for a wide range of reasons including increasing group productivity (Jessup and Valacich 1993; Dennis and Gallupe 1993), providing anonymity (Jessup and Tansik 1991; Valacich et al. 1992a), enabling collaborative working (Agres et al. 2005; Briggs et al. 2003), leveraging creativity (Nunamaker et al. 2015), knowledge management performance evaluation (Wanga et al. 2016), conflict resolution (Bose 2015), computer-supported collaborative learning (Long et al. 2013), and visual interactive modeling (Ackermann and Eden 2001) – see chapter ▶ “Group Support Systems: Past, Present, and Future” for more details regarding applications. Alongside this burgeoning range of applications, there has been a focus toward using them to facilitate the negotiation of a direction for an organization. This work includes efforts in the collaboration engineering arena (Vreede et al. 2006; de Vreede and de Bruijn 1999; van den Herik and de Vreede 2000 and chapter ▶ “Collaboration Engineering for Group Decision and Negotiation”) as well as the use of GSSs to support strategy making (Eden and Ackermann 2001a). This chapter focuses on another purpose, that of negotiating and resolving complex problems. One of the earliest definitionsdefinitions of a GSS is that it “is a set of software, hardware and language components and procedures that support a group of people in a decision related meeting” (Huber 1984: 195). Building on this definition, DeSanctis and Gallupe note that group support systems are designed to “improve the process of group decision making by removing common communication barriers, providing techniques for structuring decisions and systematically directing pattern, timing and content of the discussion” (DeSanctis and Gallupe 1987: 598). As such the raison d’etre for GSSs appears to be supporting group work – paying attention to managing both process (e.g., personalities, power, and politics) and content (management of the contributions) (Eden 1990). See also chapter ▶ “Systems Thinking, Mapping, and Group Model Building” by Andersen and Richardson.

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In addition, there is the focus on supporting effective communication. All three of these elements (process, content, and communication) are key considerations when facilitating group negotiation. Indeed, research on failed decisions specifically records failures with respect to insufficient attention of many of the above design features of a GSS (Nutt 2002). This chapter focuses upon on how group support systems are able to support group negotiation in resolving complex problems, in particular from the perspective of “soft” negotiation. The chapter starts by discussing in more detail a number of concepts incorporated within, or which usefully extend, GSSs and that allow “soft” negotiation to take place. Next, the chapter considers one particular GSS and how it attends to soft negotiation, before moving on to explore a number of soft negotiation implications through reference to a real case. Finally, the chapter concludes with some observations and recommendations. Thus, the chapter uses analysis of a real GSS case where expectations of “soft” successful negotiation were paramount, taking into account key assertions derived from (i) GSS literature, (ii) established negotiation recommendations, and (iii) where appropriate, Nutt’s research into failed decisions.

Group Support Systems: Concepts and Principles Anonymity and Higher Group Productivity from a GSS One of the key features of a GSS is anonymity. By allowing participants to put their contributions into the system anonymously, participants are more able to be open and not so pressured by social conformity issues, for example, group think (Janis 1972) and the “Abilene paradox” (Harvey 1984), where everyone ends up agreeing to something nobody wanted. This feature allows contradictory views to be surfaced along with challenges to ways of working, established myths, etc. In addition, by allowing participants to directly enter their views, into a developing group model representing all of those views, they are able to talk “simultaneously” and “listen” to the views of others in their own time (Valacich et al. 1992b; chapter ▶ “Group Support Systems: Past, Present, and Future” by Ackermann). The additional feature of direct entry results in higher productivity which in turn helps ensure that the perspectives of different constituencies are heard, rather than a single view or perspective dominating, and that ideas are captured as they are considered rather than risking being lost. One of the consequences of GSSs providing both these features – anonymity and “direct entry” – is that the comprehensiveness of the views expressed increases, contributing to procedural rationality (Simon 1976). However, an increase in comprehensiveness means an increase in complexity, and so a process for managing this increased complexity is required. In some GSSs, this is achieved through lists, categories (clustering), and voting. In other GSSs, it is managed through development of causal networks. Both forms allow for participants to explore their and other’s thinking in a safer and more structured space and thus facilitate negotiation. In addition most GSSs have some form of electronic “voting” or means for expressing “preferences” about importance, choice, and the relative leverage of

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options with respect to specific outcomes. A designed anonymous process within the GSS for expressing preferences can be used either as a way of creating a process end point or, more importantly, when considering negotiation, as a dialectic to determine participants’ views and positions and determining the degree of consensus within the group.

GSS as a Means to Create New Options GSSs can also capitalize upon a particular qualitative or “soft” negotiation approach underpinned by propositions from the field of international conciliation (Fisher and Ury 1982). Most significantly this approach to conciliation draws upon the propositions within “Getting to Yes” (Fisher and Ury 1982) and “Building Agreement” (Fisher and Shapiro 2007) where the emphasis is on reaching agreements and changing thinking. A significant aspect of Fisher and colleague’s work is that of developing new options rather than fighting over “old” options. The more groups are able to generate creative new options that emerge from seeing the views of all participants (rather than those originating from one single member of the group), the more they are able to build on, and integrate, the views into new contributions. In addition, these jointly created options garner greater ownership and thus increase the likelihood of implementation. As such, providing the ability to surface simultaneously and allowing anonymity facilitates new option generation. The GSS’s ability to make multiple changes to contributions also enables an option to have multiple owners as each contributes to its construction and refinement further assisting negotiation.

The GSS as a Means to Attend to Procedural Justice Effective “soft” negotiation additionally can be supported through attention to “procedural justice” (Kim and Mauborgne 1995; Kim and Mauborgne 1997) and institutional justice (Tyler and Blader 2003). Procedural justice is about enabling group members to have their say and be listened to in full, rather than being left out of the decision-making process (see chapter ▶ “Procedural Justice in Group Decision Support” by Kaur and Carreras). Anonymity embedded within the GSS supports participant’s ability to “have a say” and be listened to as the contributions are presented on the public screen, are woven into the overall body of argument, and are given equal weighting. Thus, a GSS provides not only the ability to contribute but also that the contributions will be viewed alongside one another and given attention.

The GSS as a “Transitional and Boundary Object” A further benefit of using a GSS when working with groups is that the publicly displayed model provides the group with a “transitional object” (de Geus 1988;

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Winnicott 1953) and “boundary object” (Carlile 2004; Franco 2013) reflecting the continuous transition of the changing views of the group and members of the group. Typically a GSS-supported meeting will commence with some form of data capture where the individual views are elicited and projected on the public display. A natural corollary of this process is that edits, additions, and deletions take place, shifting the initial disaggregated representation to one that over the course of time reflects the group’s emergent understanding without putting pressure on individuals. The model is always in transition. This shifting process from divergence to convergence typically results in many of the views and particularly options being revised (touching on the above consideration regarding new option generation). New options emerge as the captured material provides a powerful stepping stone to enabling creativity (Jelassi and Beauclair 1987). As such, the GSS is able to facilitate the process of creating new options. Moreover, the GSS facilitates another “soft” negotiation feature – that of encouraging members to change the way they see the situation from their idiosyncratic perspective to a view that encompasses aspects of the perspectives of other members of the group. Finally, by having the views anonymously displayed on a public screen that can be seen by all, it is possible to separate the proponent of a contribution from the contribution itself so that, when appropriate, the contributions can be judged on their merit alone. This is notwithstanding the fact that when appropriate, the author of a contribution is able to acknowledge ownership and intervene personally to persuade others of its merit. Thus, while each of these four concepts provides value to the development of GSS in their own right, they also build on one another. For example, when considering anonymity, elements of procedural justice are possible, and the use of boundary objects enables new option generation.

Group Explorer: A Group Support System for Soft Negotiation Group Explorer has been developed from a research interest in assisting decisionmakers working on complex and messy problems, problems that are messy, in part, because of differing perspectives. The GSS has its origins in the Strategic Options Development and Analysis (SODA) methodology (Eden and Ackermann 2001b) which seeks to attend to social and political considerations and manage the complexity generated through the capture of different perspectives. Because of the focus on differences in cognition, complexity is mapped and managed through the use of a modeling technique based upon a form of cognitive mapping (Eden 1988) which has its theoretical underpinnings in personal construct theory (Kelly 1955). Personal construct theory asserts that each of us makes sense of our world by interpreting new phenomena against our own experience – assessing both their similarity and differences to past experiences. Thus, we make sense of a situation through a mental construct system comprising bipolar constructs that capture similarity and contrast and also reflecting the relationships between constructs. The particular part of a construct system that relates to a situation expresses an attempt to

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make sense of the situation and act within it – by proffering possible explanations and consequences of action. Thus, a cognitive map seeks to capture the constructs and relationships in the form of a directed graph or network (an example of a small part of a cognitive map is shown in Fig. 1). When a cognitive map is constructed by a group, it becomes a “group cause map” as it does not represent the thinking of any one person. The map as a model/object enables members of the group to begin to appreciate how others’ think (through enhanced appreciation of both the content and the context) and therefore begin to develop a shared understanding through the representation of socially constructed reality (Berger and Luckmann 1966). The different perspectives are structured using the mapping technique to reveal the chains of argument, thus allowing for further reflection, extension, and debate among group members. This move toward convergence is a result of adopting the formalisms associated with the mapping technique which demand that not just the statements are captured but also their consequences and explanations – the context of assumed causality. Usually the term “cause” map is used when the map comprises the views of a number of different individuals, whereas a “cognitive” map is when the maps reflect individual thinking (cognition). The GSS, Group Explorer, enables the group cause map to be constructed jointly, where statements and links in the map are created and amended by the members

recognise the industry is now aligned on importance of delivering high safety performance ... simply high regulatory compliance

move away from add on design and writing safety cases to operational safety

regulator and licensee together address the peer review results (poor stds of operating & maintenance)

move away from increasing safety for remote events towards a focus on operational safety

ensure measures of success for inspectors meets both safety needs and business needs

recognise inspectors need to demonstrate existence

recognise that staff needs feeling of self worth

find ways for inspectors and experts to get “the big picture” ... focus on single expert views

regulator and licensee create jointly a new approach to new build

licensee and peer review members don’t see that UK is efficient or effective on world stage

encourage peer review of regulatory bodies

assessors inability/ unwillingness to exercise judgement

the regulator does not have a process to challenge or question themselves

Fig. 1 An example of a part of a cognitive map (statements have been changed to protect confidentiality): dashed arrows indicate parts of the map not shown in the figure. . .

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themselves (although assistance may be provided by a facilitator) and the map emerges on a computer display that can be seen by all (see Fig. 2). The contributions by members may be anonymous if required when conformity pressures are considered present. Figure 2 illustrates Group Explorer being used with the GSS enabling views of the participants to be displayed on a public screen as statements and causal links. These views can then be explored in more detail by the other members in the group, either through verbal discussion captured by a facilitator or the group members themselves contributing further comments. Thus, the material captured in the model, as transitional object, shifts gradually from being a collection of individual views (a state of divergence) toward the development of a shared representation (state of convergence) – whether the object is a map (in the case of Group Explorer) or a clustered combined list (in the case of Group Systems – see chapter ▶ “Group Support Systems: Past, Present, and Future” by Ackermann) – allowing participants to converge on a common understanding. The GSS captures the statements through language rather than tight mathematical judgments, and so the model/object provides a degree of “fuzziness” that more easily allows participants to change their mind incrementally and without the issues of “face-saving” (Eden et al. 2009). The meaning of statements grows and shifts as the context (statements associated with them) changes and where new explanations and consequences added by others gradually shift the original meanings. Over the course

Fig. 2 A photograph of a management team using the GSS

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of a meeting, the varying “underdeveloped” and diverse understandings are subtly shifted to a view that is owned to a greater extent by the entire group. Because the model is displayed in front of the group, participants have the time to read the views of others at any time after they are contributed – they can “listen” in their own time and have time to reflect on the content rather than having to immediately respond with the associated dangers of inappropriate emotion. Participants, therefore, are more able to appreciate the different points of view – particularly as the process encourages views to be elaborated upon and their meaning clarified. As a result, less stark positions are taken and procedural justice is achieved. The mapping technique therefore provides a type of “scaffolding” (Vygotsky 1978) providing not only the means for gaining a better understanding of what is meant by the contribution being made but also assisting the process of integrating the different views together.

Group Support Systems: In Practice Using a GSS to Facilitate “Soft” Negotiation: Negotiating a Way of Working Between a Nuclear Power Station Owner and the Regulator The case used to illustrate GSS concepts and principles focuses upon work undertaken over a 3-year period with a regulator and the owner of nuclear power stations (the “licensee”). Testing the use of a GSS in real negotiations is both problematic and important: experiments with students cannot replicate real issues of management (Eden 1995; Finlay 1998), and gaining access to senior managers negotiating on sensitive problems is rarely possible unless they see potentially positive outcomes in advance (Pettigrew 1992). These problems often lead to action research being viewed as the most appropriate research methodology. By working in a “researchoriented action research” format (Eden and Huxham 2006; Eden and Ackermann 2018) specifically following the cyclical research process (proposed originally by Susman and Evered 1978), in-depth data and insights can be obtained. Confidence in the use of the GSS to facilitate this particular negotiation followed from the authors having worked with the regulator on a number of significant internal issues. One of the concerns emerging from this early work was a general feeling of disquiet regarding their dysfunctional relationship with a particular licensee. Importantly it was believed that the licensee also viewed the relationship as dysfunctional. Evidence to support this view stemmed from the fact that over the previous 2 years, various exercises had been undertaken to try to alleviate the situation, but without success. While it was recognized that this relationship would always be, to some extent, adversarial due to the nature of licensees and regulators, many of those involved felt that there was considerable opportunity for improvement. Consequently the regulator suggested to the licensee that using a GSS – specifically Group Explorer – might provide a constructive way forward for both parties, and the licensee was prepared to “give it a try.” The illustrative case in this chapter is based upon the reflections undertaken during this project which involved three 1-day meetings with the top management teams.

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The research data that formed the basis for the reflections includes a combination of notes and observations as well as the computer-captured information. One set of notes was generated by the two facilitators running the meeting. These notes were based upon observations made during the meetings and encompassed both process and content management insights. In addition, an independent observer provided further observations and comments. Additionally there were extensive comments from members of both organizations. As the engagement had involved the assistance of one “partner”/observer from each organization (someone senior enough to know what was happening within the organization but with the time to help make arrangements, provide insights into organizational workings, and ensure feedback) who was present but not participating at each meeting, they also were able to provide valuable observations. The computer-generated research data consisted of the data captured in the model during the interventions (each meeting resulting in an updated version of the model allowing changes in the material to be assessed longitudinally) along with a computer log produced by the GSS which recorded on a time-stamped basis each and every contribution made through the system. Taking account of the focus on “soft” negotiation, the case is structured so as to both provide an illustration of a GSS use in negotiation and highlight important implications pertinent to the design of a GSS for “soft” negotiation. These implications are, where appropriate, framed and informed by the research undertaken by Paul Nutt (2002) on failed decisions. In Nutt’s research on decisions that failed, he is concerned, in part, with a lack of attention to key aspects of negotiation among participants (power brokers) and other stakeholders. In addition, GSS design considerations will be noted.

Emergent Implications from Case Study Exploration Getting the Right People to the Meeting Case: As noted in the above description of the situation, there were two parties involved in the negotiation – the regulator and the licensee. Careful consideration therefore would be needed when determining how many, and which, participants from each organization should attend. Involving six to eight key participants on either side allowed for a relatively even attendance at the workshop and ensured perceived equality in terms of contribution. Furthermore it emerged from discussions with the leads from both organizations that a variety of roles would be represented by these identified participants and therefore each of the participants for each organization was likely to present different views about the reasons for the dysfunctionality. This would provide a diversity of view and ensure a comprehensive appreciation of the situation. GSS Implication: One significant consideration in GSS use is that of carefully choosing the participants who should be involved in any negotiation or problem solving event. This is for three reasons. The first relates to ensuring that a good capture of the range of views is possible – a form of procedural rationality (Simon 1976). The second relates to ensuring that

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those attending have the authority or informal power to implement what is agreed upon. The third is to ensure equality in voice which touches on the above concept regarding procedural justice (Kim and Mauborgne 1995, 1997). The GSS features of direct entry and anonymity facilitate capture of the breadth reducing the likelihood of ‘group-think’. Ensuring a range of perspectives is likely to encourage creativity from the ability of a GSS to merge perspectives and so see new options.

Nutt (2002: 4) comments that “nearly everyone knows that participation prompts acceptance but participation is rarely used” and thus ownership and commitment to the outcomes are found wanting. This speaks directly to the need to ensure engagement, not only to ensure comprehensiveness of the views but also commitment to the outcomes.

Ensuring a Level Playing Field: For Participants and the Facilitator Case: Both sides wanted an opportunity to describe the situation, with its various nuances, as they saw it. They were keen to do this before getting together in a joint meeting so that there was a platform upon which to build a joint understanding. Thus, there was a strong incentive for the facilitators to meet with each group and listen to their point of view in advance of the group meeting. As a result of the original work conducted with the regulator, members of this group were satisfied that the facilitators had a fairly clear understanding of the views from their perspective. Nevertheless, it was important for the facilitators to set out their understanding and check it with the regulator team. As the regulator had already developed a view of the effectiveness of causal maps as a way of communicating understandings, this was the chosen way of reporting their views as seen by the facilitators. However, the position was different for the licensee. It was likely that licensee members saw themselves at some disadvantage because they were aware of the existing working relationship between the regulator and facilitators and their familiarity with the modeling approach (causal mapping). Therefore a visit to the licensee was appropriate so that the facilitators could listen at length to their views and also familiarize the licensee members with the modeling approach. To achieve these two objectives, the views from the licensees were also captured through taking notes in the form of a causal map that was subsequently declared and explained to the licensee group. The resultant causal map became the means for checking the facilitators’ emergent understanding of the licensee group viewpoints. A second meeting with the licensee served the purpose of further checking the understanding and adding any missing elements and further familiarized the licensee to causal mapping as a representation of their views. The licensee members seemed to be pleased to see their views as a causal map and reported that the map showed how carefully they had been listened to and that they had gained a better sense of their own thinking. GSS Implications: Although the above process was particular to the energy case, it is likely that in any workshop participants will have their own definitions and understandings of the situation and therefore it is important for the negotiation to get this ‘out in the open’. Equally participants will wish to ensure that they start from a level playing field – this too is key in any negotiation.

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In addition, it is likely to be helpful for the facilitator to have a good understanding of the different points of view in advance of the workshop (Ackermann 1996) as they will be able to better design the workshop to support the negotiation. Where it is not possible to meet with each participant in advance, it might be also achieved through conversations with the client and production of pen portraits. (Ackermann and Eden 2011a: 277) As noted in the beginning of this chapter, all GSS’s utilize particular formats of communication and some introduction to the GSS format before a meeting reduces some potential stress about new ways of working. In particular, an understanding of the role of the format that is to be used to help with the listening process, and negotiation, will introduce some confidence to the anticipated proceedings (Mantei 1988). This is particularly the case where different forms of data presentation take place, for example, visualizing the data in the form of maps.

Ensuring a Good Start Case: Having established that each of their views was represented with a reasonable level of accuracy, it was agreed with both parties that the facilitators would extract aspects of each party’s views that might usefully be discussed in a joint meeting. The intention was to choose material that could fully exploit the “soft” negotiation potential of the GSS as well as represent the situation. In particular, the facilitators were keen to persuade each party that it would be helpful to display some views about their own weaknesses in the relationship in order to gradually build trust (Ackermann et al. 2016). Their conversations had been dominated, prior to the meeting, by complaints – suggesting that it was only the other party that was at fault. At the start of the meeting, there was considerable tension, and although participants were seated in a U- shaped formation, the setting dynamics exuded the appearance of two teams about to do battle! There had been no conversation across the two groups during the coffee period immediately prior to the meeting – both organizational groups keeping very much to themselves. The first session of the meeting had been designed to absorb the first half of the day, with the period up to coffee break taken to be critical in establishing with most participants the potential for the rest of the day being constructive. Allowing each side to have the opportunity to view not only their own material but that of the other side, without having to respond, meant that deep listening could take place. The GSS enabled a more reflective stance to be taken as participants didn’t need to respond immediately. After the first hour, most, but not all, participants in each group behaved as if they were prepared to accept the possibility that the views of the other party were reasonable, even if not acceptable. There was the beginnings of an appreciation of both sides’ difficulties. Designed procedural justice appeared to be paying off, and in particular, the self-critical points produced humor as well as the potential of both parties thinking together. The research observer (and the two observers from the organizations) particularly noticed the extent to which the GSS had been able to “separate the people from the problem” – the interests from the positions. The observers reported that at the coffee break, there was still no conversation across the groups, but each group was more relaxed and good-humored, and there were signs of positive expectations for the day. Providing anonymity, a balanced structuring of views, and time for deep listening facilitates negotiation.

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GSS implications: It is critical to get a good start to any group meeting as this will set the tenor for the day. This view is strongly supported by Phillips and Phillips (1993) who note that it is critical to get a good start to any group meeting. Using the public screen to project the range of views in a manner that allows consideration rather than immediate response.

Designing Deep Listening Case: As touched on above, preparation work prior to the meeting had been very carefully undertaken: a series of causal maps that included perspectives from both parties were produced with each map encompassing a particular theme of dysfunctionality. The order in which these maps were to be presented to the group also had been carefully considered – taking into account both process (e.g., not starting with the most confrontational) and content (e.g., attending to themes that were central to the overall map structure) considerations. Care had been taken to ensure that each map utilized approximately the same number of statements from each party, and in addition that causality linked the views of one party to the views of the other. In this way, the views of each party were expected to be less stark as they were a mix of criticism, admission, and possible ways forward, a good starting point for negotiation. The implied options that had emerged from the interviews and earlier engagement were also seen as a useful resource to help resolve the situation depicted under the theme displayed. It had been clear that each party acted as if their view was the only right view and that, therefore, for them, a satisfactory outcome would be win/lose. However when the views were considered alongside each other, the possibility of generating new options that would facilitate a win-win (Fisher and Ury 1982) increased. During the first part of the meeting, the GSS was used in “single user mode” (rather than using the networked GSS) (Ackermann and Eden 2001) where one of the facilitators was modifying, elaborating, and developing each of the group maps as a result of reactions and comments. This was to allow both parties to concentrate on the material and interact without concentrating on using technology as well as reacting. The first part of the meeting also helped ensure that both parties became more equally familiar with causal mapping used in a live group setting. The anonymity from individual interviews reduced the face-to-face tensions of a normal meeting. The ability of the GSS to capture the changes in real time also meant the causal map was in continual transition – the “transitional object” allowing the group to slowly transition from two opposing camps to appreciating the wider set of views. GSS implication: Designing the GSS so that it allows participants to ‘hear’ one another without prejudice and thus listen effectively facilitates negotiative behavior. This is achieved through both allowing for anonymous contributions but also through presenting contributions in the context of alternative views. This design to encourage deep thinking helps getting off to a good start. A GSS that uses causal maps enables the suggestion of several possible portfolios of options that are not the same as any single option. The totality of the map of causality is addressed by the group – each participant (rather than adversary) can add to, reflect upon, and suggest alternatives anonymously and at the same time.

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Nutt’s (2002) research suggests that the notion of a claim – a single clearly stated “solution” – implies a firmness of proposal that tends to take a group down the route of agreement or disagreement with little hope for the creation of new options. The use of a GSS seeks to counter this possibility.

Providing the Opportunity for “Face-Saving” Case: Having established with each party those aspects of their views that they were prepared to have declared during the meeting, these two sets of views were merged together. In addition, each statement was deliberately not tagged with any identification regarding the source. Typically, participants believe that they can guess the source of the point of view; however, the facilitators expected that it was likely that, by encompassing the admissions of both party’s failure, there would be some growing confusion about attribution as the views were explored. As was argued above, the role of anonymity is significant in negotiation. In this case, the facilitators had designed the meeting so that the GSS would utilize anonymity extensively particularly when further views and responses were being sought. As such, there was no need to worry about the social dynamics of presenting a view – they were all anonymously presented on the public screen. GSS Implication: The use of both anonymity of contribution and the model as a transitional object enables participants to easily and gradually negotiate a new group view as well as manage their emotions more effectively. They are able to change their mind imperceptibly and thus avoid losing face by changing their mind publically. The role of a visual representation for sharing weaknesses from all perspectives combined with the opportunity to use the GSS to ‘discuss’ anonymously the views without the social costs of individual ‘face-saving’ provides a powerful meeting design that would be difficult to attain without this combination. (Connolly et al. 1990)

Attending to the Emotion: Ensure There Is the Opportunity for Catharsis Case: The first stage of the meeting started from “where each participant is at” – their immediate and personal/role concerns, claims, and issues. In doing this it was felt that it would not only enable both organizations to develop a new joint understanding of their different points of view both across and within teams but also act as catharsis – a release of anger, tension, and frustration. By using the GSS as a transitional object, the views would be taken to belong to participants but nevertheless be depersonalized and in addition could be continuously developed by the whole group in real time. GSS Implications. The process of getting concerns ‘out on the table’ provides important catharsis opportunities for participants and thus assist with face saving, and getting a good start. Without a GSS some participants are dominant and discourage others from expressing their views and therefore the impact of catharsis is uneven, and tensions can emerge. Acknowledging the importance of attending to emotion and its impact is a growing area of research. (Tully et al. 2018)

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Establishing Priorities and Judging Consensus Case: Before the break for lunch, all of the themes had been presented, explored, and elaborated. The elaboration had produced more rather than less equivocality of views – suggesting that the positions of each side were softening. A deliberate last stage prior to lunch was the process of asking all participants to individually express an anonymous rating depicting their views of the relative leverage and practicality of resolving the dysfunctional issues under each theme. This would inform the process after lunch. The first step of this procedure was to ask each participant to rate the relative contribution that resolving each theme in turn might have to reduce dysfunctionality. To ensure appropriate anchor points, each participant was required to, at least, rate the resolution of one theme at the highest level and one at the lowest level. For the second step, participants were asked to make a judgment, on the same rating scale and using the same anchoring process, about the relative practicality of any solutions that might be devised. The underlying rationale for this procedure was to gain insight into both the aggregation of judgments made and the degree of consensus both across all participants and within each of the parties. GSS Implication: Build in regular activities to frequently determine the extent of consensus across the group regarding the definition of the situation and thus priorities of the group. Monitoring consensus can assist the facilitator and group in the negotiation process. Although many ‘manual’ approaches to reaching agreements use a form of voting (for example, using ‘sticky colored blobs’), the power of a computer based GSS to enable full anonymity in expressing views and priorities with immediate statistical reports of degrees of consensus provides procedural justice. In addition the process permits the group to explore more honest differences in views and so the extent of agreement across different constituents (Watson et al. 1988). GSS facilities permit the dimensions of analysis to be quickly and easily varied – in this case an evaluation of options for the degree of leverage and practicality of options.

Managing Conformity Issues: Avoiding “Group Think” Case: Surprisingly there was no consensus within each of the parties. The facilitators and participants had expected that there would be relative consensus within each party about both leverage and practicality but less so across the parties. Without identifying who had said what, the results were displayed and the lack of consensus within each party highlighted. The GSS enabled a display of the average rating and the variance (the degree of consensus). The system also showed the rating of every participant but without identification of the participant. The results demonstrated that there was considerably less consensus of view among those from within the regulator party than from those within the licensee. This latter result was of particular interest to both the facilitators and the participants as it confirmed earlier impressions from viewing the themes from the aggregated map. One of the dysfunctional theme maps appeared to contain a relative commonality of view, and reasons for it, from within the licensee, as compared to the independence, and independent views, of the inspectors within the regulator. For the whole group to see, this discrepancy in opinion proved to be both amusing and helpful in establishing a shared appreciation

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of the dysfunctionalities and the multiple views held. The observers reported later that they thought this was probably the turning point in progressing toward a successful negotiation. Notwithstanding that there had not been consensus within the parties, there was nevertheless a reasonable consensus about the top three themes, in terms of both leverage and practicality – enough consensus for the group to feel comfortable about focusing on addressing these three themes as a priority and a good use of their time for the rest of the day. The agenda seemed clear. GSS implication: Using GSS features such as anonymity helps in reducing conformity behaviors such as Group Think. Recognizing different perspectives within the same department or organization as well as across organizations is easier with a GSS because social pressures to conform within a party are considerably less when anonymity is permitted. Additionally the GSSs quick and frequent analysis of the differences in views provides the facilitator with powerful help in facilitating negotiation.

The Power of Social Skills Case: As a result of this “turning point” prior to the lunch break, lunch proved to be more sociable across the parties than had been seen earlier in the day. The view of the observers and facilitators was that most participants felt reasonably buoyant about the prospects for the afternoon. This was partly due to having got a number of things “out in the open” and being able to talk about them, as well as having a relatively shared view of where to go next (rather than one side dominating the direction). GSS Implication: Enabling participants to be more open through anonymous entry and prioritization processes can start the process of effective engagement and social behavior. One party in a negotiation sometimes has better skills to present their point of view. In this case the licensee was articulate and pugnacious, and the regulator would often start presenting a view only to become overwhelmed by responses from the licensee. A GSS can equalize this type of perceived or real inequality – power derives from the perception of power as well as from the actuality of it. As such managing the impact of differential social skills assists in both ensuring procedural rationality and justice is attended to further facilitating the negotiation.

Developing Agreements Through Option Generation Case: The afternoon started with more good-humored banter between all participants, and this continued for all of the afternoon. The group returned to reconsider the causal map representing the top priority theme. Each participant was invited to use their laptop to communicate directly with the public screen – focusing upon the map of the prioritized theme. They were asked to suggest options (means of resolving the issue) that might remove the dysfunctionality represented by the material representing the theme. This stage added to the material that had been captured when elaborating each theme during discussion in the morning. As participants generated options, they appeared on the public screen in a random position. To try to help manage the growing complexity, one facilitator moved each into a position close to the statement that might be resolved by the option (to the best

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of their ability). At this stage of using the GSS, all a participant was asked to do was to type a short statement of six to eight words representing their proposed option and submit it. They were encouraged to ensure that there was an active verb in the statement, in order to suggest an action orientation. The attribution of statements appearing on the public screen was completely anonymous to the participants; however, the GSS provided the facilitator with an awareness of who contributed which statement. The second stage of this option generation activity was to ask the participants to submit their own views about causality – in other words, if an option they generated was to be implemented which of the issues would it help resolve. For a participant this is a simple process: each statement is tagged with the reference number, and links between one statement and another entailed typing, for example, 54+23, which “generates” an arrow from statement 54 to statement 23, implying that statement 54 may impact statement 23. Participants were invited to make links between any option and any other statement or option, regardless of whether they had contributed the option or statement. The process ensured that, for the most part, participants “listened” to the views of others by reading each of the suggested options and considering their potential impact (Ackermann and Eden 2011b; Shaw et al. 2009). GSS Implication: Encouraging participants to not only generate possible options but do so considering their causal context assists with the negotiation. Setting new options within the context of others ensures that they are less ‘claim’ like and more likely to develop consensus. Each generated option is seen to do something about the situation because it is causally linked, either by the proponent and/or other participants, to possible outcomes. The specific GSS feature used for this task ‘forces’ participants to address the consequences of suggested options. Other participants are able to add alternative and sometimes negative consequences by adding new outcomes or simply linking options to existing outcomes thus building up the representation and understanding.

Nutt’s research suggests that developing “decisions with multiple options are more successful” (p. 126). Using a GSS that enables, and encourages, the fast creation of a number of options taps into the wisdom and experience of group members. In addition, his research argues for asking the “what-for” question: “moving up the ladder answers the ‘why’ question . . . moving down the ladder answers the ‘how’ question” (pp. 126–7). Group Explorer, as a GSS, uses causal mapping which focuses on the use of a laddering technique to create a hierarchy of objectives and, once generated, explore and discuss the hierarchy to find the most appropriate objectives to follow. The process helps with respect to two difficulties: firstly, participants becoming fixated on one particular objective and secondly showing there are a large number of interconnected objectives uncovered by the group. The productivity gains derived from a GSS provide more opportunity to consider multiple options and multiple consequences within the context of a network of objectives.

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Quiet Participants! Case: As these tasks unfolded, the facilitator was able to monitor the number, and rate, of contributions being made by each participant. This enabled both facilitators to make judgments about the relative dominance of each participant and also to encourage and support those who were relatively “quiet.” It also allowed the facilitators to ensure that each party was represented relatively equally so as to increase the ownership of the resultant outcomes. Through this shared creation, there would also be more understanding of the different considerations further assisting in increasing the likelihood of action. GSS Implication: Encourage all participants to engage, and feel engaged, in the process through active participation independent of social skills. This is more likely to ensure a wide range of views and more equal contribution rates from all participants, leading to a greater probability of a ‘buy-in’ to agreements. Although one of the positively viewed features of a GSS is anonymity, having this facility doesn’t always inspire participants to contribute, and a little support from the facilitator can have a big impact. As such, the provision in a GSS of knowing the rate and range of contributions can help the facilitator to encourage equality of view and engagement.

A Group View from Individual Perspectives: Splitting Adversarial Positions Case: The public screen, by now, was reasonably cluttered – there was no shortage of suggested options for the top priority theme. Nevertheless, because the material was structured into a causal map, it was possible to structure the newly generated material into clusters. Some options supported other options and so created a hierarchical tree of options. Options at the top of these trees, in effect, summarized the options further down the hierarchy. Some options had an impact on several different parts of the theme – making them potentially potent. Furthermore the GSS information to the facilitator showed contributions from both parties revealing a shared approach to seeking a resolution of the situation they jointly faced. Given the cluster’s hierarchy, it was not necessary for the group to evaluate every option but rather evaluate the “summary” options (those that had a lot of options linking into them) and those options that had multiple impacts. Not surprisingly, as a proposal to use the GSS to evaluate these summary options was put to the group, participants sought to make additions and changes to the options in order to refocus the group’s attention to their own options (making these options more connected). However, it was also interesting to see some participants gradually remove themselves from a commitment to options they had suggested and seek to focus attention to the options of others that they personally favored. New wording for some options was proposed, sometimes under the guise of delivering greater clarity but actually seeking to subtly shift the meaning of the option and at other times simply elaborating in order to give clarity to meaning. During this time the facilitators sought to attend to the shifting meanings without

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losing ownership from the original proponents. As the observers commented later, the ownership of some options became extended to many members of both parties as the wording was gradually changed. In effect new options were being created, and old options became less identifiable, at least at the level of the summary options. The causal mapping appeared to have become second nature to all participants by this stage of the meeting, and it was not problematic to remind participants that the meaning of any option was related not just to the wording but also to what it was expected to achieve – the causal links out – and to the ways of making it happen, the causal links in (Eden and Ackermann 2010). The observers, and later examination of the log of the meeting produced by the GSS, demonstrated that the two parties had become a group of multiple parties each with a point of view that was becoming difficult to attribute to one party or the other. The GSS was, at this stage, again being used in a single user mode where the facilitators were proposing and making the changes in response to suggestions by participants. The GSS could have been a simple word processor in order to achieve this function. That said, the power of an action-oriented way of understanding what an option was for (out-arrows) and how it could be achieved (in-arrows) helped create new options (following the mapping technique) that achieve the agreed objectives. Continuously editing causal links and wording encouraged participants, and importantly the two parties, to no longer fight over old options but create new options (Fisher and Ury 1982). GSS Implication: Continue to play with options seeking agreement and clarity – through having the material presented on a public screen and embarking upon a process of continual refinement as this ensures that the options are owned by many as well as being refined in terms of meaning. Having an efficient process for the identification and evaluation of options also ensures that the group’s time is effectively used and progress seen to occur further stimulating the group.

The process supported by the GSS ensures that the search for options is not limiting but rather encourages “uncovering ideas” (Nutt 2002: 43). Additionally the search process echoes Nutt’s research which indicates that “decision makers also frame things to indicate what is wanted, the results a decision seeks to provide” (Nutt 2002: 111).

Closure Case: In the final stages of the meeting, some sense of closure was crucial for the group (Phillips and Phillips 1993). The group could have spent considerably more time focusing on the process of rewording and adding new options to each of the three themes that had been prioritized; however, an end point was required. The concluding process of seeking to reach some agreements was undertaken using the “preferencing” facility in the GSS. The questions asked of the group were practical: (i) “you have only a restricted amount of resource across the two organizations, and this resource is largely your time and energy; given this restricted amount of resource to use to make progress against each of your prioritized themes, choose how to distribute it,” and (ii) “we are looking for a reasonable level of consensus, if possible,

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but recognize that there may be some options that you personally regard as ridiculous; to the extent that you might surreptitiously sabotage them if they were to be agreed by a majority as actionable – thus you have the opportunity anonymously to block these options.” For each theme in turn, each participant was provided with electronic resources through the GSS – positive resources and blockers – and asked to allocate them. They were invited to use blockers only if they felt strongly and negatively about an option; however, they were asked to make use of all of their resources to support options. The GSS permits the facilitators to see statistics relating to the degree of consensus, the variability of resources allocated, the range of participants using blockers with respect to any option, and the degree of consensus within one party compared to the other. With some relief on the part of all of the attendees (facilitators, observers, and participants), there was a high degree of consensus about the top three options against each theme, but little consensus against other options. While on reflection the outcome might have been predicted by a careful analysis of the involvement of participants in the rewording and elaboration process, it nevertheless came as a surprise to all and was regarded as a remarkable success for the day. For each theme, the top three options were much preferred over the others, there was a high degree of consensus, and no blockers had been used against these top options. However, worryingly, in almost all instances, there was one participant within the regulator who was an outlier – an observation derived from the GSS statistics produced for the facilitator in real time. The facilitators were concerned that this could result in a possible significant lack of enthusiasm and so commitment to delivery. At the time, it was not possible to think of any useful way of using this data with the group, but both facilitators resolved to raise the issue in the wrap-up meeting with the observers which was due to take place the next day. The very last part of the meeting was devoted to identifying whether some “quick wins” might be achieved from within these largely consensual top options. In this case the rating procedure of the GSS was used. Here participants were given a time horizon of 1 year and participants invited to indicate the time required for each option to deliver its expected and desired outcomes. Somewhat unsurprisingly there was less consensus. When the group explored the anonymous results, it became clear that each participant had very different views about what determined a successful delivery of an outcome. Time constraints meant this outcome could not be explored further. GSS implications Allow participants to confirm support for options anonymously to ensure consensus for the outcomes, and provide an opportunity to indicate severe dislike of an option so that political feasibility can be explored. While electronic voting and rating systems offer significant gains in facilitating negotiation, unless the participants see similar meanings of statements being rated then the results might suggest spurious agreements. (Watson et al. 1988)

Planning Next Steps Case: The following day, the two facilitators and two observers met for 4 h. The purpose of this meeting was twofold: (i) to construct a document that would provide

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a summary of meeting agreements to be circulated to all participants and (ii) to provide the facilitators, as researchers, with detailed feedback and commentary from the observers. The first 2 h was devoted to the first of these purposes and provided both research data and a context for constructing a document that paid adequate attention to political feasibility (Eden and Ackermann 1998). Although the document was intended primarily for participants, it was likely that it would be circulated more widely. Each of the observers represented one of the parties, and during the process of crafting the document, each of the observers sought to slant the responsibility for agreements being delivered to the other party. Without the availability of the computer log, the agreements made by participants might have become distorted by the observers. Both of the observers commented that this was the first opportunity they had been given to influence the meeting hence their wish to shape the material. Given the enormity of differences in opinion at the start, both facilitators and observers were pessimistic about the probability of the emotional commitment created during the meeting continuing into the future – “will it last” (Sankaran and Bui 2008). There remained some concern about the position and power base of the outlier – however, this particular person was regarded as an outlier in normal work situations, and so there was a view from the observers that his behavior may not have serious consequences for that of the rest of the group. Nevertheless it was important to put in place some mechanisms for ensuring the good will, and progress did not get lost. Following the construction of the feedback document, two proposals were made and would be put to the participants by the observers: (i) there should be a 6-monthly review of progress to be undertaken by the facilitators and (ii) all of the participants should meet again in 12 months for another GSS managed meeting. GSS implications: Follow up with producing concrete ‘minutes’ based solely on the GSS material that notes the agreements and next steps and provides appendices showing the pictures the group had used during the workshop).

Summary and Conclusions Conclusions As discussed above, there are a number of implications associated with using GSS for negotiation. A list of the actions associated with these implications is noted below. Facilitators should: • Carefully choose the participants who should be involved in any negotiation or problem-solving event • Have a good understanding of the different points of view in advance • Provide an introduction to the GSS format • Put effort into getting a good start to any meeting • Allow participants to “hear” one another without prejudice

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Use the model as a transitional object Provide catharsis opportunities Frequently determine the level of group consensus Explore more honest differences in views Evaluate options for the degree of leverage and practicality of options Reduce conformity behaviors Recognize different perspectives within the same department or organization as well as across organizations Enable participants to be more open Equalize perceived or real inequality Generate possible options but do so considering their contribution and context “Force” participants to address the consequences of suggested options. Encourage all participants to engage and feel engaged Play with options Embark upon a process of continual refinement Ensure that the options are owned by many Confirm support for options anonymously Produce concrete “minutes” using the GSS material

While these implications are noted in a list form, most have impacts on others. Attendance to the entire suite will promote more successful negotiation. One of the most notable aspects of the above summary is an emergence of the significance of the role of anonymity – a significant feature of electronic GSSs. While the advantages of anonymity are not new (Valacich et al. 1992a, b), combining this facility with other features such as the use of a transitional object can extend the power both processually (a means for designing procedural justice and reducing social pressures) and contentfully (avoiding being trapped by particular claims on the future). As the case above illustrates, GSSs have a crucial role to play in “soft” negotiations – acknowledging some of the negotiation literature and extending the view that negotiation need not just be “hard.” Group decision-making thus can be viewed as a form of soft negotiation where the principles of negotiation discussed in this chapter can play a powerful role. Extending this role to help reduce the possibility of falling into some of the traps associated with failed decisions, such as those reported by Paul Nutt, can further assist groups in making better decisions. Soft negotiations, as shown above, require subtle shifts in meanings through the presence of equivocality, allowing thinking to gradually shift and agreements reached (Eden et al. 2009). Through facilitating the process of option creation and consequences in a “safe” environment, both emotional and cognitive shifts can be achieved. One process that could particularly benefit from GSSs supporting “soft” negotiation is the area of strategy making. Here top management teams using such a GSS would be better placed to consider issues, raise alternatives, appreciate consequences (particularly confirming goals), and slowly develop a shared sense of organizational direction (Eden and Ackermann 2000; Ackermann and Eden 2011a).

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Understanding the processes of social negotiation, behavioral, cognitive, and emotional, is growing in the area of group decision and negotiation support (see chapter ▶ “Role of Emotion in Group Decision and Negotiation” by Martinovski, Franco, Adam-Ledunois, and Damart), not only for the support of multiple stakeholders seeking effective shared outcomes as reported in this chapter but also through seeking to understand better the micro processes required to support groups (Tavella and Franco 2015), to ensure socially optimal allocations when considering resource allocation problems (Nongaillard and Mathieu 2014) and the role of situation and personality when initiating negotiations (Kapoutsis et al. 2013).

Postscript All participants of the first GSS meeting, reported above, agreed without hesitation to an annual review meeting utilizing the GSS. One-on-one conversations with each participant suggested that each of them regarded the first meeting as a major breakthrough. Each of them could describe critical incidents during the meeting that they could not imagine occurring using any other form of meeting. The annual review, that took place almost exactly 12 months later, reported a continuing commitment to the agreed themes (which, as expected, showed mixed progress). The review reported that the highest priority theme had shown the most significant progress – interestingly, this theme was related to the need to create a developing trust between the parties in relation to working practices. Trust had, of course, been increased simply as a result of the GSS meeting itself. The second annual review (the third meeting using a GSS) occurred a year later and further built on the progress made. It was extremely clear to the facilitators how much progress had been made to both as members from both organizations chatted, joked, and shared concerns together. There was an increased openness, an appreciation of the difficulties faced by both organizations, and a keen desire to continue to work together effectively. Although some have written about the low chances of workshops of this sort actually achieving anything of significance (Hodgkinson et al. 2006), this case (and others which have involved the use of the GSS) shows that significant achievements are possible.

Cross-References ▶ Behavioral Considerations in Group Support ▶ Group Support Systems: Experiments with an Online System and Implications for Same-Time/Different-Places Working ▶ Group Support Systems: Past, Present, and Future ▶ Looking Back on a Framework for Thinking About Group Support Systems ▶ Procedural Justice in Group Decision Support ▶ Systems Thinking, Mapping, and Group Model Building

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Fisher R, Ury W (1982) Getting to yes. Hutchinson, London Franco LA (2013) Rethinking soft OR interventions: models as boundary objects. Eur J Oper Res 231:720–733 Harvey JB (1984) The Abilene paradox: The management of agreement. Organizational dynamics. 3(1):63–80 Hodgkinson GP, Whittington R, Johnson G, Schwarz M (2006) The role of strategy workshops in strategy development processes: formality, communication, co-ordination and inclusion. Long Range Plan 39:479–496 Huber G (1984) Issues in the design of group decision support systems. MIS Q 8:195–204 Janis IL (1972) Victims of group think. Houghton Mifflin, Boston Jelassi MT, Beauclair RA (1987) An integrated framework for group decision support system design. Inf Manag 12:143–153 Jessup LM, Tansik DA (1991) Decision making in an automated environment: the effects of anonymity and proximity with a group decision support system. Decis Sci 22:266–279 Jessup L, Valacich J (1993) Group support systems: new perspectives. Macmillan, New York Kapoutsis I, Volkema RJ, Nikolopoulos AG (2013) Initiating negotiations: the role of Machiavellianism, risk propensity and bargaining power. Group Decis Negot 22:1081–1101 Kelly GA (1955) The psychology of personal constructs. Norton, New York Kim WC, Mauborgne RA (1995) A procedural justice model of strategic decision making. Organ Sci 6:44–61 Kim WC, Mauborgne RA (1997) Fair process: managing in the knowledge based economy. Harv Bus Rev 75:65 Long Y, Fui-Hoon Nah F, Eschenbrenner B, Schoonover T (2013) Computer- supported collaborative learning: a research framework. Ind Manag Data Syst 113:605–623 Mantei M (1988) Capturing the capture lab concepts: a case study in the design of computer supported meeting environments. In: Greif I (ed) Proceedings of the 1988 ACM conference on computer-supported cooperative work, Portland, pp 257–270 Nongaillard A, Mathieu P (2014) Agent-based reallocation problem on social networks. Group Decis Negot 23:1067–1083 Nunamaker JFJ, Briggs RO, Derrick DC, Schwabe G (2015) The last research mile: achieving both rigor and relevance in information systems research. J Manag Inf Syst 32(3):10 Nutt PC (2002) Why decisions fail: avoiding the blunders and traps that lead to debacles. BerrettKoehler, San Francisco Pettigrew AM (1992) On studying managerial elites. Strateg Manag J 13:163–182 Phillips L, Phillips MC (1993) Facilitated work groups: theory and practice. J Oper Res Soc 44:533–549 Sankaran S, Bui T (2008) An organizational model for transitional negotiations: concepts, design and applications. Group Decis Negot 17:157–173 Shaw D, Eden C, Ackermann F (2009) Mapping causal knowledge: how managers consider their environment during meetings. Int J Manag Decis Mak 10:321–340 Simon HA (1976) From substantive to procedural rationality. In: Latsis SJ (ed) Method and appraisal in economics. Cambridge University Press, Cambridge Susman G, Evered R (1978) An assessment of the scientific merits of action research. Adm Sci Q 23:582–603 Tavella E, Franco AL (2015) Dynamics of group knowledge production in facilitated modelling workshops: an exploratory study. Group Decis Negot 24:451 Tully P, White L, Yearworth M (2018) The value paradox of problem structuring methods. Syst Res Behav Sci. https://doi.org/10.1002/sres.2557 Tyler TR, Blader SL (2003) The group engagement model: procedural justice, social identity, and cooperative behavior. Personal Soc Psychol Rev 7:349–361 Valacich J, Jessup L, Dennis A, Nunamaker J (1992a) A conceptual framework of anonymity in group support systems. Group Decis Negot 1:219–242

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Systems Thinking, Mapping, and Group Model Building George P. Richardson and David F. Andersen

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Merging GDN Practice with System Simulation – A Group Model Building Approach . . . . . Roles in System Dynamics Group Model Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boundary Objects in Group Model Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The System Dynamics Group Modeling Process, in Brief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elements of System Dynamics Group Model Building Meetings: Scripts . . . . . . . . . . . . . . . . . . . . Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introducing Elements of System Dynamics Modeling: Concept Models . . . . . . . . . . . . . . . . . . Initiating Systems Mapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Model Formulation, Testing, and Refinement: Ownership . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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The use of systems modeling and simulation contributes an endogenous dynamic perspective to group negotiations and decision-making. In the field of system dynamics, group (participatory) model building has a rich history and growing literature. This chapter provides an introduction. It discusses the roles required to handle the intricacies of facilitation and group modeling and identifies the tension inherent in models as “microworlds” or “boundary objects.” It overviews the group model building process and focuses most extensively on an accumulating body of scripts for group modeling, including scripts for introducing model concepts, initiating systems mapping, eliciting system feedback structure, G. P. Richardson (*) · D. F. Andersen Rockefeller College of Public Affairs and Policy, University at Albany, State University of New York, Albany, NY, USA e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_19

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formulating formal models with client groups, and using them to help build a negotiated consensual view of their shared mental models. The keys to the success of group modeling building efforts appear to be engaging stakeholders, sharing mental models formally, assembling and managing complexity, using simulation to test scenarios and support or refute hypotheses, working toward alignment, and empowering people to have confidence in the strategies that emerge. Keywords

Group decision and negotiation · Group support systems · Discussion and deliberation · System dynamics mapping and modeling · Participatory model building · Mental and formal models

Introduction The problems had been growing. Responsible people in the agency had some disagreements about the sources of the problems, and they had different perceptions about how they would play out in the future. Past efforts to deal with the problems hadn’t worked out as people thought they would. They knew that decisions taken now would influence not only the future of the agency but also its environment, and those changes would influence other stakeholders and feed back to alter the playing field. Addressing the problems meant not only trying to understand that complex dynamic playing field and policies that might improve the agency’s place in it but also working with the intricate stakeholder relationships within the agency and outside in order to build consensus toward policies that could actually be implemented. They decided to bring in a group strategy support team skilled in using group facilitation and system dynamics modeling.

Such a setting is made to order for the potential contributions of system dynamics modeling in group decision and negotiation. Each of the characteristics mentioned are key: the problems are dynamic (developing over time); root causes of the dynamics aren’t clear; different stakeholders have different perceptions; past solutions haven’t worked; solutions that fail to take into account how the system will respond will surely fail to produce desirable long-term results; and implementing change within the agency will require aligning powerful stakeholders around policies that they agree have the highest likelihood of long-term success. The fields of systems thinking and system dynamics modeling1 bring four important patterns of thought to GDN: Thinking dynamically, thinking in stocks and flows, thinking in feedback loops, and thinking endogenously. • Thinking dynamically refers to thinking about problems as they have developed over time and will play out in the future. The principle tool to facilitate dynamic

1 Important texts in the field include Ford (1999), Forrester (1961), Maani and Cavana (2000), Richardson and Pugh (1981), Senge (1990), Sterman (2000), and Wolstenholme (1990).

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thinking is graphs over time. Sketching graphs over time helps groups move from a focus on separate dramatic events to a focus on the persistent, often almost continuous pressures giving rise to the discrete events we see (Howick et al. 2006). • Thinking in stocks and the flows (accumulations and their rates of change) that change them focuses on populations, physical stocks, inventories, backlogs, and other accumulating characteristics central to the problem, and on the production capacities, resources, and distinctive competencies available to deal with the problem (Warren 2002). Stocks change gradually over the time frame of interest, growing or declining as inflows compete with outflows. System capacities result not from quick changes, but from sustained investment. System policies must work through flows to change key stocks over time. • Thinking in feedback loops focuses on circular causality, the likely extended ramifying effects of actions taken by actors in the system (Richardson 1991). Feedback loops are a source of policy resistance: Exposing reinforcing and balancing feedback loops active or latent in system structure gives planners the opportunity to avoid the natural tendencies of complex systems to compensate for or counteract well-intentioned policy initiatives. • Thinking endogenously is the most powerful aspect of systems thinking. It grows out of feedback thought, but is really the foundation for it (Forrester 1968, 1969; Richardson 1991). Thinking endogenously refers to the effort to see the “system as cause,” to extend the boundary we naturally place around our thinking about a problem to the point that root causes are seen not as independent forces from outside but linked in circular causal loops with internal forces over which we might have some control. “Systems thinking” drives many apparently diverse schools of thought, but at the core of them all is the mental effort to uncover endogenous sources of system behavior.

Merging GDN Practice with System Simulation – A Group Model Building Approach In the system dynamics literature, GDN using systems tools is referred to as “group model building” (Vennix et al. 1992; Vennix 1995; Andersen et al. 2007; Rouwette et al. 2002). It could be said to trace its origins back to one of the early practices in the field, using a “model reference group” of experts (Stenberg 1980) to help guide problem definition, system conceptualization, model building and refinement, and model use.2 However, until the late 1980s, virtually all system dynamics modeling

2

Another source of the originating ideas stems from the Group Decision Support Systems literature, including in particular Decision Conferencing (Milter and Rohrbaugh 1985; Quinn et al. 1985; Schuman and Rohrbaugh 1991; Rohrbaugh 2000). Other supporting literatures include strategic management (e.g., Eden and Ackermann 1998) and the European traditions that fall under the heading of soft operations research (see Lane 1994).

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work supporting group decision and negotiation took place out of sight of the client groups, surfacing at various times to show model structure and behavior, policy experiments, and model-based insights. The first suggestion that model building could take place not in the closet but in front of a relatively large client group, in fact with the active participation of the group, comes from work done with the New York State Insurance Department striving to decide among policies to recommend to the state legislature to solve the impending bankruptcy of the state’s five medical malpractice insurance companies (Reagan-Cirincione et al. 1991). From that early beginning, the field has experienced a rather dramatic growth in diverse efforts to bring more and more of the modeling process into public forums.3 The goals of engaging a relatively large client group in the actual processes of model building are a wider resource base for insightful model structure, extended group ownership of the formal model and its implications, and acceleration of the process of model building for group decision support. However, the pitfalls generated by mixing group processes and the modeling process are formidable.

Roles in System Dynamics Group Model Building Early in the development of system dynamics group model building, it was realized that adding the complexities of group process to the arts and technicalities of model building created intricate and complicated conversations. At times the modeler would be working to facilitate the group’s conversations and to elicit information about system structure, parameters, and behavior. At other times the modeler would be in the rather contradictory role of trying to explain something about the system dynamics approach or the structure or behavior of the model under development, in effect talking and teaching rather than listening and learning. Throughout a group model building intervention, the group modeler’s attention would be split between being sensitive to group process on the one hand and on the other hand concentrating on translating what was being said into technical details of model structure. The solution to these problems in the group modeling process was the recognition that there were multiple roles involved and that these multiple roles were best handled by different people. In their seminal article “Teamwork in Group Model Building,” Richardson and Andersen (1995) outlined five distinct roles in system dynamics group model building, which they termed the “facilitator/knowledge elicitor,” the “modeler/reflector,” the “process coach,” the “recorder,” and the “gatekeeper.” • The facilitator/knowledge elicitor works with the group to facilitate the conversation, to draw out knowledge of the dynamic problem, its systemic structure, necessary data and parameter values, and so on. The facilitator/knowledge elicitor 3 See, e.g., Vennix (1996), Vennix et al. (1997), and the special issue of the System Dynamics Review on Group Model Building that that article introduces.

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translates the group’s conversation into the stocks and flows and feedback loops of system dynamics model structure. This person pays constant attention to group process, the roles of individuals in the group, and the business of drawing out knowledge and insights from the group. This role is the most visible of the five roles, constantly working with the group to further the model building effort. The modeler/reflector works more behind the scenes, listening hard to what is being said, thinking about how to clarify and improve the maps being created on the fly by the facilitator and the group. He or she focuses on the model that is being explicitly (and sometimes implicitly) formulated by the facilitator and the group. The modeler/reflector serves both the facilitator and the group. This person thinks and sketches on his or her own, reflects information back to the group, restructures formulations, exposes unstated assumptions that need to be explicit, and, in general, serves to crystallize important aspects of structure and behavior. Both the facilitator and the modeler/reflector must be experienced system dynamics modelers. They can trade roles in the middle of the process. The process coach focuses not at all on content but rather on the dynamics of individuals and subgroups within the group. Often not necessary in small group efforts (where the facilitator and reflector can often substitute), the role can be important in large group efforts. This person need not be a system dynamics practitioner. In fact, it may be advantageous that the person is not: such a person can observe unwanted impacts of jargon in word and icon missed by people closer to the field. The process coach tends to serve the facilitator; his or her efforts are largely invisible to the client group. The recorder (there may be more than one) strives to write down or sketch the important parts of the group proceedings. Together with the notes of the modeler/ reflector and the transparencies or notes of the facilitator, the text and drawings made by the recorder should allow a reconstruction of the thinking of the group. This person must be experienced enough as a modeler to know what to record and what to ignore. The gatekeeper is a person within, or related to, the client group who carries internal responsibility for the project, usually initiates it, helps frame the problem, identifies the appropriate participants, works with the modeling support team to structure the sessions, and participates as a member of the group. The gatekeeper is an advocate in two directions: within the client organization he or she speaks for the modeling process, and with the modeling support team he or she speaks for the client group and the problem. The locus of the gatekeeper in the client organization will significantly influence the process and the impact of the results.

In practice, experienced group modelers can get along with perhaps just two individuals taking (at various times) the first four roles. It should be noted that this formulation of the roles comes from the work of one set of practitioners. But the recognition of the differing natures of these roles, and skill in performing them, are essential to success in group model building efforts. Because of the difficulties of mixing modeling with group process, it is likely that all practitioners, whether or not they know of the writings on teamwork in group model building, carry out their work with groups in teams rather than as individuals (Andersen et al. 2006).

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Boundary Objects in Group Model Building Zagonel (2002, 2003) and Zagonel dos Santos (2004) identified an archetypical dichotomy in system dynamics group model building between building “microworlds” and facilitating a conversation using “boundary objects.” The distinction is blurred in practice, but nonetheless important to note. A “microworld,” as Zagonel used the term, is a model that is intended by its creators and users to be a close replica of some slice of the real world, a reliably accurate recreation, in smaller form of course, of the problematic piece of reality central to the group’s problems of negotiation and decision-making. A “boundary object” (Black 2002; Carlile 2002; Star and Griesemer 1989) is intended by its creators to be a tool for facilitating conversation that spans the boundaries that separate perspectives, constituencies, and turf present in a group struggling with a tough decision. In this sense, system dynamics modelers always strive in some sense for accurate microworlds; but group modelers must also realize the role of the model as a boundary object. In systems practice, such boundary-spanning objects are maps and models constructed by the group (with help) that enable participants to move toward a shared view of a complex system and connects that shared structural view with endogenous system dynamics. Sometimes the process involves only pictures, stories, and diagrams developed by the group, and sometimes the process employs simulation. Figure 1 presents a schematic overview of how this process works in practice. The facilitator/knowledge elicitor works in teams with other skilled system dynamics modelers to help the client group produce pictures, sketches, word-and-arrow diagrams, and other boundary objects that are both based on the client group’s prior mental models while at the same time conform to specific format and syntax defined by good system dynamics modeling principles.

Modeling Zone

Client Group’s Mental Models

Facilitation Zone

Current GMB Boundary Object

Already Completed Boundary Objects

SD Modeling Principles

Remembering and Displaying

Fig. 1 Boundary objects in system dynamics group model building

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The System Dynamics Group Modeling Process, in Brief The system dynamics group model building process involves a series of meetings much like those of any GDN support process. A typical sequence might look like the following: • Problem definition meeting (small group of project leaders) • Group modeling meetings (large group of stakeholders, with full group model building team, perhaps meeting more than once) • Formal model formulation, testing, and refinement (modeling team) • Reviewing model with model building team (modeling team with stakeholder group; this and the previous step usually iterate) • Rolling out model with the community (modeling team, the stakeholder group involved in model construction, and a larger group of potential stakeholders) • Working with flight simulator (interested actors, working with the model in an accessible “learning environment” format; not a common part of the process, but possible) • Making change happen (stakeholders, with facilitation, making decisions). Vennix (1996) describes several other structured designs, exemplified in three cases. In a qualitative modeling intervention on the Dutch health care system he and his colleagues used a Delphi-like approach to elicit knowledge about the system from some 60 participants. The process enabled the group to function “at a distance” as well as in face-to-face meetings (p. 189): • Policy problem • Knowledge elicitation cycles • Questionnaire • Workbook • Structured workshop • Final conceptual model • Project results and implementations The reader will find other variations of group model building processes in several chapters in Morecroft and Sterman (1994).

Elements of System Dynamics Group Model Building Meetings: Scripts Dynamics The problems that the field of system dynamics modeling and simulation can help with are dynamic, that is, they play out over time. Furthermore, vital aspects of their dynamic behavior come from endogenous forces and interactions, that is,

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pressures that emerge from within some appropriate system boundary. Thus, the initial stages of a system dynamics group modeling process help the group to focus on dynamics over time. The principle method for drawing out dynamics is the simple tool of graphs over time. Working in pairs, clients in the group are asked to sketch graphs over time of variables that they think are central to the problem and the decisions that have to be made. Participants are advised to put “now” somewhere in the center of the horizontal time axis, so that dynamics of the past and hopes and fears for the future can be represented. Participants describe their graphs, and the group model building team clusters them to try to tell visually the interacting stories the participants are describing. We call such a repeatable process a group model building script (Andersen and Richardson 1997; Andersen et al. 1997; Luna-Reyes et al. 2006; Richardson and Andersen 1995). This graphing script is a divergent group process that usually results in a wide diversity of candidate variables and their dynamic behaviors, which help the group to move toward dynamic thinking, to focus on key variables of interest, and to see each others’ understandings of the dynamic problem.

Introducing Elements of System Dynamics Modeling: Concept Models A puzzle for system dynamics group modelers is how to give the client group enough of a familiarity with the approach and its iconography of stocks and flows and feedback loops without spending much time doing that. One solution to that puzzle is a short sequence of what we term “concept models” (Richardson 2006). The term reflects the conceptual nature of these little models in two senses. The models introduce concepts, iconography, and points of view of the system dynamics approach. In addition, the models are designed to try to approach the group’s own concepts of its problem in its systemic context. The intent is to begin with a sequence of simulatable pictures so simple and selfexplanatory, in the domain and language of the group’s problem, that the group is quickly and naturally drawn into the system dynamics approach. Within 30 min or less, we’d like to work with the group on their problem in their terms, listening hard to what they have to say, facilitating their conversations, and structuring their views of the problem. Figure 2 shows a concept model sequence used in several group model building sessions on US welfare reform (Zagonel et al. 2004). The diagrams on the left show the sequence of models, moving from a simple view of population stocks and flows of families at risk, to the addition of a feedback loop, and ending with the addition of structure capturing the loss of assistance, which was at the heart of the welfare reform legislation. Each of these three figures was initially drawn on a white board in front of the client group, using the same hand-sketching techniques that the group would later use in mapping system structure on that same white board. When the hand sketch was completed, the computer-drawn images as shown in Fig. 2 were

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Fig. 2 A concept model sequence for a group model building workshop on welfare reform, introducing elements of the system dynamics approach

projected next to the hand drawn sketch. The point was immediately made that the system sketch created the basis for a formal simulation model. Each view in Fig. 2 is increasingly complicated; one increasingly complicated hand sketch supported this elaboration of the concept model. Again, the point being hammered home is that the group could elaborate the formal model just by making a richer and more complete sketch on the white board. The graphs on the right of Fig. 2 show the dynamics of each of these little models, moving from what the drafters of the welfare reform legislation intended (more people in jobs, fewer on assistance) to eventually a “better before worse” situation in which the employment improvement is short-lived and many end up unemployed and ineligible for Federal assistance. Seeing this sequence, participants understood the stock-and-flow iconography, saw examples of how a model can be repeatedly refined, saw that changing model structure changes behavior, and were champing at

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the bit to correct these overly simplified, agonizingly inadequate pictures, all in less than 30 min.

Initiating Systems Mapping Continuing the group model building process, three potential ways of helping the group to begin to conceptualize their complex system are in common use: • Working from the concept model to expand a conserved system of stocks and flows that can form a “backbone” on which to hang feedback structure • Identifying and drawing feedback loops implicit in the graphs over time drawn by the group • Identifying stakeholder goals and perceptions, and sketching the feedback loops that result when pressures from those goal-gaps result in actions that feed back to alter perceptions Figure 3 shows an example of the results of the first strategy. The figure shows the stock-and-flow structure of families in the US welfare system, as developed during the first day of a group model building workshop. The rich picture grew from group discussions that started from the simple concept model in Fig. 2. Beginning with loops rather than stocks and flows is somewhat more difficult to manage. People don’t naturally think in feedback loops. But people do think occasionally about self-fulfilling prophecies, vicious and virtuous cycles, band-

Fig. 3 Stocks and flows of families in the US welfare system, as developed by a group of experts in a group model building workshop (TANF stands for Temporary Assistance to Needy Families)

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wagon effects, and similar self-reinforcing processes; some of those may be apparent in the clustered graphs over time and can be identified, sketched, and expanded to initiate systems feedback mapping. Balancing loops tend to be initially less evident for most decision makers, but ultimately more ubiquitous. An excellent place to start focuses on stakeholder goals and perceptions; it is a small step from the gap between a goal and its related system condition to efforts to close the gap. Figure 4 shows the generic goal-gap feedback loop in bold, surrounded by other complicating influences. While the client group may not have a picture such as Fig. 4 in their heads, the facilitator/knowledge elicitor does, and he or she can use that image to guide the formulation of questions and the interpretation and visual representation of group suggestions. There are numerous other scripts for eliciting feedback structure (see e.g., Akkermans 1995; Andersen and Richardson 1997; Andersen et al. 1997; LunaReyes et al. 2006; Rouwette 2003; Vennix 1996). One particularly generative example is the so-called ratio script in which some need in the system is compared to some identified capacity or resource striving to meet the need (Richardson and Andersen 1995). Figure 5 shows an example from a group model building workshop focusing on care of dementia suffers in an area of the UK. The load on community care is a comparison (ratio?) of the number of dementia clients in community care and the capacity of the community care services to deal with them. Participants in the workshop were asked what would happen if that load became too great. Three obvious feedback loops immediately result: increasing capacity, increasing transfers to palliative care, and decreasing the admission of dementia clients to community

Goal

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Fig. 4 The generic goal-seeking feedback loop (in bold) showing how the gap between goals and perceptions generates action and intended outcomes striving to close the gap. Other influences and feedback loops complicate the picture suggesting sources of policy resistance

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Community services capacity

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migrating or dying

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Fig. 5 A portion of a stock-and-flow map illustrating a group model building script in which the load on community care generates pressures that close feedback loops participants can articulate

care (and there may be more, reaching further through the system). The group then talked in detail about what those aggregate feedback loops actually represented in the system.

Model Formulation, Testing, and Refinement: Ownership Much of the system structure necessary to build a formal, quantified system dynamics model is developed in scripts such as these by the participants in group model building sessions, aided by the facilitator, the modeler/reflector, and the model building team. Some of the equations that would appear in a formal model are clear and explicit in the maps the group generates in this guided process. Most of the necessary data is elicited from the group (in other scripts not discussed here). But details always remain that are best handled by professional modelers offline. At this point, a central concern is group ownership of the model, its structure and behavior, and its implications for policy and decision-making. The group knows the maps produced in the group model building sessions came from the group itself, with help from the modeling team. Now the group must come to own the formal model the modeling team produces from all that rich work. A key in the process of extending group ownership from the maps they generated to the resulting formal model is maintaining diagrammatic consistency.

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The formal model must look like the maps drawn by the group. The most recognizable features, the stocks and flows, must appear in the formal model just as they do in the maps developed by the group. There will be more detail, more equations, and some refinements necessary to support the thinking of the group and principles of good model building, but the formal model must look very familiar to the group. The process of transferring ownership to the formal model involves careful comparison of the structure of the earlier maps with the structure of the formal model, with the facilitator gaining the group’s advice and consent at every step. The process of model testing, evaluation, and refinement can also be carried out with very large groups communicating as a virtual group. See Vennix et al. 1990 and Vennix 1996 for details and examples.

Simulation Ownership of the formal model also grows from simulation experiments participants propose. The robust, nonlinear structure of good system dynamics models means that they should behave plausibly under virtually any scenario one might propose (Forrester 1961). Group model building projects make use of that robustness by offering the formal model to the group to propose any set of parameter changes designed to test possible policies to implement or to try to “break” the model. The richer the set of simulation experiments, the more the group can come to have confidence in the model it has developed (Forrester and Senge 1980; Richardson and Pugh 1981; Sterman 2000). It may take more than one group meeting, with intervening work by the group and the modeling team, but eventually the group will have explored the dynamic implications of their thinking and will have developed confidence in the policies and decisions they want to make to influence the future course of events. At this point, the model developed by the group and the group model building team is likely to be large and detailed. Client understandings of the details of why the model behaves as it does come partly from their understandings of the formal model they helped to create but also from their deep knowledge of the real system they are dealing with. A well-developed formal model will do what it does for the same reasons the real world does what it would do under the same circumstances, so explanations grounded in real world understandings transfer to the model and vice versa. Understanding surprising simulation results is often facilitated by building a small model to capture an insight embedded in the much larger complex system model. Figure 6 shows an example that emerged from group model building work on welfare reform (see Figs. 2 and 3), which resulted in a structurally and dynamically complex model of more than 400 equations. The large model tended to show that policies designed to improve welfare by accelerating the rate of job placement for Families on TANF (the major measured goal of then current national welfare reform policy) were less effective than those

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+

(R)

Probability of + recidivism

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– Families on Post TANF TANF (B) employed Enter TANF Job finding To mainstream rate employment Load on TANF (R) Load on employment (R) support capacity support capacity Time to find first job TANF support Post TANF capacity employment support capacity

At risk populations 6,000

families

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Time (Month) Families on TANF : tanf Post TANF employed : tanf Total families at risk : tanf

Fig. 6 Structure and behavior of a surprising simulation insight

that focused on the “edges” of the system (such as policies aimed at stemming recidivism or moving former TANF clients from supported employment to mainstream employment) (Zagonel et al. 2004). Paradoxically, policies focused strictly on job finding tended to make the system worse in some respects. The tiny model shown in Fig. 6, and the graphs over time it produces, reproduce this result in a surprising way and provide the beginnings of an explanation for the behavior of the larger model. The tiny model shows that adding capacity upstream in the welfare system can speed the flow of families downstream, swamp downstream resources, and significantly increase recidivism, resulting eventually over time in more families on TANF and more total families at risk. Thus, a well-intentioned policy designed to improve the situation for families on temporary assistance shows the classic “better-beforeworse” behavior in which the system overall is eventually made worse.

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Discussion Group model-building using system mapping and modeling is effective because it joins the minds of managers and policy makers in an emergent dialogue that relies on formal modeling to integrate data, other empirical insights, and mental models into strategy and policy processes (Rouwette 2003). Strategic policy making begins with the preexisting mental models and policy stories that managers bring with them into the room. Strategic policy consensus and direction emerge from a process that combines social facilitation with technical modeling and analysis. The method blends dialogue with data. It begins with an emergent discussion and ends with an analytic framework that moves from “what is” baseline knowledge to informed “what if” insights about future policy directions. The key to the success of all these interventions is a formal computer simulation model that reflects a negotiated, consensual view of the “shared mental models” (Senge 1990) of the managers in the room. The final simulation models that emerge from this process are crossbreeds, sharing much in common with data-based social scientific research while at the same time being comparable to the rough-and-ready intuitive analyses emerging from backroom conversations. In sum, we believe that a number of the process features related to building these models contribute to their appeal for front line managers: • Engagement. Key managers are in the room as the model is evolving, and their own expertise and insights drive all aspect of the analysis. • Mental models. The model building process uses the language and concepts that managers bring to the room with them, making explicit the assumptions and causal mental models managers use to make their decisions. • Complexity. The resulting nonlinear simulation models lead to insights about how system structure influences system behavior, revealing understandable but initially counterintuitive tendencies like policy resistance or “worse before better” behavior. • Alignment. The modeling process benefits from diverse, sometimes competing points of view as stakeholders have a chance to wrestle with causal assumptions in a group context. Often these discussions realign thinking and are among the most valuable portions of the overall group modeling effort. • Refutability. The resulting formal model yields testable propositions, enabling managers to see how well their implicit theories match available data about overall system performance. • Empowerment. Using the model, managers can see how actions under their control can change the future of the system. Group modeling merges managers’ causal and structural thinking with the available data, drawing upon expert judgment to fill in the gaps concerning possible futures. The resulting simulation models provide powerful tools for strategy and policy development.

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Cross-References ▶ Advances in Defining a Right Problem in Group Decision and Negotiation ▶ Group Support Systems: Concepts to Practice ▶ Group Support Systems: Past, Present, and Future ▶ Participatory Modeling for Group Decision Support ▶ Supporting Community Decisions

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Collaboration Engineering for Group Decision and Negotiation Gert-Jan de Vreede, Robert O. Briggs, and Gwendolyn L. Kolfschoten

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Business Case of Collaboration Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Collaboration Engineering Approach to Designing and Deploying Collaboration Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Investment Decision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Task Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Implementation and Sustained Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ThinkLets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Generate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reduce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clarify . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Organize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Consensus Building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ThinkLet Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Case Study: Transferring a ThinkLets-Based Collaboration Process Design for IntegrityAassessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Research Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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G.-J. de Vreede (*) University of South Florida, Tampa, FL, USA e-mail: [email protected] R. O. Briggs San Diego State University, San Diego, CA, USA e-mail: [email protected] G. L. Kolfschoten Better Samenwerken, Delft, The Netherlands e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_21

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Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Collaborative work is essential to the success of modern organizations. Many organizations could benefit from the use of advanced collaboration technologies and collaboration professionals, such as facilitators. However, these technologies are often too complex for practitioners to use without professional support, and collaboration professionals are too expensive for many groups who could benefit from their help. To address this challenge, researchers developed and tested the collaboration engineering approach. Collaboration engineering is an approach to designing collaborative work practices for high-value recurring tasks and deploying those designs for practitioners to execute for themselves without ongoing support from expert facilitators. Collaboration engineers design collaborative work practices using a facilitation pattern language consisting of “thinkLets.” ThinkLets are facilitation techniques that create predictable patterns of collaboration. Extensive research and practice demonstrate the feasibility and effectiveness of the approach. This chapter summarizes the collaboration engineering approach in general and the thinkLet concept in detail using an illustrative case in a governmental organization. Keywords

Group decision · Group support systems · Collaboration · Facilitation · Collaboration engineering · Group support · ThinkLets · Case study

Introduction Group work is challenging, especially when it involves negotiation and decision making. Group collaboration processes can benefit from both tool support and process support. Key examples of these are Group Support Systems (GSS) and Facilitators. Groups can use a GSS software suite to focus and structure their deliberations in ways that reduce the cognitive costs of communication, deliberation, information access, and distraction among members as they make joint cognitive effort toward their goals (Davison and Briggs 2000; de Vreede 2014). A GSS offers an integrated set of tools to support groups moving through their work practices to achieve their goals. However, extensive field experience with GSS show that the technology can be challenging for an organization to use in a sustained way, and so to reap ongoing benefits (Agres et al. 2004; Briggs et al. 2003a). Researchers have developed the Collaboration Engineering (CE) approach to address this issue. CE is an approach to designing collaborative work practices for high-value recurring tasks, and deploying those designs for practitioners to execute for themselves without ongoing support from professional facilitators (de

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Vreede and Briggs 2019). CE offers a sustainable approach to the deployment of collaboration support to improve group decision-making and negotiations. This chapter will explain the CE approach and the ways in which it helps to overcome the challenges in the design and implementation of collaboration support to improve group work and group decision and negotiation. Collaboration is a critical skill and competence in organizations (Boughzala and de Vreede 2015). Frost and Sullivan surveyed 946 decision makers using a collaboration index and found that collaboration is a key driver of performance in organizations. Its impact is twice the impact of strategic orientation and five times the impact of market and technological turbulence (Frost and Sullivan 2007). However, unsupervised groups face many challenges with collaboration, including but not limited to free riding, dominance, group think, and inefficiency (Nunamaker et al. 1997; Schwarz 1994). Especially when group size increases, productivity tends to decrease, while conflict tends to increase (Steiner 1972). Another factor that may increase the challenges of collaboration is the involvement of multiple actors and stakeholders, which intensifies interdependencies and the complexity of conflict resolution (Bruijn and Heuvelhof 2008). Thus, it is not surprising that there is a growing need for guidance, including social- and behavioral rules (Haan and Hof 2006). To overcome the challenges of collaboration, groups can benefit from collaboration support. Collaboration support can enable groups to accomplish their goals more efficiently and effectively (e. g., Fjermestad and Hiltz 2001; de Vreede et al. 2003b; de Vreede 2014). Groups can use support from facilitators, people that are skilled in creating interventions to support effective and efficient collaboration (Kolfschoten et al. 2012b), or they can use collaboration support technology such as Group (Decision) Support Systems (chapters ▶ “Group Support Systems: Past, Present, and Future,” ▶ “Group Support Systems: Concepts to Practice,” ▶ “Procedural Justice in Group Decision Support,” and ▶ “Group Support Systems: Experiments with an Online System and Implications for Same-Time/Different-Places Working”). Yet, the business case for return on collaboration support investment remains an issue (Agres et al. 2005; Briggs et al. 1999, 2003a; Post 1993). To address this issue, two strategies are possible: eliminating the need for the distinct role of process leader or facilitator, through integration of rules in the technology (e.g., Briggs et al. 2013), and task separation for the facilitation role, separating the design task from the execution task (e.g., Kolfschoten et al. 2008). CE is an approach in line with the second strategy. In CE, a master facilitator (called collaboration engineer) designs a collaborative work practice. This work practice is documented and then transferred through training to practitioners. Practitioners are domain experts without significant facilitation experience. The cornerstone of the CE approach is the thinkLet: The smallest unit of intellectual capital to create a pattern of collaboration (Briggs et al. 2003a). A thinkLet provides a transferable, reusable, and predictable building block for the design of a collaboration process (de Vreede et al. 2006a). In short, thinkLets are facilitation best practices. The use of thinkLets helps to increase the transferability and predictability of the process design (Kolfschoten et al. 2011, 2012a). In this chapter we will first articulate the business case for collaboration support. Next, we will describe the CE approach and the thinkLet concept in more detail, and discuss their role in the design and deployment of sustainable collaborative work

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practices. Finally, we will present a case study in which the CE approach was used to support the transfer of a recurring collaborative work practice in a governmental setting.

The Business Case of Collaboration Support In the field, GSS supported meetings have often been judged to be more efficient and effective than manual meetings and participants are more satisfied in a GSS meeting than in a traditional meeting (Fjermestad and Hiltz 2001; de Vreede 2014). In a benchmark study where Boeing, ING-NN, IBM, and EADS-M were compared, efficiency improvements of more than 50% were reported both in terms of meeting time (person hours) and project duration. In one organization, GSS users responded to a survey where they rated, “effectiveness compared to manual” and “user satisfaction” at 4.1 on a 5-point scale (de Vreede et al. 2003b). At each of these sites, the meetings were designed and guided by internal (IBM and Boeing) or external (INGNN and EADS-M) facilitators. A key task of facilitators lies in choosing the right tools and techniques, which requires significant skill and expertise that is not always available in the group. Such groups can therefore benefit from the support of facilitators (Ackermann 1996; Dennis and Wixom 2002; Griffith et al. 1998; Kolfschoten et al. 2012b; Wheeler and Valacich 1996). De Vreede et al. (2002) found that from a user perspective, the facilitator is the most critical success factor in a GSS meeting. As Clawson et al. (1993) point out, a facilitator has a large number of tasks that require skills and expertise. Notwithstanding their reported benefits, case studies have indicated that implementing GSS and facilitation support in organizations is particularly difficult to sustain over the long term and may lead to abandonment (Agres et al. 2005; Briggs et al. 1999; Munkvold and Anson 2001; Vician et al. 1992). In the organizational setting, group meetings are diverse and present many difficulties to those organizing them (Clawson and Bostrom 1996). As a result, group facilitation requires complex cognitive skills (Ackermann 1996; Hengst et al. 2005). Training a GSS facilitator takes time and should involve the experience of facilitating and influencing group dynamics (Ackermann 1996; Clawson and Bostrom 1996; Kolfschoten et al. 2011, 2012b; Post 1993; Yoong 1995). This makes facilitation support difficult to implement and sustain in organizations. However, even if a skilled facilitator is found, sustaining such support in organizations is challenging. Sustained use is very dependent on a champion in the organization that advocates and stimulates use (Briggs et al. 2003a; Munkvold and Anson 2001; Pollard 2003). Besides the deployment challenges discussed above, it is difficult to create a business case for the implementation of collaboration support in an organization (Agres et al. 2005; Briggs et al. 2003a; Post 1993). Although the added value is substantial (Fjermestad and Hiltz 2001; de Vreede et al. 2003b), it is difficult to predict and document this added value (Briggs et al. 2003a). This difficulty may be due, in part, to the fact that collaboration support (facilitator and GSS technology) poses highly visible costs whereas improvements may be less visible and are difficult

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to measure and assign to specific budget categories. Collaboration often contributes to important processes in the organization, but not often to the central production process. Further, collaboration support is often required for “special” events, which do not occur on a frequent basis, making the generated value unpredictable in a budget plan (Briggs 2006). This makes it easier to eliminate such facilities during a budget crunch (Agres et al. 2005; Briggs et al. 2003a). In the next section we introduce the CE approach that is aimed at addressing these challenges.

The Collaboration Engineering Approach to Designing and Deploying Collaboration Support Collaboration Engineering (CE) is an approach to designing collaboration processes. The following definition outlines both the scope and key elements of the CE approach (Briggs et al. 2006): Collaboration Engineering is an approach to create sustained collaboration support by designing collaborative work practices for high-value recurring tasks, and deploying those as collaboration process prescriptions for practitioners to execute for themselves without ongoing support from professionals.

In CE, we aim to offer process and/or technology support in a way that enables the organization to derive value from this collaboration support on an on-going basis without the need to rely on collaboration professionals such as facilitators (Briggs et al. 2003a; de Vreede and Briggs 2019). CE focuses on the design of collaborative work practices to accomplish a specific type of task in an organization: a recurring, high value task. This focus has several reasons. First, the return of investment on the resources devoted to the CE effort increases each time the work practice is executed. Second, the return of investment on the effort to train employees to run the collaboration process is high, and their learning curve will be faster as they can learn from previous mistakes instead of experiencing new challenges each unique session they facilitate. Additionally, the recurring benefits for a high value task make supporting it important so that it decreases the likelihood that it will be abandoned (Kolfschoten et al. 2008; de Vreede and Briggs 2019). Collaboration support exists of process and technology or tool support. For these two types of support we can distinguish a design task (to design the process and the technology), an application task (to apply the process and to use the technology) and a management task (to manage the implementation and control of the process and to manage the maintenance of the technology). Many organizations, however, distinguish only one role for collaboration support: a facilitator (Kolfschoten et al. 2012b). The facilitator often is responsible for the design and execution of the collaboration process and in many cases also takes care of the project management (e.g., acquisition of sessions, management of the facilitation team, and business administration) and technology application (operating the technology). External roles are often the

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design of the technology and the maintenance of the technology (hardware and software maintenance) (Kolfschoten et al. 2008, 2012b). In CE, the abovementioned tasks are divided among several roles which enables outsourcing and dividing the workload of collaboration support (Kolfschoten et al. 2012b). The two new roles introduced in the CE approach are the Practitioner and the Collaboration Engineer. Further, the project management with respect to the collaboration support is organized differently. Practitioners are domain experts, trained to become experts in conducting one specific collaboration process. They execute the designed collaboration process as part of their regular work (de Vreede and Briggs 2019). Practitioners are not allround facilitators. They neither have the skills to design collaborative work practices nor the experience to be flexible and adapt collaboration processes when the needs of a group change during the process’ execution. When using collaboration support technology, the technical execution can be performed by a single practitioner, or two practitioners may work together, one moderating the process while the other runs the technology. However, since this would be a standardized, routine process, there would be no need for skilled professional technical facilitators (also called chauffeurs or technographers) who know all features and functions of the technology platform and can make informed choices about which function to use in response to unanticipated demands. Rather, practitioners need to know only the configurations and operations relevant to their specific process (Briggs et al. 2013). The skills required for the application roles in collaboration support according to the CE approach are therefore much more limited compared to those of the professional facilitator. Since the practitioner will not have the skills to adapt the process on the fly, and the collaboration engineer will not be on hand to correct any deficiencies in the process design as it is executed by the practitioner (Kolfschoten et al. 2005), there is a need for a much more robust and predictable collaboration process design. Therefore, the process design skills required by the collaboration engineer are much more extensive than those required by either a facilitator or a practitioner. The processes collaboration engineers create must be well-tested, predictable, reusable, and easily transferable to practitioners who are not group process professionals. To create such a process design, a collaboration engineer must be able to predict the effect of the interventions that are prescribed in the process design. Therefore, collaboration engineers need to be highly experienced facilitators (de Vreede and Briggs 2019). In CE, the overall responsibility for the recurring task and the roll-out of the designed collaboration process is mostly not in the hands of a practitioner but of a process implementation manager. A process implementation manager is responsible for the organizational deployment process and for monitoring progress and outcomes. Also, the technology is often managed by another person. Most organizations have a special department for technology support and maintenance and such a department could also maintain the technology for collaboration support. The new role division is displayed in Fig. 1.

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Scope

Task process design

process application

process management

technology design

technology application

technology maintenance

External

Internal

Fig. 1 Role division in Collaboration Engineering (Kolfschoten et al. 2008)

Determine CE scope Determine added value CE Investment decision Interview stakeholders Elicit requirements Task analysis Decomposition Choice Validation Design Design phase

Transfer training Practitioner preparation Execution Transfer Full scale implementation Develop expertise Implementation Sustain organizational ownership Sustained use Deployment phase

Fig. 2 The collaboration engineering approach

The CE approach consists of an iterative sequence of steps from an investment decision to collaboration process design and full deployment. The process is visualized in Fig. 2. First the collaboration engineer evaluates if the work practice can be supported and improved by means of a repeatable collaboration process (Briggs and Murphy 2011). Next, the decision to invest in the design of the process and in the acquisition and training of collaboration support tools is made. To design the collaborative work practice, the task and stakeholders involved will be analyzed to determine relevant process requirements. Based on this, the collaboration process design will be composed as a sequence of steps. This process design is piloted and validated to ensure it fits the requirements and renders predictable, high quality results. Once the process design is approved, it is deployed in the organization. Practitioners are selected and trained, and the first practitioners will run the collaborative work practice. Based on this experience, the process can be adapted again. Finally, the complete practitioner team is trained, and they are encouraged to form a community of practice. This community will take ownership of the collaborative work practice and continuously improve it. We will describe these steps in more detail below.

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Investment Decision CE has a rather distinct scope. This scope has three components; the economic component, the collaboration component, and the domain of application. First, to meet the economic scope, the process should be recurring and of sufficient value to justify the development and deployment of collaboration support. Second, it should be a truly collaborative task, meaning that it requires high interaction between participants. Third, it should be a knowledge intensive and goal-oriented task. CE is not meant for general teambuilding, negotiation, or conflict resolution.

Task Analysis In the task analysis phase, a team is formed with stakeholders from the organization among which the project manager of the CE project. The team analyzes the task and defines the goal, deliverable, and other requirements. Interviews or meetings with the relevant stakeholders will give insight into the goal and task. A goal can be to deliver a tangible result, for example, to make a decision or to solve a problem. A goal can also be a state or group experience, like increasing awareness about a problem or creating shared understanding.

Design In this phase, the collaboration process is build based on the requirements established in the task analysis phase. The approach for collaboration process design will resemble a design approach or problem-solving method, with one key difference: instead of creating solutions or alternatives from scratch, a library of known techniques is used as a source to select and combine techniques to form a collaboration process design. There are three key steps in the design phase: the decomposition of the process in small activities, the choice of facilitation techniques for each activity, and the validation of the design. During the decomposition step, the discrete activities that a group has to complete to achieve their goal are determined. During the next step, facilitation techniques necessary to execute each of these activities collaboratively are selected. For this purpose, the CE design approach uses a repertoire of thinkLets. Experience has shown that practitioners and novice facilitators can use thinkLets and indeed create the intended patterns of collaboration (see, e.g., Giesbrecht et al. 2017; Kolfschoten and Veen 2005; Simmert et al. 2017; de Vreede 2014). In the third and final step, the design is validated based on several criteria, e.g., goal achievement and match between process complexity and practitioner competence. The design steps have an iterative nature, similar to iterative approaches in software engineering. The validation is, however, a key step in the process; it is critical that the design has sufficient quality since flaws will result in unsuccessful transfer to, and execution by, the practitioners, which could lead to abandonment of the project.

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Transfer In the transfer phase, the collaboration engineer transfers the collaboration process prescription to the practitioners through training and coaching effort (Kolfschoten et al. 2011; de Vreede 2014). To this end, the collaboration engineer documents the process prescription such that it becomes as easy as possible for the practitioners to grasp the process and internalize it (Kolfschoten et al. 2012a). The transfer phase also includes the first time that the practitioner prepares for the application of the process. She/he then has to execute the process prescription with a specific group in their organization and needs to prepare and instantiate different aspects of the process prescription. The last learning and transfer effort occurs during the first trials of the collaboration process execution, as the practitioners gain more and more experience with the process execution. During the transfer phase, shortcomings to the collaboration process design may be discovered and the design may consequently be updated.

Implementation and Sustained Use When the transfer phase is complete, the process can be implemented on a full scale. This requires planning and organization. Like in facilitation, the success of the practitioner is key to the successful implementation of the process (Nunamaker et al. 1997; de Vreede et al. 2003a). When practitioners are trained and have performed well at their first sessions, the process should be rolled out in the organization and the organization should slowly take ownership of the process. To establish this, management should stimulate the use of the collaboration process through controls and incentives. Furthermore, when the project involves multiple practitioners, it may be valuable to set-up a community of practice to exchange experiences and lessons learned. Finally, it is important that the process and its benefits are evaluated on a regular basis.

ThinkLets To design a predictable, transferable, reusable collaboration process, the CE approach uses design patterns called thinkLets. ThinkLets represent a pattern language for designing collaborative work practices (Kolfschoten et al. 2006; de Vreede et al. 2006a). Design patterns were first described by Alexander (1979) as reusable solutions to address frequently occurring problems. In Alexander’s words: “a [design] pattern describes a problem which occurs over and over again and then describes the core of the solution to that problem, in such a way that you can use this solution a million times over, without ever doing it the same way twice” (1979). A thinkLet is a design pattern of a collaborative activity that moves a group toward its goals in predictable, repeatable ways (Kolfschoten et al. 2006; de Vreede et al. 2006a). ThinkLets can be

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combined to create a sequence of steps that can be used by a group to execute the steps of a collaborative work practice in order to achieve collaborative goals. As with other pattern languages, thinkLets are used as design patterns, as design documentation, as a language for discussing complex and subtle design choices, and as training devices for transferring designs to practitioners in organizations (Kolfschoten et al. 2011, 2012a; de Vreede et al. 2006a; de Vreede 2014). A thinkLet provides all information required for a team to create a pattern of collaboration. Six generic patterns of collaboration have been identified, and for each, several subpatterns are recognized (Briggs et al. 2006; Kolfschoten et al. 2014):

Generate The generate pattern is defined as moving from having fewer to having more concepts in the pool of concepts shared by a group. There are three subpatterns: • Creativity: Move from having fewer to having more new concepts in the pool of concepts shared by the group. • Gathering: Move from having fewer to having more complete and relevant information shared by the group. • Reflecting (see also Evaluate): Move from less to more understanding of the relative value or quality of a property or characteristic of a concept shared by the group.

Reduce The reduce pattern of collaboration deals with moving from having many concepts to a focus on fewer concepts that a group deems worthy of further attention. There are three subpatterns: • Filtering: Move from having many concepts to fewer concepts that meet specific criteria according to the group members. • Summarizing: Move from having many concepts to having a focus on fewer concepts that represent the knowledge shared by group members. • Abstracting: Move from having many detailed concepts to fewer more generic concepts that reduce complexity.

Clarify The clarify pattern of collaboration deals with moving from having less to having more shared understanding of concepts, words, and information. There are two subpatterns:

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• Sensemaking: Move from having less to having more shared meaning of context, and possible actions in order to support principled, informed action. • Building shared understanding: Move from having less to more shared understanding of the concepts shared by the group and the words and phrases used to express them.

Organize The organize pattern involves moving from less to more understanding of the relationships among concepts the group is considering. There are three subpatterns: • Categorizing: Move from less to more understanding of the categorical relationships among concepts the group is considering. • Sequencing: Move from less to more understanding of the sequential relationships among concepts the group is considering. • Causal decomposition: Move from less to more understanding of the causal relationships among concepts the group is considering.

Evaluate The evaluate pattern involves moving from less to more understanding of the relative value of the concepts under consideration. There are three subpatterns: • Choice social/rational: Move from less to more understanding of the concept(s) most preferred by the group. • Communication of preference: Move from less to more understanding of the perspective of participants with respect to the preference of concepts the group is considering. • Reflecting (see also Generate): Move from less to more understanding of the relative value or quality of a property or characteristic of a concept shared by the group.

Consensus Building Consensus is usually defined as an agreement, acceptance, lack of disagreement, or some other indication that stakeholders commit to a proposal. There are two subpatterns: • Building agreement: Move from less to more shared preferences among participants with respect to concepts the group is considering. • Building commitment: Move from less to more willingness to commit among participants with respect to proposals the group is considering.

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ThinkLet Structure ThinkLets are based on a core set of elementary behavioral rules that, when combined, create predictable dynamics in the group and yield a deliverable with a predictable structure (Kolfschoten et al. 2006; Kolfschoten and Houten 2007; de Vreede et al. 2006a). To some extent, thinkLets also produce predictable states of mind among participants (e.g., greater understanding, broader perspectives, and more willingness to commit). Facilitators, collaboration engineers, and practitioners have executed thinkLets repeatedly in a variety of contexts for almost two decades and report that each execution produces a similar pattern of collaboration, and a similar result in terms of participants’ behaviors (see, e.g., Acosta and Guerrero 2006; Bragge et al. 2005; Fruhling and de Vreede 2005; Giesbrecht et al. 2017; Harder et al. 2005; Marques and Ochoa 2014; Simmert et al. 2017; de Vreede 2014). Thus, thinkLets have predictable effects on group process and their outcomes, and these effects have been recorded in thinkLet documentation. Researchers have also verified these effects by reviewing the transcripts of hundreds of GSS sessions (Kolfschoten et al. 2004). For some thinkLets, experimental research has been performed to compare their effects (Santanen et al. 2004). To further increase predictability, for some thinkLets theoretical models have been developed to understand their effects on the patterns of collaboration and results that are created when they are used (e.g., Briggs et al. 2006; Santanen et al. 2004; Seeber et al. 2017). Through the use of parsimonious rules, misunderstanding can be reduced, which is likely to strengthen the predictability of group behavior and process outcomes (Santanen 2005; de Vreede et al. 2006a). Many books and websites describe useful, well-tested facilitation techniques. A key distinction between such techniques and thinkLets is in the degree to which they have been formally documented according to the design pattern principles. The current documentation convention (Kolfschoten et al. 2006, 2012a; de Vreede et al. 2006a) includes the following: Identification Each thinkLet has a unique name. These names are typically selected to be catchy and amusing so as to be memorable and easy to teach to others (Buzan 1974). The name is also selected to invoke a metaphor that reminds the user of the pattern of collaboration the thinkLet will invoke, and visualized with an icon. Further, thinkLets are summarized to give an overview of the technique. The names, combined with the metaphor and icon, constitute the basis for a shared language. Rule–Based Script Each thinkLet must specify a set of rules that prescribe the actions that people in different roles must take using the capabilities provided to them under some set of constraints specified in parameters. ThinkLets can include several roles. For example, during brainstorming there can be a regular participant role and a devil’s advocate role (Janis 1972). Everything a practitioner could do and say to instruct

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the group in performing their actions based on the rules in the thinkLet is captured in the script. The script makes the thinkLet more readily transferable, because it frames the rules as spoken instructions and guided actions for the user. With the rules as a basis for the script, practitioners can adjust the script to their style while keeping the instructions that are essential for the thinkLet to succeed. Selection Guidance Each thinkLet must explain the pattern of collaboration that will emerge when the thinkLet is executed, and must include guidance about the conditions under which the thinkLet would be useful, and the conditions under which it is known not to be useful. To further support thinkLet selection, combinations, alternatives, and variations to the thinkLet are documented. Further, thinkLets are classified to the pattern of collaboration they evoke and the type of result they intend to create. Last, to help the collaboration engineer in understanding the thinkLet, insights, tips, and lessons learned from the field to further clarify the way a thinkLet might be used and how it may affect a group are documented. What Will Happen? For the practitioner it is important to understand what will happen when the thinkLet is executed. In this part the result and effects of the thinkLet are explained. For this purpose, known pitfalls that might interfere with its success and suggested ways to avoid them are captured. Additionally, insights are offered to the practitioner about (a) the role of the thinkLet in the process, (b) the time allocated for the thinkLet, and (c) how to deal with delays in the process. Also, each thinkLet documentation must include at least one success story of how a thinkLet was used in a real-life task. Success stories help the user understand how the thinkLet might play out in a group working on a real task. Some documenters of thinkLet also include failure stories to illustrate the consequences of specific execution errors or misapplications of the thinkLet. ThinkLets, like other design patterns, can be used in a variety of circumstances. They are documented in a way that a collaboration engineer can implement them with different technologies or tools, in different domains, and with different types of groups. Most thinkLets can be performed with pen and paper (de Vreede 2014). Some require data processing capacity as offered in GSS or stand-alone tools such as spreadsheets. Each thinkLet has a number of constraints that can be instantiated at process-design time or at execution time, to customize the thinkLet for a specific task in a specific domain. ThinkLets mostly define one participant role but can be modified to accommodate different roles. Last, thinkLets can be modified or instantiated to fit different time constraints within some range. These features enable collaboration engineers to create a reusable process with thinkLets, as they support accommodating the available resources, while at the same time offering the flexibility required to accommodate changes in the available resources among different instances of the recurring task. In this way, a recurring collaborative work practice can be supported using a thinkLet-based collaboration process design.

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Many hundreds of facilitators, students, and practitioners have been trained to use thinkLets to support collaborative efforts (de Vreede and Briggs 2019). ThinkLets are easy to learn because their documentation is structured to contain the essential information thus limiting their complexity to a minimum (Kolfschoten et al. 2012a). Furthermore, they have mnemonics to make it easier to memorize them and to use them as a shared language in communities of practice (de Vreede et al. 2006a). Therefore, thinkLets offer a good basis for the training of practitioners to become skilled and independent in their ability to support the collaborative work practice (Kolfschoten et al. 2011).

Case Study: Transferring a ThinkLets-Based Collaboration Process Design for IntegrityAassessment Integrity of government organizations and institutions is one of the key pillars of a successful democracy. While procedures and policy can be used to avoid integrity violations, integrity of the organization depends on the integrity of its agents. Nonetheless, a government organization is obliged to eliminate or control “tempting situations” in which agents have the opportunity to violate principles of integrity. Therefore, it is important for government organizations to assess the integrity risks in their organization and to find solutions for the most tempting situations regarding integrity violations. The integrity assessment described in this chapter was created by the Dutch national office for promoting ethics and integrity in the public sector. It was expected that many government organizations would want to use the integrity risk assessment instrument. For this purpose, additional facilitators needed to be trained in a relative short period to support groups in the assessments. This task was outsourced to one of five future centers in the Netherlands, named “het Buitenhuis.” The integrity support agency and the future center embraced the CE approach for two reasons: First, it needed to expand its cadre of practitioners to run the assessments. Second, they wanted to structure and standardize the integrity workshops to ensure their quality, even when they would be performed by different practitioners. Furthermore, the center believes that groups would feel more comfortable in an integrity assessment facilitated by a member of their own or a similar organization, i.e., an integrity assessment practitioner. The session is an integrity assessment of the organization, which is similar to a risk assessment but focused on possible integrity violations. This topic is possibly sensitive and the anonymity of GSS support was therefore considered to be of great value. Each session would take a full day and contains mostly evaluation steps, both qualitative and quantitative. However, group discussion would be required to build consensus and to integrate brainstorming results to produce a group result. The agency’s existing integrity assessment process was used as a starting point for the design of a repeatable thinkLets-based collaboration process that was to be transferred to other integrity assessment practitioners. The integrity assessment started with a guided discussion to increase awareness of integrity violations, followed by a “risk analysis” of integrity violations and an assessment of both

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hard and soft integrity measures to see how the organization dealt with integrity and how well that worked. Finally, suggestions for improvement were collected. The actual design and deployment of the new integrity assessment process following the CE approach was performed by the third author of this chapter. We modified only a few steps in the original process to simplify the process and to avoid unpredictable outcomes of some of the steps. Furthermore, some of the instructions were changed to clarify the process and the intended result. To make these modifications, two practitioners from the future center were observed while they executed the process. Proposed changes were discussed with both the integrity support agency and the future center. Next, the thinkLets needed for the process were selected using the choice criteria as discussed in Kolfschoten and Rouwette (2006) and the collaboration process was documented according to the collaboration process prescription template (Kolfschoten and Hulst 2006; Kolfschoten et al. 2012a). To validate the resulting process design, it was discussed again with the practitioners from the future center and a pilot session based on the new process prescription was facilitated by the researcher. To evaluate the value of the CE approach in the case study, we wanted to study whether practitioners, trained with a thinkLet-based collaboration process, could support the collaboration process with similar results as expert facilitators would. To this end, we tested the following hypothesis: A practitioner who executes a collaboration process design created and transferred according to the CE approach is not outperformed by a professional facilitator in terms of collaboration process’ participant’s perceptions of quality of the process in terms of: (a) Satisfaction with the process. (b) Satisfaction with the results. (c) Commitment to the process. (d) Efficiency of the process. (e) Effectiveness of the process. (f) Productivity of the process. As this is a so-called 0-hypothesis, it cannot be confirmed. However, we can collect evidence from different sources to show that the participants’ perceptions of the quality of this recurring collaborative task should not be significantly different in two treatments: • Process guidance by a practitioner (trained novice facilitator). • Process guidance by a professional facilitator. Besides collecting quality perceptions from participants, we collected data that allowed us to distinguish practitioners from professional facilitators. Furthermore, we wanted to know whether the practitioners felt supported by the training and collaboration process prescription they received, and whether the process was executed as intended and resulted in predictable patterns of collaboration and results. We thus distinguished the following roles:

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• Practitioner: (trainee, novice facilitator) A person from a government organization, who is involved in or is an expert on integrity matters without significant facilitation experience, and to whom the process design will be transferred. • Professional facilitator: A person who facilitates group processes on a regular basis as part of his/her job. • Participant: a person participating in an integrity assessment workshop. • Chauffeur: A person operating the GSS during an integrity assessment to assist the facilitator or practitioner who does not address the group to give instructions. The researcher performed the role of observer, professional facilitator, and chauffeur. For the study, the pilot of the new integrity assessment process was used as a benchmark. The pilot was executed with the researcher and several other professional facilitators in the role of the facilitator. At the conclusion of the pilot, the participant’s perceptions on the quality of collaboration process were measured. Practitioners that were to execute future integrity assessments were trained using the CE training program described in Kolfschoten et al. (2009a) and Kolfschoten et al. (2011). In addition, the practitioners’ perception of the transfer and supportiveness of the collaboration process prescription and training were evaluated. After being trained, the practitioners executed the process design while being observed by the researcher. At the end of each process execution, the participants’ perception on the success of the process was measured. Finally, also the practitioners’ perception on their performance and on the transferability of the collaboration process design was evaluated.

Research Instruments We used the following research instruments; details on the questionnaires and interview protocols can be found in Kolfschoten (2007): • A questionnaire to measure the participant’s perception on the quality of the collaboration process. • A questionnaire to evaluate the initial experience of the practitioners with facilitation, GSS, and group support. • A questionnaire to evaluate the practitioner’s perception on the transfer and supportiveness of the collaboration process prescription and training. • An interview protocol to evaluate the practitioner’s perception on his performance and the transferability of the collaboration process prescription.

Participant’s Perception on Quality of Collaboration We evaluated the quality of a collaboration process from a participant perspective. Each group that performed the collaborative integrity assessment task can judge the quality of the process and the quality of the outcome. For integrity assessments, outside objective judgments of the quality of the results are very difficult to acquire, as the outcome of the process is a perception on the integrity risks in the organization,

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and as such can conflict with the perception of an outsider. The collaboration quality questionnaire measured six constructs: efficiency, effectiveness, productivity, commitment of resources, and satisfaction with results and process. For each construct, five questions were used with a Likert scale from 1 (strongly disagree) to 7 (strongly agree). The questions for satisfaction were taken from Briggs et al. (2003b).

Questionnaire for Practitioner Experience in Group Support To evaluate the experience of the practitioner in group support, we used an interview protocol to determine different roles in group support (Kolfschoten et al. 2008). From this protocol, we used only the questions that addressed the respondents’ experience with group support. Questionnaire for Training Evaluation To evaluate the training, we collected perceptions on the usefulness of the thinkLets, the completeness of the training, the quality of the training, and the cognitive load of the training. The questions for this instrument were taken from Duivenvoorde et al. (2009). Interview Protocol for Session Evaluation To evaluate the practitioner performance and the support of the CE approach in transferring collaboration process designs we evaluated the following constructs: • • • •

Predictability of the process design. Supportiveness of the process design. Difficulty of execution. Cognitive load of execution.

Results The Pilot Results Both the researcher and the professional facilitators of the future center had facilitated many sessions with a variety of organizations. All facilitators charged a fee for the sessions they facilitated. They facilitated in service of clients of the organization Table 1 Quality of collaboration as a result of facilitation by professional facilitators. Scale 1–7, 1 being very low, 7 being very high Construct Satisfaction process Satisfaction outcome Commitment Efficiency Effectiveness Productivity

N 50 50 50 50 50 50

Mean 5,36 4,79 5,68 5,48 4,68 5,16

stdev 1,07 1,07 0,90 1,01 1,03 0,99

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for which they worked, and thus could be regarded as professional facilitators. For this study, each professional facilitator roughly performed the same process as described in the integrity assessment process design with only marginal differences in the way thinkLets were applied and instructions were given to the group. The results concerning the quality of the collaboration are presented in Table 1. The differences between the performances of the facilitators are marginal and the standard deviations are not very high either. We used these results as a benchmark to assess the practitioners’ performance.

The Practitioners The practitioners in the study were all employed by large government organizations. Some had a function related to integrity and some had some affinity with (technical) facilitation. None of the practitioners had had to perform the integrity assessment process as part of their formal job description. Most of the practitioners had some experience with supporting groups, either in the role of trainer, teacher, or project leader. Some had facilitated workshops or had worked as a technical facilitator but not for many sessions. Most had received higher education. The average age was 43, four were female, and three were male. We were not involved in any way in the recruitment of practitioners for the study. The Training The seven practitioners participated in two separate training sessions, lasting two days each. Six handed in the evaluation of the training and integrity assessment design. The results are listed in Table 2. The manual describing the details of the process design was considered complete and all aspects were considered useful. Each aspect of the training was rated as sufficient. The manual was considered quite extensive, and some more organization of the different parts would have been useful. Most of the process steps were focused on the evaluation or assessment of an organization and since the practitioners worked at different organizations, it was difficult to exercise or simulate these steps. As a result, some steps could not be experienced. This was recommended by the practitioners as an improvement for the training, yet it was recognized that this would be difficult to implement. Some practitioners had the opportunity to attend a session before they first executed it. The difficulty and mental effort of the training were estimated medium. Practitioners Table 2 Evaluation of the training and integrity assessment process design Question scale: 1–7 Was the manual complete? What did you think of the usefulness of the thinkLets? How do you estimate the mental effort of preparation and training? (low-high) How difficult was the training? Do you feel equipped to facilitate the session? Were you satisfied with the training?

Average 6.17 4.50 4.33

stdev 0.75 1.76 1.37

N 6 6 6

4.00 4.33 5.00

1.41 1.03 0.63

6 6 6

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felt equipped to execute integrity assessments but indicated that they wanted to see a real session before they executed their own, if possible. Overall, the training was evaluated satisfactory.

The Practitioner Performance Four practitioners executed the process. The three “drop-out” practitioners either felt uncomfortable with the GSS technology (1 practitioner) or did not run a session due to inability to schedule such event within the timeframe of the study (2 practitioners). We observed the sessions and intervened to support the practitioner in guiding the group only when this was absolutely necessary. In one session, the researcher was not able to observe and act as chauffeur; the chauffeur role was performed by someone else. The practitioners reported back on several questions through written self-reflections and interviews. The observer also made notes about deviations from the script and interventions that were made to support the group that should have been made by the practitioner. One practitioner did not prepare the execution and therefore presented the group with the instructions and background of the session by more or less “reading the slides out loud.” Although the participants noticed this, they were not disappointed in the results and were generally satisfied with the process. This indicates that the transferability of the instructions had become substantial. The integrity assessment process leads to an outcome that is in most cases instrumental for the organization, while it is generally not very instrumental to the participants, except when it enables the participants to reveal significant problems in which they are a stakeholder. This poses a challenge as commitment can be lower, but at the same time, the lack of significant stakes in the outcome makes the process less likely to evoke conflict and emotions. Over all sessions, it was observed that the practitioners’ ratings of mental effort increased if they had to deal with conflict in the group. The practitioners that had a background in integrity were sometimes tempted to make normative comments with respect to the integrity risks of the organization, which could be problematic, as some risks might be very different in different cultures and contexts. The results of the practitioners are shown in Table 3. We compared the results from the practitioners with the results of the professional facilitators using an independent-samples t-test with a significance level of 0.01.

Table 3 Quality of the practitioner sessions from a participant perspective Construct Satisfaction process Satisfaction outcome Commitment Efficiency Effectiveness Productivity

n 46 46 46 46 46 46

Mean 5,42 5,06 5,72 5,49 4,87 5,23

stdev 0,92 1,04 1,03 1,02 1,03 1,06

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Table 4 Independent-samples t-test practitioner’s vs. professional facilitators Construct Satisfaction process Satisfaction outcome Commitment Efficiency Effectiveness Productivity

Sig. α 0.01 0.800 0.191 0.863 0.980 0.365 0.762

Effect size 0.0009 0.0236 0.0004 0.0009 0.0114 0.0013

The groups we compared are the participants in sessions performed by professional facilitators (n = 50) and the participants in sessions performed by practitioners (n = 46). The results are depicted in Table 4. We found that for all quality dimensions, there was no significant difference between practitioners and facilitators (α =0.01). Also, the effect size eta squared was calculated. According to Cohen (1988), this is a very small effect: less than 3% of the effects is explained by the difference between facilitators and practitioners.

Limitations A key limitation in this study is the observing role of the researcher. As the sessions are held in a commercial setting, the researcher cannot allow the session to go wrong entirely, and thus, when a practitioner mal-performs, the researcher has to intervene. Although interventions were limited to a few incidents, the interventions as reported may have had an effect on the quality ratings. Another limitation is that while the task is identical, the groups are not and due to the sensitive topic of this case, some sessions can be significantly more difficult than others. This poses a limitation to the comparisons across sessions. A last limitation is the relatively low number of practitioners and professional facilitators. A laboratory setting or noncommercial setting would not resolve these problems as the session and thus the facilitation challenges would not be as realistic and are actually different (Fjermestad and Hiltz 2001; Kolfschoten et al. 2009b). To increase the robustness of the results, the number of sessions should therefore be increased.

Discussion and Conclusions During our study, no significant difference between facilitators and practitioners was found. With respect to both the training and the facilitation, practitioners did not report very high mental effort. This indicates that the facilitation task in this case has become transferable. Both practitioners and professional facilitators received positive scores on the perceived quality of the collaboration process. Practitioners could most improve their support to the group with respect to the outcomes of the sessions. Supporting the group to create high quality results is very difficult without a frame of

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reference with respect to the quality of the outcome. When practitioners execute the session for the first time, it is therefore difficult to manage the quality of the outcomes. The results of the case study lend support for the value of the CE approach. We submit that this approach offers a learning path for novice facilitators, that is, more effective and efficient than traditional methods. The training for an all-round facilitator typically takes weeks, if not months, instead of 2 days. An apprenticeship with coaching is required, especially with respect to the preparation of the process for the first sessions. Therefore, the training investment and the quality of the first sessions are much more in balance when using the CE approach than when traditional facilitation training is used. Further, we expect that when practitioners will execute the process on a recurring basis, they will be able to correct mistakes and learn from recurring challenges, while a normal apprentice facilitator will be confronted with different challenges each session, resulting in less opportunity to experiment with solutions. Examples of other CE projects include, but are not limited to, the following (see also de Vreede and Briggs 2019): • A process for collaborative usability testing was successfully employed for the development of a governmental health emergency management system (Fruhling and de Vreede 2005). • Dozens of groups engaged in effective software requirements negotiations using the EasyWinWin process (Boehm et al. 2001; Briggs and Grünbacher 2001). • A collaborative software code inspection process based on Fagan’s inspection standards was successfully employed at Union Pacific (de Vreede et al. 2006b). • A process for continuous end-user reflection on information systems development efforts was used in a large educational institution (Bragge et al. 2005). • Various collaborative learning practices where successfully designed and implemented leading to improvements in terms of learning effectiveness and student satisfaction (see e.g. Cheng et al. 2016). • A backlog creation process was developed and fine-tuned for Howard Hughes Medical Institute that adopted it as a key part of its new agile approach in their IT department (de Vreede 2014). • A process for innovation ideation was successfully designed and transferred at Verisk Analytics (de Vreede 2014). These studies and others provide ample evidence that the CE approach helps towards overcoming the barriers that we identified with respect to the sustained deployment of GSS and collaborative work practices. CE facilitates the transfer of collaboration process designs to practitioners, who can run these by themselves with similar results as those obtained by professional facilitators. Using the CE approach, we can make collaboration support available for recurring high value collaboration processes in organizations. In such cases, the support tools and the practitioners are contributing to a recurring process and the added value of the training and technology investment can be more easily estimated and visualized. Costs can be assigned

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to the collaborative work practice and in this way the business case can be made more easily. The need for a champion will remain, but the role of the champion will be to ensure the performance and quality of a collaborative work practice, instead of maintaining and “selling” a support system. Further research is required both in terms of field studies to understand the impact of collaboration support according to the CE approach and in terms of theoretical understandings of collaboration and outcomes of group interaction. From a practical perspective, to improve the transferability of thinkLets and thinkLet-based collaboration processes, it will be important to analyze the learning curve of the practitioners (how do they perform in subsequent sessions) and to apply the approach in more cases, possibly with the same practitioners to further evaluate the value of this approach compared to the master-apprentice approach. Also, longitudinal research is required to further evaluate the sustainability of new work practices that are designed and deployed using the CE approach. Next, recent advances with intelligent and configurable collaboration support tools to help practitioners in their task to instruct the group and to intervene in the collaboration process need to be expanded upon (Briggs et al. 2013). Also, it will help to use tools that are restricted to the functionalities that fulfill the capabilities required for the thinkLet (Briggs et al. 2013). This will reduce the cognitive load of using complex GSS technology for both practitioners and participants. From a theoretical and empirical perspective, it would be interesting to further understand and predict the effects of thinkLets, and to gain empirical evidence of their effects. Previous research often evaluates the effect of “the GSS” without distinguishing specific capabilities and associated interventions to create specific effects. We think that thinkLets offer a new lens for research in collaboration support that enables more specific analysis of successful and unsuccessful interventions to support collaboration. From a theoretical perspective, additional research is also required on the patterns of collaboration. While some initial theoretical work on creativity, convergence (i.e., reduction and clarification), evaluation, and consensus building has been done (for an overview, see de Vreede and Briggs 2019), more work is needed, especially on the organizing pattern of collaboration. The patterns of collaboration describe complex cognitive processes in a group setting that are not yet fully understood.

Cross-References ▶ Behavioral Considerations in Group Support ▶ Crowd-Scale Deliberation for Group Decision-Making ▶ Discussion and Negotiation Support for Crowd-Scale Consensus ▶ Group Decision Support Practice “as it happens” ▶ Group Support Systems: Concepts to Practice ▶ Group Support Systems: Experiments with an Online System and Implications for Same-Time/Different-Places Working ▶ Group Support Systems: Past, Present, and Future

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▶ Looking Back on a Framework for Thinking About Group Support Systems ▶ Participatory Modeling for Group Decision Support ▶ Procedural Justice in Group Decision Support ▶ Systems Thinking, Mapping, and Group Model Building ▶ Time, Technology, and Teams: From GSS to Collective Action

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Behavioral Considerations in Group Support Colin Eden

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Decision Support as Facilitating Negotiation Using Analytical Support . . . . . . . . . . . . . . Balancing Managing Process with Managing Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Political Feasibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Attending to Past and Future of the Group: Participants Are Not Free Agents . . . . . . . . . . . . . . . The Principles of “Getting to Yes” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cognitive Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Boundary Objects and Transitional Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Building and Monitoring Emotional Commitment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Procedural Rationality and Procedural Justice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem “Finishing” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Political Feasibility and the Consultant-Client Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Developing the Consultant-Client Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relationship Between Method, Facilitator, and Situation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stage Management and Disaster Planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Expectation Setting: Contracts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . What Do Clients Want: “Selling” GDN Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

A series of interrelated issues are presented that significantly affect the success and failure to provide facilitated group support for decision and negotiation. The issues are derived from the GDN experience of the author, accumulated over 40 years and hundreds of GDN interventions. After each issue is presented, the implications for facilitation and the design of a group support system are noted with reference to other chapters in the Handbook. While discussions of the C. Eden (*) Strathclyde Business School, University of Strathclyde, Glasgow, UK e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_34

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issues refers to some of the well-established literature on the topic, they are not based on formal empirical analysis of interventions. The issues all raise behavioral considerations. In particular, it is suggested that, notwithstanding a recent focus on microanalysis in GDN, these issues are still worthy of greater research and debate within the GDN research community. Keywords

Group decision and negotiation · Group support systems · Group behavior · Boundary object · Client group · Facilitation · Consultant-client relationship · Emotion

Introduction This chapter identifies issues in facilitating group decision support as a result of the author reflecting on many years of GDN facilitation experiences. These issues are not identified through a designed research program but rather collect together the theoretical and practical issues that the author addresses as GDN workshops are designed and fulfilled. The literature used is inevitably largely focused on the published views of the author as they developed over 40 years of research and practice. The issues addressed are inter-related and these are noted as the chapter unfolds. As the sections within the chapter develop the implications for the design of GDN support tools are explored, and in addition indicate chapters in this handbook that discuss topics that relate to the section in this chapter.

Group Decision Support as Facilitating Negotiation Using Analytical Support Because there are multiple perspectives on problem situations (at least if there is an effective team), then any agreed actions are the result of negotiation – indeed the essence of both Operational Research (Eden 1989; Rouwette 2003) and Group Decision and Negotiation is that of supporting and managing a negotiation. The extent to which facilitation explicitly attends to the need for the group to enact the agreed decisions will depend on maintaining the social working of the group in relation to other issues they need to work with one another. In the provision of effective group support, this means the facilitator must pay attention to both balancing socially negotiated order (negotiated relationships) with negotiated social order (a negotiated solution) (Day and Day 1977; Strauss and Schatzman 1963; Strauss 1978; Eden and Ackermann 1998). Alongside this consideration sits another requirement to enable the group to appreciate that the process followed “makes sense”: evidence of procedural rationality (Simon 1976). For group decision and negotiation, this means that the steps taken by the group

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are obviously sensible if the group is to arrive at a decision; it also means an avoidance of “black box” analysis where the group sees the work of a model as opaque. Implication: Exploit the benefits of a team. Attend to the design of process as well as working towards an outcome. Related chapters: In many chapters, authors discuss the development of the team – ▶ “Procedural Justice in Group Decision Support”; ▶ “Group Support Systems: Concepts to Practice”; ▶ “Group Decision Support Practice “as it happens””; ▶ “Systems Thinking, Mapping, and Group Model Building”; ▶ “Impact of Cognitive Style on Group Decision and Negotiation.”

Balancing Managing Process with Managing Content There are two extremes to facilitation style: that of the Organization Development (OD) consultant who wishes to attend to the behavior of the group as a group and so help the group operate more successfully; and that of the decision science consultant who is committed to supporting the group with rational analysis such as that provided by traditional Operational Research (OR) modeling (Eden 1978). These extremes of process management [P] compared to content management [C] are in practice blurred. The significance of a PxC conceptualization (Eden 1990b) captures the essence of the tension between pure OD focus and pure content focus. The equation symbolizes that process with no content focus (OD) achieves little and content with no attention to process (often referred to as “hard-OR”) also achieves little. It is still too often the case that excellent analysis does not get implemented because the process of model building pays no attention to the client’s view of his/her situation. Huxham and Cropper (1994) further developed the conceptualization to encompass the role of “substantive” knowledge of the facilitator (PxCxS). The focus of the facilitator along these dimensions, and the way in which the facilitator expects one to inform the other, is important in managing a facilitation episode. Effective group decision and negotiation is significantly aided by employing the multiplier effect between the skills of process management and the skills of content management (Eden 1987), where the multiplier comes from treating the two skills as intimately and continuously informing each other. Similarly, the particular decision modeling, or problem structuring and analysis, focus of the facilitator is likely to influence significantly the nature of process support to a group. For example, many facilitators are oriented to decision analysis and others are oriented to simulation modeling as the appropriate decision support procedure. Implication: GSS tools need to provide support for the facilitator as well as the group given the excessive demands of managing both content and process (Ackermann and Eden 1999). Related chapters: ▶ “Group Support Systems: Concepts to Practice” use software that provides the facilitator with information about the behavior of participants – the rate of contribution, the extent of developing consensus, the specific nature of contributions, etc.

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Political Feasibility Organizational politics is the essence of organizational life (Jones and Lakin 1978 provide a fascinating account of the range of politics of organizational life). “Organisations must be seen as tools. . . organisations are tools for shaping the world as one wishes it to be shaped” (Perrow 1986, p 14). Politics exists because of people wanting to make personal gain and enjoy an enhanced career. But what matters for good decision-making is that politics also arise from managers fighting for what they genuinely believe is best for the organization. In any effective team, there should be different perspectives on a decision situation (see the next section on cognitive change). When there are multiple perspectives the fight for the “right” perspective generates politics, where coalitions are formed “issue selling” and “claims on the future” take place (Dutton et al. 1983, 2001; Nutt 1984, 2002). When there is no politics around decision making then there is a great danger of narrow-mindedness and “group-think.” It does not matter how analytically rational a decision is, if a decision cannot influence the future in the way it was intended, then it cannot be regarded as an effective decision. The decision must be politically feasible for the designed organizational change to follow. Importantly, in problem definition managers do not save considerations of implementation to a separate stage in the process of problem-solving. The term implementation tends to connote its consideration as being separate from the other processes of problem-solving such as problem construction, problem defining, evaluating alternatives, and so on. Managers consider the practicality of possible solutions at the same time as problems are formulated (Eden 1987). As Chester Barnard 1938 (1938) stated: “the decision as to whether an order has authority or not lies with the persons to whom it is addressed. . . there is no principle of executive conduct better established than that orders will not be issued that cannot or will not be obeyed” (pp. 163–167). The role of equivocality in managing content may be significant in facilitating a shift in perspective for participants in such a way that they have not won or lost, with concomitant consequences for future working. The precision of analysis has to be balanced with fuzziness and a recognition of uncertainty in the results of analysis. The effectiveness of facilitation can be founded on devising some sort of dialectic (Eden 1992b) which can act as the energy to aid creativity and negotiation within the group, but finding the right time to shift from equivocality to precision as a dialectical force is not easy. The politics of problem solving in teams can be viewed as the “management of meaning” (Pettigrew 1977). Implication: GDN practice must combine the dispassionate and “objective” activities of science combined with aspects of the behavioral sciences which can encompass the passion of “issue selling.” Encourage, acknowledge, and manage multiple perspectives. Related chapters: Szapiro presents the role of intuition and tacit knowledge.

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Attending to Past and Future of the Group: Participants Are Not Free Agents The history of the group and organization and the emergent properties of the group and organization influences the politically feasibility of agreements. What sort, if any, of “organizational memory” is used to enable respect for the future? The notion of “organizational memory” involves not just a record of the meeting in the form of “minutes” but rather something that captures the essence of the meeting and so signifies an emotional connection with the GDN workshop. Developing some initial “shared meaning” (a complex notion which is discussed extensively by Scheper 1991 and Scheper and Faber 1994), a cathartic experience, and some personal problem solving prior to meeting the group can be an important preface to a group workshop. Political feasibility (Eden 1992b) is influenced by the need for a group decision to account for the impact the decision will have on the future working relationships of the group members, as well as attending to organisational politics. As Geoffrey Vickers 1965 (1965) argued “the goals we seek are changes in our relations or in our opportunity for relating; but the bulk of our activity consists in ‘relating’ itself. . . the most important aspect of activities, the ongoing maintenance of our on-going activities and their ongoing satisfactions” (p33).

Implication: Facilitate changes in relationships as well as the “physics” of a situation. Emotion is important to gaining commitment. Related chapters: Martinovski discusses the significance of emotion in GDN.

The Principles of “Getting to Yes” Fisher and Ury (1982) published an important text on the principles of negotiation (see also Fisher and Brown 1988; Fisher and Shapiro 2007; Fisher et al. 2011). For group decision and negotiation key principles are: • “Face-saving reflects the persons need to reconcile the stand he takes in a negotiation or an agreement with his principles and with his past words and deeds” p29 Any group decision support process or tool must recognize the significance of a provision for face-saving. • “Structuring of the negotiating game in ways that separate the substantive problem from the relationship and protect people’s egos from getting involved in substantive discussions” p38 Many group support systems (GSS) are designed to use anonymity at some stage during the process – typically during the problem structuring phase. • “If the first impediment to creative thinking is premature criticism, the second is premature closure. By looking from the outset for the single best answer, you are likely to short-circuit a wiser decision making process in which you select from a large number of possible answers” p61

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Nutt (2002) reinforces the importance of developing a large set of possible options. Option surfacing must be seen as a key part of the group decision and negotiation process. • “Rather than ask about their positions he asks about their interests: not how big a window the wife wants, but why she wants it” p119 Understanding goals (and “negative goals” – Eden and Ackermann 2013) and the relationship between options and goals (the causal links) enables the group to understand the means-ends relationships associated with agreements. These principles are each fundamental to group decision and negotiation. Implication: Use multiple perspectives to drive creativity through the synergistic combination of many options. Ensure that agreement is not only focused on actions but also on the reasons for them. Related chapters: ▶ “Just Negotiations, Stable Peace Agreements, and Durable Peace” present aspects of more formal negotiation situations; ▶ “Negotiation Process Modelling: From Soft and Tacit to Deliberate” considers how to utilize tacit knowledge; ▶ “Group Support Systems: Concepts to Practice,” and ▶ “Procedural Justice in Group Decision Support” consider the process of sharing knowledge.

Cognitive Change During group decision and negotiation, a person thinks, reconstrues, and socially interacts and so changes their mind. It is a gradual and subtle process within which GDN models play a more significant part when they can be a processual “toy” (Eden 1993) that can be played with in an engaging manner. Cognition is in transition as negotiation unfolds. Without cognitive change, negotiation cannot proceed. The key to understanding how cognition can change is an acceptance that problems are socially constructed (Berger and Luckmann 1966) and that the act of construal of situations is as important as the act of perception. The act of construal is filtering in not filtering out (Berger 1974). Meaning is given to perceived events and that meaning varies from one person to another as they each try to make sense and give meaning to the event. Meanings are derived from the cognitive context of perception (Berger 1974). Differences in construal explain why different people see different things in what is “objectively” the same situation. Negotiation depends, then, upon negotiating meanings – managing meaning (Pettigrew 1977). Because meaning is personal then it is always the case that there will be multiple perspectives on any situation – from the point of view of GDN then these need to be recognized and exploited. Recognizing and working with multiple perspectives reduces the likelihood of the danger of “group-think” (Janis 1972, 1989) and the group “going to Abilene” – a place nobody wanted to go to (Harvey 1988). Implication: Organizational change comes from managing meanings – focus on the tool allowing for meanings to be in transition. Related chapters: ▶ “Communication Media and Negotiation: A Review” considers the role of communication media; ▶ “Group Support Systems: Concepts to Practice” use theory from cognitive psychology; ▶ “Negotiation as a Cooperative

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Game” presents negotiation as a cooperative game; ▶ “Procedural Justice in Group Decision Support” use cognitive mapping; ▶ “Neuroscience Tools for Group Decision and Negotiation” explore the neuroscience to GDN.

Boundary Objects and Transitional Objects Boundary objects (Black and Andersen 2012; Carlile 2002; Franco 2013; Quick and Feldman 2014) of some sort are fundamental to negotiation and cognitive change – they are at the boundary of all the different perspectives and belong to no one person but are expected to belong to the group. However, for a boundary object to be effective, the object (decision model, in my case a causal map) needs to be in continual transition to reflect the changing thinking of the group. Simple boundary objects such as a flip chart sheet, perhaps with a rich picture, can help – but only as long as they are in transition – become transitional objects (Eden and Ackermann 2018; Ackermann and Eden 2010, 2011b; Ackermann et al. 2016; de Geus 1988; Eden 1994; Eden and Ackermann 2004; Winnicott 1953). Most simple boundary objects are too difficult to keep in transition; the continually developing rich picture sometimes need to change in a fundamental way, post-it/ hexagon/oval maps do not get changed often enough because it is too tedious, and the time taken can lose the group. Boundary objects play a significant role in developing emotional commitment as well as cognitive commitment (Eden and Ackermann 1998). Boundary objects and transitional objects play an important role in the “the creation of legitimacy for certain ideas, values, and demands-not just action performed as a result of previously acquired legitimacy” – in the management of meaning (Pettigrew 1977, p85). Implication: Tools must reflect multiple perspectives and so act as a boundary between different perspectives, and yet also be in continual change. Related chapters: ▶ “Systems Thinking, Mapping, and Group Model Building” introduce group modeling procedures that seek to ensure the construction of an appropriate boundary object – a simulation model; ▶ “Group Support Systems: Concepts to Practice”; ▶ “Procedural Justice in Group Decision Support” illustrate the use of causal mapping as a boundary object; and ▶ “Group Support Systems: Concepts to Practice” emphasize the significance of a causal map as a transitional object.

Building and Monitoring Emotional Commitment Procedural Rationality and Procedural Justice The interest and commitment of group members can be significantly influenced by two aspects of process. If the procedure follows what participants regard as a sense step by step process where each step appears a sensible follow on from the previous step then the process is likely to be regarded as rational. Similarly when participants are convinced that they have been listened to then they are more likely to commit to

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an alternative view even if different from their own (Thibaut and Walker 1975; Tyler and Blader 2000; Kim and Mauborgne 1998). The two aspects are related and while appearing to be arguing for increased democracy in groups and organizations, they can be a key to manipulating and managing commitment. Related chapters: ▶ “Procedural Justice in Group Decision Support” tell a real story of the impact of procedural justices.

Problem “Finishing” In an organizational setting, a problem is mostly finished (with) rather than solved. Problem finishing is a common phenomenon explained by many psychological and social psychological reasons, other than a solution having been attained. In early papers, I have depicted the social business of working on problems as a cycle of “presenting a portfolio of solution/options,” “problem construction,” “pondering upon” and “making sense of the situation” and “defining the situation” (Eden and Sims 1982; Eden 1987). Negotiation is most likely to take place at the problem construction stage. This means that the group decision and negotiation process is aimed at a “solution” falling out from the “making sense” and “definition” that follows “construction.” Thus, implementation is not a stage in a process of working on a problem, but rather is embedded in the negotiation about the nature of the problem. People do not construe problems without also considering how to get things done. Ackoff and Emery (1972) usefully distinguish dissolving from resolving from problem finishing. Dissolving problems: a change in an individual’s intentions, change in the relationship between a person’s value system and their belief system, change in the salience of particular values for construing the situation, downward change in expectations. Resolving problems: arbitrary choice: “the dice man.” “Solving”/Finishing/Alleviation: replace dissatisfaction with satisfaction, “satisficing,” individual “feels that it is obvious what must be done” – the action is felt to be robust, by doing it few options for future action are closed off, unknown worry/anxiety disappears even if course of action not defined, a complex “mess” is organized into a system of interacting tractable problems, “I don’t know what I will do, but I know I will be able to decide when I need to.”

A group of individuals will become “finished” with a problem at different times. The forming and reforming of coalitions means that each person’s expectations of what is possible/practical will be continually changing and so involves seeing negotiation as a psychological as well as social process. There are dangers of “socially negotiated order” being crowded out by “negotiated social order” (Harvey 1988). Implication: In group decision and negotiation, attention must be paid to the early part of group work where the “problem” is constructed and defined. For the facilitator, there is a need to monitor the attitude of the group to stages of agreement, so that the commitment of the group to agreements is not lost through the facilitator/ analyst encouraging the group to refine their “solutions” by too much “rational analysis” that does not recognize earlier emotional commitment.

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Chapters: ▶ “Advances in Defining a Right Problem in Group Decision and Negotiation” explore getting at the problem; ▶ “Group Decision Support Practice “as it happens”” uses microanalysis to understand the group process “as it happens.”

Political Feasibility and the Consultant-Client Relationship Building trust with the client and the group can significantly affect the success of a GDN workshop. The starting point for an involvement with a client and a group typically recognizes some degree of trust in the alleged competence of the facilitator. However, many client groups have poor experiences of facilitated workshops, where the group has been the recipient of a design that has not understood either the nature of the situation facing the group, or the contextual nature of the organizations within which the group members reside. The facilitator uses a standard workshop script often based on no substantive discussion with the client or any attempt to “read up” on the context, and so build trust before a GDN intervention (see Eden and Ackermann 2004; Tully et al. 2018). Clearly an external facilitator cannot, and should not, pretend to understand fully the situation – indeed often it is the “naïve” questions asked by a facilitator that can sometimes help a group. But having some understanding of the “pain” felt by the group is crucial. Without understanding the pain and working to resolve it (or “finish” with it (Eden 1987)), the workshop deals with the problem as defined by the facilitator rather than that faced by the group. The gradual process of building trust, through effectively addressing the pain – as defined by the client group – leads to the facilitator being treated as someone whose views about the substance of the problem are sought: PxC expertise leads to PxCxS contributions. Building trust demands flexibility of script (Ackermann et al. 2011). The facilitator has to “earn the right” to be respected rather than relying on trust from their appointment to manage the task. Implication: Build mutual trust between consultant and the client group. Chapters: ▶ “Procedural Justice in Group Decision Support” discuss the care and methods they took in developing and understanding the client group prior to a GDN workshop. ▶ “Group Decision Support Practice “as it happens”” presents, through microanalysis of group behavior, some of the significant episodes in the GDN process.

Developing the Consultant-Client Relationship Facilitators may, or may not, specifically address the nature of the relationship between consultant/facilitator and a client who is not “the organization” but rather a particular individual. Thus, the facilitation may be expected to meet a number of objectives, including “invisible objectives” (Friend and Hickling 1987, p 103) such as the resolution of interpersonal disputes and the management of political agendas.

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Rarely is the facilitation episode of a “quick in and out” manner, but rather the project engages with the client through a developing relationship between consultant, method, and client. Negotiating and establishing clear expectations may be taken to be crucial to the success of the facilitation (Ackermann 1996; Eden and Sims 1979). The way in which the consultant-client relationship is managed is expected to have a profound influence on the outcome of the group support and so upon the success of facilitation. Issues that may be significant in managing the consultant-client relationship in a designed manner are: working with the client in the choice of group participants, analyzing the power of participants in relation to the specific issue being addressed, determining the particular method of follow through after decisions have been made in a group situation. These issues are related to the need to attend to the existing social order of the group prior to a workshop and the process of creating a new social order which can be maintained after the workshop. This discussion with the client hopes to elicit some of the invisible objectives of the GDN workshop (Friend and Hickling 1987) and the organizational politics (Eden et al. 1979). Conversations that accept the significance of organizational politics typically show the client that the consultant has some understanding of the reality of organizational life and can positively impact consultant-client trust. Politics in problem solving does not, as is often presumed, only involve personal ambitions but usually derives from genuine differences of view about what is best for the organization, and so fighting for making “claims” (Nutt 2002) and building coalitions to support those views. Managing this negotiation across a range of claims is the key aim of a GDN workshop. Implication: Organizational politics is inevitable – don’t ignore it. Related chapters: Kaur and Carreras consider the early preparations for a GDN workshop.

Relationship Between Method, Facilitator, and Situation The extent to which method and facilitator and setting are able to converge can be regarded as a significant dimension in evaluating facilitation. Thus issues of matching personal style to method are often considered important (see Cropper 1990); however, the congruence between style, method, and the problem setting needs to be considered in relation to success of facilitation. The ability of the facilitator reflects a system of three aspects: facilitator, methodology, and group support; so that a contingency approach can be taken to managing a wide range of characteristics of the situation. Implication: Don’t use a hammer to drive a screw.

Stage Management and Disaster Planning There is anecdotal evidence that successful facilitators are pessimists, in the sense that they prepare for facilitation episodes from a disaster planning perspective. Robust planning which recognizes a wide “trumpet of uncertainty” (Rosenhead

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1989) – may relate to accepting the need for interactive facilitation, rather than either reactive or proactive facilitation. It seems clear that many facilitators pay particular attention to physical environment and “trivialities” (Eden 1990a; Hickling 1990; Huxham 1990). The setting for GDN episodes can be important. The requirement for off-site workshops means that facilitators can, if not careful, be subjected to the bizarre settings determined by the overnight staff in the hotel, who take it upon themselves to “tidy” the careful setup created earlier by the facilitator. Hotel staff have a fondness for the “board-room” setup. The facilitator dependence of creating a boundary object that is transition (e.g., flip chart papers) can find walls where attaching flip chart sheets is not permitted, wood paneling means there is no flat wall, etc. Implication: Being realistic about the potential for disaster is not the same as being pessimistic.

Expectation Setting: Contracts Some facilitation episodes involve a lengthy intervention involving work on strategic issues that are intractable and messy. Facilitation approaches may or may not reflect the contingent development of the intervention – contingencies that may for example dictate a brief intervention of a couple of hours, or a two-day workshop, or one full day workshop each month for a couple of years. Lengthy interventions often require the use of a “tight” contract of engagement for the facilitator. Contracts can be disastrous for the effectiveness of an intervention. By the nature of a consultant-client relationship, the effective intervention by the facilitator/consultant means that the nature of the situation to be addressed will (or should) change over time (Eden and Ackermann 2004). If the situation is changing then the nature of the engagement changes and so the contract becomes outdated. However, it is usually very difficult to change the contract and so both client and consultant find themselves working on the wrong problem (Shakun and Martinovski; Mitroff and Featheringham 1974). Developing contracts for GDN workshops can be highly problematic because of what Tully et al. (2018) call the “value paradox”: the “consultant attempting to sell a [GDN] intervention will struggle to articulate value to clients in terms that are commercially meaningful prior to the intervention being enacted. Thus, in order to win a contract to deliver a [GDN] intervention, the consultant must first resolve this puzzle” (p1). Implication: When possible the “contract” should be established (not necessarily written) so that the assignment can be staged, with a “new” contract written often. For example, with one-day GDN workshops it is possible to contract for one-day and then reassess the contract at the end of the workshop, with an option for the requirement of no further involvement of the consultant, because enough has been achieved.

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What Do Clients Want: “Selling” GDN Support “I want to get our thinking straight” is probably the most common phrase used when discussing what a client wants from the use of a GSS. However, this implies they have at least some understanding of a GSS. This understanding typically comes from (in order of likelihood): (i) word of mouth from those having experienced a GDN/ GSS workshop, (ii) having had a direct experience as a participant, or (iii) having read something about them. In all of these instances a follow-up, prior to a workshop, with a brief and punchy one-page description has been important. Very often demand comes from a client who has “tried all other methods to resolve the issue we face” – in other words desperation. Desperation can provide an experience which is successful and so leads to other uses by the same client/group (see Ackermann and Eden in this book). But success does not come from the use of the GSS (or GDN method) alone, rather it comes as much from the professionalism of the facilitator. A key aspect of professionalism derives from sympathy and empathy for the realities of managerial life. A recognition that organizational politics inevitably follows from agreeing ways forward. Change of any sort implies winners and losers. Relieving some “pain” of the client must be regarded as a crucial first step of the intervention (Eden and Ackermann 2004). But the reality of organizational life means “the salience and surfacing of issues comes and goes within the complex milieu of organizational life (Dutton and Ashford 1993; Dutton et al. 1983)” (from Eden and Ackermann 2004). This means that the nature of the “pain” will likely change during the use of the GSS – the GSS work leads to a restructuring of the issue. The “script” (Ackermann et al. 2011) for the intervention needs to be flexible, recognizing also that agreements are often reached before analysis is complete. But also the notion of “pain” recognizes the significance of emotion in problem definition. Of course all of these issues of professionalism imply that facilitation is as important, or more important, than the GSS as a tool – a good process badly facilitated will not help (Ackermann and Eden 2011a). Good facilitation means paying attention to trivialities – the “boring” aspects of ensuring success such as room design and refreshment design (Eden 1990a; Hickling 1990; Huxham 1990). Finally, it is sometimes important to remember that the symbolic use of external “help” is designed to give the impression of action (Brewer 1981) rather than to lead to action. Tully et al. (2018) recently provided one of the first discussions about the issues in selling soft-OR (akin to GDN support). The issues they discuss have similarity to some of the issues in selling the use of GGN methods and tools to organizations.

Future Research A special issue of the GDN journal (October 2018) focused on Micro-Processes in Group Decision and Negotiation: Practices and Routines for Supporting Decision Making in GDN type workshops. This issue of the journal was the first to explore in

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depth a range of behavioral aspects of decision support through detailed analysis of workshops providing group decision support. This chapter follows from this attention to behavioral issues and recognizes the research developments demonstrated by this issue of the journal. The recent developments in the microanalysis of GDN workshops are moving the field forwards at an impressive rate (Tavella and Franco 2015). The renewed focus that develops the focus of researchers in the 1970s and 1980s (Eden 1993; Eden et al. 1983; Eden et al. 1981; Jackson and Keys P. (Eds.) 1987; Jackson et al. 1989; Sims et al. 1981) on what is now labeled as Behavioral OR is building more interest in the softer aspects of group decision and negotiation. Most of the 14 topics presented in this chapter warrant further exploration through focused research. However research in the GDN field is problematic. Much can be discovered and used in GDN developments through traditional controlled experiments (to the extent they can be controlled. “A theory of subatomic particles or of the universe – right or wrong – does not change the behaviors of those particles or of the universe. If a theory assumes that the sun goes round the earth, it does not change what the sun actually does. So, if the theory is wrong, the truth is preserved for discovery by someone else. In contrast, a management theory – if it gains sufficient currency – changes the behaviors of managers who start acting in accordance with the theory” (Ghoshal 2005 p77: my emphasis). This simple statement suggests that Action Research (Eden and Ackermann 2018) might be, at least as helpful, or possibly more helpful in moving the GDN field forward (see also the debate: Finlay 1998, Eden 2000). Beyond the above recent developments, the following topics are particularly deserving of more attention: • The role of emotion in negotiation and the ways of managing emotion – extending and building on the work of, in particular, Martinovski (2010, 2014) in the GDN field (Martinovski). • More attention to operationalizing some of the attractive negotiation theories that are relevant to group decision making and exploring how apparently conflicting theories appear to work in practice (Howick and Ackermann 2011). • The impact of the requirements for traditional contracts when both internal and external facilitators are used. • How trust develops between consultant and client and facilitator and group. • How to judge the balance between seeking enough consensus to gain the energy for implementation versus encouraging “group-think” through too much consensus. A better understanding of “problem finishing.” • How to make better use of the power of analysis techniques in GDN (for example, MCDM, Game Theory in its developed forms) that imply precision and a static definition of the situation and cannot be flexible (in transition) enough to recognize their role in changing cognition. These research topics imply a better use of multidisciplinary research teams that can bring to bear more variety in theory. However, these research topics imply

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attention to the reality of organizational life and less emphasis on research undertaken with student groups who have no future and no past (even though much can be learned from such research).

Cross-References ▶ Context and Environment in Negotiation ▶ Group Decision Support Practice “as it happens” ▶ Group Support Systems: Concepts to Practice ▶ Procedural Justice in Group Decision Support ▶ Role of Emotion in Group Decision and Negotiation ▶ Systems Thinking, Mapping, and Group Model Building

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Group Decision Support Practice “as it happens” L. Alberto Franco and Christian Greiffenhagen

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Getting Close to GDS Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ethnomethodology and the Analysis of Everyday Conduct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GDS Practice in situ: An Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix: Transcription Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Getting close to the work of group decision support (GDS) practitioners do in “real time” has received increasing attention from GDS scholars in recent years. What motivates this interest is the recognition that to develop better GDS practice, one must first pay attention to those engaged with the practice in situ. By zooming in on what GDS practitioners actually do with their craft, and the critical role of these doings on generating group outputs and outcomes, a more nuanced understanding of GDS practice can be achieved. Furthermore, this understanding can inform the development of more effective GDS practi-

L. A. Franco (*) School of Business and Economics, Loughborough University, Leicestershire, UK Universidad del Pacifico, Lima, Peru e-mail: [email protected] C. Greiffenhagen Department of Sociology, The Chinese University of Hong Kong, Shatin, Hong Kong e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_54

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tioner training and teaching materials. One approach of studying GDS practice “as it happens” on the ground is based on ethnomethodology (EM). To illustrate the approach, an example of its application to study GDS practice in a facilitated, computer-supported causal mapping workshop is provided. Overall, the analysis shows the various ways in which actual GDS practice is accomplished over time and with what effects. Specifically, GDS practice is revealed as a “skilled accomplishment”: an achievement based on the contingent and coordinated assembling of material and conversational resources. Following the analysis, departures from current theorizing about GDS practice resulting from the adoption of an ethnomethodologically-informed perspective are discussed. Two potentially useful avenues for future research are then proposed. Keywords

Group decision and negotiation · Group support systems · Group behavior · Facilitation · Causal mapping · Group decision support practice · Ethnomethodology · Workshops

Introduction This chapter is concerned with getting close to GDS practice when using a particular type of GDS approach, namely, a facilitated model-driven GDS system (Morton et al. 2003). GDS scholars share a long standing concern with understanding and unpacking the complexities associated with GDS practice (e.g., Eden 1992; see also chapter ▶ “Behavioral Considerations in Group Support”), and yet empirical analyses of “live” GDS practice as it happens on the ground remain rare within the literature. Nevertheless, some relevant research is beginning to appear following calls to conduct microlevel studies of GDS practice within the operational research (Franco and Greiffenhagen 2018; White et al. 2016) and group decision and negotiation (Ackermann et al. 2018; Tavella and Franco 2015) communities. We begin the chapter by outlining earlier attempts to get close to actual GDS practice by surveying the relevant literature. The aim is not to survey these efforts fully but to underline a key empirical issue, which will provide the grounds for introducing a particular and distinctive way of studying GDS practice based on ethnomethodology (EM) and conversation analysis (CA). To illustrate the approach, we provide an example of its application to study GDS practice in a facilitated modeling workshop (Franco and Montibeller 2010) that uses computer-supported causal mapping (Bryson et al. 2004) as the GDS approach. Overall, the analysis will reveal the various ways in which actual GDS practice is actually accomplished over time, as it happens, and with what effects. We conclude the chapter with a summary of the unique contribution that this type of fine-grained studies makes to GDS theory and practice, and two proposals for future research.

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Getting Close to GDS Practice There is a growing body of literature that adopts a theory-informed approach to reveal the complex dynamic processes of actual GDS interventions (e.g., Brocklesby 2009; Ormerod 2014). Three exemplars of this type of research are briefly mentioned here as an illustration. White (2009) uses Actor Network Theory (Callon 1986; Latour 2005) and Narrative Analysis (Greimas 1990) to show how the success of a GDS intervention is contingent on the effective integration of networks of actors, interests, and models. Franco (2013) draws on Carlile’s (2004) knowledge management framework to show that the models created in GDS interventions can enable the development of shared language, shared meaning, and shared commitment if they act as “boundary objects” (Henderson 1991; Star and Griesemer 1989) performing specific roles (transferring, translating, transforming). Furthermore, their effective performance is contingent to the possibilities for action they afford to the actors involved during the modeling process. More recently, Thompson et al. (2016) use constructivist learning theories (e.g., Doolittle 2014; Fox 2001) to investigate participants’ experiences of GDS projects. They provide evidence that changes in participants’ mental models were connected with the occurrence of critical learning incidents during the projects. Furthermore, the timing of these incidents was linked to a variety of factors, including the type of GDS tool used, its designed aims, and the project stage in which it was used. Research studies such as the above offer useful insights into real GDS practice and its impacts. However, these are studies about, rather than of, GDS practice. Their actual treatment of GDS practice is, therefore, rather vague. Notably, the materials chosen in these studies for empirical analysis inhibit the prospect of improving our understanding of the minutiae of GDS in situ and how these shape GDS outcomes. In White’s case, theoretically informed introspection is supplemented with analysis that relies heavily on observational notes, but the analysis steers clear of investigating live GDS conduct. Similarly, in Franco’s and Thompson et al.’s studies, data collection is guided by the chosen theory but, once again, analysis is built mostly on empirical materials such as post hoc interviews with GDS participants, which are far removed from the fluctuations of real-time GDS practice. A few empirical studies have sought to reassemble the unfolding nature of real-time GDS practice to understand its developmental character (Franco and Rouwette 2011). Empirically, these studies do not base their analyses on post hoc sources but on participants’ logged contributions in computer-supported GDS workshops. Of these, two studies are worthy of attention. In the study by Ackermann and Eden (2011), patterns of participant contributions are traced over time and linked to modes of making sense. Specifically, their study shows how participant contributions to building a group causal map follow a bi-modal pattern, that is, initially participants focus on their own contributions (issues or links), and only after they have exhausted their most immediate concerns they shift their attention to the contributions of others. This pattern happens during both the issue gather and linking stages of a casual mapping workshop

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(Ackermann and Eden 2011). Furthermore, examination of participants’ preferences for prioritizing key issues or options to implement reveals a similar pattern. Similarly, in the study by Ackermann et al. (2016), time logs and the causal maps produced by participants in two separate workshops are used to characterize model-supported conflict management as a broad linear sequence comprised of three phases. First, there is a cathartic phase in which participants express their views (mostly accusations) anonymously and without interruption via a group support system. Next, there is a reflective phase where participants shift the tone of their contributions (from accusatory to more conciliatory statements, explanations, and admissions) as they read the preceding individual contributions on a public display and begin to add and elaborate material. The final stage is an integrative phase, where participants negotiate their understandings of the conflict by giving new meanings to the contributions made in the preceding two phases through linking them on the public display and thus taking ownership for each other’s ideas. The studies by Ackermann and colleagues are significant because they start to disentangle the temporal aspects of GDS practice more directly. They provide teleological explanations that stress the purposiveness of the group and the structures provided by the GDS environment as the motor for cognitive change. Yet as in the other studies introduced earlier, explanations of what goes on within the practice of GDS rely heavily on the researcher’s own interpretations. Overall, the studies briefly reviewed so far share a key methodological issue: neither their empirical materials nor their proposed interpretations make apparent the complexities and situated specifics of GDS practice they are intended to unpack. A different approach is thus needed, and one way to address this issue is by using live recordings of actual GDS practice. With such empirical materials at hand, the possibility to improve our understanding of the intricacies of the ebb-and-flow of GDS practice becomes a real prospect. The use of live recordings remains rare within the group decision and negotiation literature, but three recent studies that use such materials as the basis for empirical analysis are worthy of note here and will be considered further below. The study by Tavella and Franco (2015) examines real-time model-supported knowledge creation in an audio recorded strategy workshop. They conduct sequential analyses of participants’ interactions with a viable system model (VSM) (Espejo and Harden 1989) to identify links between behaviors and knowledge outcomes. Specifically, they show that participants produce different types of knowledge by engaging in specific behaviors: new or shared knowledge was produced by expanding, combining or reframing their contributions, whereas “old” knowledge was re-produced by using the model to fix the meaning of their contributions. Using a similar analytic strategy, the study of experts and novice facilitators by Tavella and Papadopoulos (2015a) shows that experts and novices share common conversational patterns in the way they manage a workshop, contrary to the claim in the mainstream literature that they behave differently. Finally, the study by Velez-Castiblanco et al. (2016) investigates the conversational games that consultants employ in the moment of designing a GDS intervention: a particular combination of moves (“set,” “follow,”

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“enhance,” “wander outside,” “challenge,” “probe”) triggers a negotiation about intervention boundaries that can result in different intervention designs. The above three studies are particularly noteworthy for two reasons. Firstly, these studies scrutinize GDS practice through meticulous examination of audio recordings of in situ activity. Secondly, they demonstrate a specific concern with GDS practice as put into action via talk. Still, the material elements of GDS practice (e.g., the “models” used, talked about, and oriented to in interactions; the technologies used to support their creation) remain somewhat covert. Consequently, in order to foreground the materiality of GDS practice, we need to capture not only talk, but also body language, movement, and the models and supporting technologies through which GDS is enacted. This takes us to our final group of studies that use live recordings of GDS practice. The study by White et al. (2016) adopts activity theory (Engeström 1987, 2000; Miettinen 2005) to guide the analysis of a decision support project focused on energy efficient planning in a UK city1. By adopting a detailed coding scheme, the authors show how participants in a GDSGDS workshop use mediating artifacts to deal with the concept of a “zero carbon zone,” and demonstrate how a shared activity system is developed to accommodate contradictions between participants’ motives. More recently, Velez-Castiblanco et al. (2018) report from their close observation of the development of a problem structure that actors can produce multimodal communications by combining speech, writing, gesture and image (e.g., a model) that alter the assumptions they hold. Finally, the study by Burger et al. (2018) shows how actors deliberately use humor (see also chapter ▶ “Role of Emotion in Group Decision and Negotiation”) to enable others to experience a problem situation of mutual concern from multiple perspectives and make progress towards action. Thus, consideration of epistemic and physical interactions with a model to produce group outcomes (e.g., learning) is not enough: playful cognitive-affective scaffolding may also be needed. What makes these last three studies particularly distinctive compared to those briefly reviewed earlier is their use of video-based analysis to scrutinize what GDS participants actually do with the technologies at hand and each other, and highlight the (interactional) effects of these “doings.” In this respect, the approach adopted in these studies is perhaps the closest to the one we advocate in this chapter. Our approach also uses video recordings to examine real-time GDS practice. However, and this will become clearer in the sections that follow, what distinguishes our videobased analysis approach is that it does not stay within the single snapshot of group decision and negotiation activity (as in Burger et al.’s case) to reveal the intricacies of live GDS practice, nor it relies on predetermined coding schemes to steer empirical investigations (as in White et al.’s and Velez-Castiblanco et al.’s studies). Instead,

1

Whilst the most common approach to qualitative research is to derive theory from observation inductively using a grounded theoretical approach to coding, White et al use theory (and the coding scheme associated with the theory) to guide their empirical observations, so that the theory gets further specified through a process of abductive reasoning.

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our approach brings to light a wider range of micro-level GDS practices through repeated viewings and close examination of video data. To conclude, studies that use live recordings of actual GDS practice as empirical materials are just beginning to appear within the group decision and negotiation literature. Taken altogether, they provide a collective response to calls for opening the “black box” of GDS practice at the micro-level (Ackermann et al. 2018; Franco and Rouwette 2011; Tavella and Franco 2015). It is against this background that we position this chapter’s intended contribution. If we are serious about revealing the intricate dynamics and situated specifics of GDS practice as it happens on the ground, then we must adopt an approach capable of foregrounding its material and interactional features. Furthermore, we need to study such features as a “bundle” rather than as separate, discrete dimensions. One such approach draws from ethnomethodology, which we briefly introduce next.

Ethnomethodology and the Analysis of Everyday Conduct Originating in sociology, ethnomethodology (EM) aims to study the methods that individuals use in “doing” social life (Garfinkel 1967). This approach proposes a bottom-up perspective to examine ordinary members’ own sense-making and practices to accomplish their everyday activities, that is, how people “do” things. In that sense, ethnomethodology makes what people’s everyday knowledge the topic of investigation. As Garfinkel (1967: 36) argues, the primary aim of the ethnomethodological approach is therefore to make familiar the “seen but unnoticed” of everyday life. The challenge is thus often not having more data, but how to make visible what people know, that is, to “help the goldfish become aware of the water it swims in” (Watson 2009: 68). Conversation analysis (CA) was deeply inspired by an ethnomethodological approach and developed by Harvey Sacks in collaboration with Emanuel Schegloff and Gail Jefferson (Sacks 1992; Sacks et al. 1974). CA initially used audio-recordings of naturally occurring everyday conversations as the basis to investigate the organization of talk-in-interaction. By “naturally occurring,” CA argues against using data that have been produced or arranged for the purpose of the research (Potter 2002: 541). Instead, researchers collect data that is everyday and commonplace. The pioneering conversation analytical research worked with audio recordings of telephone conversations (Schegloff 1968). With the technological advances and the realization of the important interplay of talk and other embodied communicative resources, the field has increasingly made use of video recordings (Goodwin 1993; Heath et al. 2010) which allows to capture the visual conduct of activities. Although both EM and CA started with studies of everyday activities, they both subsequently investigated the conduct of professional work, either as ethnomethodological studies of work (Garfinkel 1986; Rouncefield and Tolmie 2016) or studies of institutional talk (Drew and Heritage 1992). Compared to the studies of everyday life, new challenges arise for researchers in conducting the studies of work. According to Garfinkel, researchers need to acquire the “unique adequacy” of an

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adept practitioner to become not only a researcher but also a competent member immersed in that practice (Garfinkel and Wieder 1992). For example, Garfinkel’s student Livingston spent several years in graduate school as a mathematician in order to prepare his ethnomethodological study of mathematics (Lynch 1993, footnote 25). In our case, the first author (Franco) became a practitioner of a range of GDS approaches by first working as an apprentice and afterwards as an academic consultant along GDS experts for a number of years before starting research on the nature and impact of GDS practice. In the past three decades, ethnomethodological studies of work have a particular influence in the study and evaluation of how technologies transform workplace practices. This has led to various ethnomethodological investigations within the field of Computer-Supported Cooperative Work (CSCW) and Human-Computer Interaction (HCI) (Button 1993; Luff et al. 2000). For example, early studies explored the work of collaboration and control in London Underground control rooms (Heath and Luff 1992). More recently, there has been research on the properties of virtual reality (Hindmarsh et al. 2006) or interaction with Amazon’s Alexa (Porcheron et al. 2018). These studies offered important insights into the way that new technologies transform work practices and social relationships.

GDS Practice in situ: An Illustration In this section we draw heavily on the data analyzed in Franco and Greiffenhagen (2018), which was generated from a facilitated modeling workshop (Franco and Montibeller 2010) with the top management team of a medium-sized enterprise in the UK. The facilitated modeling approach used in the workshop was the group causal mapping technique supported by Group Explorer, a group support system developed by Colin Eden and Fran Ackermann at the University of Strathclyde (Bryson et al. 2004; Eden and Ackermann 2001; see also chapter ▶ “Group Support Systems: Concepts to Practice”). Group Explorer2 enables the construction and use of causal maps to support group decision and negotiation in a strategy making or problem-solving context. Group members typically sit at small tables arranged in a horseshoe-shaped layout and enter their contributions in to the system via a mobile device (e.g., laptop, tablet). A facilitator controls the system and organizes the entered contributions using specific coding guidelines (Eden 1988, 2004) to produce a map displayed on a large public screen. The constructed map is thus visible to all group members and becomes the focal point for group discussions, always in transition as discussions develop. Figure 1 shows the Group Explorer setup during the causal mapping workshop.

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Group Explorer has now been upgraded to support same-time/different-places workshops -see Group Support Systems: Experiments with an Online System and Implications for Same-Time/ Different-Places Working.

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Fig. 1 Computer-supported group causal mapping workshop

In what follows, we adopt an ethnomethodological perspective to examine a core activity in group causal mapping workshops: the creation and use of causal links, and the ensuing discussions on how the direction of links could or should be interpreted. In the fragment below, group members start a discussion about the causality of the links around the strategic issue of “growth.” The discussion follows a “brainwriting” activity that had asked group members to raise key strategic issues facing their organization (as they saw them). Each issue is represented by a statement or “node” that was subsequently grouped into thematic clusters by the facilitator. Group members were then invited by the facilitator to create possible links between nodes, before collectively examine the links that had been created. A link represents the belief that the issue captured in one node can lead to, impact on, or influence the issue captured in another node. Group discussions about such links support the exploration of intersubjective issues and their eventual resolution (Eden et al. 1981). Figure 2 shows that there is currently a link from the node “coping with growth” (number tag 1) to the node “growth management” (number tag 8). Linking gives meaning to each node by setting it within a context that makes clear why the issue captured in the statement matters (consequences) and what needs to be done to address it (explanations). Indeed, according to the coding protocols of cognitive and causal mapping, the meaning of a node depends more on the causal context within which it sits than on the wording used to describe it (Eden 1988, 2004; Eden and Ackermann 2010). Yet querying the meaning of the wording of nodes is not uncommon in practice and, in fact, happens often (Franco and Greiffenhagen 2018). Thus, previously agreed links can be re-examined as a result of such queries, and this is illustrated in Fragment 1 shown in Fig. 3 below. The

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Fig. 2 Map excerpt showing the link between nodes 1 and 8

fragment opens by group member B asking for the meaning of node 1, “coping with growth.” (See the appendix for details of the transcription symbols used in this and other fragments in this chapter.) In Fragment 1 (see Fig. 3), B starts by asking about the meaning of node 1, “coping with growth” (lines 1–3; see Fig. 3a). This is taken up by another group member, S, who utters “Depends on what you view to be the issue?” (lines 5–6). This utterance is clearly not a direct answer to B’s question, but seems to divert the problem: the meaning of “coping with growth” is dependent on what “the issue” is (i.e., node 1 or node 8). In lines 10–11, S elaborates on this, by voicing his understanding of what “management” is, which can be heard as an elaboration of the other node, “growth management” (in that sense, S is explaining the meaning of node 1 by explaining the meaning of node 8). After a long 4-second pause (line 12), B makes a tentative but somewhat unclear suggestion of how to reformulate node 1 (“Can’t you say ‘coping with growth’ for ‘growth’?”). Immediately afterwards, another group member, K, formulates another proposal, namely that “growth” (in itself) is the issue (line 14). At this point, the facilitator F tries to reign in the interaction, by refocusing the participants’ attention on which of the two nodes under discussion is “the issue.” Specifically, F asks whether “coping with growth” is the issue (line 16) and seeks a response from S by looking at S (line 19). In response, S confirms that this is the case (line 20; see Fig. 3b). F then seeks further confirmation from the rest of the group members but does not get a response (line 23). After a pause, B formulates the link between nodes 1 and 8 by stating that “Growth management enables you to cope with growth” (lines 25–27). This gets a supportive reaction from S, who confirms that “[coping with growth] is something that comes out of [growth management].”

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B:

S:

B: S:

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F: S: F: F: B:

S:

((looking at display)) What does it mean to ‘coping with growth’? (3.0) Depends on what you view to be the issue? (1.0) 3[a] ((looks at S then at display, then at S again)) You see, I think management is a thing that you do in order to address a particular issue (4.0) rowth’ for growth?= Can’t you say ‘coping with growth’ sue, isn’t it? =Growth itself (.) is the issue, (1.0) Is- Is ‘coping with growth’ the issue then? [ (inaudible) ((looks at S)) It is for me ((scanning the room)) (1.5) What do you think, huh? (1.5) d l)) ) ((gazing at S while looking at model)) 3[b] Growth management enables you to cope with growth >Absolutely! (0.7) So, it is something that comes out of it ((moves both hands in north-west direction)) for- >in the way I see it

Fig. 3 Fragment 1

Finally, S gestures the suggested direction of the link by moving both of his hands in north-west direction, to indicate that the link should be re-drawn to from node 8 to node 1. We can see here that the original link from node 1 to node 8 (Fig. 2) prompts one group member to interrogate the meaning of one of the nodes. Various other members make suggestions of how they understand the two nodes and the direction that the arrow should go. In this fragment, group members’ individuality (Kelly 1955) becomes salient in the ways they express their expertise, wisdom, and experience of the world (e. g., “management is a thing that you do in order to address a particular issue”), a feature that is commonly claimed to be associated with group causal mapping interactions (Ackermann and Eden 2010; Eden et al. 1981). It is worth noting that the whole discussion stays at the verbal level; the model is not modified. Thus, in a sense, the different understandings are left standing beside each other.

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We’ve talked-)((points at prompt on laptop)) >You have to go back to the original statement.What’s your original statement? (3.0) So basically ((looks at map, then highlights node 1 on map)) 4[a] ((looks at S)) ((turns to S)) you are saying that that’s basically the issue? That is for me, but- [((opens arms to rest of group)) [((nods whilst looking at S)) okay ((looks at group members to his left side)) (5.0) ((looks at group members to his right side)) Is that the issue then? ((reads prompt question on laptop)) >We are saying [if you were to be as successful 4[b] [((looks at S and nodes)) as you are being today, what are the key strategic challenges/issues that [((company name)) will be facing= [((turns to look at map))

Fig. 4 Fragment 2

These different understandings continue for a while until S invokes the “prompt question” during the next fragment. In causal mapping workshops, a prompt question is often used at the start of the workshop to brainstorm the strategic issues captured and displayed as nodes in the causal map. Fragment 2 (see Fig. 4) starts with S proposing to go back to the original statement (the “prompt question”) they have been given as the workshop task (lines 1–5; Fig. 4a). After a pause, F steps in and formulates a candidate solution by highlighting node 1 (“coping with growth”) on the public screen and then uttering: “you are saying that that’s basically the issue?” (lines 10–11). S agrees with this formulation but indicates that other members of the group may have a different view (“That is for me, but. . .[opens arms to rest of group],” lines 12–13). When nobody responds to this (note the long pause of 5 seconds in line 17), F restates the question (“Is that the issue then?” line 19) but nobody responds. Instead, S reads out the prompt question (lines 20–26; Fig. 4b).

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It is worth noting how the “prompt question” is brought into the discussion here. The whole sequence was started off with a participant interrogating the meaning of a node prompted by the direction of a particular link between that node and another node. As a result of them not being able to resolve their questions, one of the group members now brings back the original prompt that they were given at the start of the workshop. What is interesting is that all of these “moves” are not initiated by the facilitator F or the GDS technology, but by the group members themselves in response to what they see displayed in the model in front of them. This implies a type of agency on the part of group members that is generally overlooked in GDS research (we will return to this issue in the “Discussion” section). The next and final fragment will show how F prompts the group to reach a conclusion regarding the direction of the link between nodes 1 and 8. In Fragment 3 (see Fig. 5), the facilitator F tries to bring the discussion to a close. F proposes that node 1 (“coping with growth”) really should be the issue, which then would mean that node 8 should be reformulated, perhaps into “ensure successful growth management” (lines 1–7). This proposal is accepted first by S (line 8) and then by then C (line 10). F then moves on to implement the changes into the model (lines 11–14). While the facilitator F is doing this, there is another exchange between B and S (lines 15–23). However, F does not pick up on this as he appears already committed to changing the wording of node 8. In lines 24–25, F finishes re-wording node 8 and also changes the font style and color of node 8. F then formulates a conclusion while simultaneously drawing an arrow from node 8 to node 1 (lines 28–31). Once that has been done, he looks into the room (lines 32) and tries to assess whether everybody in the room accepts this new formulation, which is shown in Fig. 6. It is worth noting the work of the facilitator F in this fragment. It is the facilitator who tries to bring the discussion to a (temporary) close, by making an explicit formulation or proposal (“. . .then 8 could become something like ‘ensure. . .successful growth management’”). Furthermore, when no one objects to this, F quickly moves on to implement his proposal into the model, thereby transforming the proposal from a purely verbal one to a permanent one that is now visible in the model. The sequential and interactional nature of the facilitated modeling process brings to the fore the ways F’s turns were designed to select particular actions, such as participants’ agreement on the wording of an issue or the direction of a link. What is also important to note is the fact that the work of facilitating is not just done verbally (by, for example, asking the right questions or trying to suggest “compromises”), but also materially: only the facilitator can change the model on the display and thereby transform transient, verbal proposals into persistent, material ones. In other words, the facilitator is here “solidifying” the proposal. It still could be challenged or changed – but at this point it stands “there”: not just as a verbal formulation in the room, but as a material representation on the display. The empirical fragments examined above show how agreement on model content is a temporal interactional accomplishment: a situated process where “intersubjective alignment” (Hindmarsh and Heath 2000; Samra-Fredericks 2010) is temporally gained and constantly worked upon by the facilitator. Let us quickly summarize how the

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((looks at map and opens hands)) So so (.) if if >if 1 is the issue then 8 could become something like uhh (0.5)‘ensure’, you know?, [((looks at S))‘successful growth management’? [((nodding)) ˚Yeah 5[a] Something like that 5[a] ˚Yeah So it’s an enabler [on its own [˚But (inaudible) [˚Yeah ((starts changing the wording in the node)) For me, 1 could be ‘growth’ like you were saying (it). We don’t have to be careful with growth, it’s growth Yes, it could be (0.3) could be. And all the other things are (0.3) how do you cope with it? it’s just- >it articulates the issue 5[b] ((moves to changing font style and colour of node 8 to red italics)) Yeah. So:: Is that? (one way the arrow goes?) (2.0) ((draws arrow from 8 to 1)) ((looks at Sam)) Yeah? (0.5) Does that make more sense? (1.5) So basically- >yeah? ((looks at G, B, C, K and A)) Yeah. Okay.

Fig. 5 Fragment 3

model has changed in this fragment. Initially, the model is open for scrutiny by group members and, in particular, the meaning of node 1 (¼“coping with growth”). Discussion about the meaning of node 1 leads to a discussion of the meaning of node 8 (¼“growth management”), and of the link between node 1 to node 8. At the end, the direction of the arrow is changed, from node 8 to node 1, but now node 8 is reformulated (¼“ensure successful growth management”). As already stated, a core aspect of group causal mapping involves linking nodes that capture issues of concern

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Fig. 6 Map excerpt showing final version

to those involved in the GDS activity. The direction of the links implies causality – that is, issue to issue, means to ends, option to outcome. However, which direction is eventually captured in a map will depend on the value system of the individual (or group) involved in the mapping. Ackerman and Eden (2010) highlight this dilemma with their example of the relationship between “buying a new computer” and the “backlog of processing is too big”: while some could see the latter as a good reason for realizing the former, others could see the former is the only option to effectively address the latter. As a consequence, it is not uncommon for the direction of links to be re-evaluated as new perspectives on the issues are surfaced and explored. This might explain the apparent conflict between the way S interpreted the direction of the link between nodes 1 and 8 and what was displayed initially in the model, as these represented their own beliefs about causality, which were not challenged by the facilitator during the discussion. These differences do get resolved in the end by the facilitator’s reformulation of node 8. This resolution will have interactional consequences for the group’s subsequent discussions during the workshop, as the meaning and relationships of these nodes becomes (visually) permanent in the model.

Discussion The preceding analysis portrays causal mapping practice as a “skilled accomplishment”: an achievement based on the contingent and coordinated assembling of material and conversational resources. By adopting an ethnomethodologically informed perspective, we were able to take a glance at some of the intricacies and situated specifics of live GDS practice. Specifically, the analysis presented in this

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chapter suggests that actual GDS practice in general, and computer-supported causal mapping practice in particular, may be more usefully conceptualized as a contingent, interactional, and sequential performance involving the “collaborative viewing” of models: a socio-material process where issues are “seen” and understood through the interplay between a model subject to the close scrutiny of those involved, and a set of conversational and embodied practices employed within the process. Within a computer-supported causal mapping workshop, these practices involve “talking” as well as “seeing,” “looking,” and “watching”; “coding” group members’ contributions into means, ends, issues, goals, and so forth; and “highlighting” through bodily gestures such as pointing, or materially changing the style of a node or link in a map. In and through these practices, group members display an orientation to both the model and the sequential character of the GDS process. It should be noted that GDS practitioners are certainly well acquainted with the interactional and contingent aspects of their practice, but perhaps these are less known to those new to, and interested in, this area. An ethnomethodologically informed perspective provides several departures from current theorizing about GDS practice in general, and model-driven GDS practice (Morton et al. 2003) in particular. The first one relates to the commonly accepted notion of facilitation as a neutral activity. Indeed, the argument that effective model-driven GDS relies on the facilitator not contributing to the content of group discussions is well known (Eden 1990a; Phillips and Phillips 1993; see also chapter ▶ “Behavioral Considerations in Group Support”) but hardly explored empirically. And yet in the fragments presented we see the facilitator contributing to content by re-formulating group members’ contributions as a response to previous talk (“if 1 is the issue then 8 could become something like ‘ensure successful growth management’”). This is only one instance of the use of formulations by the facilitator: if we paid closer attention to the entire group discussion we would notice that formulations are used often and take different forms including, for example, invitations to elaborate on an issue, reintroduction of previous talk, testing hypothesis about what is going on, and as candidate preclosings (see, for example, Franco and Nielsen 2018). Granted, facilitators may use formulations only as cautious response to prior talk rather than assessments of the group discussion, and in this sense they may actually serve to preserve the facilitator’s intended neutrality. Notwithstanding this, it is evident that the facilitator’s use of a formulation in Fig. 5 shapes the way in which the group are able to make progress. A second notable departure from current theorizing about GDS practice concerns established assumptions about group members’ behavior. Traditionally, GDS research assumes that the behavior of group members is affected by their individual cognitive structures (e.g., personality traits, decision styles, abilities; see also chapter ▶ “Impact of Cognitive Style on Group Decision and Negotiation”) or their environment, including their GDS environment (e.g. Eden 1990b; Hickling 1990). In other words, group members’ behavior is taken to be determined, directed or guided, giving them little agency to act and be accountable for their actions. By contrast, as Figs. 3 and 4 make clear, the behavior of group members plays a key role in determining how GDS interactions unfold. This suggests a more “voluntarist” notion

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of behavior, where decisions and choices about how to engage with GDS processes and tools are made by the group members, and while both the facilitator and designed GDS provide a scripted guidance for interactions, control over how to interact lies ultimately with the group members themselves. Another departure relates to the notion of “shared understanding,” one of the claimed impacts of the use of model-driven GDS systems. Advocates of these systems argue that it is the collective development and analysis of model content that helps to produce a shared understanding of the situation being addressed by the group, and of potentially useful ways to address that situation (e.g., Eden 1992; Franco and Montibeller 2010; Phillips 2007). Not surprisingly then, a key concern of scholars wishing to evaluate the claimed impacts of model-driven GDS systems (e.g., Rouwette et al. 2002) is to find the most robust and reliable way to assess shared understanding along with other impacts. It should be noted, however, that the assessment of shared understanding is a task for the group members and not just a task for the researcher/evaluator. A group member shows an appreciation of another member’s prior turn through her or his reaction to that member’s prior turn. Such appreciation can, every so often, be rectified, acknowledged, or contested in situ (Sacks et al. 1974). The question then is: how shared understanding of issues such as “growth” or “management” is achieved turn by turn? In this regard, the empirical evidence presented in this chapter demonstrates how the range of discursive and embodied practices displayed during interaction provided a context within which group members made assessments about their indexical appreciations of the model. And although it cannot be claimed that shared understanding is really attained, the illustrative fragments presented here suggest that, at a minimum, a transitory “intersubjective alignment” (Eden et al. 1981; Hindmarsh and Heath 2000; Samra-Fredericks 2010) towards that model is achieved. A direct conclusion of our empirical analysis is that the sense and impact of the models produced in GDS workshops is continually accomplished. Thus, a fourth departure from current theorizing concerns the use of “scripts” (e.g., Ackermann et al. 2011; Andersen and Richardson 1997; Bryson et al. 2004) as a means to guide and improve model-driven GDS practice. Such scripts are claimed to be exemplars of effective practice and contain a predefined and documented set of behaviors that participants in a GDS process are expected to follow. For example, step 4 of the script for “building graphs over time” reported in Herrera et al. (2016: 1307) states that the facilitator “asks participants to draw one variable over time per piece of paper” and that the participants “should be given the option of including hoped for behaviour, expected behaviour, and feared behaviour on the same graph” (italics added). Scripts such as the one just described have been developed by experienced GDS practitioners, many of whom are the original developers of particular GDS systems. In this respect, scripts are indeed close enough to practice. However, while they can act as helpful reminders of planned GDS activity, they fall short of representing some of GDS practice’s richness and complexity. Put differently, “scripts” have to be accomplished and therefore do not determine or prescribe what the facilitator or group members actually do in practice (cf. Schmidt 1999).

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Finally, the ethnomethodologically informed perspective adopted here both complements and broadens the research approach used to study changes associated with the use of GDS. With respect to the research approach, changes are often determined by testing causal explanations that connect independent variables representing the important aspects or attributes of the particular GDS design under study, and dependent variables that typically focus on surrogates of group behavior such as performance, choice, learning, and efficiency, as well as perceptions about GDS outcomes (e.g., Barkhi and Pirkul 1999; Beroggi 2000; Herrera et al. 2016; Melzer and Schoop 2016; Rouwette et al. 2002; Škraba et al. 2007). Although valuable, this approach “blackboxes” many critical and interesting aspects of changes linked to GDS use. A research approach that adopts a focus on process at the microlevel (Ackermann et al. 2018) can alleviate these shortcomings by delving deeper into the intricacies of the ebb-and-flow of GDS practice, as illustrated in the analyses presented above.

Conclusion The argument advanced in this chapter is that if we are serious about improving GDS practice, then we must first pay attention to how it is actually used by those who engage with it. Such consideration will prevent us from developing cursory understandings of what GDS participants actually do on the ground, and of the crucial role of these doings in producing GDS outputs. It should be noted that while the adoption of an ethnomethodologically informed perspective allows us to show what may seem at first ordinary events of practice, the choice of events for empirical scrutiny (and why) is always guided by the GDS researcher’s theoretical and practical considerations (e.g., how group members attain shared understanding). There are considerable opportunities for further research using the approach adopted here, and we outline two potentially useful avenues. The first one concerns further testing the relation between GDS and group members as not entirely determinist, given that groups can have agency to decide and choose how to engage with GDS. A very small proportion of studies within the group decision and negotiation domain are beginning to show that group members can adapt GDS processes and tools to suit their needs in unexpected ways (e.g., Franco 2013; Franco et al. 2016; Poole et al. 1991). As illustrated in the present chapter, the adoption of an ethnomethodologically informed perspective in future research could also bring into light the interactional and nonneutral nature of GDS activity, in which the agency of actors (e.g., clients, analysts, facilitators, model users) and “nonactors” (e.g., models, text, language, software) play a mutually reinforcing role (e.g., Burger et al. 2018; Franco and Greiffenhagen 2018; Velez-Castiblanco et al. 2018). The implications for the role of the GDS facilitator are clear: without providing proper guidance, individuals and groups may end up using GDS processes and tools in ways that might seem opposite to their intended design. DeSanctis and Poole (1994) call this phenomenon an “ironic” appropriation of decision support technology.

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Whether this is a good or a bad thing remains an empirical question to be investigated. A second and connected avenue for further research concerns the development of GDS competences (Keys 2006; Kolfschoten et al. 2011, 2015; Ormerod 2008; Tavella and Papadopoulos 2015b). To develop the future generation of GDS practitioners, we need to create training materials based on real GDS practice in workshops as well as other settings such as, for example, elicitation interviews, progress meetings, and project presentations. Fine-grained analyses of multiple instances of video recorded GDS practice in these settings can identify the actual trajectories of different micro-level GDS tasks (e.g., starting an “issue linking” task, explaining how to perform the linking task, performing the linking task, closing the linking task), with a view to distinguish successful from unsuccessful trajectories. Building a corpus comprised of such empirically generated knowledge would enable the development of training materials based on actual, rather than simulated, GDS practice. For example, the use of “role play” is common for training. With the approach suggested here, “role-plays” grounded in the actual activities of anonymized GDS facilitators can be developed. The structure of such role-plays would be designed in a way that the successful trajectory of a given microlevel GDS task would only be revealed after the trainees do something at a particular point in interactional time. The approach to skills training suggested here has been advocated in cognate fields such as mediation services (e.g., Stokoe 2013, 2014), and GDS scholars concerned with the development of GDS competences are encouraged to consult this work. It should be noted that the time and effort needed to implement an ethnomethodologically informed approach to research GDS practice is perhaps its most obvious limitation. Indeed, getting access, recording, watching, listening, transcribing, conducting, summarizing, and writing up fine-grained analyses can all become a substantial undertaking. However, if the interest is to reveal what is actually done as GDS practice, and not what is said about GDS practice, then undertaking this type of research is a needed and complementary addition to more conventional studies aimed at improving practice. It has been our contention throughout this chapter that proper attention to the situated, interactional, and material features of GDS practice will move the GDS research agenda closer to the reality experienced by those who practice GDS on the ground.

Cross-References ▶ Behavioral Considerations in Group Support ▶ Group Support Systems: Concepts to Practice ▶ Group Support Systems: Experiments with an Online System and Implications for Same-Time/Different-Places Working ▶ Impact of Cognitive Style on Group Decision and Negotiation ▶ Role of Emotion in Group Decision and Negotiation

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Appendix: Transcription Symbols For the analysis presented in this chapter, we followed the conversation analytic transcript conventions developed by Gail Jefferson (2004). The most important are the following: • • • • • • • •

Double parentheses [“(( ))”] are used to mark transcriber’s descriptions of events. Single parentheses [“( )”] indicate uncertainty on the transcriber’s part. Underlined items [“item”] are hearably stressed. Colons [“a::]” indicate prolongation of the immediately prior sound. The degree sign [“°”] is used as a softener. A dash [“-”] indicates a cut-off. An inbreath is denoted by a preceding circle [“°h”]. Numbers in parentheses [e.g., “(0.3)”] denote a silence in tenth of seconds, while “(.)” denotes a micropause of less than 0.2 seconds. • The onset of overlap is indicated either through square brackets between lines [“[“], or in case of “latching” through an equal sign [“¼”]. • An arrow is used to indicate particular lines of interest.

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Rouwette EAJA, Vennix JAM, Van Mullekom T (2002) Group model building effectiveness. A review of assessment studies. Syst Dyn Rev 18(1):5–45 Sacks H (1992) In: Jefferson G (ed) Lectures on conversation. Basil Blackwell, Oxford Sacks H, Schegloff EA, Jefferson G (1974) A simplest systematics for the organization of turntaking for conversation. Language 50(4):696–735 Samra-Fredericks D (2010) The interactional accomplishment of a strategic plan. In: Llewellyn N, Hindmarsh J (eds) Organization, interaction and practice: studies in ethnomethodology and conversation analysis. Cambridge University Press, Cambridge, pp 198–217 Schegloff EA (1968) Sequencing in conversational openings 1. Am Anthropol 70(6):1075–1095 Schmidt K (1999) Of maps and scripts: the status of formal constructs in cooperative work. J Inf Softw Technol 41(6):319–329 Škraba A, Kljajić M, Borštnar MK (2007) The role of information feedback in the management group decision-making process applying System Dynamics models. Group Decis Negot 16 (1):77–95 Star SL, Griesemer RJ (1989) Institutional ecology, ‘Translations’, and boundary objects: amateurs and professionals in Berkeley’s Museum of Vertebrae Zoology. Soc Stud Sci 19:387–420 Stokoe E (2013) The (in)authenticity of simulated talk: comparing role-played and actual conversation and the implications for communication training. Res Lang Soc Interact 46(2):1–21 Stokoe E (2014) The Conversation Analytic Role-play Method (CARM): a method for training communication skills as an alternative to simulated role-play. Res Lang Soc Interact 47(3):255–265 Tavella E, Franco LA (2015) Dynamics of group knowledge production in facilitated modelling workshops: An exploratory study. Group Decis Negot 24(3):451–475 Tavella E, Papadopoulos T (2015a) Expert and novice facilitated modelling: a case of a Viable System Model workshop in a local food network. J Oper Res Soc 66(2):247–264 Tavella E, Papadopoulos T (2015b) Novice facilitators and the use of scripts for managing facilitated modelling workshops. J Oper Res Soc 66(12):1967–1988 Thompson JP, Howick S, Belton V (2016) Critical learning incidents in system dynamics modelling engagements. Eur J Oper Res 249(3):945–958 Velez-Castiblanco J, Brocklesby J, Midgley G (2016) Boundary games: how teams of OR practitioners explore the boundaries of intervention. Eur J Oper Res 249(3):968–982 Velez-Castiblanco J, Londono-Correa D, Naranjo-Rivera O (2018) The structure of problem structuring conversations: a boundary games approach. Group Decis Negot 27(5):853–884 Watson R (2009) Analysing practical and professional texts: a naturalistic approach. Ashgate, London White L (2009) Understanding problem structuring methods interventions. Eur J Oper Res 99 (3):823–833 White L, Burger K, Yearworth M (2016) Understanding behaviour in problem structuring methods interventions with activity theory. Eur J Oper Res 249(3):983–1004

Procedural Justice in Group Decision Support Parmjit Kaur and Ashley L. Carreras

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Case of Negotiating Strategic Priorities: A Client Case Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pre-workshop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Workshop: Three Days at Off-Site Venue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aligning the Dual Facilitation Process with Procedural Justice Principles . . . . . . . . . . . . . . . . . . . . Treatment Issues in Procedural Justice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

A case study explicitly considers dimensions of procedural justice in the negotiation of new “working contracts” in a large organization. The case outlines how using a causal mapping group support system (GSS) helped in a specific client intervention to deliver a new negotiated contract. Following key stages from the strategy making approach known as “JOURNEY Making,” the findings illustrate the development of an agreed identity and vision of the organization and the strategic priorities that were identified and prioritized. One particular area of focus centers on a contentious and difficult political negotiation of revenue contracts between the central decision-making executive of a multinational chain of health care practices and the practitioners who run the chain of practices. The intervention resulted in the acceptance of a new collective agreement on working P. Kaur (*) Department of Economics and Marketing, Faculty of Business and Law, De Montfort University, Leicester, UK e-mail: [email protected] A. L. Carreras School of Business and Economics, Loughborough University, Leicestershire, UK e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_55

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contracts between the center and the practices opening the door to rapid expansion of the business. The focus in the workshops on the dimensions of “procedural justice,” using a “dual facilitation process,” helped to support positive extra rule behaviors in turn fostering the successful renegotiation to be delivered. Keywords

Group decision · Group support systems · Procedural justice · Causal mapping · Case study · Facilitation · Group support

Introduction This chapter presents a case study examination of a workshop intervention that allowed a client organization to develop a plan for growth. The chapter sets out the steps undertaken in the workshops and is an example of how causal mapping workshops can be used to determine strategic priorities. The examination also seeks to explain why the use of Group Support Systems can be an effective way of undertaking workshops with clients. This is discussed through the lens of procedural justice literature. The literature is examined, and links are drawn between the key aspects noted in procedural justice literature and the “dual facilitation” process used in the workshops; the dual facilitation process is comprised of the electronic workshop process combined with human facilitation. A working model of the dual facilitation process has been developed by the authors (see Fig. 1), which illustrates

Conflict Divergence

Surfacing issues /ideas/differences

“Groan Zone”

Convergence

Workshop dynamic develops Responsibility of Group Facilitator

Dynamic monitored

Ensure workshop allows equal participation and collection of accurate data. Electronic gathering ensures that incorrect information is corrected.

Ensure that process is consistently applied

Develop extra role behaviours (more authentic qualitative data)

Increase focus group effectiveness

Improve procedural justice Responsibility of Software Facilitator Box A

Fig. 1 Working model of the dual facilitation process

Observe focus group behaviour

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how the “fair process and extra-role behaviors” noted in procedural justice literature are inherently “present” in causal mapping group support interventions, by the nature of the process (electronic gathering of ideas in a facilitated group workshop). At the top of Fig. 1 is the standard notion of the “Groan Zone,” as discussed by Kaner (2005) and (2007), explaining the typical process in workshops. Initially the workshop participants diverge in thinking, and the dual facilitation process will move them onto convergence of thinking. The dual facilitation aspect is discussed by Kaur and Carreras (2018). The arrows in the looped feedback process represent the dual facilitation process in action. The right-hand side of the diagram emphasizes how the dual facilitation process encourages the display of desired extra-role behaviors (Kim and Mauborgne 1998) in the workshops. The literature for this is discussed in section “Aligning the Dual Facilitation Process with Procedural Justice Principles.” The chapter will be of particular interest to readers interested in facilitation using the problem structuring approach of causal mapping and those wanting exposure to procedural justice literature applied in an organizational context.

The Case of Negotiating Strategic Priorities: A Client Case Study A consultancy team (the authors) was invited to discuss with the CEO of a national chain of dental care providers, the possibility of running a workshop with the senior executive team. The CEO was charged with the expansion of the national chain of dental practices in both numbers and regions. This required substantial capital investment from the parent company, who wished to see a coherent strategic plan to justify this investment in the upgrading and rebranding of the franchised dental practices. After two initial scoping meetings and brief demonstration of the GSS software to be used (Group Explorer – see Ackermann and Eden, and Ackermann), a 3-day workshop was agreed at an off-site location. The workshop was to focus on the development of a plan of action to enable the national chain of dental care providers to move the current, or future, business forward. The workshop was designed to achieve a shared understanding of the issues, expectations, and aspirations of the senior executive team and to use this to contextualize the design of a plan of action, delivering expansion of growth requiring additional venture capital funding so as to take the chain to the next phase. The workshop process was loosely based upon the approach of JOURNEY Making (JOintly Understanding, Reflecting, and NEgotiating strategY (see Eden and Ackermann (1998)). The process was adjusted to take account of some specific issues that the client wanted addressing, regarding team dynamics and decisionmaking. We shall proceed by outlining the workshop (intervention) process followed with a discussion after each part relating it to the dimensions of procedural justice that dovetail with the workshop process discussed. The whole intervention can be divided into two stages:

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Stage 1: Pre-workshop comprising of project scoping, stakeholder mapping, individual interviews, and an executive team survey Stage 2: 3-day workshop comprising three phases: agreement on group approach to interaction, agreement of goals and aspirations, and agreement and prioritization of key actions

Pre-workshop Two scoping sessions were held with the CEO to determine the structure and focus of the workshop. Part of these discussions focused on who would be present at the workshops. Following a brief stakeholder mapping process (see Bryson 2004), it was agreed that the senior executive team would be present plus four other key members of the organization, one person responsible for the information technology strategy and two people representing clinical practitioners who run franchise dental practices. One additional member of the finance team was also included. This was a deliberate decision to ensure the representation of the franchisees’ interests and perspective were placed alongside the parent company’s financial interests. Here we have the first reference to procedural justice characteristics, in that this inclusivity mirrors the procedural justice aspect of allowing “voice” for stakeholders. The aspect of “voice” and how the workshop process services to provide this opportunity to participants in a workshop environment is discussed more fully in part 2. The off-site workshop employed a causal mapping approach to strategy and intraorganizational collaboration, co-facilitated by the authors. The intervention was supported by the Decision Explorer1 mapping software and the computersupported network system Group Explorer. We also conducted a regular survey of the participants’ perceptions on how they worked as a team; these results were collated and analyzed using Excel and SPSS, shown in Table 1.

Individual Interviews and Surveys From the individual interviews, a series of seven causal maps were constructed and analyzed independently by the two facilitators. Five common main themes were found across the whole team: Contracts and their need for renegotiation The Branding of the franchise The Commercial-Clinical Interface, how the commercial imperatives of the organization affected the operations of the clinical practitioners who were the franchisees Internal Processes, improving the day-to-day operations of the organization Teamwork, how the senior team worked together and interacted with the key stakeholders

1

Decision Explorer is available from Banxia.com and was developed at the University of Strathclyde.

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Table 1 Survey of senior executive team Question Goals and objectives are clearly understood and accepted by all members Everyone is involved and heard during group discussions. There is no “tyranny of a minority” Team members are consulted on matters concerning them The group is both objective and effective at reaching decisions When action is planned, clear assignments are made and accepted The team has clear rules, methods, and procedures to guide it. There are agreed-to methods for problem-solving Communication between members is open and honest. Members listen actively Difficult or uncomfortable issues are openly worked through, and conflicts are not avoided Team members are open in their transactions, and there are no hidden agendas. Members feel free to be candid Team members are committed to deadlines, meetings, and other team activities Members pull for and help each other, including when one person makes a mistake Individuals feel they can try new things and risk failure. The team encourages risk taking The team atmosphere is informal, comfortable, and relaxed Leadership roles are shared. The same people do not dominate or control The team routinely stops and evaluates how it’s doing in order to improve Meetings are orderly, well planned, and productive There is an “esprit de corps” or sense of fun on this team

Mean 2.4286 2.5714 3.0000 2.0000 3.2857 2.0000 2.0000 2.4286 2.1429 2.5714 3.0000 2.4286 3.2857 2.1429 1.8571 1.8571 2.8571

Questionnaire based upon questionnaires from Bens (2005) and Kaner (2007)

The survey results (from activity 2), based upon a 5-point Likert scale where 1 signified totally disagree and 5 signified totally agree, are displayed below with no averages indicating significant positive agreement and low degree of variability in the responses. From these results it was clear that time would need to be spent at the workshop improving teamwork as this was seen to be adversely affecting the decision-making in the team and leading to potential conflicts. Consequently, it was decided that part of the first day would involve developing an agreement on how the team would work together as a group during the workshop and in the future in the workplace. The subsequent 3-day workshop was constructed to meet the dual objectives of providing a set of prioritized actions to help the organization meet its stated objectives while simultaneously improving the overall team performance and decisionmaking culture.

Workshop: Three Days at Off-Site Venue Phase 1: Agreement on Group Approach to Interaction The first session included a review of the interview maps that were merged into a combined map. With the views of the individual members of the team displayed as a series of combined maps based upon the identified themes above. This demonstrated

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to the team that they had identified common themes. The overall map indicated the degree of complexity of the issues surfaced and a brief explanation of the process used to determine the main themes (for a full consideration of this approach to combining individual maps, see Ackermann and Eden (2005)). Each of the themed maps was presented to the team on a central public display. Care was taken to ensure that no individuals’ response could be directly attributed to them unless they volunteered to do so in the group; this included the removal of any idiosyncratic language. This was to reassure the team that their responses would be anonymized throughout the process and identities only revealed by the member who was responsible if they chose to do so. Showing the maps demonstrated that all of the concerns raised by the individuals could be addressed during the process. This was a deliberate strategy to show that all contributions were valued. This is the second reference to the procedural justice characteristics of the “fair process effect,” which allows participants process control over the qualitative data they input in the workshops. The value of this is that participants then engage more meaningfully in the workshop. This will be discussed further in section “Aligning the Dual Facilitation Process with Procedural Justice Principles,” when picking up on the six determinants of procedural justice, with the final 6th one citing stakeholders need a “clear and transparent” voice. The pre-workshop executive team survey was used to legitimize the first activity of gaining a team agreement on how they would interact during the workshop and possibly beyond in their future meetings. This can be seen to relate to the notion of “interactional justice and treatment effects,” to be discussed in section “Aligning the Dual Facilitation Process with Procedural Justice Principles.” To do this we invited them to enter suggestions on what they saw as important behaviors in team meetings. The anonymized responses from this fresh gather were put up on the central screen with the group invited to view their responses and suggest emergent themes (Fig. 2).

Fig. 2 Gathering from participants of suggested workshop behaviors

Procedural Justice in Group Decision Support Table 2 Group norms

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Group Norms 1. Seek first to understand before being understood 2. Feedback should be considered and constructive 3. Be open-minded 4. We have the freedom to express and explore without judgement 5. We encourage equal participation, reflection and healthy challenge 6. We have a responsibility to contribute 7. Be respectful of each other 8. It’s OK to disagree

A facilitated discussion with the group led to the generation of a set of rules of behavior or group norms (see Table 2) that would be followed during the rest of the workshop. These workshop norms were posted around the room as a reminder for the team on their agreed way of working together. The group norms developed resonance with themes procedural justice literature. Norms 1, 2, 4, 7, and 8 emphasize the treatment or interactional aspects of procedural justice, while 5 and 6 capture the notion of fairness inherent in procedural justice. The literature examination in section “Aligning the Dual Facilitation Process with Procedural Justice Principles” explains these concepts further, and in doing so it becomes easier to argue that the dual facilitating process adopted in the workshops in procedurally fair. Some team building activities were also used before the workshop progressed to the strategic decision-making process. This ensured that the group felt refreshed and alert before they started in earnest.

Phase 2: Agreement of Goals and Aspirations We started by asking the group what they each expected to achieve by the end of the workshop and gathered their answers again on the central screen before grouping them into themes (Fig. 3). Clustering these hopes around the six themes in Fig. 3 helped create a sense of direction and establish reasonable expectations for the 3-day workshop as well as indicating what was and was not in scope. Next we conducted a “gathering” of issues through anonymous brainstorming based upon the prompt question “What can the senior team do to meet its objectives in 1 and 5 years?.” The question was designed to be open, so as to avoid self-censorship of ideas, but also had a clear time frame. This gather was further developed to include all of the issues/concepts/ideas that emerged during the workshop and is indicative of the complexity of the issues facing the organization. From the initial gathering, we clustered the concepts into themes crossreferencing them against the themes from the interviews to ensure none were missed. The team then followed an exercise in indicating their preferences, using the

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Fig. 3 Workshop hopes

Fig. 4 Preferences on cluster from initial gathering

software for prioritizing the themes to be worked upon during the workshop. The anonymized preferencing was based on the premise that toward the end of the workshop, the group would work on creating work streams for the key actions or projects that would be identified as the workshop progress. To indicate the teams’ collective preference for the order in which we would work through the cluster, each team member was given a number of green tokens and a number of red tokens. Green tokens against a cluster would indicate a desire to work on this cluster, red tokens indicating that while of importance that cluster was not a priority for discussion in this workshop. Typically, thrice as many green tokens as red tokens are offered, and there are fewer tokens per person than clusters. This encourages the group to prioritize and not simply evenly spread their electronic votes. Participants can also place more than one of their tokens against a particular cluster to indicate a strength of preference. Though we urge caution with this approach as participants can learn to behave strategically if this process is repeated, a number of times to ensure a specific agenda are followed (Fig. 4). In this instance there were nine clusters, so the participants were offered six green tokens but only two red tokens. While all of the green tokens were allocated, with some people placing more than one against a particular cluster (Process and

Procedural Justice in Group Decision Support

146 Establish a human resource plan that anticipates grow 291 An investment approach to building teams 314 identify how to spread "equity" interest wider in the organisation 133 develop a unifying vision and values shared by all employees and associat 317 Remove blame culture 316 communicate across functional areas

318 To have the ability to react to need for growth of support staff and clincians in the business

315 Create empowered teams

320 create a reward and recognition strategy

118 have the right staff skills and resources

282 Roll out pursuit of excellenace

302 develop and use a talent mapping process

299 develop strengths and recognise weaknesses 296 Develope the ability to grow teams at pace with minimal impact on team performance 123 create a world class support system

321 create a 360 degree feedback system

306 To empower practices teams to deliver results

319 create a solutions culture with a can do attitude 257 decide our behavioural norms

288 restructure practice teams to ensure most efficient and customer focused set-up 304 Review and fully utilise the apprasisal system 313 be clear about the goals roll down process 297 create role descriptions for each role

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115 Retain & attract the best people to work for us

285 strong pipeline of dentists 309 Create a world class HR function 300 Development & training for all team members 293 training on systems and process changes for practice teams

310 Create effective knowledge management and knowledge transfer processes 289 Clear roles and responsibilities 312 Understand others roles, responsibilities and the interdependencies

303 A group of people who have different skills experience and abilities that achive or deliver joint objectives

126 recruit to all our existing and anticipated dentist vacancies 290 To have a team that is aligned to deliver world class service

284 continuous professional development of clinicians

311 aligned group of individuals working towards goals

286 Ensure existing teams buy in to our unified vision, values and culture

301 Ensure all new recruits have and maintain the right attitude

323 Develop an intra-net 270 develop and support the support centre teams

305 Clear progression plans

292 leadership training for practice managers and field teams 307 develop a succession plan

268 develop and support the field base teams (including CCDs)

181 recognise and incorporate variety of motivations at senior levels

Fig. 5 Teams

systems), not many people used their red tokens. Again the “fair process and voice” aspects of procedural justice are part of the process to ensure the working order of the days schedule. This allows the group to see that the structure and content of the workshop is “collectively agreed” through discussion, which should produce a higher level of buy into the outputs developed as a result of the intervention. The spread of votes on clusters was discussed by the group to see if any surprising results had arisen and that the order indicated by the preferencing was what the group wished to follow. Such a discussion can also help members understand why some clusters have received red tokens and that the team have a sufficiently similar understanding of what each of the clusters encapsulate. The group moved onto mapping each of the identified clusters, through the addition of causal links, in order of indicated group preference. Taking each agreed cluster in turn, we moved the related concepts to a separate screen and checked them for accuracy and meaning; see “Teams” in Fig. 5 as an example. The group first linked the individual concepts in the cluster using the standard notion of causal links. The arrows between the items are causal, i.e., an arrow from “A” to “B” means that “A” may lead to (or influence) “B” or that “B” is caused by (or influenced by) “A.” Arrows can also be negative; this would mean a reduction or reduce likelihood of “B” due to the influence of “A.” Figure 6 shows the more developed map with the potential for additional concepts being added later as more clusters were discussed and links between the cluster understood. The numbering on the concepts act as reference numbers and are indicative of the order in which they were entered into either the participants’ laptops or by the facilitator.

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303 A group of people who have 126 recruit to all different skills our existing and experience and 115 Retain & attract anticipated dentist abilities that the best people to vacancies achive or deliver work for us 146 Establish a joint objectives human resource plan 290 To have a team that anticipates 285 strong pipeline that is aligned to grow of dentists deliver world class 315 Create empowered service 291 An investment 311 aligned group of teams approach to building individuals working 284 continuous teams towards goals 320 create a reward 309 Create a world 118 have the right professional and recognition 314 identify how to class HR function development of staff skills and strategy spread "equity" resources clinicians interest wider in 286 Ensure existing 301 Ensure all new 302 develop and use the organisation teams buy in to our recruits have and a talent mapping 300 Development & 282 Roll out pursuit unified vision, 133 develop a maintain the right process training for all of excellenace values and culture unifying vision and attitude team members values shared by all 323 Develop an employees and intra-net associat 299 develop stregnths and 288 restructure 270 develop and recognise weaknesses 293 training on 317 Remove blame practice teams to support the support systems and process culture ensure most centre teams changes for practice efficient and 296 Develope the teams 305 Clear customer focused 292 leadership ability to grow progression plans set-up training for 316 communicate teams at pace with 310 Create effective practice managers across functional minimal impact on knowledge management and field teams areas team performance 304 Review and fully 268 develop and and knowledge utilise the 307 develop a support the field transfer processes apprasisal system succession plan 123 create a world base teams 321 create a 360 class support system (including CCDs) 289 Clear roles and degree feedback 319 create a responsibilities system 181 recognise and solutions culture 313 be clear about incorporate variety with a can do the goals roll down 312 Understand of motivations at attitude 297 create role process others roles, senior levels descriptions for responsibilities and 257 decide our each role the behavioural norms interdependencies 318 To have the ability to react to 306 To empower need for growth practices teams of support staff to deliver results and clincians in the business

Fig. 6 The “Teams” cluster with causal links

The approach adopted was to have concepts with causal links going out to other concepts toward the bottom and those primarily with causal links feeding in placed toward the top. The software provides a useful function to aid this process of establishing a loose hierarchy of concepts. This structure facilitates the next stage of understanding how carrying out these actions benefits the organization. Each of the maps was developed following the process of “laddering” up to understand how resolving or working on actions suggested would benefit the organization. This revealed a system of interlinked goals or aspirations that the organization wished to fulfill (Eden and Ackermann 2013). To enable the team to gain an understanding of each other’s motivations for the development of the business, we took the group of issues that centered on the key issues of developing and extended them by asking why it is important to resolve or carry out the identified action. The goals across the themes were then placed in single screen along with the key actions thought most likely to significantly add to their realization (Fig. 7). The map was enhanced using a function of the software that captures both the direct links between the concepts and the indirect links, where a casual chain from one concept on the map leads to another on the map through a series of other concepts. The six end goals or aspirations are the concepts with oval borders. These are facilitated by the key actions in red font and provisional key performance indicators in the green font.

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Fig. 7 Goals and aspirations

The CEO reported that this map of agreed goals proved to be a significant milestone in the workshop and for the organization as a whole. It demonstrated that a number of key actions would simultaneously meet the pressing commercial needs of the company’s owners (121 and 131) and be aligned with the stated aims of the franchise owners who held an ethical medical imperative and duty of care to their customers (342, 352 and 358). A catch-all goal that seemed to capture both cultural strands within the developing organization was represented by 344 “A sense of pride” which later developed to inform the rebranding of the organization. Once a full discussion of these complimentary goals had taken place, the third phase of the workshop began. This is an important stage in the workshop process and can be linked to one of the six key determinants of procedural justice. Table 4 will look at these six determinants.

Phase 3: Agreement and Prioritization of Key Actions Now there was some consensus on what the organization was seeking to achieve; the participants were invited to review each cluster and select the actions they thought were critical within the context of that cluster. These key actions were then collated onto a single screen. We used the “domain” function to help us identify those concepts that were linked to large numbers of other concepts as groups can find this useful when reviewing very busy and highly interrelated maps. This can also be done by eye, with the group members invited to individually select concepts, and

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Table 3 Ratings on impact of key issues/actions

then the domain function used to check for any missed potential candidates. Following this process ensures that the group retains the sense that they have chosen the concepts to be taken forward. Using the software‘s rating function, we invited the group to prioritize the identified key actions. This was done by asking the question “Which of the key issues in the business plan has the greatest impact in helping the company in the direction of the prompt question?.” The participants gave a rating of 100 to the action that they expected would have of the greatest impact, a zero score to the issue with the lowest expected impact, and the others placed within that normalized range. The average scores from the team and their standard deviations are listed next to the issues in Table. A partial view of the table is presented in Table 3. For example, concept 114 “Implement a robust, flexible information systems infrastructure” had an average rating of 82 and standard deviation of 13.5 represented by the yellow line above the scores which would indicate a relatively high degree of consensus compared with the standard deviation for concept 137. The anonymized individual scores are also indicated which again help demonstrate the relative degree of consensus. Because some concepts seemed to indicate a lack of consensus on expected impact (e.g., 137), a discussion took place as to whether or not this was because there was real difference of opinion or simply a difference in understanding of what

Procedural Justice in Group Decision Support

146 Establish a human resource plan that anticipates grow

303 A group of people who have 318 To have the 126 recruit to all different skills ability to react to 306 To empower 115 Retain & attract our existing and experience and need for growth practices teams to the best people to anticipated dentist abilities that deliver results of support staff vacancies achive or deliver work for Oasis and clincians in the joint objectives business 290 To have a team 285 strong pipeline that is aligned to of dentists [R 87 deliver world class 12] 315 Create empowered service teams 311 aligned group of

291 An investment approach to building teams 320 create a reward 118 have the right and recognition 314 identify how to staff skills and strategy [R 37 26] spread "equity" resources interest wider in 302 develop and use the organisation a talent mapping 282 Roll out pursuit 133 develop a process of excellenace unifying vision and values shared by all employees and associat 299 develop stregnths and 288 restructure recognise weaknesses 317 Remove blame practice teams to culture ensure most efficient and 296 Develope the customer focused ability to grow set-up 316 communicate teams at pace with across functional areas [R 67 27]

321 create a 360 degree feedback system

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309 Create a world class HR function

300 Development & training for all team members

individuals working 284 continuous towards goals professional development of clinicians 286 Ensure existing301 Ensure all new teams buy in to our recruits have and unified vision, maintain the right values and culture attitude 323 Develop an intra-net

293 training on systems and process changes for practice teams

270 develop and support the support centre teams 292 leadership 305 Clear training for progression plans practice managers

310 Create effective and field teams knowledge management 268 develop and and knowledge 307 develop a support the field transfer processes succession plan 123 create a world base teams (including CCDs) class support system 289 Clear roles and 319 create a 181 recognise and responsibilities solutions culture incorporate variety 313 be clear about with a can do of motivations at the goals roll down 312 Understand attitude 297 create role senior levels process others roles, descriptions for responsibilities and 257 decide our each role the behavioural norms interdependencies minimal impact on team performance

304 Review and fully utilise the apprasisal system [R 25 22]

Fig. 8 “Teams” with key actions highlighted

the concepts meant. After the discussion a second rating exercise took place to check if there was any movement in the ratings and the degree of consensus. The second rating confirmed the results for the first with a reduced degree of variability. These scores were captured by the software and attached to the concepts in the map, where the potential key action/issues had their font altered to help focus attention in their original clusters. Only a few were selected from the teams cluster to represent the cluster in the ratings process above and were thought to be sufficiently linked to the rest that they were representative of a key element within that cluster (Fig. 8). Each of the key actions with a high-impact rating where then considered in more detail. They were taken to a separate view so as to enable a clearer focus, and the links to the overall goal clearly indicated. If we focus on the concept 285, “Strong pipeline of dentists” (which had a mean rating of 87 and a standard deviation of 12), then we can see how the development and maintenance of this feeds into all of the end goals via a series of causal chains (see Fig. 9). This activity was done for each of the identified key actions. Following this process of prioritization, the team then spent the final day agreeing the work teams for each of the key actions, with the participants asked to first volunteer for taking charge of specific work streams. The team started to make a distinction between strategic objectives and key actions that would enable them.

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121 Improve EBITDA

131 Attract the right buyer

358 Meet the needs of our professional teams

352 Improve nations oral health

140 ensure all contracted xxxxxxxxxx 's are delivered 349 Make dentists more productive

344 A sense of pride

345 Making a contribution to society

151 Growth by acquisitions & new builds

102 Improve it's margins 183 successful mutual agreement of associates contracts

342 Meeting the patients interests

339 out perform the competitors

337 Develop a sense of purpose 119 To become the place dentists and 191 Dentist contract other staff want to renegotiation needs to be communicated work clearly 280 Have a clear 184 Engagement with 146 Establish a road map for appropriate human resource plan contract change that anticipates stakeholders process [R 77 10] grow 275 Use forums to gain input prior to 281 Need to build a 278 Put plans in defining final benefits case place to manage 285 strong pipeline contract risks and of dentists [R 87 communications 12] 326 create a world class organisation

126 recruit to all our existing and anticipated dentist vacancies

341 Win the hearts and minds of our practice teams

284 continuous professional development of clinicians

Fig. 9 Strong pipeline of dentists

These strategic actions were identified and others added as the team built up an understanding of how these might fit together as a series of projects. As projects were identified as being sufficiently discrete from each other, they were added to an Excel spreadsheet and assigned a sponsor and project leader. The projects were then filled with suitably aligned key actions with an agreement that the project leader would return to the management team at a later date with a provisional timeline for the key actions. Members of the wider team were assigned ownership of specific key actions within projects relevant to their roles and positions within the organization. Project leaders were identified for each work stream with key supporting team members. Getting the commitment for leading these projects and being part of other projects, teams were relatively easy as the participants could see the impact each project would have for the part of the organization for which they were responsible, and how cooperating with other members could directly or indirectly have positive impacts for them. A final map was produced to demonstrate the degree of interrelatedness that the work streams had (see Fig. 10), where the solid lines represent direct links and the broken line indirect links. For each set of strategic actions (which have a red font with rectangular border), one action was identified as embodying the nature of a project and given a black font with rectangular background. The client was able to understand the complexities around activities that would the required, as a result of the visual representation of the causal map. The intervention resulted in a large amount of qualitative data generated and captured through the intervention. We worked with the client on a number of follow-up workshops to help them dig deeper into the specific projects that had been identified through this process. This enabled them to provide plans for additional investment finance to expand the organization and significantly renegotiate their contracts with their dental

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829 156 Ensure terms of financing agreements continue to be met [R 93 9]

183 Successful mutual agreement of associates contracts

134 Provide a quality service to patients

137 Develop a nationwide consumer recognised brand [R 28 30] 285 strong pipeline of dentists [R 87 12]

282 Roll out pursuit of excellence

174 Gain buy in to the process from all stakeholders

133 Develop a unifying vision and values shared by all employees and associates [R 78 17]

146 Establish a human resource plan that anticipates growth [R 65 21]

147 Open and acquire the budgeted number of practices [R 78 11]

141 Develop an information systems processes & proceduresstrategy to be able to grow effectively [R 70 21]

114 Implement a robust, flexible information systems infrastructure [R 84 13]

359 Implement robust and flexible process and procedures

Fig. 10 Project dependencies

practitioners as they could see the combined benefits of the actions proposed. The dentists agree to pay a greater proportion of their revenue to the parent company in return for the investment in marketing and processes that took place. Involving the dental practitioners in the procedurally fair decision-making process opened up the possibility of them accepting a distributional outcome that at the outset would have been deemed unacceptable. Having examined the case study in detail, the second part of the chapter moves to look at the literature in the field of procedural justice, to seek answers on what make group workshop interventions using GSS more effective.

Aligning the Dual Facilitation Process with Procedural Justice Principles Here we use procedural justice as the theoretical lens to assess how the process of investigation serves to illustrate the development of the commitment and engagement of the participants in strategic development workshops. This section examines how this method of undertaking interventions mirrors the dimensions of a “fair” process, as is discussed in procedural justice (PJ) literature and explored in Ackermann and Eden 2011 The lack of research in this applied area is noted: The relatively small amount of research in group decision making is surprising considering its importance for both practice and theory. One possible explanation for this scarcity is the absence of an effective tool of for measuring fairness of procedures in a group context. (Jacobs et al. 2009, p. 386)

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This section aims to draw the links between the facilitated, software-driven group process used in the study and the characteristics of procedural justice. In the field of organizational research, justice is considered to be socially constructed (see Wagner and Druckman). In the workshop space, it is proposed that this subjective aspect of a socially constructed reality can be “managed” and “controlled” via human facilitation and use of group decision negotiation software, such that the overall structured process used in this group study becomes fairer in the vein of procedural justice. It has been noted that “voice” has value beyond its ability to shape decisionmaking processes and outcomes (Tyler and Blader 2003, p. 351). In this context the facilitation process that the organization set up is indicative of the policy maker showing respect and allowing all participants in the intervention to voice their concerns, in an attempt to improve interactional justice (Bies and Moag 1986; Tyler and Bies 1990). This posits that being treated with dignity and politeness positively reinforces people’s identity judgements since the interpersonal experience shows one is valued by others. In organizational justice research, concerns about fairness are based on the interrelated aspects of organizations, such as how resources are distributed – distributive justice; the fairness of decision-making processes – procedural justice; the nature of interpersonal treatment received from others – interactional justice; and collectively these justice dimensions are known as organizational justice (Colquitt et al. 2005). Of these justice dimensions, the one which was the main aim of examination was procedural justice, since fairness of process is expected to enhance the group outcomes, in terms of levels of firstly meaningful engagement with the process and secondly the richness and authenticity of the qualitative data generated throughout the workshop intervention. The work on justice literature has developed in waves with each dimension receiving prominence in certain decades: distributive (1950–1970), procedural (mid-1970s to mid-1990s), and integrative (mid-1980s to present). Increasingly when examining the area of social justice, there has been a movement away from “distributive justice” to “procedural justice” (PJ) concerns. The aspect of justice in organizational literature is a subjective notion of justice that states that certain process and procedure types can enhance fairness judgments (Lind and Tyler 1988, p. 3). “Procedures can refer to official rules of how things are done, how decisions are made, etc. This represents the traditional view which in this study we refer to as Procedural Justice Narrow (PJN). An alternative and possibly more inclusive understanding of procedures can comprise all processes and interactions that occur in the context of organizational life” (Blader and Tyler 2003, p. 123), which here is referred to as Procedural Justice Wide (PJW). While this broader view of process and procedures helps us understand how the process we used may affect the participants perception of their relationship within the organization, the more focused concern was on how ensuring PJN impacts upon the quality of the outcomes of the workshops. The quality of the sessions is indicated by the authenticity of the data generated and the number of concepts/statements that are volunteered in the session. There is a further distinction in the literature that helps understanding. Organizational justice can be seen to operate at two distinct but potentially interrelated levels.

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The individual self-interest models that state that participants are interested in fairness purely from improving their individual outcomes (Kovonosky 2000, p. 493) and the group oriented models which reflect the concerns of all the group members and are thus more complex in nature (Lind and Tyler 1988; Tyler and Blader 2000, 2003). As a group process was used that did not involve making decisions that would necessarily directly affect their individual outcomes, it is argued that the group-orientated models are more appropriate in framing this examination and this will be discussed further below under treatment issues in PJ. In the area of PJ, the work of Thibaut and Walker (1975) paid particular attention to the “level of control”; the participants believed they had in a process and the subsequent decisions arrived at through that process. They noted that participants reported higher levels of satisfaction when the process was seen as fair and as such even second best final decisions could be accepted by the participants so long as they had experienced control and fair participation in the earlier, process stage (Colquitt et al. 2001, p. 426). “Disputants viewed the procedure as fair if they perceived that they had process control (that is, control over the presentation and sufficient time to present their case). This process control effect is often referred to as the “fair process effect “or “voice” effect (Lind and Tyler 1988; Folger and Cropanzano 1998). In this context fair decision-making would allow participants control over the procedures that determine the outcome, as opposed to the outcomes themselves. Linking this to our work, in an organizational context with a hierarchical structure, direct decision-making tends to reside at the top (at CEO level) and given that participants recognize this as the correct structure; they are hence prepared to accept “indirect opportunities” to impact on decision-making as acceptable. This indirect aspect is termed “process control” by Thibaut and Walker (1975) or the opportunity to express “voice.” The dual facilitation process used in the study allowed all participants to directly input their concepts (thoughts) into the Group Explorer system, without any censoring of views; hence we propose that the power to express “voice” for the participants is unrivalled by any other process. Colquitt et al. (2001) note that Leventhal broadened the determinants of procedural justice to points beyond process control (Leventhal et al. 1980). This requires six criteria to be met if procedure is to be perceived as fair (Colquitt et al. 2001, p. 426). These six determinants are compared to the characteristics of the dual facilitation process used in the study in Table 4. By aligning the six determinants of procedural justice to the dual facilitation process, it can be understood how the workshop process ensures that it has kept to the tenants of procedural justice. In making this connection, we are seeking to show that this helps to develop the help “extra-role” behaviors, discussed below. When processes of investigation are embodying PJ determinants, the participants show commitment to the decisions made and will exhibit extra-role behaviors (Kim and Mauborgne 1998). PJ also enhances the levels of voluntary contribution by “invoking the side of human behavior that goes beyond the outcome-driven self-interest” in exhibiting the extra-role behaviors (Kim and Mauborgne 1998). All participants in the workshop needed to experience a “fair” process of focus group investigation so as to engage meaningfully. In this study, the extra-role behavior would be to divulge information that participants are not normally obliged to divulge

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Table 4 Colquitt et al. 2001, p. 426 [8] Determinant; Colquitt et al. A) Procedures should be applied consistently across people and across time

B) Procedures should be free from bias, i.e., ensuring that a third part has no vested interest in a particular settlement C) Procedures should ensure that accurate information is collected and used in making decisions D) Procedures should have a mechanism to correct flawed or incorrect decisions

E) Procedures should conform to prevailing standards of ethics or morality F) Procedures should ensure opinions of various groups affected by the decision which have been taken into account

Workshop Process; Dual facilitation We conduct the workshops using a laptop/ tablet laboratory setting. This ensures uniformity over time of both the steps followed and the reporting process of results to participants and organization As facilitators should be seen by the participants as independent of the senior executive/organization and cannot impact on policy formulation at senior level Electronic gather of statements/concepts directly from the participants ensures accurate collection of qualitative/experiential data with a clear audit trail through cluster building The process can be used iteratively to ensure accuracy of information gathered Concepts and links entered can be corrected electronically if incorrect Trained independent facilitators ensure process is ethically used with a correct employment of group norms in the focus sessions Stakeholders are often not directly consulted in policy formulation, yet this process affords them a clear and transparent voice

and in doing so show “honesty” of opinion in a transparent manner. This would enable them to volunteer their individual confidential opinion/information (given the initial anonymity of the facilitated software-driven process) relating to which areas of organizational activity need improvement, agreement on goals and aspirations for the business, and prioritization of key actions. As the inputting is anonymous electronic inputting to individual PCs, participants are less likely to self-sensor and will be more likely to engage in exhibiting extra-role behaviors and allow to surface individual opinions, which otherwise they would not feel safe to express. The construction of the maps enables the facilitators to understand the conversation so that they may help surface more meaningful qualitative data. To understand how we are enabling Procedural Justice Narrow (PJN) in the workshop process discussed above, which in turn may enhance Procedural Justice Wide (PJW), also called organizational justice, we need to consider a more recent refinement of PJ terms.

Treatment Issues in Procedural Justice The group engagement model of Tyler and Blader (2003) gives a prominent role to procedural justice and is used to contextualize the work in this study. Within their model treatment issues are examined – participants value PJ

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(operationalized by voice or process control) because it aids the decisionmaker’s ability to make equitable judgments. In the post-1990s’ examination of PJ, more attention is given to the interpersonal aspects of procedures. This attention to interpersonal aspects recognizes that any process or procedure used in a group context will be a setting where participants are involved in social interaction and is known as the treatment aspect. Interpersonal experience can range from being polite, rude, respectful, and with hostility. The process used in the interventions exhibits interpersonal fairness as one of the key functions of the facilitators is to ensure that the group conducts itself in a way that reinforces interpersonal fairness positively. The workshop sessions open with a slide on eight “workshop conventions and norms” of operation, and as these are presented to the participants, it is emphasized that the facilitator will intervene in discussions to bring the use of the norms on track, if the group appears to be overlooking them. This shift in PJ, from a focus on decision-making to interpersonal treatment aspects, shows the development of PJ literature. It increasingly emphasizes “prosocial outcomes, such as how to build trust, encourage responsibility and obligation, generate intrinsic motivation, and stimulate voluntary cooperation with others” (Tyler and Blader 2000). All of the above are a fundamental necessity in workshops as they ensure the surfacing of meaningful qualitative data. In terms of interactional justice, the workshop study ensured equality in contribution, such that fair interpersonal treatment was attained within the groups. All participants had access to an individual laptop to input an “equal number” of concepts on the prompt question, such that no one participant had a louder voice. This process was overseen and “policed” by the facilitators using the software that notes all concepts entered and by whom. This dual use of facilitation with Group Explorer software improves interpersonal fairness and can very quickly generate rich qualitative data. In summary, in the area of Organizational Justice Research, there are very few practitioner orientated reviews, and there is a lack of practice-based theory development (Page 2009). The examination here is firmly “practice based” in terms of context, as it illustrates a live case of negotiation of strategic priorities for the senior executive of a multinational healthcare chain. The electronic gather of qualitative statements (known as concepts) on the prompt question allows the participants a clear “voice,” which would then impact higher up in the strategy development process. “Fair procedures reassure people that stereotypes are not and will not be applied” (Tyler and Blader 2003, p. 358). Research has been undertaken to show that fair decision-making procedures are important in judgments about racial profiling (Tyler and Blader 2003, p. 359). In the workshop, it was imperative that the process and procedure be seen to be fair; otherwise the respondents would not engage with the study, and the qualitative data would be banal, of no illuminating value. Participants would opt not to express their voice (not exhibit extra-role behaviors) as they would have no faith in the process, in terms of upholding their respect and interpersonal treatment issues.

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By starting with only one initial question and allowing the participants to determine what the main factors and themes are, the participants have implicitly been involved in the development of the workshop process which has led to what we call Procedural Justice Narrow. This has had the added advantage of changing the underlying nature of the workshop from a cognitive/discursive type to a cultural, analytical, or linguistic approach with the shared experiences of the group being surfaced and a more authentic voice being heard. This in turn can only help to serve to improve the Procedural Justice Wide dimension of participant’s engagement in policy making at the organizational level.

Conclusion Group Support Systems (GSS), such as the one used in the case study referred to in this chapter, are an effective approach to supporting organizations seeking to develop strategic priorities that can help to support organizational growth. The case study details the steps in a particular client intervention. This process however can be generalized as an appropriate structure for most interventions aiming to determine organizational goals, aspirations, and key priorities for action. The chapter also examines procedural justice literature, which has led the authors to model the dual facilitation process used in group workshops and the dimensions of procedural justice. The crossover between the dimensions of procedural justice and the dual facilitation workshop process shows a strong alignment. This has been used as evidence that supports the effectiveness of GSS in aiding the development of organizations.

Cross-References ▶ Behavioral Considerations in Group Support ▶ Group Support Systems: Concepts to Practice ▶ Group Support Systems: Past, Present, and Future ▶ Just Negotiations, Stable Peace Agreements, and Durable Peace

References Ackermann F, Eden C (2005) The practice of making strategy: a step-by-step guide. Sage, London Ackermann F, Eden C (2011) Making strategy: mapping out strategic success. Sage, London Bens I (2005) Facilitating with ease!, 2nd edn. Wiley, San Francisco Bies RJ, Moag JS (1986) Interactional justice; communication criteria of fairness. In: Lewicki R, Sheppard B, Bazermann BH (eds) Research on negotiations in organizations, vol 1. JAI press, Greenwich, pp 43–55 Blader SL, Tyler TR (2003) What constitutes fairness in work settings? A four- component model of procedural justice. Hum Resour Manag Rev 13:107–126 Bryson JM (2004) What to do when stakeholders matter. Public Manag Rev 6(1):21–53

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Colquitt JA et al (2001) Justice at the millennium: a meta-analaytic review of 12 years of organisational justice research. J Appl Psychol 86(3):425–445 Colquitt JA et al (2005) What is organizational justice? A historical overview. In: Colquitt JA, Greenberg J (eds) Handbook of organizational justice. Lawrence Erlbaum Associates, Inc, Hillsdale, pp 3–56 Eden C, Ackermann F (1998) Making strategy: the journey of strategic management. Sage, London Eden C, Ackermann F (2013) Problem structuring: on the nature of, and reaching agreement about, goals. EURO J Decis Process 1(1):7–28 Folger R, Cropanzano R (1998) Organizational justice and human resource management. Sage, Thousand Oaks Jacobs E et al (2009) Of practicalities and perspective: what is fair in group decision making? J Soc Issues 65(2):383–407 Kaner S (2005) Promoting mutual understanding for effective collaboration in cross-functional groups with multiple stakeholders. In: Schuman S (ed) The IAF handbook of group facilitation: best practices from the leading organisation in facilitation. Jossey-Bass, San Francisco Kaner S (2007) Facilitator’s guide to participatory decision making. Jossey-Bass, San Francisco Kaur P, Carreras AL (2018) Capturing the participants’ voice: using causal mapping supported by group decision software to enhance procedural justice. In: Published in the edited book of referred proceedings of the 18th international conference of GDN 2018. Lectures notes in business information processing (LNBIP 315) a Springer publication, pp 113–126 Kim WC, Mauborgne RA (1998) Procedural justice, strategic decision making, and the knowledge economy. Strateg Manag J 19(4):323 Kovonosky MA (2000) Understanding procedural justice and its impact on business. J Manag 26(3):489–563 Leventhal GS et al (1980) Beyond fairness: a theory of allocation preferences. In: Minkula G (ed) Justice and social interaction. Spinger, New York, pp 167–218 Lind EA, Tyler TR (1988) The social psychology of procedural justice. Plenum, New York Page K (2009) Unlocking engagement and building social capital using procedural justice. PhD thesis Strathclyde University, UK Thibaut J, Walker L (1975) Procedural justice. Lawrence Erlbaum Associates, Inc, Hillsdale Tyler TR, Bies RJ (1990) Interpersonal aspects of procedural justice. In: Carroll JS (ed) Applied social psychology in business settings. Erlbaum, Hillsdale, pp 77–98 Tyler TR, Blader SL (2000) Cooperation in groups: procedural justice, social identity, and behavioural engagement, Taylor & Francis Group, Philadelphia Tyler TR, Blader SL (2003) The group engagement model: procedural justice, social identity, and cooperative behavior. Personal Soc Psychol Rev 7(4):349–361. Lawrence Erlbaum Associate

Looking Back on a Framework for Thinking About Group Support Systems Viktor Dörfler

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Approaches for Considering Success of GDSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GDSS: To Support or to Substitute? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Brave New World of Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dimensions of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Political Feasibility: Focusing on Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Meeting Productivity: Time Is of Essence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Nature of Negotiation: The Role of the Transitional Object . . . . . . . . . . . . . . . . . . . . . . . . . . . Creativity and Intuition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GDSS, Big Data, and Artificial Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concluding Remarks Through Personal Reflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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The thinking framework for group decision support systems (GDSS) proposed by Colin Eden 30 years ago is revisited. Like the source paper, this chapter is a personal take on the topic; however it is a personal take rooted in substantial experience in the broad area of decision-making and modeling and in some specific narrow areas of decision support. There have been major developments in the broad context surrounding GDSS, including the improved understanding of decisions on the conceptual side, and many aspects of computer development, such as artificial intelligence and big data on the technical side. Considering the volume of these changes, it is surprising how much the observations, arguments, and conclusions offered in the source paper are still valid today. The most important component of any GDSS is still the facilitator, and the most valuable ingredients of the GDSS process are the participants’ intuitions, creativity, V. Dörfler (*) Management Science Department, University of Strathclyde Business School, Glasgow, UK e-mail: viktor.dorfl[email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_32

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opinions, arguments, agendas, personalities, and networks. The outcome of the GDSS process is only valuable if it is politically feasible. Today we have a better understanding of transitional objects and their role in the GDSS process; their significance is the second after the facilitator. Artificial intelligence can be useful for GDSS in several different ways, but it cannot replace the facilitator. Keywords

Group decision and negotiation · Group support systems · Political feasibility · Causal mapping · Facilitation · Intuition · Boundary object · Transitional object

Introduction This chapter has the same title as a paper published by Colin Eden, nearly 30 years ago, in Group Decision and Negotiation (Eden 1992a). In that paper, Eden showcased the framework he developed for thinking about Group Decision Support Systems (GDSS). The purpose of this chapter is to revisit the topic explored by Eden and explore whether the claims made in that paper still make sense. To this end, I examine whether the scope of validity has changed and consider the shifts in trends identified in the original paper. In other words, this chapter offers an updated version of Eden’s framework for thinking about GDSS for the age of big data and artificial intelligence. I pick up where Eden left off, and work my way backwards through Eden’s paper, indicating the changes I have observed in the field of GDSS over the last three decades. As pointed out in the source paper, creating a framework for thinking about GDSS is tricky for several reasons: 1. There is no agreement in the broad area of decision support and operational research about whether a particular tool, method, or approach is a GDSS. For instance, Eden noted that while he regarded Soft System Methodology (Checkland 1999; Checkland and Scholes 1999) a GDSS, he was not sure whether Peter Checkland (the originator) would accept the label. 2. There is no common set of objectives for all GDSSs. However, supportive of pluralism of GDSS, Eden (1992a: 214) emphasized that “it is not important to agree the purposes of GDSSs but rather that the designer be explicit about them in each individual case.” 3. The conceptual underpinnings of different GDSS are different and are worked out at varying levels of sophistication. Some, such as SSM (Soft System Methodology) or SODA (Strategic Options Development and Analysis), are built from explicit philosophical and conceptual basis, while others, such as Group Systems (see chapter ▶ “Group Support Systems: Past, Present, and Future”), ignore the conceptual level altogether and focus on technicalities instead. 4. There is no agreement about what GDSS stands for as a technical term. For instance, Eden (see also Eden 1990) notes the typically American idiosyncrasy of

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the term GDSS being reserved exclusively for systems that support groups with dedicated computer hardware and software, excluding many solutions developed elsewhere. These reasons also imply that comparing GDSSs to each other in an attempt to figure out which one is generally the best is both hopeless and useless. So, what is the real purpose of a thinking framework for GDSS? As I see it, the primary purpose is to bring some order to a messy field and provide markers for orientation to scholars and practitioners who engage with the field and want to use GDSS. The secondary purpose, not less important, but unsound without the primary one, is to assist GDSS users in figuring out what distinctive benefits a particular GDSS can bring to addressing a specific problem situation – even if it may not be possible to assess whether one GDSS is better than another. In what follows, I first revisit the three approaches to considering the success of GDSS, which constituted the outcome of Eden’s original exploration of the topic. My conclusion is that the three suggested approaches, namely controlled experiments, comparing GDSS to their underlying conceptual backgrounds and asking the user, are as valid now as they were at the time when they were introduced. Next, I get back to Eden’s consideration of the roles and significance of computers in GDSS. There is one, relatively small change in this area, the development of virtual reality, which may have significant consequences in the future. Then, I look into the conceptualizations of decision-making that underline GDSS. Subsequently, I revisit the dimensions along which Eden conducted his analysis. In each of these dimensions, I will look into what has changed and how. The source article was one of the earliest mentions of “transitional objects” in the GDSS context; I assign a more prominent role to this concept, as its significance has substantially increased since the publication of the source article. Finally, I offer a personal view on what role(s) big data (BD) and artificial intelligence (AI) may play in the future of GDSSs.

Approaches for Considering Success of GDSS When I went to school, they asked me what I wanted to be when I grew up.I wrote down ‘happy’. They told me I didn’t understand the assignment,and I told them they didn’t understand life.John Lennon (1940–1980)

It is perhaps trivial, today, to say that GDSSs are necessarily complex. This was less obvious 30 years ago, but Eden (1992a: 212) offered a sound argument, based on the assumption that “a GDSS is only likely to be economically viable when used to support ill-structured, complex, and probably strategic1 decision making.” This assumption, in turn, derives from the author’s experience and that of others using 1

This notion of strategic does not necessarily refer to the overall corporate strategy but can also mean strategy at the level of an organisational unit or team, whatever we are supporting with the GDSS.

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GDSS in real-world settings with real clients. I believe that this assumption is as valid today as it was 30 years ago. Then, drawing on Ashby’s Law of Requisite Variety, Eden suggested that in order to provide an adequate support in such complex situations, “GDSSs are, and will be, a complex system of computer hardware, computer software, procedures, environments, and facilitation in a mix of proportions” (ibid.: 212). I believe that they still are and they will be for the foreseeable future. This is one of the trends that has kept the same direction, perhaps has become even more forceful. I make a few comments later on how the recent developments in big data (BD) and artificial intelligence (AI) relate to this and what role they may play in GDSS. It is an important consequence of the necessary complexity of GDSS, that a thinking framework and any evaluation criteria of success are also necessarily complex. This also means that any sort of experimental approach is likely to be futile, as even if their experimental validity is high (if such situations occurred, the response would be what the experiment had predicted), as we cannot know anything about their ecological or mundane validity (how close real-world situations can be to the experimental situations) (Kvavilashvili and Ellis 2004). In Eden’s (1992a: 212) words: If the system is designed specifically to address real groups (with a history and a future) working on complex issues, then it is no use taking out those very characteristics that make it complex in order to control experiments. Research with students using structured problems will say absolutely nothing about the performance of a GDSS in relation to its designed aims.

This does not mean that such controlled experiments cannot be useful, only that this usefulness is limited to a specific aspect(s) of GDSS, namely to understand better the micro-characteristics of the designed GDSS and of the conceptual models underpinning the design. With the development of technology, much of validation through controlled experiments can be automated using simulations. However, the judgment cannot be fully automated, as it requires an understanding of the conceptual background and of the decision situations which, however simplified, may still involve a degree of complexity beyond the machines’ capability. Regardless of the degree of automation, this approach will only help to make sure that the GDSS is consistent. The second (not in order) type of evaluation discussed in the source paper is comparing the designed GDSS with the conceptual background that was used to determine the design. As explored later in more detail, there are many different, mutually incompatible conceptualizations of decisions. These different conceptualizations do not even work with the same concepts as building elements; what is central to one may be regarded non-existing by another, and the same concepts may carry different meanings in different models. Therefore, one of the meaningful questions to ask about GDSS is how well it reflects the conceptual model(s) it is based on. (If there is more than one model, these also need to be compatible with each other; ultimately it should be possible, at least in principle, to synthesize these into a single model.) To achieve some clarity in this regard, Eden (1992a: 213–214) urged GDSS designers to be explicit about “the nature of group decision making as a

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process; the nature of decision making in organizations (including the nature of problems, problem solving/alleviation/finishing, and of implementation); and the nature of support and intervention by a ‘system,’ be it facilitator/chauffeur/consultant/ software tool in relation to a group.” If these were not made explicit, we would not know what to compare the designed GDSS to at this level of validation. I believe that this level of evaluation gained in significance over the past 30 years, particularly as the conceptualizations of decision-making have multiplied. Furthermore, I believe that the significance of this type of validation is not limited to GDSS field but would be sorely needed in all areas of modelling. In all areas of management and organization studies, we find a multitude of mutually incompatible models (and unexamined compatibility does not imply compatibility), and these are often used without critical examination. But why would we question whether the designed GDSS (or any model or solution) reflects the conceptual model that determined that design? The short answer would be experience. Because we have all seen models, including GDSS, that, by the time they were ready, got in contradiction with the conceptual underpinnings on which they were based. Daniel Dennett (1995: 21) said once that “there is no such thing as philosophy-free science; there is only science whose philosophical baggage is taken on board without examination.” In a similar manner, there is a significant danger that some conceptual baggage is taken on, without examination, resulting in a model that is self-contradictory. Although a particular GDSS may not account for every single feature of its conceptual background, it must be fully in harmony with it, otherwise we cannot use it having that conceptual framework on mind. In other words, the GDSS must be relevant to the conceptual background that informed its design. Finally, the third approach for considering success brings GDSS to the people and situation to which it is applied and asking whether it is applicable to the situation. In the source paper, Eden (1992a: 215) suggested to “ask the client to explain, in his/her own language, what goes on when using a GDSS and compare with the conceptual framework of the designers.” I do not think it is possible to overstate the significance of this approach. If any model or artifact is used for something else than it was designed for, it may not be simply useless, it can be outright harmful or, at least, dangerous. I still remember, from my student years, a particular finite element modelling package which some architects used to perform some design calculations for a bridge. They did not check the underpinning conceptual framework (the tool was, at the time, designed for a particular type of mechanical engineering problems) and the bridge collapsed, killing a dozen people. While consequences of misapplying GDSS are rarely so severe (at least the consequences are not so directly linked), they are not necessarily less disappointing. Overall, the three suggested approaches for considering the success of GDSS – through controlled experiments, by comparing GDSS to their conceptual underpinnings, and by asking the users – are as valid today as they were three decades ago. It may be possible to replace some controlled experiments with computerized simulations but that does not affect the logic of the three approaches. When I started to study these approaches, I did not know that I will connect it to the notions of consistency, relevance, and applicability, which I previously used in different

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contexts for knowledge validation (e.g., Velencei et al. 2016). The significance of this coincidence is that if we can observe similar patterns in different validation situations, we may trust it more, as this means that from different starting points, following different routes, we arrived at similar considerations of what works well.

GDSS: To Support or to Substitute? [. . .] not everything that can be counted counts,and not everything that counts can be counted.William Bruce Cameron: Informal Sociology2

Based on an earlier conference paper version of Ackermann and Eden (1994), the source paper distinguishes three categories of GDSS with respect to the role(s) computers play in the process: 1. Computer-driven GDSS involves direct entry from members of the group, e.g., Group Systems; if there is a human facilitator involved in these systems, their role is primarily to help the participants feed the input into the system the right way, so that its algorithms can deliver the best performance. 2. Facilitator-driven computer-supported GDSS involves real-time computing that is integral to the activity of the group, e.g., Decision Conferencing (using HiView, now Hieview3), SODA (at the time using COPE, later Decision Explorer, and now strategyfinder), Metagame Analysis (using CONAN), and Strategic Choice (using STRAD). 3. Facilitator-driven GDSS with no computer support, such as SSM and Strategic Choice (as practiced by Hickling 1974), solely relies on the facilitator, there is no computer involved in the process in any way. Although he was (and is) interested in the role of the facilitator and the process of facilitation, Eden (1992a: 200) opted for concentrating on the first two categories, i.e., “GDSSs within which a computer plays an important role.” This was not an obvious choice at the time, but it is perfectly justified with hindsight – most GDSS now come with computer support. In turn, the gap between the first two categories has increased, partly due to the technology development and partly due to the current hype of big data, and the nearly hysterical insistence of some managers, consultants, and scholars to get rid of everything that is subjective. The best way of achieving this seems to be eliminating the “human factor” and leave all the work to computers. However, this also means that such systems cannot meet anymore the above noted complexity requirements, captured in a carefully formulated yet firm viewpoint:

2

Maxim, technically a chiasmus, usually attributed to Albert Einstein (allegedly he once wrote it on his blackboard), but it seems that it was first brought together, at least in writing by Cameron (1963: 13).

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Clearly the more central the computer is in determining process, the more problems there are in the system identifying when a group is ‘finished’ with the problem. Nevertheless several GDSS designers seemingly are determined to design facilitator-less (and chauffeurless) systems. I cannot envisage such a system having a sophisticated enough ‘expert system’ qua facilitator embedded within it for this ever to be a sensible proposition – unless the group is working on highly structured tasks, and even then I am dubious. Eden (1992a: 203)

Only completely well-structured tasks that are solely based on factual data, without any need for judgment or opinion, can be fully computer-supported. Basically, we are not talking about much beyond what database transactions can cover. There has been an incredible progress in computer technology over the past 30 years, so it is reasonable to expect that GDSS has been significantly affected. Indeed, GDSS has been significantly affected, at least at a surface level. But there has been no significant impact at the deep, thinking level. Inputs from participants now must work from their own devices, these must include tablets and mobile phones, it is expected that everything works with more or less no setup and seamless connection (typically using TCP/IP protocol), and all interfaces must be intuitively usable. This is a long way from the keyboard input and wired networks. However, it does not change the basic premises that there is user input, a joint display of the emerging model, and some analytical capabilities provided by the computer. In some cases, specific technology can be of great interest, for instance, approaches such as the Metagame Analysis could substantially benefit from virtual reality (VR). Any approach that displays a model of high complexity can also make use of VR for displaying 3D versions of the model, get the users inside the models to move around and explore parts in more detail, but these are only minor improvements in usability, that can be, at least for now, prohibitively expensive. It is possible to make use of 3D modelling to display richer information and possibly increase interactivity as well but, as far as I know, such developments are in early stages for now. GDSS can also be used in online distributed settings, with or without VR, but as many experienced facilitators will emphasize, there is significant advantage in being in the same physical space, seeing one another’s facial expressions, body language, hearing the tone of voice, etc., rather than just receiving smileys and similar symbols. Once we can have a real-time shared VR over great physical distances, the situation could be significantly improved, but for now, this is closer to science fiction. Based on the previous train of thought, today I would only distinguish between computer-driven and facilitator-driven GDSS. These are, however, not separate boxes anymore but rather ends of a continuum. On the one end, we find computerdriven GDSS that works with minimal human input and with no facilitator. In the extreme cases, these will be fully automated systems aimed at substituting rather than supporting the decision makers. On the other end, we find facilitator-driven GDSS that is fully focused on the human (personal, transpersonal, interpersonal, group, organizational, and possibly social) aspects. This does not mean that the computer does not play an important role in the GDSS process, only that its role is not focal. I like to describe the role of computers in these systems as a support for the facilitator. It makes the facilitator’s work easier in terms of getting the input from the participants, and it provides the facilitator with real-time analytics, but the

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facilitator decides how to make use of the output of the analysis. Similarly, the computer can provide further back-office data for subsequent reports and learning of the facilitator. Eden noted his suspicion that GDSS had been more successful with top managers than forms of DSS and EIS that did not involve a facilitation, as the facilitator’s role is crucial. My personal experience matches this suspicion. For many years, I have been involved in developing a knowledge-based expert system (KBS).3 We predominantly supported top executives using the software; sometimes working with groups of experts and at other times with individual decision makers – and we always provided facilitation. Doctus was well received by senior managers, and they often emphasized that it was all about the facilitation. So much so, that when we tried to sell the software, the response was that it would not make sense to buy it, as it did not work without us. In every variant of GDSS, with the exception of the fully automated system, the most significant role of the computer is to display the evolving model, the so-called “transitional object”; this point is discussed in further detail below. Before getting to the dimensions of analysis, it is useful to take a quick look at how the conceptualizations of decision-making have evolved since 1992.

The Brave New World of Decisions Alice: Which way should I go?Cat: That depends on where you are going.Alice: I don’t know.Cat: Then it doesn’t matter which way you go.Lewis Carroll: Alice in Wonderland

A former MBA student said many years ago: “you know, those decisions that you talk about in your lectures, do not exist in our organisations or, at least, they are extremely rare.” This sentence keeps haunting me, particularly if I look into what is taught in MBA programs about decisions. The purpose of this section is twofold. On the one hand, I want to have a quick look at how the conceptualizations of decisions have evolved in the recent times. On the other hand, I want to show that, even though he could not have known about these newer conceptualizations, Eden’s comments suggest a very similar understanding. The most significant advancement in understanding decisions happened about the same time when the source paper was published. It was James March’s (1991) seminal “How Decisions Happen in Organizations” that made this leap forward. After that a few other important reconsiderations took place, such as the role of intuition was taken more center stage (Sinclair and Ashkanasy 2005; Kahneman and Klein 2009), rationality was even more forcefully questioned (Ariely 2009; Ariely and Trower 2019), and some underlying aspects of our choices have been explored as never before (Iyengar 2011).

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It is the Doctus KBS (www.doctuskbs.com), started and owned by Zoltán Baracskai.

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At the time of source paper, the dominant views of decisions were brought together and divided by the concept of rationality (Simon 1947, 1955, 1956). On the one end, we have total rationality, with the assumption of fully measurable and calculable variables, complete information, including the knowledge of consequences of alternative actions, and computing power that allows for optimization. On the other end, we have bounded rationality, providing a counterpoint to balance the nonexistent world of totally rational decisions towards real-world decisions. In the real world, not everything is measurable and even what is, not necessarily on the same scale, information is incomplete, time and computing power are limited, decision alternatives may not be readily available, goals may contradict each other, and the consequences of different courses of action are rarely known. Between the two extremes, there are a variety of approaches to handling risks, uncertainty, ambiguity, and conflict. This is also what an MBA course would cover regarding decisions; occasionally we may come across heuristics and biases (Tversky and Kahneman 1974; Kahneman et al. 1982), decision traps (Hammond et al. 1998) and possibly superficial mentions of intuition and emotions (Simon 1987). All these models address the thinking of the individual decision maker, and they come a long way explaining how an isolated person would make decisions. However, decision makers do not exist in isolation and thus March argues that decisions in real organizations look very different. March suggests that that decisions “happen” rather than “being made” and therefore the organizational processes that result in decisions “may be poorly comprehended by a conception of intentional, future-oriented choice” (March 1991: 97). As the first reconsideration of the rational choice approach, March suggests looking into rules, including organizational procedures, traditions, cultural norms, considerations of what is appropriate, obligations, duties, and the advices or actions of others. Decision makers often observe these, while ignoring their own, fully conscious preferences. Of course, there are always too many rules that apply in a particular situation and, just like the goals, they can be conflicting. Therefore, the logic that March suggests is to describe the situation using all the rules, then ask the Don Quixotean question of “who am I?,” and then match the two. So the logic of decision-making becomes “what is appropriate for me to do in this situation?,” which is an approach focused on the starting point rather than on the consequences of the choice (rational or otherwise). Things get even more interesting, if we consider that decision makers may be misbehaving (Thaler 2015; Baracskai and Dörfler 2017), i.e., not doing what they think is appropriate. While the first reconsideration shifts the focus from the consequences of the choice to the situation in which the choice happens, it is still about the choice. As the second level of reconsideration, March suggests moving away from the choice, as in real organizations: Many things are happening at once; technologies are changing and poorly understood; alliances, preferences, and perceptions are changing; problems, solutions, opportunities, ideas, people, and outcomes are mixed together in ways that make their interpretation uncertain and their connections unclear; actions in one part of an organization appear to be

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only loosely coupled to actions in another; solutions seem to have only modest connection to problems; policies are not implemented; decision makers seem to wander in and out of decision arenas. (March 1991: 107–108)

From this starting point, March arrives at a series of provocative observations – however, no one with experience in decisions in organizations can deny them. The first point is fairly trivial, i.e., that decisions do not happen in hierarchies but rather in constantly changing and partially overlapping networks of people and objects within and among organizations (cf Mintzberg and van der Heyden 1999). The second, less obvious, point is that orders tend to be temporal rather than consequential. The reason for this is that people are simultaneously involved in many different things. In addition, problems, decision alternatives, and decision makers are time dependent, both in arrival and life span. Furthermore, some people, activities, ideas, etc. are more attractive to a person than others, and this attractiveness also has a temporal aspect. Thus attention becomes a valuable currency – when people attend to some things, they do not attend to other things (cf Davenport and Beck 2001). As a consequence, problems, solutions, etc. get linked not because they are in meansends relationship but because of their temporal proximity. The third point is about symbols and values in construction of meaning. March (1991: 110) observes that “[i] ndividuals fight for the right to participate in decision processes, but then do not exercise the right.” The reason, according to March, is that decisions are opportunities to demonstrate virtues or explain what is going on, to reconsider or reaffirm alliances and make new ones, to socialize, to educate newcomers, and have a good time being involved in the decision. (This reasoning parallels that of Eden and Ackermann 1998: 48–49; this will be discussed in more detail in the section on negotiation.) The three points raised by March together induce a surprising picture: decision makers request great deal of information (outcome of analyses) for their decisions, but then they barely use them, instead, they are scanning the horizon for ideas, opportunities, and people. Outcomes of particular decisions are significantly affected by aspects with no apparent connection to those particular decisions, as they are happening around the same time, as others are interested or disinterested in them, and as they have a particular value or affect particular networks. March (1991: 110) goes so far to say that “decision processes are only partly – and often almost incidentally – concerned with making decisions.” Although this sounds shocking when brought together this way, anyone who has facilitated decision-making groups in organizations or participated in such groups can confirm that this picture resembles reality. On a superficial look, it may seem that the first part, the rational choice approach is more linked to substantive rationality, while the other two are closer to procedural rationality (Simon 1976). However, on a closer examination, we can realize that this is not the case. Each of the three approaches described above have an aspect of substantial as well as procedural rationality. If we think about the decision outcomes, in any of the above three approaches, in terms of whether the outcome makes sense, whether it can be justified, explained, and communicated, we are within substantive rationality. If we look into the behavioral and social processes that led to the

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outcome, the realm of examination is procedural rationality. Eden is very firm in pointing out that a GDSS must feature both forms of rationality, particularly because both are necessary for achieving political feasibility. Of course, how we approach political feasibility will also affect, and be affected by, how we approach decisions in terms of the above three categories, when designing a GDSS. It is remarkable that from the duality of substantive and procedural rationality and some observations, Eden paints a picture of GDSS that covers virtually every aspect of the two revisions of decision approaches suggested by March. This is well reflected in the SODA approach to Making Strategy that Eden has developed with various collaborators (Eden and Ackermann 1998, 2001, 2009; Ackermann and Eden 2011a). Typically such GDSS workshops start from the burning issues of the participants (see chapters ▶ “Group Support Systems: Concepts to Practice” and ▶ “Procedural Justice in Group Decision Support”), there is attention paid to the dynamics, courses of action, values, and preferences are negotiated, the causal map is co-constructed, the aim is to achieve a consensus, power brokers are included, intuitions and expert opinions of participants are explicitly welcome, emotional commitment is not only fostered but also declared. Having reviewed the approaches to considering the success of GDSS, having had a quick look into the role of the computers and having overviewed the recent changes in the conceptualizations of decision-making, the scene is now set for revisiting the dimensions of analysis used by Eden in the source paper.

Dimensions of Analysis There are more things in heaven and earth, Horatio,than are dreamt of in your philosophy. William Shakespeare: Hamlet

In the source paper, Eden conducted his analysis along four dimensions: political feasibility (with coordination and cooperation being featured particularly prominently), meeting productivity, negotiation, and creativity. The scope of the analysis was developments of GDSS at the time and what was then a likely future, including the past 30 years. And his declared purpose was the following: The purpose of this discussion, at the level of conceptual and theoretical assertions, is intended to inform a further debate about the implications for the effective design of GDSSs. Thus the article is specifically seeking to relate decision making in a group to issues in the design of a group decision support system. (ibid.: 200)

I stick approximately to the same dimensions of analysis. There are two differences: 1. Together with creativity, I also include intuition, for several reasons. The scholarly literature on intuition has significantly developed over the past two decades. Creativity involves intuition, and consulting experience repeatedly highlighted the immense value of intuition in GDSS.

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2. I am more prominently emphasizing the notion of “transitional objects,” as today we have a much better understanding of their role in GDSS and any setting where interpersonal relationships matter. I primarily talk about this in the dimension of negotiations. In what follows, I address these dimensions one by one, exploring the claims from the source paper and, where possible, providing updates.

Political Feasibility: Focusing on Implementation Political feasibility is a very simple concept, which acquires extremely high complexity when it manifests in the real world. Other chapters in this handbook deal with political feasibility (chapters ▶ “Group Support Systems: Concepts to Practice” and ▶ “Procedural Justice in Group Decision Support”) from a somewhat different perspective; the chapters are complementary rather than overlapping. The chapters use the same approach to political feasibility, namely that regardless how good (or sound, or rational, etc.) a decision is, if it is not politically feasible, it will be ineffective, that is, it will not bring about the intended change. Political feasibility is further elaborated elsewhere (Eden 1992b) in relation to decision-making groups: The manoeuvring of people along Machiavellian dimensions is relatively easy to identify, but it is, in my experience, much less common than the politics that results from the wish to define reality. This latter form of politics is the essence of human life, it derives from honest people believing they know what is best for the organization. (Eden 1992b: 803)

The notion of political feasibility is closely linked with the notion of implementation. This means that we need to get beyond Simon’s (1977) decision phases (intelligence, design, choice, implementation), as in reality all the participants think about the implementation from the very beginning, as soon as they start to formulate the problem (Eden 1987). It helps if the phases are refined using cycles (Eden 1987: 103), and these can be reasonably well observed in GDSS if they are allowed and supported. I tend to describe the phases as paradoxical, in the sense that each phase seems to contain all the other phases. The second thing, closely related to implementation, is that participants of any decision think about from the outset is the stakeholders (Eden et al. 2019) – how the decision will affect whom and how they will respond (Ackermann and Eden 2011c; Eden et al. 2019). The stakeholders are thus determinants of political feasibility. It seems therefore, that the practicalities of implementation are only to very small extent technical issues, they are primarily political issues. Therefore Eden argues that “[c]ommitment to solutions developed using GDSS is increased because of their ability to manage negotiation and develop coordination and cooperation in relation to the practicalities of implementation” (Eden 1992a: 200). Facilitating the processes underlying political feasibility is complex, as the participants will hold different

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beliefs regarding what is best for the organization, they will have different agendas, intentions, and inclinations, be in different alliances, etc. Therefore, a full reconciliation of all the differences is impossible – but it is also not necessary. As March suggests: In political treatments, however, the emphasis is less on designing a system of contracts between principals and agents, or partners, than it is on understanding a political process that allows decisions to happen without necessarily resolving conflicts among the parties. (March 1991: 103)

What we need to achieve is sufficient alignment between the players regarding the particular actions at hand. In other words, political feasibility will enable enactment (cf Weick 1979, 1995). This will have two aspects, as political feasibility links back to substantive and procedural rationality. For any decision alternative, or course of action, to be politically feasible, it must be both appropriate in itself as well as arrived at through appropriate processes. Therefore, the GDSS has to offer a method for influencing both the analysis of the outcomes as well as the attitudes of the participants (chapter ▶ “Behavioral Considerations in Group Support”). The term order (instead of solution or decision) is useful for increasing political feasibility, as it implies settlement, harmony, progression, and arrangement, which are well aligned with being satisfactory in terms of both substantive and procedural rationality. The notion of order is also more consistent with decisions not being only about creating (with a very inappropriate word generating) alternatives and choosing among them. “Decision making is influenced by the way in which issues are presented, the identification of their significance, their exploration as the group constructs a shared understanding of them, and the point at which a negotiated settlement is likely.” (Eden 1992a: 204). Thus negotiating this order is the most crucial element of political feasibility. Any GDSS, in order to ensure an egalitarian participation and the free expression of ideas, takes away power from some people and gives them to others, as power and social skills would otherwise determine who is heard, how often, for how long, and with how much impact. Based on Kim and Mauborgne (1991), Ackermann and Eden (2010, 2011b) call this redistribution of power procedural justice (see chapter ▶ “Procedural Justice in Group Decision Support”), and they emphasize that procedural justice is not about democracy but about good management. In the first approximation, this is important as it enhances information exchange. Everyone should be heard and listened to. However, participation is not solely about information exchange. As March explained, people often fight to get into a decision-making position but then they often do not exercise their role. We do not only need people to get a seat around the table, we need them to want to be part of the group processes, to participate the best they can. Creating the sense of procedural justice through temporarily redistributing power disturbs the social order. This is very useful in obtaining expert opinions (which is frequently the highest quality information available), as the experts are less likely to try to guess what their bosses want to hear. Of course, we need to be attentive that the disturbance of the social order remains temporary. Finally, as will be emphasized below, procedural justice is tightly

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linked with emotional commitment, which is of paramount importance. On the technical side, anonymity can help a lot with achieving procedural justice, and this is easily achieved when using computers – which, as said above, characterize all GDSS today. Procedural justice helps everyone’s perspectives, opinions, intuitions getting “on the table,” but this is only the first step of achieving political feasibility. However, if all is on the table that anyone wanted to add, we are up to a good start. Assuming that the decision participants are sensible people who are good at what they do, it is plausible that each participant will comprehend what the other participants mean, their respective priorities, issues, etc. The facilitator’s role is as crucial in the subsequent stages, as it was in the initial stage in achieving political feasibility. Time is of essence, as even a politically feasible solution will be ineffective if it is achieved too late, therefore the facilitator also needs to make the group work productive.

Meeting Productivity: Time Is of Essence The topic of meeting productivity sounds trivial. This was also my impression when I came across some literature on decision-making, many years ago, getting into very fine details about the size and shape of the room, about the furniture and the facilities within it, about the color, shape, and size of the post-its and pens (or whatever else they were using), making suggestions on how to gain a few minutes here, and a bit better performance there (see more details in Huxham 1990). While these things really do not make for a particularly interesting intellectual journey, they are of immense importance once we come to the practice of GDSS. Of course, the pen-andpaper issues are now superseded by their computerized counterparts, but the principles are pretty much the same. So meeting productivity is concerned with achieving a reasonably good outcome in a reasonably short time. Experienced decision makers often say that a relatively good decision right now is usually much better than a perfect decision later. Increasing commitment and improving decisions both point towards increased group size. These help achieving improvements both along substantive as well as procedural rationality. However, running a GDSS process with more participants takes more time, and the time increase can be exponential with substantially higher numbers. And the available time is limited, decisions are usually urgent. Many in the GDSS arena, including Nunamaker and Eden (Nunamaker et al. 1988), argued that meeting productivity is an important aspect of good GDSS. In principle, the story is relatively simple here. Not so much when we get our feet on the ground in the real world, to design a GDSS and work with it. There has been significant progress achieved over the past three decades in GDSS design, both in designing the social process as well as the software that supports it, in the area of meeting productivity. This progress has been the result of a series of miniscule steps, tiny gains, but there is a very large number of them and the tiny gains add up to substantial gains. For outsiders, some of these will seem trivial, others unnecessary or even

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counterintuitive. For instance, in SODA, one recommendation for facilitators is to add links between concepts using a keyboard shortcut. In today’s mouse- and touchscreen-oriented world, this does not seem to make sense. It took me several sessions to realize how much faster it is. Perhaps only a fraction of a second in some cases, a few seconds in other cases, but a few hundred times these seconds and fractions can add up to many minutes. In addition, the process gets less fragmented, which can bring additional minutes. And there are dozens of such speed gains that, together, make a significant difference. With Doctus (the software mentioned earlier), such speed gains did not appear to matter. We were paid by the hour, the hourly rates were limited, but the hours were not. Our clients did not seem to be in a rush. We did create several efficiency gaining shorthand solutions anyway, and the clients were not interested in using them, so we stopped. Then, quite suddenly, we realized that we were slow. We could not deliver a full GDSS (or DSS) process in 1–2 days, and we lost numerous opportunities, as speed became expected. It did not even matter that the quality that we produced was excellent. Increasing meeting productivity is not a simple matter, in spite of the simple tiny gains described before. These worked, as they increased speed at an elementary level, by speeding up individual steps. However, these steps do not exist in isolation, and their interconnectedness is nonlinear. In other words, as already said before, the GDSS process is complex. Therefore, we need to be very careful not to end up in the situation of Mintzberg’s (http://www.mintzberg.org/blog/orchestra) hypothetical MBA student, trying to increase the efficiency of the symphony orchestra. He suggested removing two of the four oboes and distributing their activity more evenly, as they had nothing to do for considerable periods of time, drastically reducing the number of violins, as they were often playing the same notes, rounding up the notes, removing the repetitions, and replacing the several hundred years old instrument of the first violin with a newer model. It is so absurd and funny, and devastating. However, very often, similar things are done in organizations in the name of productivity, only the absurdity is less obvious. I have noted previously that, as the decision situations are complex, GDSS design must be complex too. The same applies to increasing the meeting productivity. I find it very worrying when it is suggested that productivity can be increased by improved software design. I categorically say NO to this. Software design cannot improve productivity. Approaching the problem as complex as it is, we must design processes, with a complex systemic attitude, involving excellent facilitators with considerable experience, listening to their intuitions, listening to experienced participants. All software design can do is to support the redesigned processes – and this is very important. Although the best software will not be worth much without good processes, a poorly functioning software can destroy otherwise excellent processes. The reason for this is that GDSS is all about the human-social aspects. Therefore, it needs excellent facilitators conducting excellent processes, so that the participants can productively negotiate politically feasible new orders. Next, we look into some aspects of the nature of negotiation.

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The Nature of Negotiation: The Role of the Transitional Object Linking back to political feasibility, I have noted that it is a new order that is negotiated; this new order has two interrelated features. The first one is called socially negotiated order, emphasizing that the new order is socially constructed, linking to procedural rationality. The second one is called negotiated social order (cf to March’s comments on participation in decision-making and see Eden and Ackermann 1998: 48–49 for more details), emphasizing that the new order, through organizational change, impacts the social relationships, linking to substantive rationality. A politically feasible GDSS process will balance the two aspects of negotiating the new order (Eden 1992b; Eden and Ackermann 2010); the facilitator plays an important role in this process that can be understood primarily by exploring the behavioral aspects of it. The role of the facilitator is discussed in detail in other chapters; here I focus on the role of the transitional object. Whichever GDSS approach we consider, there is always a model which is developed in the GDSS process. This model is a boundary object, as it is at the boundary of the different individual perspectives, and it is also what de Geus (1988) calls a transitional object, as it is constantly changing during the GDSS process. Although Eden and others keep these two “objects” as separable notions, henceforth, in this chapter, I consider the concept of transitional object to cover the notion of boundary object as well. So why are transitional objects important for GDSS? First, transitional objects help to get the right distance from what is happening in the workshop. The “right distance” means not being so close, embedded in the process, that we get lost in the details, losing sight of the big picture, but we are also not so far that we cannot see the details anymore. The transitional object therefore helps “seeing the essence,” which means seeing both the detail and the big picture and swiftly switching between the two (Dörfler and Eden 2019). Furthermore, having the right distance means that discussing what is being said becomes easier, as it is not the other participant one is commenting on but the transitional object. At the same time, the transitional object displays the various perspectives, helping the participants not only the make sense of each other’s views but also to develop an appreciation of each other’s priorities. The participants can see their views represented in the transitional object, so even if what they thought of as a high priority issue is deprioritized during the GDSS process, they will have an appreciation of how this happened. Experience shows that the participants find it much more acceptable to have their views acknowledged and then deprioritized than simply denying them without consideration. Second, the transitional object helps develop an emotional commitment and the sense of ownership. The participants’ sense of ownership does not come as a surprise; each of them was a creator of the transitional object. However, as the transitional object stands for something beyond itself, it represents the new order inthe-making, and they will also have a sense of ownership for that new order. Furthermore, as they co-created the transitional object and the new order it represents, it is a sense of shared ownership. The process of co-creation brings the participants closer together, and they develop commitment not only to the new

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order but also to each other. Beyond learning to appreciate each other’s views and priorities, they also learn to appreciate each other. Therefore, the developing commitment will have a strong emotional dimension. For a long time, in the “Age of Reason” (Enlightenment), emotions were considered a disturbance at best and serious obstacles to good decisions at worst (chapter ▶ “Role of Emotion in Group Decision and Negotiation”). Unfortunately, we can still often hear that we need to get rid of emotions and focus on data instead, in an objective manner, in order to make optimal decisions. Those who hold such views do not seem to know that we have come a long way since the Age of Reason (Simon 1983; Handy 1991). It was still during the Enlightenment that David Hume famously declared that: Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve and obey them. (Hume 1739: Book 2, Part III, Section 3)

But it is not only philosophy but also hard science that teaches us about the significance of emotions. Antonio Damasio (1995), working with a patient referred to as “poor Elliot,” whose emotions were disabled due to an injury, found that emotions are necessary for decisions. Elliot was able to rationally argue about various alternatives, to analyze pros and cons, to evaluate different aspects, but he could not decide. If we just think about any of the most significant decisions of our lives, such as what profession to choose, with whom to spend our lives, where to live, we take all these decisions on emotional basis. Perhaps less obviously, all decisions are like that. What we want to do is mostly emotional and how we go about it, has more to do with reason. In order to acknowledge the significance of emotions, in psychology as well as in management and organization studies, today scholars talk about “cold cognition” and “hot cognition,” where the former refers to the detached reason while the latter to an involved emotional stance (Healey and Hodgkinson 2017; Hodgkinson and Sadler-Smith 2017). In GDSS, emotions play a particularly important role (Martinovski 2010, 2015), especially in relation to the transitional object, as they enhance the GDSS process as well as the sense of ownership. Finally, the transitional object helps enhancing the quality of the new order. This has several components. As all the ideas are displayed in it, the transitional object also supports obtaining further ideas by prompting additional thinking. This is not limited to the volume of ideas, and there will also be further cohesion, as the new ideas will relate to what is already there. It will also become easier to spot if there is a hole in the big picture, so the hole can be filled and the big picture becomes more complete. With the transitional object, it is less likely that something is forgotten or not considered. The developing big picture will also help the participants change their minds. Nobody else can change one’s mind but oneself, but the transitional object enables the internal dialogue as a reference point. This dynamics of changing minds, with the assistance of an excellent facilitator, helps achieving consensus. The consensus, together with the sense of ownership and the emotional commitment, goes a long way in achieving political feasibility.

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What has been discussed about transitional objects so far in this section has been known for a while from the GDSS literature and from the related consultancy experience. So far I have brought together what has been fragmented in the literature, but I want to go a step further. When they were exploring what makes Communities of Practice (CoPs) work, Pyrko et al. (2017) introduced the concept of “thinking together” as the core process of CoPs. Thinking together is a transpersonal thinking process that can be conceptualized based on Polányi’s (1962) notion of indwelling. In CoPs, indwelling is interlocked on the real-life problems the CoP members care about, based on their shared knowledge tradition (see also Pyrko et al. 2019). Dörfler and Stierand (2018) have subsequently explored different modes of indwelling and argued that in different contexts, indwelling can be locked or interlocked on different things, for instance, personal tacit knowing in locked on the subject of study. Based on this, I propose that in a GDSS process, thinking together can happen by the indwelling being interlocked on the transitional object. The GDSS participants may care about some of the same problems but they will also care about some different ones, and usually they will not have a shared knowledge tradition. This raises obstacles to thinking together, and the transitional object can serve the purpose. It can act as an enabler of thinking together, although it will not make it happen on its own, the eagerness of the participants and an excellent facilitator will be essential. In GDSS, particularly if the participants think together, creativity and intuition plays an important role – this is what I explore below, as the last dimension of analysis.

Creativity and Intuition Above I have noted that the transitional object enables creating new ideas in the GDSS process. The significance of these new ideas is that instead of fighting over old options, the participants create new ones. These new options make it easier to achieve consensus while supporting the development of emotional commitment and of the sense of shared ownership. The new options require creativity, which is typically defined as new and useful ideas (Amabile 1983, 1996). This is perhaps sufficient to justify the importance of creativity in the GDSS process. The greatest benefit that GDSS can bring to the organization is realized through the political feasibility, supported by the consensus, emotional commitment, and sense of shared ownership. For this, it is of paramount significance that the participants create new options rather than fight over old ones. An excellent facilitator could achieve a conflict resolution through compromise based on old options; however, consensus can be achieved, at least more easily, on the basis of new options. Moreover, there is more to creativity in GDSS than just adding new options. The participants also synthesize options already displayed in the transitional object as well as the newly added ones, and this leads to further synergies. It is trivial that, when they come to the table, the participants bring their often conflicting goals and viewpoints. Synthesizing the old and new options helps getting the participants’ directions aligned, and this alignment is not forced upon them from the outside but emerges from the GDSS process. While each GDSS process will have a different take on fostering the creativity of the group, there are three commonalities: it is anchored in the transitional object, it is

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fostered by the facilitator, and it does not resemble the brainstorming processes often advocated in the creativity management literature. According to Eden, the reason is that brainstorming works better in situations when the participants have expertise (preferably from the same discipline or problem domain) but no decision-making prerogative. Furthermore, processes like brainstorming may be harmful, as they may interfere with the problem-solving process that is at the heart of any GDSS (Eden 1992a: 210). The social aspect of the problem-solving process is important here, and therefore, creativity in GDSS is highly linked with the relationship-building that takes place. The computerization does not help relationship-building, which is why Eden (1992a: 211) repeatedly argued that GDSS is usually too tedious and not enough fun, that it lacks humor. This becomes even more important, if we take into consideration that the underlying logic of creativity is in essence the same as the logic of jokes (Dörfler et al. 2010). A good facilitator will make humor part of the GDSS process, but this is done in nontrivial ways rather than following a recipe, as creativity is a complex systemic process (Stierand et al. 2014), just like everything else in GDSS. Creativity also makes the story of the GDSS process more interesting, and this story is important. The initial options brought to the table by the participants can be considered an antenarrative, while the resulting model could be considered the final story (cf Stierand et al. 2019). Intuition is relevant to GDSS at least in two different ways. First, in relation to creativity, as creativity requires intuition, namely what we call “intuitive insight” (Dörfler and Ackermann 2012; Stierand and Dörfler 2016). The significance of intuitive insight is that in any GDSS, the creative ideas are not scrutinized on the basis of justification but rather based on whether they make sense in the context of the decision(s) at hand. Second, “intuitive judgments” (Dörfler and Ackermann 2012) brought to the table by the participants are useful for evaluating the options, the ways forward, and everything that has a value attached to it. It is important that intuitions are the intuitions of experts, as intuition works reliably at a high level of expertise (Kahneman and Klein 2009; Dörfler and Stierand 2017). In both cases, intuition is considered to be a form of tacit knowing (chapter ▶ “Negotiation Process Modelling: From Soft and Tacit to Deliberate”), and I would go so far to argue that a GDSS can be only as good as much it makes use of the participants’ intuitions.

GDSS, Big Data, and Artificial Intelligence The prospect of machine interpretation is not only whimsical; it is absurd. Interpretation belongs solely to a living mind in exactly the same way that birth belongs solely to a living body. Disconnected from a mind, ‘interpretation’ becomes what ‘birth’ becomes when it does not refer to a body: a metaphor.Theodore Roszak: The Cult of Information

The increased computerization of GDSS and the more general hype of big data and artificial intelligence (AI) makes it necessary to consider what they can bring to GDSS – but not to become uncritical enthusiasts. There are possible benefits, but these are limited; intuitively this is obvious from the complexity of GDSS and from the importance of the facilitator.

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It is frequently asserted that, more often than not, focusing on big data leads to “big data – small insight.” Instead, Michael Pidd (2017) recommends “small data and big thinking.” At first sight, big data seems to be irrelevant to GDSS anyway, as even a comparatively large number of participants would still conveniently fit within the scope of “small data.” Furthermore, as thinking, and even better, thinking together is at the center of GDSS, we should and often do achieve “small data and big thinking.” However, this is not the complete picture. The GDSS participants do not come to the table empty-handed; they bring with them the analyses that they have conducted before or that they are familiar with. Eden suggested on multiple occasions (see, e.g., Ackermann and Eden 2011a) that analysis, at least good analysis, can and should inform the GDSS process. This means that big data, more precisely big data analytics (BDA), can serve as a useful input, and it can inform the GDSS process. While BDA was relatively straightforward to deal with, this is not the case with AI; to a large extent, this is due to misunderstandings and misrepresentations of AI. In order to figure out what role AI can play in GDSS, it is useful to distinguish between GDSSs that are AI-based and that are not. In AI-based GDSS, the model that becomes the transitional object is created or supported by AI; these include, among others, knowledge-based expert systems (KBS) and artificial neural networks (ANN). I will not discuss these here, as the role of AI would be specific to the particular GDSS – but I would be concerned of any AI-based GDSS that puts more emphasis on AI than on the facilitation process. As a colleague of mine said, the less AI the expert system contains, the better it is. The reason is the misrepresentation surrounding AI. The data processing underlying AI is not akin to thinking, as only a very small part of thinking is data processing. The reinforcement learning, used by ANN, is not akin to learning, as only a very small part of learning is done through reinforcement (see the TEDx talk at https://youtu.be/KAXfo-cZ8oY for a more detailed account). In short, AI and humans are good at different things. This difference is what we should be focusing on; we can make the best use of AI in the GDSS process if we use what AI is particularly good at and humans are not. As Thomas Davenport (2018: 44) says, AI is only “analytics on steroids.” There are many who suggest that AI should replace the facilitator. With more than 20 years of experience in using and developing AI, I believe that this is never going to happen, at least not in a beneficial way. AI will never replace an excellent facilitator. However, as AI can be excellent in analyzing the data generated by the participants real-time, and I am not primarily talking about what they put in the model, but about behavioral data, and this can be supplied in the form of real-time support to the facilitator, who can then decide what to do about it. The facilitator’s perception of the group and her/ his intuitive judgment of the patterns suggested by AI are crucial for an excellent GDSS process. Finally, it is important to ask what role AI can play in creativity, specifically in the context of GDSS. I have explored the topic of AI creativity in detail elsewhere (Dörfler forthcoming), here I just want to outline the conclusions. First, I believe that AI cannot be creative. As knowledge in AI is limited to explicit knowledge and creativity requires intuition, which is a form of tacit knowing, AI creativity cannot

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happen. Surely AI may produce something that satisfies the two criteria of creativity, something that is new and useful. However, there is a hidden third requirement: it has to be an idea. AI does not have ideas – but if AI suggest something that people find new and useful, they can transform it into an idea. Thus AI can support human creativity by providing some sort of preprocessing. There is, however, another, perhaps somewhat counterintuitive way how I believe AI can help human creativity: AI is not affected by “tunnel vision” or “group think,” and therefore, AI can help us think “outside the box” by showing patterns that we may not allow ourselves to see imposing unnecessary limitations. I have to note that what I said about AI is a personal view – even if it is a personal view that is rooted in two decades of experience. Many AI experts would disagree with me. I allow the possibility that they may be right and I may be wrong about some details, but these do not affect what role AI can play in GDSS today or in the near future.

Concluding Remarks Through Personal Reflection I have experience with two types of DSS/GDSS: for 20+ years I have been doing consultancy work with knowledge-based expert systems, leading related software development, using it in my research, and teaching about the subject. In addition, for the past few years, I have been involved in using causal mapping (specifically the SODA approach), although primarily in teaching and research. Both these experiences informed my argument in this chapter. Admittedly, this is still only a personal opinion, and it is as much based on beliefs and opinion as on facts. However, it is a well-informed personal opinion. I have found that the context of GDSS has considerably changed over the past three decades, particularly, now we have a very different understanding of how decisions happen and the underlying computer technology has significantly evolved. Although these are both of great interest to studying GDSS, they seem to be less significant in terms of the paper that served as my starting point, as Colin Eden has approached it 30 years ago in a way that is consistent with the changed understanding of decisions and he only focused on computerized GDSS in the first place. It has also been reinforced that we need to design GDSS processes with a complex systemic mindset, and all computers can do is to support these processes – software design cannot substitute system design. The dimensions of analysis that Eden used in that paper can still be meaningfully maintained, as it is indispensable for a viable output of the GDSS process to be politically feasible, and to achieve this, we need to conduct productive meetings, enable negotiation, and foster creativity and intuition. While computers can help a lot with the GDSS process, at the core of it are the GDSS participants, with their intuitions, creative ideas, social relationships, agendas, arguments, and personalities. The first of the two main changes that happened in the last 30 years is that despite all the computerization, the role of the facilitator is confirmed as exceptionally important, perhaps the most important ingredient of good GDSS. The reason that I

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see this as a change rather than remaining the same is that it is a completely different world in terms of computers, big data and AI – and I argue that a good facilitator cannot and never will be replaced by AI. The second change is that we have a much better understanding of transitional objects, their role, significance, and modus operandi in the DSS/GDSS context. I maintain that further technological development will primarily benefit GDSS through creating better transitional objects, at least, in the short term.

Cross-References ▶ Group Decision Support Practice “as it happens” ▶ Group Support Systems: Concepts to Practice ▶ Group Support Systems: Past, Present, and Future ▶ Negotiation Process Modelling: From Soft and Tacit to Deliberate ▶ Procedural Justice in Group Decision Support

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Part VII Multiple Criteria Analysis for Group Decisions

Multicriteria Methods for Group Decision Processes: An Overview Ahti Salo, Raimo P. Ha¨ma¨la¨inen, and Tuomas J. Lahtinen

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rationales for Using MCDA Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phases of MCDA-Assisted Group Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiattribute Value and Utility Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Analytic Hierarchy Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methodological Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Behavioral Issues and Biases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guidelines for Designing MCDA-Assisted Decision Support Processes . . . . . . . . . . . . . . . . . . . . . . MCDA Methods in Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outlook for the Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Important decisions are often taken by groups of decision makers who need to choose among several alternatives in view of multiple objectives, in recognition of the interests of stakeholders. Such decision problems can be supported with the methods and processes of multicriteria decision analysis (MCDA) which foster collaboration, lend structure to the decision process, and help in managing problem complexity. In this chapter, we examine rationales for using MCDA methods in group decision processes, outline typical phases of these processes, summarize widely used MCDA methods, and discuss some of their recent methodological extensions. We also provide guidelines for the design and implementation of

A. Salo (*) · R. P. Hämäläinen · T. J. Lahtinen Systems Analysis Laboratory, Department of Mathematics and Systems Analysis, Aalto University School of Science, Aalto, Finland e-mail: ahti.salo@aalto.fi; raimo.hamalainen@aalto.fi; tuomas.j.lahtinen@aalto.fi © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_16

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MCDA-assisted group decision processes, based on an examination of behavioral factors and a structured review of selected case studies as well. We conclude with an outlook for the future in light of recent developments and trends. Keywords

Group decision · Multiple criteria analysis · Preferences · Multiple attribute decision-making · Multiple participant-multiple criteria · Negotiation process · Preference modeling

Introduction Important decisions with multiple objectives and alternatives often involve group decision-making (see, e.g., Keeney and Kirkwood 1975, French 1986, Belton and Stewart 2002, French et al. 2009, Greco et al. 2016). The problem is to find a course of action that contributes to the attainment of objectives that are seen as important by the members of the decision-making group. Even if the decision is taken by a single individual, the decision typically affects several stakeholders whose interests need to be recognized. Thus, it may be helpful to design and implement structured decision support processes in which these stakeholders’ views are systematically charted. The literature on multicriteria decision analysis (MCDA) offers numerous methods for addressing problems characterized by multiple objectives (for textbooks and surveys, see, e.g., Belton and Stewart 2002, Wallenius et al. 2008, French et al. 2009, Parnell et al. 2013, Greco et al. 2016). The articulation of the objectives can be useful for many reasons: for instance, it fosters the identification, elaboration, and prioritization of alternatives (Keeney 1992). For example, the elaboration of safety-related objectives, such as reducing the number of accidents, reducing the severity of injuries in accidents, or providing faster access to first-aid services, can stimulate the generation of alternative measures for improving safety. The systematic concretization of such objectives in terms of corresponding evaluation criteria and attendant measurement scales provides a framework for assessing how the alternatives contribute to the attainment of these objectives. Within this framework, information about the decision-makers’ subjective preferences can be modeled through the elicitation of criteria weights and the evaluation of alternatives with regard to the relevant criteria. Finally, overall evaluations of the alternatives (or a ranking of the alternatives) can be produced by combining criterion weights with the criterion-specific evaluations. Thus, the MCDA methods help synthesize both values and facts, in order to generate well-founded guidance for decision-making. Typically, a notable benefit of deploying MCDA in group decision process is that of fostering increased understanding of the decision problem in its broader context. Thanks to its systematic structure, the MCDA process can help group members consider the problem from multiple perspectives, explore the possible consequences of the decision, and recognize how others perceive the problem, for

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instance. Moreover, the group can benefit from the process as a result of enhanced communication and the articulation shared as well as conflicting views. These benefits are among the key reasons for the wide adoption of MCDA methods in supporting group decision-making in application areas like environmental management (Gregory et al. 2012). From a theoretical perspective, many MCDA methods build on normative theories of decision-making that characterize what choices a decision-maker would make among alternatives, subject to the assumption that his or her preferences comply with stated rationality axioms (Keeney and Raiffa 1976; von Winterfeldt and Edwards 1986). Extensions of these theories into group settings underpin development of MCDA methods which admit and aggregate information about the group members’ preferences, which gives insights into which alternatives are preferred to others by the individual group members as well as by the group as a whole (see, e.g., Keeney and Kirkwood 1975, Keeney 2013). In MCDA processes, the group members can be, for example, decision-makers, representatives of stakeholders who are impacted by the decision, or experts providing information or methodological modeling support to the decision process. Often, there is also a process facilitator (see, e.g., Phillips and Phillips 1993, Franco and Montibeller 2010). A group decision process creates a temporary organization and assigning a leader is often useful (Hämäläinen et al. 2020). Commonly, this role is assumed by or explicitly granted to the facilitator. The number of group members involved in the decision support process may vary, for example, if web-based approaches are employed, even hundreds of group members can be consulted (see, e.g., Hämäläinen et al. 2010). In this updated version of the chapter by Salo and Hämäläinen (2010) in the previous version of the Handbook of Group Decision and Negotiation, we restrict our attention to multicriteria decision analysis. For example, we do not discuss the many variants of voting procedures considered in chapters ▶ “Group Decisions: Choosing a Winner by Voting” and ▶ “Group Decisions: Choosing Multiple Winners by Voting.” Nor do we cover game theoretic approaches discussed in chapter ▶ “Negotiation as a Cooperative Game”; conflict analysis methods covered in chapter ▶ “Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives”; multicriteria agency models (Vetschera 2000); or bargaining models where the group members (or agents) pursue different objectives (see, e.g., Ehtamo and Hämäläinen 2001, Mármol et al. 2007).

Rationales for Using MCDA Methods From the perspective of enhancing and ensuring the quality of decision processes, there are several rationales which motivate the use of MCDA methods. As shown in Table 1, these include support for the management of complexity, increased transparency and legitimacy, the formation of an audit trail, and enhanced collaborative learning:

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Table 1 Rationales for the deployment of MCDA methods Rationale Management of complexity

Brief definition MCDA offers tools for managing the complexity involved in major decision problems

Transparency

The results are based on explicitly stated values, facts, and assumptions in an understandable way Process appropriately embedded in its institutional and organizational context Availability of a track record of the consecutive steps enacted during the support process Enhanced understanding among group members about each other’s perspectives and the decision problem

Legitimacy

Audit trail

Learning

Benefits in group decision support Helps to systematically consider decision problem from multiple perspectives and to combine subjective evaluations with multiple sources of data Reduces the risk that the results are driven by biases, false assumptions, or hidden motives. Supports learning Lends authority and credibility. Facilitates the implementation of decision recommendations Permits reflective ex post evaluations of the process which enhances learning Helps find areas of agreement and disagreement. Process found rewarding by group members

• MCDA provides support for the management of complexity in many-faceted and far-reaching decision problems where the number of issues to be accounted for can be truly large. Specifically, MCDA methods lend structure to complex decision problems, which is useful for guiding discussions as well as modeling and data collection efforts, for example. They also help formulate well-founded conclusions based on the consideration of diverse perspectives and complementary sources of data. The rationale of managing complexity is particularly salient in problems of portfolio decision analysis (Salo et al. 2011), because without adequate methodological support, it may be impossible to examine all portfolios which, by definition, consist of combinations of individual alternatives. • Enhanced transparency is another key rationale. This is achieved when the group members understand the structure of the MCDA model and the interdependencies between the model outputs (e.g., the overall evaluations or the ranking of the alternatives) and the model inputs consisting of beliefs about facts (e.g., criterionspecific evaluations of alternatives) and subjective value judgments (weights of the criteria) (see Bana e Costa et al. 2006; Geldermann et al. 2009; Hodgkin et al. 2005; Mustajoki et al. 2007). Such an understanding fosters trust in the results and promotes commitment to the implementation of decision recommendations. Transparency also supports learning processes where the group members can explore interactively how changes in the input parameters will be reflected in the results (Geldermann et al. 2009; Salo 1995). • The legitimacy of the decision support process is often a key concern, particularly in problems such as environmental planning where the decisions affect several stakeholder groups (Hajkowicz 2008; Kiker et al. 2005). Indeed, even if a less formal decision support process might lead to the same decision outcome, a

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model-based approach may still be warranted because it ensures, among other things, that the alternatives will be treated consistently, systematically, and on equal terms within a comprehensive evaluation framework. • The use of MCDA methods typically leaves an audit trail that records the steps through which the decision recommendation was arrived at. The availability of such an audit trail can be particularly valuable in situations where the decision may have to be reached under considerable time pressure (e.g., emergency management; Bertsch and Geldermann 2008, Geldermann et al. 2009, Papamichail and French 2013), but where there is a need to improve the quality of these processes, which suggests that they should be subjected to scrutiny later on. Audit trails may suggest instructive “lessons learned” that serve to improve the quality of decision-making processes. The audit trail may also help reflect on how the results of the process could have been affected by behavioral phenomena such as cognitive biases and help design processes that mitigate the risk of biases (see also Lahtinen et al. 2017a; Zare et al. 2020). • The collaborative development and deployment of a shared MCDA model foster learning processes which, at best, help group members understand both the factual dimensions of the decision problem, such as the likely magnitudes of the possible consequences of the decision, and each other’s perspectives. This learning can be quite important: for instance, it may facilitate the shaping of alternatives that are likely to be accepted by all group members. It is also possible that the decision-makers’ preferences change as they learn more about the problem. In effect, learning can be an inherently rewarding experience which generates interest in model-based approaches even in further decision problems as well.

Phases of MCDA-Assisted Group Processes While MCDA methods differ in their underpinning theoretical and methodological assumptions, the processes through which they are deployed often share many similarities (e.g., Belton and Stewart 2002; French et al. 2009; Wallenius et al. 2008). At a high level of aggregation, these processes commonly consist of the following partly overlapping and iterative phases: 1. Clarification of the decision context and the identification of group members: In this phase, the aim is to clarify the overall situation in which the MCDA process takes place, including aspects such as what the broader aims of the process are, what the decision is really about, who the member of the decision-making group and the other stakeholders are, and in what role the participants will be engaged in the process (e.g., as decision-makers, sources of expertise, or representatives of their respective stakeholder groups (cf. Belton and Pictet 1997)). In high-level decisions which are to be taken by senior decision and policy makers, MCDA processes can be enacted with the aim of providing information to the actual decision-makers without involving them extensively in the process. Yet, even in

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this situation, it can be advantageous to involve at least someone from the highlevel decision-making group in the MCDA process in order to ensure that the high-level concerns are reflected in framing the problem, distilling insights, and communicating the results. Identification and explication of decision objectives: In this phase, the objectives related to the decision are identified and explicated. The objectives can relate to the full range of tangible and intangible concerns, including the aims and goals of the decision-makers and relevant stakeholders. Many kinds of techniques (e.g., in-depth interviews, workshops, questionnaires) can be used to ensure that all relevant objectives are identified. In the identification of objectives, it can be fruitful to start from the values that are important to the members of the decision-making group and stakeholders and to proceed by formulating objectives based on these (Keeney 1992, 1996). Next, the objectives need to be elaborated by developing corresponding evaluation criteria and associated measurement scales with the help of which the attainment of the objectives can be assessed (see, e.g., Keeney and Gregory 2005). Ideally, the set of criteria should be comprehensive (i.e., all relevant objectives are addressed) and nonredundant (i.e., no double counting of benefits or harms related to alternatives). Generation of decision alternatives: In this phase, the aim is to specify a representative yet manageable set of alternatives. Even if some alternatives may have been identified before the MCDA process, deliberate attempts at generating further alternatives should be made, because the process may be compromised by “errors of omission” if promising alternatives are not included in the analysis. Keeney (1992) and Siebert and Keeney (2015) describe how the objectives identified in the previous phase can be used to stimulate the generation of alternatives. Other techniques can be found, e.g., in Sternberg (1999) and Colorni and Tsoukiàs (2020). All alternatives need to be specified sufficiently well so that they can be evaluated with respect to the criteria. Elicitation of preferences: In this phase, subjective preference statements are solicited, for example, about criterion-specific weights which indicate how important the different evaluation criteria are relative to each other and how much value the group members associate with the alternatives’ performance levels on criterion-specific measurement scales. Thus, the responses by different group members typically differ due to differences in their preferences. The use of debiasing techniques is recommended (see, e.g., Montibeller and Von Winterfeldt 2015, Lahtinen et al. 2020). Evaluation of decision alternatives: All alternatives are measured with regard to every decision criterion using an associated measurement scale. These measurements can be based, among other things, on empirical data, quantitative models, or subjective judgments. The subjective judgments may be solicited from external experts or from the group members themselves. Analysis and communication of results: The results are typically represented as the overall values of the alternatives (sometimes called overall scores), computed from the elicited parameters of the decision model in keeping with the calculation

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schemes of the chosen MCDA method. Another format for presenting results is a ranking of alternatives which does not convey information about preference differences between the alternatives. Usually sensitivity analyses are carried out to examine how the results would be affected by changes in the values of numerical parameters. Interactive workshops are often held, e.g., to enhance learning, increase transparency, and support communication. It may be pertinent to revisit the earlier phases of the process and to re-specify alternatives or objectives, if this is deemed warranted due to changes in the group members’ perception of the problem. The possibility of revising earlier phases is often warranted, because the group members’ understanding of the problem evolves over time. For example, the examination of tentative results may lead to the recognition of additional objectives or stimulate the generation of further alternatives. There may be changes in the decision-makers’ preferences as well, as these preferences are partly constructed during the decision support process (see, e.g., Slovic 1995, Payne et al. 1999). Especially in entirely new decision contexts, an iterative process may be useful in that it helps generate tentative initial results for learning purposes before proceeding to the later rounds. In MCDA-assisted group processes, the facilitator often has an essential role in ensuring that the group members’ views are properly charted and that each group member has a chance of voicing his or her concerns. This is important especially in face-to-face workshops. The facilitator also has a critical role in ensuring that (i) methodologies are employed correctly, taking into account the pitfalls of human decision biases, (ii) the group members are aware of the underlying methodological and modeling assumptions, and (iii) the results of the decision model are understood. Franco and Montibeller (2010) provide an extensive discussion of the facilitator’s role and relevant facilitator skills. In some cases, the group members need not approach the problem using the same problem representation (see, e.g., Keeney 2013). In the Web-HIPRE software (Hämäläinen 2003; Mustajoki and Hämäläinen 2000), for example, the group members can first examine the problem using their own individual value trees, whereafter recommendations for the group decision can be generated by associating importance weights to the group members. Because the evaluation of alternatives with regard to the criteria builds on multiple information sources, it may be possible to carry out this activity in a decentralized mode so that the participants evaluate alternatives only with regard to those criteria they are knowledgeable about. Furthermore, the elicitation of preference information can be supported with Internet-based decision support tools (Hämäläinen et al. 2010). Such tools may be indispensable in extensive MCDA processes characterized by the need to engage a very large number of participants who represent different stakeholder groups. We next summarize the main features of two widely used MCDA methodologies, noting that there are numerous other MCDA approaches as well. Matsatsinis and Samaras (2001) discuss so-called preference disaggregation

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methods in group MCDM. See also chapters ▶ “A Group Multicriteria Approach,” ▶ “Group Decisions with Intuitionistic Fuzzy Sets,” ▶ “Multiple Criteria Decision Support,” and ▶ “Holistic Preferences and Prenegotiation Preparation” in this handbook.

Multiattribute Value and Utility Theory Multiattribute value theory (MAVT) is a methodological framework which offers prescriptive decision recommendations for making choices among alternatives x ¼ (x1, . . ., xn) which have consequences xi with regard to n attributes (Keeney and Raiffa 1976; French 1986; Belton and Stewart 2002). MAVT is based on a set of axioms that characterize rational decision-making. For example, it is postulated that a rational decision-maker has complete preferences, meaning that for any two multiattribute alternatives x and y, the decision-maker either finds that these alternatives are equally preferred or that one is preferred over the other. Moreover, the preferences are assumed to be transitive, meaning that if the decision-maker prefers alternative x over y and alternative y over z, then x is logically preferred over z. Mutual preferential independence is a key axiom in MAVT (Keeney and Raiffa 1976). This axiom holds if the decision-maker’s preferences for alternatives which have different consequences on some attributes and similar consequences on some other attributes do not change if the alternatives’ similar consequences are changed. If this axiom holds along with other, less restrictive axioms, there exists an additive multiattribute value function, defined on the alternatives’ consequences, such that alternative x is preferred to y if and only if x≽y ( V ðxÞ ¼

X

v i ðx i Þ 

i

X v i ðy i Þ ¼ V ðyÞ

ð1Þ

i

The existence of the value function has been proved using a topological approach (Debreu 1960) and an algebraic approach (Krantz et al. 1971). The value function is unique up to positive affine transformations. Thus, the preference relation that it induces on the alternatives does not change if the values are multiplied by a positive constant α > 0 or if a constant β is added to the overall values of all alternatives. Due to this property, the MAVT function in (1) can be written in the customary form V ðxÞ ¼

X

wi vi ðxi Þ,

ð2Þ

where the scores vi() are typically normalized onto the [0,1] range so that the score of the least preferred alternatives on a given attribute is zero while that of the most preferred alternative is one. Furthermore, the wi denote the attribute weights, which reflect the decision-maker’s preferences for the improvements obtained by changing consequences from the least preferred attribute level to the most preferred attribute

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level. These weights are customarily normalized so that they add up to one, i.e., iwi ¼ 1. Keeney and Raiffa (1976) extend the MAVT framework into group decisionmaking settings where the groups’ aggregate value depends on the values that are attained by the individual group members. Specifically, they show that if the requisite axioms hold, the group’s aggregate value function can be expressed as V ðx Þ ¼

X X wki vki ðxi Þ, Wk

ð3Þ

k

where Wk denotes the importance weight of the k-th decision-maker and the latter sum represents the value that alternative x will give to her. When using the MAVT framework in group decision support, the parameters of the representation (1) or (3) are first estimated whereafter the alternatives’ overall values are used for deriving decision recommendations. However, it is pertinent to check that the decision problem can be adequately modeled using MAVT and to elicit score and weight parameters carefully, with the aim of mitigating the possibility of biases.

The Analytic Hierarchy Process In the analytic hierarchy process (AHP) (Dyer and Forman 1992; Saaty 1977, 1980, 2005), the decision problem is structured as a hierarchy where the topmost element represents the overall decision objective. This element is decomposed into subobjectives which are placed on the next highest level and which are decomposed further into their respective sub-objectives until the resulting hierarchy provides a sufficiently comprehensive representation of the relevant objectives. The decision alternatives are presented at the lowest level of the hierarchy. The elicitation of preferences is based on the use of a ratio scale. Specifically, for every objective on the higher levels of the hierarchy, the DM is requested to compare the relative importance of its sub-objectives through a series of pairwise comparisons. In each such comparison, the DM is asked to state how much more important one sub-objective is than another (e.g., “Which is the more important objective, criterion, cost, or quality?”) and to indicate the answer on a 1-to-9 verbal ratio scale (1 ¼ equally important, 3 ¼ somewhat more important, 5 ¼ strongly more important, 7 ¼ very strongly more important, 9 ¼ extremely more important). For the lowest-level objectives, the DM is asked to carry out similar comparisons about which decision alternatives contribute most to the attainment of these objectives. In the AHP, the derivation of the priorities is based on the following eigenvector computations. First, the ratio statements are placed into a pairwise comparisons matrix A such that the element Aij denotes the strength of preference for the i-th subobjective over the j-th one. From this matrix, a local priority vector w is derived as a normalized solution to the equation Aw ¼ λwmaxw where λwmax is the largest eigenvalue of the matrix A. Second, using these local priorities, aggregate weights

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for the objectives are derived by first assigning a unit weight to the topmost objective. This weight then “flows” downward in the hierarchy so that the weight of an objective is obtained by multiplying the weight of the objective immediately above it with the local priority vector component that corresponds to the lower-level objective (taking the sum of such products if the lower-level objective is placed under several higher-level objectives). The weight of an alternative is obtained by summing all these products over those objectives that have not been decomposed into sub-objectives. In group settings, the AHP can be employed in many ways. For instance, stakeholder groups can be represented by “objectives” that are placed immediately below the topmost element of the hierarchy, whereafter pairwise comparisons can be elicited in order to associate corresponding importance weights with the stakeholders. Alternatively, the group members can provide their individual pairwise comparisons in a shared hierarchy where aggregation techniques are employed to synthesize their comparisons. They may also work in close collaboration, with the aim of arriving at consensual judgments for each pairwise comparison (see Basak and Saaty 1993; Forman and Peniwati 1998). Group decision-making with the AHP is discussed in chapter ▶ “Group Decision Support Using the Analytic Hierarchy Process.” Despite its popularity, the AHP has been subjected to major criticisms. In particular, the AHP may exhibit so-called rank reversals (Belton and Gear 1983) whereby the introduction of an additional alternative may change recommendations concerning the other alternatives. This possibility – which is caused by the normalization of local priority vectors – violates the rationality axioms of MAVT, and it is one of the reasons why some scholars have contested the merits of the AHP as a sound decision support methodology (Dyer 1990). Other caveats in the AHP include the insensitivity of the 1-to-9 ratio scale and the large number of pairwise comparisons that may be needed when the number of decision alternatives is large (Salo and Hämäläinen 1997). Yet, it can be shown that the pairwise comparisons are reformulated so that they pertain to value differences; then the results of the AHP analysis can be expected to coincide with those of MAVT (Salo and Hämäläinen 1997).

Methodological Extensions The above descriptions summarize the “basic” features of two commonly employed MCDA methods. These and many other methods have been extended in a number of ways: • Incorporation of partial or incomplete information. Most MCDA methods assume that information about the model parameters can be characterized through exact point estimates. Yet, the recognition that such estimates can be difficult or expensive to acquire has spurred the development of methods in which incomplete information is represented either with intervals or sets of parameter values that contain the “true” values (see, e.g., Kim and Ahn 1997; Kim and Choi 2001;

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Salo and Hämäläinen 1992, 2001; Punkka and Salo 2013). See also chapter ▶ “Multiple Criteria Group Decisions with Partial Information About Preference.” One advantage of the set inclusion representation is its simplicity in comparison with approaches such as evidential reasoning (Yang and Xu 2002) and fuzzy sets (Herrera-Viedma et al. 2007), for instance. In group decisionmaking, the intervals can be defined so that they contain the parameter values that correspond to the group members’ individual preferences (Hämäläinen et al. 1992; Salo 1995; Hämäläinen and Pöyhönen 1996; Vilkkumaa et al. 2014). While the resulting decision model may not provide conclusive recommendations for the group’s preferred alternative, it may help determine which alternatives do not merit further attention, allowing the later phases of the analysis to be focused on the other alternatives. • MCDA and multi-modeling. In many decision contexts, information about the impacts of the alternatives is generated with modeling tools such as prediction or simulation tools. In such cases, MCDA models can be usefully interfaced with or even integrated into the other tools. For example, the MCDA model can be used for the overall evaluation of strategies whose performance with respect to multiple criteria has been assessed with a system dynamics model (see, e.g., Brans et al. 1998, Santos et al. 2002). Environmental decision-making is one context in which the use of multiple modeling tools in combination is common (Voinov et al. 2016). For example, the Web-HIPRE MCDA tool has been incorporated into the RODOS decision support system for the prediction of radiation exposures associated with nuclear emergency scenarios so that the system provides timely guidance for the prioritization of countermeasures for mitigating the impacts of an emergency (Hämäläinen 2003; Geldermann et al. 2009). Furthermore, MCDA can be integrated with different problem structuring and stakeholder methods which are often important in group settings (Marttunen et al. 2017). Methods that could be used together with MCDA include also causal maps (Montibeller and Belton 2006), reasoning maps (Montibeller et al. 2008), cognitive maps (Eden 2004), reference point approaches (Lahdelma and Salminen 2001; Lahdelma et al. 2005), and argumentation analysis (Matsatsinis and Tzoannopoulos 2008). • Spatial decision-making. MCDA methods are increasingly used to help address spatial decision problems (Malczewski 2006; Greene et al. 2011; Malczewski and Jankowski 2020). Such problems typically call for the evaluation of alternative locations for industrial or other facilities or the evaluation of alternatives which have geographically varying outcomes. In this context, the multicriteria data is visualized as map layers in geographical information systems (GISs). The use of GISs brings in additional aspects such as how information can be best presented with maps and what impacts the GIS software has on the MCDA process (Ferretti and Montibeller 2016; Malczewski and Jankowski 2020). Spatial decision-making has given rise to new theoretical results, too (see, e.g., Harju et al. 2019). In siting problems such as the siting of facilities, one affected stakeholder group consists of the potential neighbors of the facility: thus, there may be a need to involve a large number of citizens in

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the decision support process (see, e.g., the wind farm siting study in which a GIS-based decision support system was developed for the collaboration between the planners and the public over the web (Simao et al. 2009)). The adequate involvement of the public can be a key enabler of perceived success, because the public can provide information and views from the local level, whereas the planners and the experts are viewing the decision problem from the strategic level. In the earlier GIS-based MCDA literature, attention has been given to the aggregation of preferences (Malczewski and Rinner 2015). Recently, there has been growing interest in considering group aspects more broadly (Jelokhani-Niaraki 2019, 2021; Malczewski and Jankowski 2020). • Portfolio decision analysis. In many problems, decision-makers have to address multiple decision items in conjunction (Salo et al. 2011). Such problems arise, for example, in environmental management, where the decision-makers may seek to identify a good set of policy actions to cut greenhouse gas emissions or to purchase many pieces of land to form a conservation network (see, e.g., Lahtinen et al. 2017b). The decision items are usually linked through shared constraints: this is the case, for example, when allocating resources to different organizational units, because the resources that are given to any one unit will have an impact on how much resources remain available for the others (see Kleinmuntz 2007). These kinds of interdependencies can be captured through methods of portfolio decision analysis (see, e.g., Liesiö et al. 2007, 2008, Phillips and e Costa 2007) which offers recommendations on all decision items jointly. Even if there are no interdependencies among the items, portfolio modeling can still be helpful, because it allows the group members to search for “win-win” decision combinations that would be acceptable to all group members. Yet caution may be needed when increasing the diversity of items that are assessed simultaneously, because it may be difficult to develop a single model which would be meaningful and applicable to very different kinds of items.

Behavioral Issues and Biases The behavioral perspective is important in the practice of MCDA because people from diverse backgrounds are involved in a process in which preferences and other subjective issues are central. Behavioral factors such as biases and socio-emotional dynamics influence the effectiveness of the MCDA process. Biases are behavior- and judgment-related tendencies. For example, the loss aversion bias refers to a tendency to assign more importance to changes that are perceived as losses instead of gains. The so-called motivational biases relate to strategic or unintentional advancement of own interest or the interests of a stakeholder. A recent review of biases in MCDA is provided by Montibeller and Von Winterfeldt (2015). For an extensive list of cognitive biases in general, see Wikipedia (2020). Behavioral issues are almost always present in model-based interventions (Hämäläinen et al. 2013; Franco and Hämäläinen 2016).

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Behavioral factors should be considered both in the design of the MCDA group process and in its actual implementation. First, it is important to become aware of behavioral factors and their possible influence. Reflecting on one’s own behavior and the behavior of the group may suggest ways to improve the process or to correct poor choices made earlier. Second, there are bias mitigation techniques and other practices which can help to reduce the risks of biases and other behavioral effects. The following ideas and questions are examples of things that can be considered: • Behavioral impacts and process design: Behavioral phenomena interact with procedural choices such as the framing of preference elicitation questions. For example, due to the loss aversion bias, it can matter whether the hypothetical questions used in preference elicitation are framed as losses or gains. Also the choice of measuring stick attributes to be used in the preference elicitation phase can impact the results (see, e.g., Anderson and Hobbs 2002, Lahtinen and Hämäläinen 2016). Due to the measuring stick bias, the alternatives that are strong in the measuring stick attribute may become favored in the process. Another example is the splitting bias, whereby an objective could receive too much weight if it has been split to too many sub-objectives (Pöyhönen et al. 2001; Hämäläinen and Alaja 2008). Procedural choices can also stimulate or hinder socio-emotional phenomena such as trust generation. The problem-solving team may consider questions such as the following: What are the behavioral factors such as cognitive or motivational biases that can influence the decision process? What are the possible impacts of these factors in each phase of the process? Do the biases and other behavioral factors pose risks and could these risks be mitigated? For example, should the risk of narrow thinking be mitigated, e.g., by increasing group heterogeneity or by appointing a “Devil’s advocate” whose role is to challenge the assumptions made by the group and to bring up alternative perspectives in discussions? How is the process documented and evaluated from the behavioral perspective? • Mitigation of biases: Biases pose a risk particularly if their effects are likely to accumulate, thereby favoring some given alternative or a subset of alternatives so that the rank order of the alternatives is affected. General approaches for mitigating biases include, e.g., the use of iterative processes with consistency checks and feedback, the use of multiple approaches, and the averaging of results obtained with different approaches. Furthermore, a number of bias mitigation techniques are presented in Montibeller and Von Winterfeldt (2015), and these may be helpful. Lahtinen et al. (2020) describe new techniques for mitigating risks related to loss aversion and the measuring stick effect and also for preventing the accumulation of biases. The design of bias mitigation can also be assisted by computational analyses. This may help to tailor the bias mitigation techniques for the situation at hand and also to help prioritize bias mitigation efforts. • Socio-emotional phenomena: Human decision-making is an emotional process, and group behavior is strongly driven by socio-emotional dynamics (Faure et al. 1990; Leppänen et al. 2018; Martinovsky 2015). See also chapters ▶ “Role of Emotion in Group Decision and Negotiation” and ▶ “Negotiation Processes:

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Empirical Insights.” This needs to be taken into account in how group members are engaged. One example of socio-emotional dynamics is the group think phenomenon (Janis 1982) in situations where the group makes consensual choices without critical consideration of alternative viewpoints. The risk is greater in highly cohesive groups. It is necessary to consider how socio-emotional effects are to be accounted for during the process and in its facilitation. A dialogical approach can be useful (see Slotte and Hämäläinen 2015). Even the location of workshops and their physical setup merit attention. • Trust and interaction: Have the group members collaborated on earlier occasions? Is it likely that strongly opposing viewpoints will be presented? What is the prior level of trust that exists among the group members? Is there a willingness to collaborate in a consensus-seeking spirit in an open dialogue? Should the facilitator promote trust among the group members and how? Furthermore, to ensure the trustworthiness of the process, it can be helpful to address considerations such as comprehensiveness and balance. For instance, are all relevant interests and sources of information duly represented? Or are some stakeholders disproportionately under/overrepresented? • Path dependency: The facilitators (and even other members) of group decision processes need to recognize that usually there are alternative paths that can be taken in the decision support process and that these paths can lead to different outcomes. Path is the sequence of steps taken in the MCDA process – it represents the actual realization of the planned process. It is created from the interactions between all the factors in the problem-solving process including the people involved and their assumptions, expertise, and interests, and also the methods used, and the contextual aspects. Major forks along the path include, for example, the choice of the group members, how the decision problem is defined, the choice of the MCDA method and the preference elicitation techniques used, and how the decision alternatives are evaluated with respect to the criteria. Considering the path offers an integrative perspective which can help understand the overall impact of behavioral phenomena (see Hämäläinen and Lahtinen 2016; Lahtinen and Hämäläinen 2016).

Guidelines for Designing MCDA-Assisted Decision Support Processes Against the backdrop of the processual, methodological, and behavioral considerations outlined in the previous sections, we next provide guiding questions and suggestions to support the design of MCDA processes. However, we also note that due to the huge variety of decision contexts and many variants of MCDA methods, it does not appear warranted to provide definitive guidelines. Yet, design steps such as the following can be considered: • Identification of the potential need for MCDA approaches. A starting point for the development of an MCDA-assisted group decision support process is the

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identification of a decision problem which can benefit from an explicit articulation of multiple criteria and alternatives. Already in this step, the initiators of the MCDA process have a tentative understanding of the decision problem and the context, the real decision-makers and the stakeholders, etc. The case for making a major commitment to and investment in a formalized decision support process is most compelling in problems where the decision consequences are significant, the decision is irreversible, and there are reasons for not postponing the decision substantially and when there is ample time for the analysis. Also, if it is expected that the same decision problem will be encountered on a recurring basis, a sizeable investment may be warranted even if it would not be justified by the significance of a single isolated decision. Depending on the problem context, the MCDA process can be limited to the initial phases without proceeding to data collection or quantitative modeling, as these initial activities may be sufficient for increased understanding and improved communication, for instance. Moreover, it may be pertinent to assess what benefits the adoption a multi-modeling approach could bring. • Setting up the project. At the outset of the design, the issue of project leadership (Hämäläinen et al. 2020) needs to be considered. Assigning the leadership role to a designated individual with sufficient knowledge and authority can help the group keep the big picture in mind while ensuring that the process is impartial and that fair documentation is produced. The leader can be, e.g., the modeling expert, facilitator, or representative of the body commissioning the study. In general, the personal and professional competence profile of the facilitator is an important design issue. Representatives of the stakeholders are rarely experts in MCDA methodologies, and consequently a facilitator with strong methodological skills can be essential in ensuring that models are deployed correctly and productively. The specific competencies and past expertise of the facilitator should be explicitly recognized during the design phase (see, e.g., Franco and Montibeller 2010; Ormerod 2014). In particular, the MCDA process should not be designed “in the abstract,” resulting in mere role descriptions, without considering the specific competencies of the individuals who will enact these roles. In this phase, it can be relevant to consider also what constraints (e.g., temporal, technical, and budgetary) apply to the decision support process. • Elaboration of decision context. This phase essentially consists of systems thinking regarding the decision problem and the interconnected systems related to the problem. This involves the explicit specification of the decision that is to be supported, assisted by guiding questions such as the following: Who are the real and final decision-makers? What is their role in relation to the decision problem? Do the decision-makers expect that the process produces a decision recommendation, or do they seek to receive information more generally, e.g., about stakeholder views or the alternatives? Which organizations and stakeholder groups are impacted by the decision and how? What commitments and time frames are involved? Is there a need to justify and legitimize the results? Can the decision be modified or revoked later on? Will the same decision problem be encountered repeatedly, or does the decision pertain to one-of-a-kind problem? Another key

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consideration is whether the decision is to be taken in isolation or in connection with other decisions. • Identification of participants. The identification of the group members who will be engaged in the MCDA process either as decision-makers, as sources of expertise, or as representatives of stakeholder groups is an important step which is largely guided by the preceding steps of problem identification and elaboration. In order to build legitimacy and trust, it is pertinent to address considerations such as comprehensiveness and diversity of participants. For instance, are all relevant interests and sources of information represented? Or are some stakeholders disproportionately under/overrepresented? Furthermore, how familiar are the group members with the decision problem? On what aspects of the decision problem do the group members have knowledge? • Design of the decision support process. The detailed design of the process involves a series of choices about which MCDA methods will be used and how they will be deployed. These design choices need to be viewed from several perspectives, including the behavioral one and the viewpoint of practicality. The temporal order of the process steps also calls for close attention, because it may have significant consequences due to behavioral effects (Hämäläinen and Lahtinen 2016). See also chapter ▶ “Behavioral Considerations in Group Support.” Checkpoints can be planned into the process, where the group can review the results from the completed steps and possibly redirect the process (Lahtinen et al. 2017a). Overall, the process design can benefit from an explicit specification of the different roles in which the group members participate in the process. Here, it can be fruitful to consider the cognitive styles of the group members; see chapter ▶ “Impact of Cognitive Style on Group Decision and Negotiation.” Some group members may take part in the identification of the relevant decision criteria, in view of their understanding of the organization’s values and objectives; but they may also take part in the process as suppliers of factual information about the impacts of the different alternatives, for example. Particularly in long-lasting policy processes, different groups may participate in different stages and in different tasks. For instance, there could be a small initial core group for the structuring of the MCDA model, followed by the prioritization activities of a larger group and the synthesis of results by a steering group. In addition, the design should acknowledge how much time and effort the group members can devote to the process and which methodological tools are best aligned with such requirements (e.g., workshops, video conferences, Internet-based surveys). Another question is which, if any, software tools should be used (see, e.g., Mustajoki and Marttunen 2017). If the group members address several decision problems together, it may be possible to apply methods of portfolio decision analysis to develop solutions that may be superior to those reached by analyzing individual problems one by one (Salo et al. 2011). The portfolio approach can help at identifying portfolios of “win-win” recommendations which are deemed acceptable by most or all group members. There is an extensive literature on the design of participation in general which could also be considered. Bayley and French (2008) provide a discussion from the perspective

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of group decision-making literature. In general, the design phase should yield a clear plan of how the process will be carried out. Such a plan is likely to enhance the legitimacy of the process. It may also serve as communication tool which clarifies how the different group members can expect to benefit from their participation (Hämäläinen et al. 1992). • Execution of the decision support process. This involves the use of the MCDA methodologies and tools in accordance with the process design, proceeding through phases such as the elaboration of the values, objectives, and criteria; elicitation of preferences; development of alternatives; assessment of decision alternatives; synthesis of decision recommendations; and discussion of results, possibly in a workshop setting. In some situations it may be pertinent to adjust the design in response to feedback that accumulates in the course of the decision support process (see, e.g., Hämäläinen et al. 2001; Marttunen and Hämäläinen 2008). The execution of the process may benefit from the involvement of a “Devil’s advocate” whose role is to challenge the assumptions made by the group and to bring up alternative perspectives in discussions. • Evaluation of the decision support process. In the ex post evaluation of the decision support, it is necessary to consider, e.g., to what extent the context may have changed and were the right stakeholders included in the process. Moreover, the ex post assessment frameworks proposed by Schilling et al. (2007) and Hamilton et al. (2019) consider criteria such as transparency, creativity, dialogue orientation, efficiency, satisfaction, and impact, to name a few. Reflecting on the possible impacts of biases and other behavioral effects is also important (see, e.g., Hämäläinen et al. 2010; Scott et al. 2016; Zare et al. 2020).

MCDA Methods in Action In this section, we exemplify the use of MCDA methods in the light of selected case studies demonstrating some key aspects of MCDA-based group decision support. Mustajoki et al. (2007) (see also Hämäläinen 1988; Hämäläinen et al. 2000; Mustajoki et al. 2006) consider the development of models for assessing alternative strategies in response to a nuclear emergency situation. These models – which were constructed through a close dialogue with key decision-makers (see also Hämäläinen et al. 2000) – made it possible to evaluate different remediation alternatives with regard to the attributes that captured main impacts (e.g., human health, social impacts, economic losses, environmental impacts). An important benefit of using these models repeatedly in facilitated workshops was that the learning experiences allowed the decision-makers to acquire a better understanding of relevant alternatives and tradeoffs. Many of these models and decision support tools (such as Web-HIPRE) have been subsequently incorporated into RODOS, a real-time online decision support system which supports the development of countermeasure strategies in recognition of different time horizons (Geldermann et al. 2009). The use of MCDA tools for nuclear power in Finland started already in the 1980s when the Parliament of Finland discussed whether or

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not a fifth nuclear reactor should be constructed. At that time, MCDA tools served to clarify differences of opinion among different political groups (Hämäläinen 1988). Könnölä et al. (2011) report a case study where national research priorities for the forestry and forest-related industries were developed in 3 months by engaging more than 150 people. Due to the tight schedule, the process relied extensively on the webbased solicitation of prospective research themes proposed by members of the research community. The themes were then commented on and evaluated by designated reviewers with regard to three criteria: feasibility, novelty, and industrial relevance. Based on these valuations, shortlists of most promising themes were generated with the Robust Portfolio Modeling (RPM) methodology (Liesiö et al. 2007). The final priorities were developed in decision workshops where the RPM results helped ensure that the attention could be focused on the most promising themes in view of the preceding consultation and multicriteria evaluation process. Analogous RPM-based processes have supported the development of strategic product portfolios (Lindstedt et al. 2008), the establishment of priorities for international research and technology development programs (Brummer et al. 2008, 2011), and the selection of infrastructure maintenance projects at the Finnish Transport Agency (Mild et al. 2015). An interesting feature of the application presented in Mild et al. (2015) is that the RPM methodology was applied repeatedly over several consecutive years. Harris-Lovett et al. (2019) describe a collaborative decision analysis process in which MCDA methods were combined with stakeholder analysis and scenario planning to support nutrient management in the San Francisco Bay Area. In this application, the aim was to engage people in thinking about the issues, to improve communication, and to collect information. More specifically, there was an interest to find areas of agreement and disagreement among stakeholders, to evaluate alternative options from a range of perspectives, and to identify issues requiring further investigation. Initially, interviews were carried out with 32 stakeholders in order to better understand the decision-making context, to develop objectives and scenarios, and also to collect ideas concerning possible nutrient management alternatives, for example. Subsequently, nine stakeholders were involved in the preference elicitation phase and in the evaluation of decision alternatives. These nine stakeholders were selected using a cluster analysis technique so that the selected stakeholders’ views would represent the opinions of the larger set of stakeholders as comprehensively as possible. The quantitative results of this study included the overall evaluations of alternatives under three future scenarios. The preference statements by different stakeholders were not aggregated. Rather, insights were sought by comparing the results based on the statements expressed by different stakeholders. Interestingly the authors suggest that the low ranking of one of the alternatives could be explained with the lack of familiarity concerning the technology that the alternative is based on. This demonstrates how the results of the MCDA process may depend on the people involved.

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Bell et al. (2003) consider uses of MCDA methods in integrated assessment (IA) where the aim is to capture interactions of physical, biological, and human systems so as to better understand long-term consequences of environmental and energy policies (e.g., limits on greenhouse gas emissions and other strategies for the mitigation of climate change). Specifically, they organized a workshop in which climate change experts used several MCDA methods to rank hypothetical policies for abating greenhouse gas emissions, using data outputs from integrated assessment models. These methods helped group members understand policy tradeoffs as well as complex interdependencies among value judgments, data outputs, and recommended decisions. Inspired by encouraging results of their case study, Bell et al. (2003) outline alternative approaches for the use of MCDA methods in integrated assessment. Bana e Costa et al. (2006) helped the Portuguese Institute for Social Welfare to adopt a systematic and transparent decision process for the development and renewal of the social infrastructures whose role is to provide funding and services to children, the elderly, and the disabled. This process – which was based on decision conferencing and multicriteria modeling – engaged key decision-makers in the three main phases of problem structuring, evaluation, and prioritization. The proposed sociotechnical process was perceived to improve the transparency of decision-making, the “rationality” of resource allocation decision, and the cost-effectiveness of decisions. Belton et al. (1997) report experiences from the development of strategic action plans for the department of a large UK hospital trust. Their case study was based on the combined use of (i) the strategic options and strategic analysis (SODA) in the problem structuring phase and (ii) the MAVT analysis during the evaluation of decision alternatives. The study was carried in a 2-day facilitated workshop where the joint use of different methodologies helped the group make progress toward the definition of a shared strategic direction while it also promoted a shared and improved understanding of key issues. Building on this case study, Belton et al. (1997) also discuss what benefits may arise from the integration of these two approaches and what implications such an integration has for the development of methodologies and tools. In many countries, MCDA tools are widely applied in problems of water and environmental management (Hajkowicz 2008; Kangas et al. 2008; Kiker et al. 2005; Linkov and Moberg 2011). For example, the Finnish Environment Institute has adopted systematic processes in order to guide its decisions on water regulation (Marttunen and Hämäläinen 2008). In many ways, these processes illustrate the different phases we have discussed in this chapter, particularly as concerns the identification and involvement of stakeholders, collaborative and iterative development of alternatives, MCDA-assisted evaluation of alternatives in workshops, and communication of results to citizens over the Internet. These processes are noteworthy in that explicit attention has been paid to potential biases and their mitigation. Most recently, there has been an interest in discovering and mitigating biases related to the structuring of the objectives hierarchy, i.e., the value tree (Marttunen et al. 2018, 2019).

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Outlook for the Future The outlook for MCDA methods appears promising due to the increasing importance of understanding, managing, and acting in complex wholes with multiple stakeholder groups and multiple interests. This endeavor calls for structured problem-solving approaches. Furthermore, in order to succeed, these approaches and accompanying tools must be applied with due care. In particular, it is crucial to pay attention to the behavioral and socio-emotional phenomena arising in the group situation as well as to the correct use of tools: 1. The behavioral perspective brings in new ideas and methods. Recently, the behavioral perspective has gained increasing attention as expressed by the introduction of the term behavioral operational research (BOR) (Hämäläinen et al. 2013; Franco and Hämäläinen 2016). Within this lively stream of research, researchers have introduced new perspectives and methods that help develop the practice of group MCDA. One example is ethnomethodology which has helped understand the phenomena occurring in real-time live situations; see chapter ▶ “Group Decision Support Practice “as it happens””. Also the role of emotions is receiving increasing interest (chapter ▶ “Role of Emotion in Group Decision and Negotiation”). These trends are likely to affect how MCDA is carried out in practice. For example, it may become possible to use emotional stimuli beneficially in creative processes or to utilize procedures designed to minimize the fear of losing face. Furthermore, advances in neuroscience help understand cognitive and emotional phenomena related to group decision-making. For example, methods of neuroscience have been recently employed to study the inquiry and advocacy modes as well as related emotions in group decisionmaking (Leppänen et al. 2018). Roselli et al. (2019) used neuroscience methods to inform the development of data visualizations. See also chapter ▶ “Neuroscience Tools for Group Decision and Negotiation”. Recently, there has also been rapid development in the areas of big data and affective computing (see, e.g., Shoumy et al. 2020). This can mean that there will be direct ways to evaluate and even to generate emotional responses in computer-supported group settings, which can give rise to ethical issues as triggering emotions can influence decision-making. Emotional criteria can perhaps be more often seen in the MCDA models used in group decision-making in the future. The mitigation of biases is an important practical question, which is attracting increasing attention. One possibility is to use computational simulations to assist in the design of bias mitigation strategies before engaging the real group members (Lahtinen et al. 2020). 2. Technological progress. Recent advances with information and communication technologies offer new possibilities for interfacing group members with MCDA models. For instance, mobile applications can be utilized to invite preference statements or other judgments from the participants. Moreover, virtual meetings over the Internet are associated with a host of new challenges and

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opportunities. It has also become easier to incorporate different kinds of inputs in decision models so that both quantitative data (e.g., scores, weights, values) and qualitative data (e.g., verbal descriptions, visual material) can be synthesized. Such an integration will enable the development of decision support tools that contain richer information, for example, in the context of e-democracy (Hämäläinen 2003; French et al. 2007). MCDA methods can help in the development of large-scale group participation systems (chapter ▶ “CrowdScale Deliberation for Group Decision-Making”), which are connected, e.g., to big data and social media. Digital platforms are becoming increasingly common in many areas, and it is likely that they will in the future include group collaboration platforms where MCDA methods could be available. The important questions to be addressed with the use of technological developments include, e.g., how remote collaboration over the web influences the formation of trust (chapter ▶ “Group Support Systems: Experiments with an Online System and Implications for Same-Time/Different-Places Working”). Gamification and serious games is an emerging technological field which offers a broad array of new methodologies that can prove useful in participatory processes. For a recent survey, see Bakhanova et al. (2020). One could use gamification, e.g., in the preliminary analysis and problem structuring phase without explicitly involving the real decision-makers. Gamification can also be used together with agent-based modeling to evaluate potential outcomes from different scenarios. It has already been tested in online preference elicitation (Aubert and Lienert 2019). Overall, technological progress will make the use of multi-modeling easier and more attractive. 3. Building on experiences and creating competencies. There is a strong need for reflective analyses of high-impact MCDA case studies. Such analyses should consider contextual problem characteristics as well as behavioral and socioemotional factors such as those highlighted in chapter ▶ “Role of Emotion in Group Decision and Negotiation.” The goal is to report lessons learned and good practices that help design and implement decision support processes in other contexts as well. For illustrative discussions in the area of environmental management, see, e.g., Hämäläinen (2015) and Lahtinen et al. (2017a). It is plausible that shared repositories of process and model templates will be created within communities of group members for specific decision problems (see, e.g., Cockerill et al. 2019). Such repositories could be embedded in online group collaboration platforms. More controlled and well-designed experiments are still needed, e.g., to design and evaluate ways of mitigating biases. At times, such experiments can be combined with real decision support processes (see, e.g., Hämäläinen and Alaja 2008). Furthermore, one needs to consider the development of professional competencies that are needed in facilitation, as discussed, e.g., chapters ▶ “Group Decision Support Practice “as it happens”” and ▶ “Behavioral Considerations in Group Support.” A further set of competencies is discussed by Hämäläinen et al. (2018) in relation to the concept of

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systems intelligence (Saarinen and Hämäläinen 2004; Hämäläinen and Saarinen 2008) which refers to “our ability to behave intelligently in the context of complex systems involving interaction, dynamics and feedback.” The systems intelligence-related competencies, i.e., systemic perception, attunement, positive attitude, spirited discovery, reflection, wise action, positive engagement, and effective responsiveness, serve to understand and improve the practice of MCDA. For example, attunement to the group problem-solving process can be important for effective collaboration.

Conclusion We conclude this chapter by reasserting our belief in the pivotal contribution that MCDA methods can bring to the solution of complex group decision-making problems. As exemplified by the growing body of reported applications, MCDA methods offer structured frameworks for addressing multifaceted problems in which group members’ preferences need to be captured and synthesized to inform decision-makers, often by way of producing well-founded decision recommendations. Many of the benefits of these methods stem from their ability to foster collective learning processes and to promote a shared understanding of the problem, including the many-faceted relations between decision objectives and decision alternatives. MCDA-assisted group decision processes are more likely to succeed when there is a sound understanding of behavioral aspects, such as socio-emotional dynamics as well as cognitive and motivational biases. These aspects need to be accounted for in the design of the MCDA-based group process and its implementation. Even the process needs to be documented to support critical reflection and learning. Overall, we believe that the potential demand for MCDA methods and tools in group decision support will continue to grow. One reason for this is that most of the significant problems faced by organizations are increasingly systemic in that they involve many interrelated issues and affect many stakeholder groups whose interests need to be acknowledged and accounted for. In addition, the development of new methodologies and technologies, combined with new perspectives into human behavior, opens up exciting opportunities for enhancing group decision processes with MCDA approaches.

Cross-References ▶ A Group Multicriteria Approach ▶ Behavioral Considerations in Group Support ▶ Conflict Resolution Using the Graph Model: Matrices, Uncertainty, and Systems Perspectives

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▶ Crowd-Scale Deliberation for Group Decision-Making ▶ Group Decision Support Practice “as it happens” ▶ Group Decision Support Using the Analytic Hierarchy Process ▶ Group Decisions: Choosing a Winner by Voting ▶ Group Decisions: Choosing Multiple Winners by Voting ▶ Group Support Systems: Experiments with an Online System and Implications for Same-Time/Different-Places Working ▶ Holistic Preferences and Prenegotiation Preparation ▶ Impact of Cognitive Style on Group Decision and Negotiation ▶ Multiple Criteria Decision Support ▶ Multiple Criteria Group Decisions with Partial Information About Preference ▶ Negotiation Processes: Empirical Insights ▶ Neuroscience Tools for Group Decision and Negotiation ▶ Participatory Modeling for Group Decision Support ▶ Role of Emotion in Group Decision and Negotiation Acknowledgments This research has been partly supported by the Platform Value Now project of the Strategic Research Council of the Academy of Finland (funding decision 314207).

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Multiple Criteria Decision Support Salvatore Corrente, José Rui Figueira, Salvatore Greco, and Roman Słowiński

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An Introduction to MCDA: Notation, Problematics, and Main Approaches . . . . . . . . . . . . . . . . . . Multiple Attribute Value Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outranking Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decision Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interaction Between Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robust Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Robust Ordinal Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stochastic Multicriteria Acceptability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recent Developments and MCDA Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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S. Corrente (*) Department of Economics and Business, University of Catania, Catania, Italy e-mail: [email protected] J. R. Figueira CEG-IST, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, Portugal e-mail: fi[email protected] S. Greco Department of Economics and Business, University of Catania, Catania, Italy Portsmouth Business School, Centre of Operations Research and Logistics (CORL), University of Portsmouth, Portsmouth, UK e-mail: [email protected] R. Słowiński Institute of Computing Science, Poznań University of Technology, Poznań, Poland Systems Research Institute, Polish Academy of Science, Warsaw, Poland e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_33

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Abstract

Multiple criteria decision support methodologies aim to assist decision makers in making difficult decisions when many conflicting viewpoints have to be considered. After introducing the main concepts and principles, some basic approaches to multiple criteria decision aiding are presented, with an emphasis on recent contributions. Three main families of aggregation methods are distinguished by the type of the preference model involved: multiple attribute value theory, outranking-based methods, and methods using sets of decision rules. They are analyzed in detail, together with the way of providing robust recommendations by means of robust ordinal regression and stochastic multicriteria acceptability analysis. A brief overview of recent trends in the field is also included. All the concepts and methods are presented from the perspective of a single decision maker since group decisions involving multiple evaluation criteria have to solve the criteria aggregation problem taking into account preferences of particular decision makers. Keywords

Group decision · Multiple criteria analysis · Preferences · Decision support system · Multiple attribute decision-making · Preference modeling

Introduction What do the terms multiple criteria decision analysis and multiple criteria decision aiding mean1? In the following, without seeking for being exhaustive, we report some statements by well-known researchers in the field, which help to characterize the goals of multiple criteria decision analysis and multiple criteria decision aiding. 1. Bell 1979: Almost all the issues that decision makers face in actuality involve multiple objectives that conflict in some measure with each other. In such issues, decisions that serve some objectives well will generally satisfy other objectives less well than alternative decisions, which, however, would not be so satisfactory for the first group. The decision maker then must select from among the possible decisions the one that somehow establishes the best mix of outcomes for his multiple conflicting objectives. (. . .) Such problems include the use of energy resources, the management of the environment, the development of water resources, and the expansion of regional development. 2. Keeney and Raiffa 1976: The theory of decision analysis is designed to help the individual make a choice among a set of prespecified alternatives. (. . .) The aim of the analysis is to get your head straightened out.

1

In this chapter, we shall use the acronym MCDA to refer to both multiple criteria decision analysis and multiple criteria decision aiding.

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3. Roy 2005: Decision aiding is the activity of the person who, through the use of explicit but not necessarily completely formalized models, helps obtain elements of responses to the questions posed by a stakeholder in a decision process. 4. Belton and Stewart 2002: (. . .) we use the expression MCDA as an umbrella term to describe a collection of formal approaches which seek to take explicit account of multiple criteria in helping individuals or groups explore decisions that matter. 5. Saaty 2005: The purpose of decision-making is to help people make decisions according to their own understanding. (. . .) decision-making is the most frequent activity of all people all the time (. . .) This book is devoted to group decision-making, but it is apparent that any group decision is originally based on the decision of each single decision maker being a component of the group. The single decision makers are all facing, in general, a multiple criteria decision problem. For this reason, in this chapter, we are going to describe the main ideas and the basic principles of multiple criteria decision aiding methodologies. The concepts used here are useful also for methodologies related to group decision introduced in chapters ▶ “Multicriteria Methods for Group Decision Processes: An Overview” and ▶ “A Group Multicriteria Approach”. Our chapter is therefore articulated in the following way: in the section “An Introduction to MCDA: Notation, Problematics and Main Approaches,” we give an introduction to MCDA presenting the notation used in the chapter, the main problematics dealt with, and the three aggregation methods being mostly used in the field, which are multiple attribute value theory (section “Multiple Attribute Value Theory”), outranking methods (section “Outranking Methods”), and decision rules (section “Decision Rules”). A discussion on interactions between criteria is provided in the section “Interaction Between Criteria.” In the section “Robust Recommendations,” we will focus our attention on the robustness concerns and, in particular, on robust ordinal regression (section “Robust Ordinal Regression”) and stochastic multicriteria acceptability analysis (section “Stochastic Multicriteria Acceptability Analysis”). Finally, section “Recent Developments and MCDA Applications” collects a brief summary of recent developments and applications of MCDA.

An Introduction to MCDA: Notation, Problematics, and Main Approaches In MCDA (see Greco et al. 2016) for an updated state-of-art survey on this topic), a finite set of alternatives A ¼ {a, b, c, . . .} is evaluated on the basis of a finite and coherent family of evaluation criteria G ¼ {g1, . . ., gj, . . ., gn} where G is coherent if it satisfies the requirements of exhaustiveness, cohesiveness, and nonredundancy (Roy 1996): • Exhaustiveness: All the relevant evaluation criteria are taken into account. This is to avoid situations in which two alternatives a and b have the same evaluation on criteria from G but a and b are not considered indifferent.

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• Cohesiveness: Given four alternatives a, b, c, d where a and b are indifferent, and c and d are obtained from a and b, respectively, by decreasing the performance of a on one criterion, thus getting c, and increasing the performance of b on also one criterion, thus getting d, then d should be considered at least as good as c. • Nonredundancy: Removing one of the criteria from G, one of the two requirements above is not satisfied anymore. This means that none of the aspects taken into account in the considered problem is counted more than once. The criteria in G are representing different aspects of evaluation of the alternatives considered in the decision problem the DM is faced with. Let Ej denote the set of all possible performance levels when considering alternative a on criterion gj. In other words, Ej is the scale of criterion gj which has a quantitative or a qualitative nature. In general, in the first case, Ej  ℝ, while in the second, Ej is composed of qualitative judgments that can assume linguistic forms such as those considered in the chapter ▶ “Group Decisions with Linguistic Information: A Survey.” For example, considering an alternative being a sport car evaluated on two criteria, acceleration and comfort, the performances of each car on the acceleration are expressed on a quantitative scale (for example, 5 secs to pass from 0 to 100 km/h), while the performances of each car on the comfort can be expressed in qualitative terms, such as bad, medium, good, and so on. In the following, by gj(a), we shall denote the quantitative or qualitative performance of a on gj, for all a  A, and for all gj  G. In general, each criterion gj is associated with an increasing or a decreasing direction of preference. On the one hand, gj has an increasing direction of preference if the greater the performance gj(a), the better is a on gj. On the other hand, gj has a decreasing direction of preference if the lower the performance gj(a), the better is a on gj. In the previous example, acceleration can be considered as a criterion having a decreasing direction of preference, while comfort can be considered as a criterion having increasing direction of preference. We used above “in general,” since there could be criteria that have not a monotone direction of preference. In this case, we are in presence of an attribute. For example, let us assume that the DM has to choose the locality where to spend his holidays next summer. To choose the best place, he will take into account the average temperature of the considered places during the summer time. Thinking about this attribute, the DM will probably prefer an average temperature of 35 to 25 or 45 . This means that this attribute has neither an increasing direction of preference (in this case, 45 had been preferred to 35 ) nor a decreasing direction of preference (in this case, 25 had been preferred to 35 ). In what follows, we shall assume that criteria have an increasing or a decreasing direction of preference. Although this is the most frequent assumption in MCDA, in recent years, many contributions have been presented taking into account nonmonotone criteria (see, for example, Doumpos 2012; Ghaderi et al. 2017; Kadziński et al. 2020; Tehrani et al. 2012). Three different decision aiding problem statements (problematics) are distinguished in MCDA: choice, ranking, and sorting. In choice problems, one has to choose the best alternative or the best subset of alternatives among those at hand

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by rejecting all the remaining alternatives, considered bad (see, for example, Bottero et al. 2019; Govindan et al. 2017; Malekmohammadi et al. 2011); in ranking problems, one has to rank-order all alternatives from the best to the worst with the possibility of some ties and incomparabilities (see, for example, Angilella et al. 2016a; Shanian and Savadogo 2006); finally, in sorting problems, one has to assign each alternative to one or more contiguous classes that have been defined a priori and ordered from the best to the worst taking into account the preferences provided by the DM (see, for example, Costa et al. 2018; Morais et al. 2014; Rocchi et al. 2018). The starting point of any decision aiding problem is the construction of the performance table.

Anyway, looking at the performance table above, the only objective information that one can see is the dominance relation in the set of alternatives, for which a dominates b if and only if a is at least as good as b for all criteria and better for at least one of them. For the sake of simplicity, and without loss of generality, we shall assume that all criteria have an increasing direction of preference. Consequently, we shall write that a dominates b if and only if gj(a) ⩾ gj(b) for all j ¼ 1, . . ., n, and there exists at least one gj  G such that gj(a) > gj(b). Even if, as stated above, the dominance relation is a really objective information that can be obtained from the performance table, it is very poor since, in general, when comparing a and b, a is better than b on some criteria, while b is better than a for the other criteria. Consequently, neither a dominates b nor the opposite situation occurs, thus the dominance relation leaves many alternatives noncomparable. To deal with one of the three problem statements mentioned above, there is, therefore, the need to aggregate the performances of alternatives on the considered evaluation criteria, aiming to get a comprehensive assessment of the alternatives at hand, and to use this assessment for working out a recommendation proposed to the DM. In order to get a recommendation that would be convincing for the DM, the aggregation must take into account DM’s preferences which underline the relative importance of evaluation criteria in the comprehensive assessment. The aggregation thus leads to a comprehensive preference model that translates a value system of the DM at the current stage of the decision process. Three different aggregation methods, very well known in MCDA literature, are associated with the following three preference models, which are value functions (Keeney and Raiffa 1976), outranking relations (Roy 1996), and decision rules (Greco et al. 2001):

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• A value function is a map U : A ! ℝ assigning to each alternative a  A a real number U(a) being representative of the comprehensive assessment of a in the considered problem; the greater the value of U(a), the better a is. • An outranking relation S is a binary relation such that aSb iff a is at least as good as b; in general, aSb iff a majority of criteria is in favor of this statement, and there is not any criterion opposing too strongly to this outranking. • Decision rules link a recommendation in the considered problem with the performances of alternatives on selected criteria; these are logical statements that put on the condition side of a rule some threshold requirements on selected criteria, and on the decision side a recommendation concerning an alternative or a pair of alternatives that satisfied the above requirements; for example, “if the consumption is at least 20 km/l and the price is at most 15,000 euros, then the car is considered at least good”; the rules identify values that drive DM’s decisions – each rule is a scenario of a causal relationship between evaluations on a subset of criteria and a comprehensive judgment. In the following sections, we are going to describe more in detail the three aggregation methods and their associated preference models, putting an emphasis on their main assumptions that differentiate them, and listing the most known MCDA methods belonging to that aggregation family. When choosing a particular method of MCDA for a real-world decision problem, an analyst, together with the DM, have to answer a series of interrelated questions concerning the nature of an expected recommendation, the character of available preference information, and the type of preference model (Roy and Słowiński 2013).

Multiple Attribute Value Theory As already stated in the previous section, a value function assigns a real number to each alternative in A representing its comprehensive assessment in the problem at hand. The value function most used in the applications is the additive one. U ðg1 ðaÞ, . . . , gn ðaÞÞ ¼

n   X uj gj ðaÞ

ð1Þ

j¼1

where uj() are nondecreasing functions of gj(a), called marginal value functions, such that if gj(a) < gj(b), then uj(gj(a)) O uj(gj(b)). In the following, for the sake of simplicity and without loss of generality, we shall write U(a) and uj(a), instead of U(g1(a), . . ., gn(a)) and uj(gj(a)). In its simplest form, this additive value function is reduced to a weighted sum. U ð aÞ ¼

n X j¼1

wj gj ðaÞ

ð2Þ

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where wj > 0 for all criteria and wj/wi represents a trade-off between criteria gi and gj, that is, how much units one is willing to renounce on gi to have an increase of one unit on gj (Belton and Stewart 2002). Let us observe that these trade-offs (or substitution rates) are therefore dependent on the scale on which the performances of alternatives are defined. A basic assumption, not always satisfied in the real applications, is that the set of criteria G is mutually preferentially independent (Keeney and Raiffa 1976; Wakker 1989), meaning that each T  G is preferentially independent Q on G\T. Formally, T is preferentially independent from G\T iff for all aT , bT  Ej and for all gj  T Q cG∖T , dG∖T  Ej , gj  G∖T

ðaT , cG∖T Þ≿ðbT , cG∖T Þ , ðaT , dG∖T Þ≿ðbT , dG∖T Þ where ≿ denotes a weak preference between alternatives, aT and bT denote partial evaluations of a and b, respectively, on criteria from T, while cG\T and dG\T denote partial evaluations of some c and d, respectively, on criteria from G\T; (aT, cG\T) and (bT, cG\T) denote alternatives a and b, respectively, that got the same evaluations cG\T on criteria from G\T; (aT, dG\T) and (bT, dG\T) are defined analogously. In practical terms, T is preferentially independent of G\T if the preference between two alternatives (a and b) in not dependent on the common evaluation on the criteria from G\T (cG\T and dG\T) but on the evaluations on criteria from T only (aT and bT). Therefore, if T is preferentially independent of G\T and aT is preferred to bT, then the replacing of the common evaluations cG\T with the common evaluations dG\T does not invert the preference of a over b. We shall see more in detail in section “Interaction Between Criteria” that, in some cases, this assumption is not satisfied. The use of a value function provides a total-preorder of the considered alternatives.2 Indeed, given the value function U, a is strictly preferred to b, and we shall write a  b, iff U(a) > U(b), while a and b are indifferent, and we shall write a  b, iff U(a) ¼ U(b). Let us observe that a  b iff a ≿ b and not(b ≿ a), while a  b iff a ≿ b and b ≿ a. Let us conclude this section by recalling that, a very well-known method in the literature that can be included among the MAVT methods is the analytic hierarchy process (AHP; Saaty 1980) which application to group decision problems will be described in the chapter ▶ “Group Decision Support Using the Analytic Hierarchy Process.”

A total-preoder on A is a reflexive and transitive binary relation on A such that for all a, b  A, aRb, or bRa. In particular, reflexive means that aRa for all a  A, while transitive means that if aRb and bRc, then aRc for all a, b, c  A. 2

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Outranking Methods Differently from MAVT where each alternative is assessed using a real number, outranking methods are based on a binary relation, here denoted by S, where aSb iff a is at least as good as b. The main differences between the methods based on value functions and outranking methods are the following: • Methods based on value functions are compensatory, while outranking methods are not; this means that in MAVT, a very bad performance on one criterion can be compensated by a very good performance on another criterion while this is not the case in the outranking methods. • On the basis of the built value functions, a preference and an indifference relation are constructed in MAVT; in the outranking methods, in addition to the preference and indifference relations,3 an incomparability relation is also defined for which a and b are incomparable iff not(aSb) and not(bSa). The most well-known families of outranking methods are ELECTRE (ELimination Et Choix Trasuidant la REalité; see Figueira et al. (2013) for a full description of the ELECTRE methods and Govindan and Jepsen (2016) for a recent review of ELECTRE methods) and PROMETHEE (Preference Ranking Organization METhod for Enrichment of Evaluations; see Brans and Vincke (1985) for the paper introducing PROMETHEE methods and Behzadian et al. (2010) for a literature review on their use in MCDA). We are now going to briefly describe methods belonging to ELECTRE and PROMETHEE families.

ELECTRE Methods All ELECTRE methods are based on the comparison of the reasons in favor and the reasons against the outranking of an alternative a over an alternative b. The ELECTRE methods differ by the way these reasons are taken into account and for the different problems they are applied to. The ELECTRE methods are based on the concept of quasi-criterion. This means that each criterion gj  G is associated with two different thresholds, indifference qj and preference threshold pj, where 0 O qj O pj. These thresholds are introduced to take into account an arbitrariness, imprecision, or lack of knowledge in defining the performances of alternatives (Roy et al. 2014). Even if, in general, these thresholds are dependent on the performances (qj(gj(a)) and pj(gj(a))), in the following, we shall assume, without loss of generality, that they are fixed. qj represents the main difference between the performances of two alternatives on gj being compatible with their indifference on gj, while pj represents the lowest difference between the

3 On one hand, a is preferred to b, and we shall write aPb, iff aSb but not(bSa); on the other hand, a and b are indifferent, and we shall write aIb, iff aSb and bSa.

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performances of two alternatives on gj compatible with the preference of one over the other on this criterion. The construction of the outranking relation starts from the computation of the partial concordance index cj(a, b) for each gj and for each pair of alternatives (a, b)  A  A. cj(a, b)  [0, 1] is a nonincreasing function of the difference gj(b)  gj(a) and it expresses how much gj is in favor of the outranking of a over b. The general definition of cj(a, b) is the following:

cj ða, bÞ ¼ f

1

if

gj ðbÞ  gj ðaÞOqj ,

ðaSj bÞ,

pj  ½gj ðbÞ  gj ðaÞ pj  qj

if

qj < gj ðbÞ  gj ðaÞ < pj ,

ðbQj aÞ,

0

if

gj ðbÞ  gj ðaÞPpj ,

ðbPj aÞ:

If cj(a, b) ¼ 0, then gj is not in favor of the outranking of a over b. If, instead, cj(a, b)  ]0, 1[, gj is partially in favor of the same outranking. gj becomes strongly in favor of the outranking of a over b iff cj(a, b) ¼ 1. Adding up all the partial concordance indices, the comprehensive concordance index C(a, b) is obtained. Cða, bÞ ¼

n X

wj cj ða, bÞ

j¼1

where wj > 0 is an importance weight of criterion gj for all j ¼ 1, . . ., n, and, in n P wj ¼ 1. Let us observe that, differently from Eq. (2), the wj have the general, j¼1

meaning of a voting power (Roy 2005). This means that the value wj represents a relative importance of criterion gj inside the family of criteria G. As a consequence, they are not dependent on the scale on which the performances of alternatives are given. C(a, b)  [0, 1] and it represents how much the criteria in G are in favor of the outranking of a over b. On the basis of C(a, b), the concordance test is therefore satisfied iff C(a, b) ⩾ λ, where λ  ]0.5,1], called cutting level, represents the minimum portion of criteria that should be in favor of the outranking of a over b. Close to the definition of an indifference and a preference threshold, the DM can define a veto threshold vj. vj represents the lowest difference between the performances of two alternatives being incompatible with the preference of one over the other. This means that, even if the concordance test regarding alternatives a and b is verified, but the difference gj(b)  gj(a) exceeds vj, then a cannot outrank b. From this definition, it is easy to observe why the ELECTRE methods are non-compensatory methods, differently from those based on value functions. Similarly to cj(a, b), that defines how much gj is in favor of the outranking of a over b for each gj, the discordance index dj(a, b) defines how much gj is against the hypothesis about outranking. dj(a, b) belongs to the interval [0, 1] and it is a nondecreasing function of the difference gj(b)  gj(a) defined as follows:

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8 1 > > h i > > < g ðbÞ  g ðaÞ  p j j j d j ða, bÞ ¼ > > v j  pj > > : 0

if

gj ðbÞ  gj ðaÞPvj ,

if

pj < gj ð bÞ  gj ð aÞ < v j ,

if

gj ðbÞ  gj ðaÞOpj :

If dj(a, b) ¼ 0, then gj is not against the outranking of a over b. If, instead, dj(a, b)  ]0, 1[, gj is partially against the same outranking. gj becomes strongly against the outranking of a over b iff dj(a, b) ¼ 1. The ELECTRE methods take into account the reasons against the outranking of an alternative over another, in two different possible ways. On one hand, the concordance and the non-discordance test are performed separately. In particular, the non-discordance test is passed iff gj(b)  gj(a) < vj for all gj  G.4 On the other hand, the reasons in favor and against the outranking of a over b are put together defining the so-called credibility index σ(a, b). σ ða, bÞ ¼

Y gj  G :

1  dj ða, bÞ : 1  Cða, bÞ

dj ða, bÞ > Cða, bÞ σ(a, b) ⩾ λ means that the credibility of outranking reached a necessary cutting level λ to state that a outranks b. σ(a, b)  [0, 1] takes into account simultaneously the reasons in favor (C(a, b)) and the reasons against (dj(a, b)) the outranking of a over b. In particular, σ(a, b) ¼ C(a, b) if no criterion is opposing to the outranking of 1d ða, bÞ a over b, while C(a, b) is reduced by multiplying it for 1Cjða, bÞ if gj is such that dj(a, b) > C(a, b). On the basis of the concepts previously defined, two main different outranking relations can be considered: O1. aS1b iff C(a, b) ⩾ λ and gj(b)  gj(a) < vj, for all gj  G, which is the definition of the outranking relation used in the ELECTRE IS method. O2. aS2b iff σ(a, b) ⩾ λ, which is the definition of the outranking relation used in the ELECTRE III method.

PROMETHEE Methods Similarly to the ELECTRE methods, the PROMETHEE methods provide recommendations on the considered problem by building two or three binary relations on the basis of the computations of different flows in a graph representing an outranking relation. First of all, for each criterion gj  G, the PROMETHEE methods build a function π j : A  A ! [0, 1], where π j(a, b) measures the degree of the preference of a over b This is equivalent to say that dj(a, b) < 1 for all gj  G.

4

Multiple Criteria Decision Support

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on gj. π j(a, b) is a nondecreasing function of the difference gj(a)  gj(b) and six different functions have been proposed in Brans and Vincke (1985), with the most used one being the V-shape function defined as follows: 8 1 > > h i > > < g ð aÞ  g ð bÞ  q j j j π j ða, bÞ ¼ > > p  q j j > > : 0

if

gj ðaÞ  gj ðbÞPpj ,

if

qj < gj ð aÞ  gj ð bÞ < pj ,

if

gj ðaÞ  gj ðbÞOqj ,

where the indifference and preference thresholds have an analogous meaning as in ELECTRE methods. As for the ELECTRE methods, the partial preference indices π j(a, b) are therefore aggregated by mean of the following weighted sum: π ða, bÞ ¼

n X

wj π j ða, bÞ

j¼1

where wj represents a relative importance of gj and it is interpreted as in the ELECTRE methods. π(a, b)  [0, 1] denotes the degree of outranking of a over b. Using π(a, b), an outranking graph can be drawn, where nodes represent the alternatives and directed arcs between them are valued by a degree of outranking. This graph is a base for calculation of a positive, a negative, and a net flow for each alternative a  A: • The positive flow, ϕ+(a), represents how much, in average, a is preferred to all other alternatives in A; it is formally computed as: ϕþ ð aÞ ¼

X 1 π ða, bÞ: j A j 1 b  A∖ a

ð3Þ

f g

• The negative flow, ϕ(a), represents how much, in average, all alternatives in A are preferred to a; it is formally computed as: ϕ  ð aÞ ¼

X 1 π ðb, aÞ: j A j 1

ð4Þ

b  A∖fag

• The net flow, ϕ(a), is a balance between the two flows defined above and it represents the comprehensive assessment of a taking into account both how much a is preferred to the other alternatives and how much the other alternatives are preferred to a; this is simply computed as: ϕðaÞ ¼ ϕþ ðaÞ  ϕ ðaÞ:

ð5Þ

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On the basis of the computed flows, several PROMETHEE methods have been defined. In the following, we shall recall the PROMETHEE I and II only, being the most popular ones. PROMETHEE I defines preference PI, indifference II, and incomparability relation RI computed as follows: • aPIb iff ϕ+(a) ⩾ ϕ+(b), ϕ(a) O ϕ(b) and at least one of the inequalities is strict • aIIb iff ϕ+(a) ¼ ϕ+(b) and ϕ(a) ¼ ϕ(b) • aRIb iff not(aPIb), not(bPIa) and not(aIIb) PROMETHEE I provides, therefore, a partial preorder on the set of alternatives A. PROMETHEE II, instead, provides a total order of the alternatives in A defining preference PII and indifference relation III on the basis of the net flows. In particular: • aPIIb iff ϕ(a) > ϕ(b) • aIIIb iff ϕ(a) ¼ ϕ(b)

Decision Rules Decision rule model is an MCDA preference model based on the dominance-based rough set approach (DRSA) proposed in Greco et al. (2001). The basic preference information supplied by the DM is composed of pairwise preference comparisons of alternatives or classification of alternatives in preference ordered classes. On the basis of this information, some decision rules explaining the preference information are induced. The two most typical syntactical forms of the induced decision rules are the following: • “if the strength of the preference of alternative x over alternative y is at least π i1 on criterion gi1 and at least π i2 on criterion gi2 and . . . and at least π ir on criterion gir , then x is at least as good as y,” with gi1 , gi2 , . . . , gir  G • “if alternative x has an evaluation not worse than li1 on criterion gi1 and not worse than li2 on criterion gi2 . . . and not worse than lir on criterion gir , then x is assigned to a class not worse than Cs,” with gi1 , gi2 , . . . , gir  G, C1, C2, . . ., Cp is a set of increasing preferentially ordered classes and Cs  {C1, C2, . . ., Cp} Two examples of decision rules are the following: R1 R2

“if student S1 is at least weakly preferred in Mathematics and strongly preferred or more in Physics over student S2, then S1 is at least as good as S2,” “if student S has an evaluation at least medium in Literature and good or better in Philosophy, then the student S is comprehensively at least medium.”

Each one of the induced decision rules is associated with the corresponding pieces of preference information, that is, pairs of alternatives for which there is the

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preference relation suggested by a pairwise comparison rule or alternatives assigned to the class by a classification rule. For example, rule R1 will be associated with the set of pairs of students (S1, S2) such that S1 is at least weakly preferred in Mathematics and strongly preferred or more in Physics over S2, and S1 is at least as good as S2. Analogously, rule R2 will be associated with students S having an evaluation at least medium in Literature and good or better in Philosophy, being comprehensively at least medium. The set of decision rules induced from the preference information supplied by the DM, constitute a preference model that after being discussed with the DM and accepted by him, can be applied on the alternatives of the decision problem at hand. This means that if rule R1 is accepted by the DM, each time that a student S1 is at least weakly preferred in Mathematics and strongly preferred or more in Physics over S2, then S1 will be considered at least as good as S2. Analogously, if rule R2 is accepted, each student S having an evaluation at least medium in Literature and good or better in Philosophy will be considered comprehensively at least medium. The advantage of this approach is that the decision model is transparent and easily understandable by the DM that can find the arguments supporting the recommended decision in the same rule defining the preference relation or the classification. For tutorials and surveys on the use of DRSA in MCDA, one can refer to Słowiński et al. (2014, 2015).

Interaction Between Criteria As observed in the section “Multiple Attribute Value Theory,” the use of an additive value function assumes that the criteria from set G are mutually preferentially independent. Let us consider a problem in which the dean of a scientifically oriented high school has to evaluate four students with respect to three subjects, such as Mathematics (M), Physics (P), and Literature (L) (Grabisch 1996). The marks of these four students on the three subjects are given in the table below using a 20-point scale:

When comparing a and b, the dean states that b is preferred to a, while when comparing c and d, he expresses his preference for c over d. These preferences can be justified in the following way. On one hand, since a and b have both high marks on Mathematics and Physics, then the dean prefers the student presenting a higher mark on Literature. On the other hand, since the performances of c and d on Physics are not very good and for the dean the scientific subjects are really important, then he prefers c over d since c has a better mark than d on Mathematics. Let us try to

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represent these preferences by using the value function from Eq. (1). On one hand, the preference of b over a is translated into the constraint: uM ð15Þ þ uP ð13Þ þ uL ð10Þ < uM ð12Þ þ uP ð13Þ þ uL ð12Þ

ð6Þ

while the preference of c over d is translated into the constraint: uM ð15Þ þ uP ð5Þ þ uL ð10Þ > uM ð12Þ þ uP ð5Þ þ uL ð12Þ:

ð7Þ

The two inequalities are obviously in contradiction since, from Eq. (6) we get that uM(15) + uL(10) < uM(12) + uL(12), while from Eq. (7), we get that uM(15) + uL(10) > uM(12) + uL(12). This means that an additive value function is not able to represent these preferences since, observing carefully the students’ marks shown in the table, one can see that the criteria {M, P, L} are not mutually preferentially independent since {M, L} is not preferentially independent of P. Indeed, considering only criteria M and L, a has the same marks as c and b has the same marks as d. Therefore, observing that a and b have the same mark on P (13) and c and d have the same mark on P (5), if {M, L} was preferentially independent of P, then the preference of b over a should imply the preference of d over c, which is not true in this case since b is preferred to a but c is preferred to d. In this case, we can say that the three criteria present a certain degree of interaction. On one hand, two criteria are positively interacting if a good performance on one criterion does not imply, in general, a good performance on the other. Consequently, one would like to give a bonus to an alternative presenting good performances on both criteria. On the other hand, two criteria are negatively interacting if a good performance on one criterion implies a good performance on the other too. In this case, one would therefore give a malus to an alternative presenting good performances on both criteria. The mentioned interaction between criteria is taken into account in different ways in the literature. In the following, we are going to briefly recall the most known methods: • Multilinear value functions (Belton and Stewart 2002; Keeney and Raiffa 1976): U ðaÞ ¼

n X j¼1

u j ð aÞ þ

n X X

uj ðaÞui ðaÞ þ . . . þ u1 ðaÞu2 ðaÞ  un ðaÞ:

j¼1 j 0, if π j ða, bÞ ¼ 0,

where π Bj ða, bÞ represents the bipolar preference of a over b on gj: if π Bj ða, bÞ > 0, then a is preferred to b on gj, while, if π Bj ða, bÞ < 0, b is preferred to a on gj. Iff π Bj ða, bÞ ¼ 0 none of the two alternatives is preferred over the other on gj. The bipolar vector π B ða, bÞ ¼ ðπ B1 ða, bÞ, . . . , π Bn ða, bÞÞ is therefore aggregated by using the bipolar Choquet integral (Grabisch and Labreuche 2005a, b).

Robust Recommendations All the methods described in the previous sections involve definitions of several parameters. For example, the marginal value functions uj() and the substitution ratios wj/wi in the additive value functions, or the importance coefficients and the thresholds in the outranking methods. These parameters can be obtained by using a

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direct or an indirect preference information (Jacquet-Lagrèze and Siskos 2001) (see also chapter ▶ “Multiple Criteria Group Decisions with Partial Information About Preference”). The DM provides a direct preference information if he gives directly values to all parameters involved in the model. In general, this way of giving preference information implies a great cognitive effort from the part of the DM who has to specify a huge number of parameters of which, in most of the cases, he does not know or understand the meaning. For this reason, the indirect preference information is preferred in practice. The DM provides an indirect preference information if he expresses his preferences through statements, like comparisons between some reference alternatives (a is preferred to b or a is indifferent to b) or comparison between criteria with respect to their importance (for example, gi is more important than gj or gi is as important as gj) or the statements on the possible interactions existing between them (for example, gi and gj are positively interacting or gi exercises an antagonistic effect over gj). From this preference information, parameters compatible with these statements can be inferred. By applying the indirect preference information one aims, therefore, to discover an instance of the preference model compatible with the information provided by the DM. This technique is known in MCDA under the name of ordinal regression and many contributions have applied this technique to different preference models. In Jacquet-Lagrèze and Siskos (1982), the authors proposed the UTA method. The underlying preference model is an additive value function as that one in Eq.(1). In UTA, each uj is a piecewise linear value function defined by the utility uj xkj of the breakpoints xkj defining the partition of the interval [αj, βj] that contains the evaluations of the alternatives on criterion gj. The DM provides a partial preorder regarding a subset of alternatives, AR  A, and this preorder is translated to inequality constraints. For example, if a is preferred to b, then U(a) > U(b), while the indifference between a and b is translated into the constraint U(a) ¼ U(b). To check for the existence of an instance of a value function compatible with these preferences, an LP problem has to be solved. The same approach is used for nonadditive integrals and, in particular, for the Choquet integral preference model (Marichal and Roubens 2000). In this case, the DM provides a partial preorder on the set of alternatives as in Jacquet-Lagrèze and Siskos (1982) together with some preferences regarding importance of criteria and interaction between criteria. Again, an instance of the capacity compatible with the preferences provided by the DM is obtained solving an LP problem. The indirect preference information is also implemented by Figueira and Roy (2002) in a revised version of the Simos method (Simos 1990a, b) called deck of cards method (DCM). The DCM, known also as SRF method, proposes a procedure to assign a value to the weights used in the outranking methods, starting from preferences provided by the DM in very natural terms. The method is composed of three steps: (i) rank-order all the criteria from the least important to the most important with the possibility of some ex-aequo; (ii) add some blank cards between successive subsets of criteria to increase the difference between their importance; and (iii) provide a ratio z between the weight of the most important criterion and the

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least important one. From these preferences, the analyst supporting the DM is therefore able to assign a single value to each criterion. All above methods using the indirect preference information provided by the DM aim at discovering a single instance of the considered preference model compatible with this preference. In general, however, there could exist more than one instance of the preference model compatible with the preferences provided by the DM (in the following, a compatible model). All compatible models give the same recommendations on the reference alternatives, that is, the alternatives in AR, but they could provide different recommendations on the non-reference alternatives. To stress this point, let us provide a very simple example involving four alternatives evaluated on two criteria with performances given in the table below.

Let us assume that the DM prefers a to b and that we translate this preference using a weighted sum as a preference model. It is straightforward to observe that: 10w1 þ 6w2 > 7w1 þ 9w2 , 3w1 > 3w2 , w1 > w2 : Considering a vector w ¼ (w1, w2), such that w1 > w2, is enough to represent this preference. Let us consider, therefore, w(1) ¼ (0.6,0.4) and w(2) ¼ (0.7,0.3). Both of them represent the preference of the DM but, comparing the other two alternatives, that is c and d, one can observe that using w(1), d is preferred to c (U(1)(d) ¼ 7.4 > U(1)(c) ¼ 7), while using w(2), c is preferred to d (U(2)(c) ¼ 7.5 > U(2)(d) ¼ 6.3). This simple example proves that the choice of the compatible model will affect the final recommendations. Therefore, more robust recommendations could be provided by taking into account not only one compatible instance of the preference model but all of them simultaneously.

Robust Ordinal Regression The robust ordinal regression (ROR) (see Greco et al. (2008) for the paper introducing ROR and Corrente et al. (2013a, 2014c) for two recent surveys on ROR) takes into account all instances of the considered preference model by defining a necessary and a possible preference relation on A. In particular, a is necessarily preferred to b, and we shall write a≿Nb, iff a is at least as good as b for all compatible models, while a is possibly preferred to b, and we shall write a≿Pb, iff a is at least as good as b for at least one compatible model. ≿N and ≿P satisfy a set of properties among which inclusion (≿N  ≿P) and completeness (for all a,

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b  A, a≿Nb or b≿ba), while the basic axioms on ROR have been studied in Giarlotta and Greco (2013). ROR has been already applied to all preference models described above and, in particular, to value functions (Corrente et al. 2012; Figueira et al. 2009b; Greco et al. 2008, 2010), ELECTRE methods (Corrente et al. 2013b; Greco et al. 2011a), PROMETHEE methods (Corrente et al. 2013b; Kadziński et al. 2012a), Choquet integral (Angilella et al. 2010b, 2016b), and decision rules (Kadziński et al. 2015, 2016). Depending on the underlying preference model used to represent the preferences provided by the DM, the necessary and possible preference relations are computed by solving LP or MILP problems. In both cases, the concept is however the same. In the following, we are going to describe how these relations are computed if the R preference model is an additive value function. Denoting by EA the set containing the constraints translating the preferences given by the DM and the technical constraints depending on the considered preference model, the two preference relations are obtained by solving the following programming problems for each pair of alternatives (a, b)  A  A: eN ða, bÞ ¼ max e, subject to ) UðbÞPU ðaÞ þ e, EN ða, bÞ R EA

eP ða, bÞ ¼ max e, subject to ) UðaÞPU ðbÞ, EP ða, bÞ AR E

On one hand, we shall conclude that a is necessarily preferred to b iff EN(a, b) is infeasible or eN(a, b) O 0. On the other hand, we shall conclude that a is possibly preferred to b if EP(a, b) is feasible and eP(a, b) > 0. Of course, in consequence of the properties holding for the two relations, not all programming problems have to be solved but just some of them. More details with respect to this aspect can be found in Corrente et al. (2016a). The necessary preference relation provides a partial preorder of the alternatives since it is a reflexive and transitive binary relation. Therefore, it is possible that some pairs of alternatives are not comparable with respect to this preference relation since neither a is necessarily preferred to b nor b is necessarily preferred to a. In some realworld problems, however, it is often required to get a complete order of the alternatives and, therefore, the results obtained by taking into account the whole set of compatible models have to be aggregated to provide a conclusive recommendation. For such a reason, among the many compatible models, the most representative one can be selected. This model is the one, among those compatible, maximizing the difference between the alternatives (a, b)  A  A for which a≿Nb but not(b≿Na) and minimizing the difference between the alternatives (a, b)  A  A for which not(a≿Nb) and not(b≿Na). The most representative model has been defined for value functions (Corrente et al. 2012; Greco et al. 2011b; Kadziński et al. 2012a, 2013), outranking methods (Kadziński et al. 2012b), and Choquet integral (Angilella et al. 2010a).

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Stochastic Multicriteria Acceptability Analysis As already observed in the previous section, the ROR provides extreme information on each pair of alternatives (a, b)  A  A. Indeed, the necessary and possible preference relations tell us only if all models agree on the fact that a is at least as good as b (a≿Nb) or if at least one model agrees on the fact that a is at least as good as b (a≿Pb). Anyway, in most of the cases, the alternatives are incomparable with respect to the necessary preference relation since there are compatible models for which a is at least as good as b (a≿Pb) and compatible models for which b is at least as good as a (b≿Pa). In these cases, nothing can be concluded regarding the comparison between the two alternatives. Therefore, to have more information on them, one should “count” the number of compatible models for which a is preferred to b and the number of compatible models for which the opposite is true. The stochastic multicriteria5 acceptability analysis (SMAA) (see Lahdelma et al. (1998) for the first paper on SMAA and Lahdelma and Salminen (2016), Pelissari et al. (2019), and Tervonen and Figueira (2008) for three surveys on the methodology), alike the ROR, takes into account simultaneously all the models compatible with the preferences provided by the DM, however, in a different way. SMAA provides information in probabilistic terms, that is, the frequency with which a certain alternative is in a ranking position or the frequency with which an alternative is preferred to another one when a big sample of compatible preference models is considered. In particular, three different indices can be defined in SMAA: • The rank acceptability index bk(a): It is the frequency with which an alternative reaches a certain ranking position; of course, it can therefore be considered if the underlying preference model produces a total ranking of the alternatives such as a value function (Lahdelma et al. 1998), the Choquet integral (Angilella et al. 2015, 2016b), or the PROMETHEE II method (Corrente et al. 2014b). • The pairwise winning index p(a, b) (Leskinen et al. 2006): It is the frequency with which the alternative a is preferred to the alternative b; it can be computed not only in case the model provides a total order of the alternatives but also in case it provides a partial preorder as for the ELECTRE III method (Corrente et al. 2017) or for the PROMETHEE I method (Corrente et al. 2014b). • The central weight vector w1(a): It is computed only for alternatives a such that b1(a) > 0 and, therefore, alternatives that can be the first for at least one compatible model. It is formally computed as a barycenter of the space of compatible models giving to a the first position and it represents, therefore, the “typical” preference giving to a the best possible position. On the basis of the mentioned indices and, in particular, of the rank acceptability indices for each alternative, one can also compute the best and worst reachable positions, the ranking positions presenting the highest frequencies, or the cumulative

5

Multiobjective and multiattribute are used as well.

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rank acceptability indices giving for each a  A and each k ¼ 1, . . ., jAj the frequency with which a reaches at least the position k (bOk(a)) or at most the position k (b⩾(a)). The formal definition of the introduced indices depends on the assumed preference model. Anyway, all of them are computed by solving multidimensional integrals that can be approximated by Monte Carlo simulations. Indeed, the preferences provided by the DM define a space of compatible models for which several instances of the assumed preference model have to be sampled. If the space of compatible models is defined by linear inequalities and equality constrains and, therefore, it constitutes a convex space, one can sample instances of its elements by using the hitand-run (HAR) method introduced in Smith (1984) but then applied to MCDA in Tervonen et al. (2013) and Van Valkenhoef et al. (2014) (see Corrente et al. (2019) for a very detailed description of the HAR method in this case). Let us conclude this section by mentioning that ROR and SMAA have been put together in Kadziński and Tervonen (2013a, b), while procedure to aggregate the rank acceptability indices and the pairwise winning indices have been proposed in Kadziński and Michalski (2016).

Recent Developments and MCDA Applications In this section, we shall briefly recall two recent developments and we shall list some research areas in which MCDA has been fruitfully applied. MCHP: In MCDA problems, it is assumed, in general, that the evaluation criteria are all at the same level. This is not the case, however, in several MCDA applications where it is possible to observe a root criterion, being the objective of the problem, some macrocriteria, being the main aspects that need to be taken into account in the problem at hand, some other criteria descending from the macrocriteria, until the bottom of the hierarchy where there are so called elementary criteria, being the criteria on which the performances of the alternatives are directly given. To deal with such problems where the evaluation criteria are structured in a hierarchical way, the multiple criteria hierarchy process (MCHP) (Corrente et al. 2012) has been proposed. It gives important advantages from the input and from the output point of view with respect to the classical MCDA methods where all evaluation criteria are considered at the same level: 1. From the input point of view, considering the indirect way of providing preference information, the DM can supply information not only comprehensively, that is taking into account simultaneously all the criteria, but also partially, that is considering only a subset of criteria corresponding to particular node in the hierarchy tree. This is beneficial since the DM could be a bit confused when being forced to provide a full information that summarizes all the aspects of the alternatives, but he could be more confident in providing a preference information on only those aspects he knows better.

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2. From the output point of view, together with the recommendations in which all aspects are taken into account simultaneously, when applying the MCHP the DM can learn if a is preferred to b on g1 or if b is preferred to a on g2 and so on. This gives the DM the possibility to get a better insight to the problem he is coping with because in this way he learns which are the weak and strong points of each alternative. The MCHP has been applied to all mentioned preference models considering also the ROR and the SMAA methodologies (Angilella et al. 2016b; Arcidiacono et al. 2018; Corrente et al. 2013b, 2016b, 2017). IEMO: In multiobjective optimization, one aims to optimize simultaneously a set of objective functions f1(x), . . ., fn(x) under some constraints c1(x) ⩾ d1, . . ., cm(x) ⩾ dm. The goal is to find the best vector of variables x optimizing the objective functions and satisfying all considered constraints. This problem is a particular case of a multiple criteria choice problem where objective functions are evaluation criteria and the set of constraints is defining a set of possible alternatives. As already observed in the introductory section, since the objective functions (criteria) are in conflict, there is not any x optimizing simultaneously all the objective functions. The best one can hope is therefore finding the Pareto set, that is the set composed of all non-dominated x. In recent years, to compute the whole Pareto set or its representative approximation, the evolutionary algorithms have been successfully applied. They mimic the evolution of the populations in biology and try to approximate the Pareto front by means of a population of solutions x. The best known of these evolutionary algorithms is NSGA-II (Deb et al. 2002). However, even if the DM would know the Pareto set, he should finally choose in this set the best solution x or a subset composed of all satisfactory solutions with respect to his preferences. For this reason, two extreme approaches can be taken into account: (i) defining a priori a value function representing the preferences of the DM and substituting all the considered objective functions, that is, U(x) ¼ U( f1(x), . . ., fn(x)). In this way, the multiobjective problem is reduced to a single objective problem where one aims to find x maximizing the utility function of the DM; and (ii) build the whole Pareto front and then deciding among these solutions the preferred one by specifying, for example, trade-offs between the different objective functions. These two approaches are equally impractical since the first assumes that the preferences of the DM can be formalized a priori by a value function, while, the second one assumes that the DM is able to provide his preferences on a set composed of many solutions described by vector evaluations (Branke et al. 2008). Interactive evolutionary multiobjective optimization (IEMO) methods represent an intermediate approach since they give to the DM the possibility of including his preferences in the search of the solution space, i.e., in the evolution of the population of solutions. This permits, in consequence, to focus the search on the most appealing part of the Pareto front with respect to his preferences. Several methods integrating MCDA and evolutionary algorithms have been proposed recently. See, for example, Branke et al. (2015, 2016), Greenwood et al. (1997), and Phelps and Köksalan (2003).

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MCDA methods have been very successful in handing many complex real-world decision problems and it is impossible to give here an exhaustive inventory of all applications. A very partial list of fields where MCDA has been successfully applied is the following: • Economics and finance (Doumpos and Zopounidis 2014; Zavadskas and Turskis 2011) • Energy planning (Diakoulaki et al. 2005; Wang et al. 2009) • Engineering (Bertola et al. 2019; Rogers et al. 2013; Zavadskas et al. 2015a, b) • Environmental problems (Cegan et al. 2017; Huang et al. 2011; Kiker et al. 2005; Linkov and Moberg 2011; Malczewski 1999; Malczewski and Rinner 2016) • Medicine (Diaby et al. 2013; Thokala et al. 2016) • Natural resource management (Mendoza and Martins 2006) Looking at the future perspectives, we believe that MCDA has to proceed in a direction in which the information required from the DM and supplied to the DM, as well as the decision model adopted are “as simple as possible, but not simpler” (Arcidiacono et al. 2020). Indeed, on one hand, the DM has to be given the possibility to express his preferences with the desired degree of detail in all their richness of contents, while, on the other hand, the DM must have the possibility of understanding all the aspects of the final recommendation including its pros and cons with respect to other decisions.

Cross-References ▶ A Group Multicriteria Approach ▶ Behavioral Considerations in Group Support ▶ Group Decision Support Using the Analytic Hierarchy Process ▶ Group Decisions with Intuitionistic Fuzzy Sets ▶ Group Decisions with Linguistic Information: A Survey ▶ Group Support Systems: Concepts to Practice ▶ Group Support Systems: Past, Present, and Future ▶ Holistic Preferences and Prenegotiation Preparation ▶ Multicriteria Methods for Group Decision Processes: An Overview ▶ Multiple Criteria Group Decisions with Partial Information About Preference ▶ Participatory Modeling for Group Decision Support Acknowledgments Salvatore Corrente and Salvatore Greco gratefully acknowledge the funding by the research project “Data analytics for entrepreneurial ecosystems, sustainable development and wellbeing indices” of the Department of Economics and Business of the University of Catania. José Rui Figueira acknowledges the support from the hSNS FCT – Research Project (PTDC/EGE-OGE/ 30546/2017) and the FCT grant SFRH/BSAB/139892/2018 under POCH Program. The research of Roman Słowiński has been partially supported by the statutory funds of Poznan University of Technology.

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Multiple Criteria Group Decisions with Partial Information About Preference Adiel Teixeira de Almeida, Eduarda Asfora Frej, Danielle Costa Morais, and Ana Paula Cabral Seixas Costa

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple Criteria Group Decision-Making and Preference Modeling . . . . . . . . . . . . . . . . . . . . . . . . . Partial Information in Preference Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MCDM/A Partial Information Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Framework for Classifying Partial Information MCDM/A Methods . . . . . . . . . . . . . . . . . . . . Group Decision-Making Under Partial Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flexible and Interactive Tradeoff for MCGDM Preference Modeling . . . . . . . . . . . . . . . . . . . . . . . . . FITradeoff Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Decision Process Based on Flexible and Interactive Elicitation . . . . . . . . . . . . . . . . . . . . Conclusions and Future Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Multiple criteria decision making/aid (MCDM/A) methods have been applied in many different contexts to deal with problems of a single decision maker (DM) or a group of them. One of the critical issues when applying this kind of method is the evaluation of DMs’ preferences and the definition of the parameters to be considered in these methods. In this context, an overview of preference modeling

A. T. de Almeida (*) · E. A. Frej · D. C. Morais CDSID – Center for Decision Systems and Information Development, Universidade Federal de Pernambuco, Recife, PE, Brazil e-mail: [email protected]; [email protected]; [email protected] A. P. C. S. Costa CDSID – Center for Decision Systems and Information Development, Universidade Federal de Pernambuco, Recife, Brazil Departamento de Engenharia de Produção, Federal University of Pernambuco, Recife, Brazil e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_50

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approaches for aiding multicriteria group decision-making (MCGDM) problems is conducted when only partial (or imprecise/incomplete) information about DMs’ preferences is available, in order to reduce the amount of information required from the DMs to recommend a final compromise solution for the group. Although this chapter is not intended as an exhaustive literature review on methods using partial information, a framework for summarizing different types of approaches for preference modeling with partial information is presented, with a focus on multi-attribute value theory (MAVT). Moreover, a flexible elicitation procedure to aid MCGDM problems under partial information throughout an interactive decision support system is also presented. Keywords

Group decision · Multiple criteria analysis · Preferences · Multiple criteria group decision making/aid · MCGDM/A · Partial information · Incomplete information · Preference modeling

Introduction Decision situations involving a specified set of alternatives and conflicting objectives usually lead to the application of multicriteria decision-making/aid (MCDM/A) techniques. Within the scope of a compensatory rationality, alternatives are scored straightforwardly through an additive aggregation function (1), in which v(aj) is the global value of alternative aj, vi(xij) is the normalized value function that represents the value of the consequence of alternative aj in criterion ci, and ki is the scaling constant of criterion ci (ki
0), normalized according to eq. (2).
 Xn
 v aj ¼ kv x i¼1 i i ij Xn

k i¼1 i

¼1

ð1Þ ð2Þ

Additive aggregation models require the establishment of parameters that are difficult to elicit from the decision makers (DMs), such as the criteria scaling constants ki. Definition of criteria weights – as these parameters are usually called – is not a trivial task, since they represent not only the level of importance of each criterion but also a scaling factor, which is crucial to the additive aggregation. The sphere of complete information in MCDM/A traditionally embraces a specified set of alternatives, a set of criteria, and a DM – or a group of them – with a welldefined stable preference structure (Weber 1987). Traditional decision-making models based on the multi-attribute value/utility theory – MAVT/MAUT (Keeney and Raiffa 1976) implicitly assume that DMs use their well-defined preferences in order to answer questions in the elicitation of criteria scaling constants or weights (Weber and Borcherding 1993). In practice, however, eliciting criteria weights is one of the most difficult tasks in MCDM/A, due to the conceptual difficulties regarding the interpretation of intangible objectives (Salo and Punkka 2005).

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Other difficulties in the elicitation process may arise due to the amount of information required to be provided, since DMs are not always able to specify their preferences in the detailed way required (Weber 1987). The main disadvantage of traditional methods with complete information is that the information required by DMs can be tedious and time-consuming (Salo and Hämäläinen 1992; Kirkwood and Sarin 1985; Kirkwood and Corner 1993). The cognitively demanding process that DMs face in traditional methods may also account for the high rate of inconsistencies observed in behavioral studies (Borcherding et al. 1991). Moreover, DMs may not be willing to provide the necessary information to elicit criteria scaling constants (Salo and Hämäläinen 1992), which brings up the opportunity of using procedures with weaker and less precise information for estimating the value/utility function. Methods using partial information (or imprecise/incomplete information) about DMs’ preferences were mainly motivated by these issues. Partial information decision problems typically include DMs who lack a well-defined preference structure, and therefore have difficulty to specify preferences at the level of detail required by complete information approaches (Weber 1987). In general, the main purpose of these methods is to narrow the gap between theoretical research and practical real-world applications, making the decision-making process easier and less cognitively demanding for DMs. When more than one decision maker takes responsibility for the decision, a group decision-making situation occurs, and thus the complexity of the problem increases even more. This chapter aims to present an overview of MCDM/A methods for preference modeling with partial/incomplete information, within the context of MAVT, embracing also group decision-making situations. A framework summarizing different types of approaches for preference modeling under partial information is presented and discussed. MCDM/A methods may be classified in different ways; one of these ways considers if they use either a compensatory or non-compensatory rationality (de Almeida et al. 2015). This chapter deals mainly with those using a compensatory rationality, in which are the majority of partial information methods. A flexible elicitation method for aiding group decision-making processes under incomplete information based on an interactive decision support system is also presented here. This chapter is structured as follows: section “Multiple Criteria Group DecisionMaking and Preference Modeling” presents some concepts related to preference modeling in group decision-making processes; section “Partial Information in Preference Modeling” presents an overview of multicriteria partial information methods for preference modeling; section “Flexible and Interactive Tradeoff for MCGDM Preference Modeling” presents an interactive method for supporting MCGDM problems based on flexible elicitation; finally, in section “Conclusions and Future Challenges,” some conclusions and future challenges are discussed.

Multiple Criteria Group Decision-Making and Preference Modeling A multiple criteria group decision-making (MCGDM) problem is characterized by two or more actors who are responsible for a decision in the context of multiple objectives. Individual decision-making situations are not trivial due to need to

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evaluate alternatives according to multiple and conflicting objectives; however, when it comes to group decision-making, the process becomes even more challenging, since different decision makers (DMs) have different and conflicting viewpoints, aspirations and preferences. Therefore, several methods for aiding group decision-making when multiple criteria are involved were developed (Salo et al., ▶ “Multicriteria Methods for Group Decision Processes: An Overview”). Furthermore, a relevant distinction has to be made, corresponding to two different conceptions of “group decision” in the literature. This distinction is related to the nature of information to be aggregated. Some studies consider group decision (GD) to be aggregation of DMs’ preferences; others regard it as the aggregation of experts’ knowledge. These two kinds of GD are associated to integrating two substantially distinct information. While the former is a kind of preferential information and latter is a kind of factual information. Each one of this kind of aggregation of information requires their own foundations. Regrettably, in some studies, this distinction is not made clearly, leading to misconceptions and inappropriate processes for building a decision model (for more details, see chap. 2 of de Almeida et al. 2015). The present chapter is particularly focused on aggregation of DMs’ preferences. Group decision-making (GDM) situations involve both interaction procedures and analytic procedures. Interaction between DMs is important in group decisionmaking (GDM) processes because this may lead to consensus and/or agreement reaching in a more efficient manner, depending on the accuracy of the communication process. By interacting with each other, DMs get to know more about their counterparts’ aspirations and viewpoints. Nevertheless, interaction situations are often not possible, due to restrictions of the actors’ agendas or other factors. In such situations, analytical procedures for aggregation of DMs’ preferences may be applied, but processes for building analytical models have to pay great attention for rationality issues regarding the actors involved. Interaction and analytical models may also be applied conjointly, depending on the situation. Regarding the cooperation among decision makers in GDM processes, it is possible that DMs have the same objective – but they do not clearly realize it – or they may have different objectives, which may be conflicting or not. The group may have a supra decision maker with a hierarchical position above the other DMs in the organization’s structure, which may impose some aggregation rule, or maybe this actor does not exist in the decision-making context and the group decision is made based on a participatory process, by developing their own aggregation rule (de Almeida et al. 2015). Those aggregation approaches generally involve the reduction of different individual preferences to a set of collective preferences, and whether or not a Supra-DM is present in the process, two types of group decision aggregation may be considered (Kim and Ahn 1999; LeyvaLópez and Fernandez-Gonzalez 2003; Dias and Clımaco 2005): aggregation of DMs’ initial preferences or aggregation of DMs’ individual final choices. In the first approach, DMs provide their initial preferences in an integrated way, because the actors are willing to give up on their own individual interests in order to find the best solution for the group as a whole, and therefore the aggregation of

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preferences is conducted in the very beginning of the process. In the second approach, each DM has his/her own final choice – or ranking – obtained no matter how, and these final results are then aggregated so as to find the final solution; this may be case of using a voting procedure for achieving a final compromise solution (Nurmi 2002). In the final choices aggregation approach, each DM chooses an alternative (or rank them) according to his/her own preferred method; if a multicriteria evaluation is performed by each of them, they do not need to consider the same criteria in their evaluation, nor the MCDM method has to be the same. Their final choices are then aggregated based on some voting procedure or some MCDM method in which ordinal inputs may be applied, such as PROMETHEE-GDSS (Mareschal et al. 1998) or ELECTRE-GD (Leyva-López and Fernandez-Gonzalez 2003). When voting procedures are applied, the main complication is the choice of a voting procedure to aggregate preferences and deal with the respective paradoxes that may arise (de Almeida and Nurmi 2015). Additive models may also be applied for group decision aggregation (Keeney and Kirkwood 1975; Keeney 1976, 2009), but a critical issue in this case is how to define weights for each DM in order to obtain the group value function, since these parameters have to consider a scaling factor related to the consequences of each DM’s choices, and not only the level of importance of each DM (Keeney 2009). When it comes to the initial preferences aggregation approach, however, there is integration between all the actors responsible for making a decision, and therefore the final results of each DM are not viewed directly, because the aggregation among DMs is developed from the initial preference data. Within this approach, the final output is the recommendation for the group regarding the initial set of alternatives. This recommendation may be given as a simple ordinal ranking of the alternatives or it may include a cardinal score for each alternative; it depends on the method applied, which is the same for all DMs. In general, the same criteria are considered for all DMs, but the intracriterion and intercriteria evaluations may be different. Considering all the aspects mentioned above, it can be seen that preference modeling in MCGDM problems is a critical issue, regardless of the approach in which preferences/choices are combined. Especially in compensatory models, specifying criteria weights is not an easy task. Elicitation of weights can be time-consuming and controversial (Kirkwood and Sarin 1985; Kirkwood and Corner 1993), and the DMs may not be willing to specify the information in the detailed way required by traditional elicitation methods (Salo and Hämäläinen 1992). DMs are often more comfortable in making natural language statements during the elicitation process, which can be converted in linear inequalities (White III and Holloway 2008). Motivated by these issues, decision-making with partial information has been widely used in MCDM problems. Partial information methods work with incomplete/imprecise preferential information obtained from the DMs, thereby reducing their cognitive burden when making decisions. The next section gives an overview of the MCDM partial information methods developed in the literature.

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Partial Information in Preference Modeling In this section, several approaches that deal with partial/incomplete information about decision makers’ preferences in multicriteria decision problems are presented. These methods are then classified according to the form in which the partial information is provided, the type of partial information, and the method of synthetizing it in order to build a recommendation for the DMs. At the end of this section, we present some key papers dealing specifically with group decisionmaking under partial information, and focusing on how to aggregate divergent points of view into a recommendation, in the context of partial information.

MCDM/A Partial Information Methods Many partial information methods dealing with MCDM/A problems can be found in the literature. Kirkwood and Sarin (1985) presented a method for ranking alternatives with partial information based on dominance relations searched in a feasible region of weights through linear programming problems (LPP). The authors present an algorithm with four steps for building a partial – or complete – ranking of the alternatives, depending on the amount of information gathered from the DM. The application of the method was illustrated with an application for evaluating materials for use in nuclear waste containment. Salo and Hämäläinen (1992) proposed the PAIRS method (Preference Assessment by Imprecise Ratio Statements), which allows DMs to specify interval judgments for the criteria scaling constants, instead of specifying exact values. With this imprecise information, it is possible to find dominance relations through linear programming problems. The process is interactive, where the solution can be found even before the specification of all judgments by the DM. A job selection problem was presented for illustrating the application of the method. The PAIRS method is particularly suitable also for group decision-making problems (Salo and Hämäläinen 1992). Partial information in the scope of hierarchical structures was also approached by Salo and Hämäläinen (1995) and Kim and Han (2000). Salo and Hamalainen (2001) also developed the PRIME method (Preference Ratios in Multiattribute Evaluation), which differs from other additive methods such as AHP, SMART, and PAIRS for three main reasons: first, the comparisons made based on ratios are explicitly related to the values of the alternatives on each criterion, which avoids the notion of weights just as relative importance; second, PRIME is able to deal with holistic preference judgments; third, decision recommendations in PRIME are complemented by an information of possible losses of value resulted from that recommendation. On the other hand, PRIME is similar to PAIRS on what comes to the following factors (Salo and Hamalainen 2001): both provide information about dominance relations; both preserve the consistency of the model; and both are suitable for group decision-making problems, since intervals may be interpreted as lower and upper bounds of the group members’ points of view. The PRIME method aims to achieve equilibrium between the solid axiomatic

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foundation of the classical tradeoff procedure and the functionality of ratio judgments (Salo and Hamalainen 2001). Claiming that it is not always necessary to gather complete information about criteria weights in order to produce a decision recommendation, Salo and Punkka (2005) proposed the RICH method (Rank Inclusion in Criteria Hierarchies), which allows DMs to provide incomplete information, and the decision recommendations are given based on dominance relations and decision rules. Later on, the same authors approached the case in which the incomplete information provided may result in a non-convex set of feasible values, so they developed a mixed integer linear formulation in order to model the problem (Punkka and Salo 2013). Mármol et al. (2002) suggested an approach in which the DM provides information in a sequential way; once he/she knows the effect that the last information provided had in the set of alternatives, he/she may learn more about the decision process, in such a way that more specific information can be provided at this point. Therefore, the DM learns about his/her preferences during the preference modeling process, in such a way that, in case of inconsistency, the DM may reconsider the information previously provided (Mármol et al. 2002). Imprecise preference interval judgments were incorporated in SMART/SWING method by Mustajoki et al. (2005). The Interval SMART/SWING differs from the traditional SMART method because the DM can choose any attribute as the reference attribute (not necessarily the most or least preferred one), and he/she can also specify an interval instead of a fixed value to compare any attribute with the reference attribute. White III and Holloway (2008) developed an approach to aid the facilitator/ analyst in the question-answering process of the ISMAUT method (Imprecisely Specified MAUT), based on a Markov process. In this method, the DM is allowed to evaluate criteria weights and value functions as a finite set of linear inequalities. Dias and Clímaco (2000) developed the VIP (Variable Independent Parameters) Analysis software, which works with progressive reduction of the number of alternatives based on imprecise information gathered from DMs in the form of bounds, linear inequalities and linear equalities, which act as constraints for linear programming problems. The authors then extended this approach for group decision-making problems (Dias and Clımaco 2005), as will be mentioned in the next subsection. Park and Kim (1997) proposed an interactive method for ranking alternatives using dominance graphs. These graphs are built based on pairwise dominance information computed from decision rules and LPP models. The method considers that partial information provided by the DM can be either about criteria weights or utility/value functions. Malakooti (2000) presented a ten-step algorithm for ranking and screening alternatives with mathematical programming. Partial information can be gathered from the DM by paired questions, statements of strengths of preference and other types of questions, but in such a way that linear inequalities can represent it. Concepts regarding dominance and potential optimality when imprecise values of weights are available were addressed by Eum et al. (2001), who considered information in form of rankings and arbitrarily linear inequalities, which can act as constraints for LPP models.

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Aguayo et al. (2014) and Mateos et al. (2014) approached the so-called dominance intensity methods, which consider incomplete information of criteria scaling constants to find pairwise dominance relations and derive dominance intensity measures in order to build a ranking of the alternatives. Other partial information approaches using dominance relations to rank order alternatives were also proposed by Athanassopoulos and Podinovski (1997), Park et al. (1997), Park (2004), and Ahn and Park (2008). Montiel and Bickel (2014) presented a Monte Carlo simulation process to test the sensitivity of multilinear utility functions with regards to changes in the scaling constants values. Any kind of partial preference information that can be expressed by linear constraints are allowed in this method. The authors apply the proposed methodology in the context of a coal-fired power plant location decision, emphasizing the flexibility of the method. Approaches based on surrogate weights are also common in the world of incomplete preference information. In the SMARTER method (Edwards and Barron 1994), criteria weights are ranked based on the swing procedure according to the DM’s preferences, and then surrogate weights are calculated based on the Rank Ordered Centroid (ROC). Therefore, the only preference information given by the DM is about the ranking of criteria weights, which turns the process easier. Other surrogate weighting approaches were presented by Stillwell et al. (1981), the rank sum (RS) and rank reciprocal (RR) weights. Danielson et al. (2014) proposed the CROC method, which extends the ROC procedure by considering numerically imprecise cardinal information in addition to the ordinal information provided in ROC. Danielson and Ekenberg (2017) stated that using only ordinal preference information may be too vague or imprecise, which leads to an evaluation of alternatives not very confident. By incorporating preference strengths in surrogate weighting, these authors proposed a new method in which the weight function combine properties of rank sum and rank reciprocal, the CSR method. This method was shown to be robust and stable compared to other surrogate weighting methods under reasonably assumptions, and it is also suitable for group decision-making (Danielson and Ekenberg 2017). Sarabando and Dias (2009) compared different decision rules for MCDM problems with partial information available, and one of their conclusions is that the ROC rule is one of the rules with best performance. Inspired on the ROC weights, Sarabando and Dias (2010) proposed new decision-rules based on surrogate values (ROC values) for MCDM problems in which incomplete information regarding the criteria weights and the alternatives’ values on each criterion is available. The ROC method was also applied for determining criteria weights in the PROMETHEE method (Morais et al. 2015). In most of these previously described partial information methods, the information is gathered from DMs in many possible ways, and in general, there is not a structured process in order to guide the elicitation process. In some cases, the elicitation is structured following the swing procedure (Von Winterfeldt and Edwards 1986), which uses linear approximations to single-dimension utility/value functions (Edwards and Barron 1994). Another procedure for structuring elicitation

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of criteria scaling constants is the classical tradeoff developed by Keeney and Raiffa (1976), which has a strong axiomatic foundation (Weber and Borcherding 1993), but, on the other hand, it is not often used due to the high inconsistency rate presented when applied – around 67%, according to behavioral studies (Borcherding et al. 1991). In order to try to lower such a high inconsistency rate and to improve the applicability of the tradeoff procedure for DMs, de Almeida et al. (2016) developed the FITradeoff method (Flexible and Interactive Tradeoff). FITradeoff works with partial information about DMs preferences, but with a structured elicitation process keeping all the axiomatic structure of the classical tradeoff. The cognitive effort spent by DMs is reduced in FITradeoff because the elicitation process is based on strict preference statements, which are easier to provide (de Almeida et al. 2016). A more detailed explanation of FITradeoff method as well as its applicability for solving group decision-making problems is presented later on in this chapter, in section “Flexible and Interactive Tradeoff for MCGDM Preference Modeling.” De Almeida et al. (2016) also presented a framework to classify MCDM/A methods that use partial information for elicitation of criteria weights in additive models with respect to preference statements, forms of partial information, and synthesis step. In order to summarize and complement the content of this section, the next section presents a classification for all partial information methods mentioned in this section according to this framework.

A Framework for Classifying Partial Information MCDM/A Methods Methods that use partial information about DMs’ preferences in the elicitation process of scaling constants in additive models can by classified according to the framework presented in Fig. 1 (de Almeida et al. 2016). The first class is about preference statements, and it is divided in three subclasses. The first subclass concerns about the structure of the elicitation process: an elicitation procedure may be structured if there is an organized support mechanism to guide the process in which DMs state their preferences. For example, methods based on the swing or tradeoff procedure can be considered as having a structured elicitation

FORMS OF PARTIAL INFORMATION

PREFERENCE STATEMENTS ü ü

Structured Elicitation; Non structured elicitation.

ü ü

All at once; Interactive.

ü ü

Flexible process; Fixed process.

ü ü ü ü

Ranking; Bounds; Holistic Judgments; Arbitrarily linear inequalities.

SYNTHESIS STEP ü ü ü ü

Surrogate weights; Decision rules; Linear programming problems; Simulation/sensitivity analysis.

Fig. 1 Framework for classification of partial information methods. (Adapted from de Almeida et al. 2016)

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process. In other cases, the elicitation is conducted in a nonstructured manner, because it is either assumed that the information is previously given (without a defined process to gather it), or that DMs can give information in any format at any time. The second subclass is about the interactivity of the elicitation process: in interactive methods, the DM gives information in an interactive manner, in such way that, at each step of the process, additional information is gathered, and new results are computed; on the other hand, in noninteractive methods, DMs give all the information only once. Finally, the third subclass concerns about the flexibility of the process, which allows DMs can to conduct the elicitation process in a more flexible way, without a fixed defined process. The second class is about the forms of partial information provided by the DM in the elicitation process, which can be in various ways, such as ranking of criteria scaling constants, bounds of these parameters, holistic judgments between alternatives or even arbitrarily linear inequalities. This step represents an interface between the preference statements step and the synthesis step. The third and last class is the information synthesis step. Some methods use surrogate values for weights, which can be obtained based only on the ranking of criteria weights. Other methods use decision rules, such as maximin and minimax, in order to find a recommendation. Other widely applied technique is to incorporate linear inequalities obtained from ranking, bounds, or arbitrarily as constraints to linear programming problem models, in order to search for dominance relations and/or potential optimality. Another possibility for synthesis is conducting simulation and sensitivity analysis, so as to test the robustness of the results obtained. Table 1 shows the classification of the methods mentioned in this section according to the framework presented in Fig. 1. Darkened squares mean that the chapter fits within the corresponding classification. From Table 1, it can be observed that, when it comes to preference statements, 81% of the methods analyzed have a nonstructured elicitation process, so that it is assumed that the information is previously given by DMs without a specified process for gathering it. Sixty-six percentage of the methods analyzed have no interactive process with DMs, and the information is given all at once. Moreover, 75% of the methods have a fixed process, without providing flexibility for DMs in the elicitation procedure. The method proposed by de Almeida et al. (2016) should be highlighted here, since it has a structured elicitation process based on tradeoffs, is an interactive procedure, and also provides flexibility for DMs in terms of graphical visualization of partial results (de Almeida et al. 2016). As for forms of partial information, most of the methods use rankings (75%), bounds (59%), and arbitrarily linear inequalities (66%). Holistic judgments are not very often used, since only 19% of the methods consider this kind of information. For the synthesis step, the majority of the methods (78%) use linear programming problem models in order to define dominance relations and potential optimality. Only 19% of the methods are based on surrogate weights, in which only the information about the ranking of criteria weights is necessary. However, on the other hand, providing only ranking information may be vague or imprecise in terms on

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Table 1 Classification of partial information methods

Simulation/sensitivity analysis

LPP models

Decision Rules

Surrogate weights

Synthesis step Arbitrarily linear inequalities

Holistic judgements

Bounds

Fixed process

Flexible

Interactive

All at once

No Structured

Structured

Ranking

Forms of Partial Information

Preference statements

Stillwell et al (1981) Kirkwood and Sarin (1985) Weber (1987) Salo and Hamalainen (1992) Edwards and Barron (1994) Salo & Hamalainen (1995) Athanassopoulos and Podinovski (1997) Park and Kim (1997) Park et al. (1997) Kim and Ahn (1999) Malakooti (2000) Kim and Han (2000) Dias and Clímaco (2000) Salo and Hamalainen (2001) Eum et al. (2001) Mármol et al. (2002) Salo and Punkka (2005) Park (2004) Mustajoki et al. (2005) Ahn and Park (2008) White III and Holloway (2008) Sarabando and Dias (2010) Punkka and Salo (2013) Danielson et al (2014) Aguayo et al. (2014) Montiel and Bickel (2014) Mateos et al. (2014) de Almeida et al. (2016) Danielson and Ekenberg (2017)

confidence and may not express the real preferences of the DM. The method proposed by Danielson and Ekenberg (2017) aims to overcome such issues, by combining a simplified decision-making process with the realistic information of preferences by incorporating cardinality on surrogate weights.

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Group Decision-Making Under Partial Information Most of the methods presented already are focused on preference modeling when decision makers present incomplete information. For group decision problems, the complexity increases because the incomplete data on preference must be aggregated across decision makers. Therefore, we have selected some key papers in the literature of group decision-making that deal specially with this issue, in order to illustrate the possible ways in which a group decision process can be approached under partial information. There are five major ways to conduct a group decision-making process under partial information obtained from the actors. The first one consists in using indicators and decision rules, such as maximax, minimax regret, maximin, central value, and others. The second one relies on the aggregation of decision makers, by considering the relative importance of each DM and establishing weights for them; this approach has to be carefully applied due to issues related to the real meaning of these weights, as previously discussed in section “Multiple Criteria Group Decision-Making and Preference Modeling.” The third approach considers that the final group decision is made throughout a participatory process, in which the DMs try to reach a consensus. The fourth one is based on constructing a common interval model for the group, which can be conducted based on the union and/or intersection of the individual interval models. Finally, the last approach considers voting tools for dealing with group decision under partial information. Table 2 presents a summarized classification of some papers that deal with preference modeling for group decision-making. Hämäläinen and Pöyhönen (1996) propose a decision support technique in which DMs give preference considering their own value model, and then their Table 2 Classification for group decision synthesis approach

Indicators and Decision Rules Hamalainen & Poyhonen (1996) Kim & Ahn (1997) Kim et al. (1998) Kim & Ahn (1999) Baucells & Sarin (2003) Dias & Climaco (2005) Contreas & Marmol (2006) Keeney (2009) Adla et al (2011) Hinojosa & Marmol (2011) Chen et al (2012) Ackerman et al (2013) Jimenez-Martin et al (2017) Sarabando et al (2019)

SYSNTHESIS APPROACH Common Consensus interval reaching model

Aggregation of DMs

Voting procedures

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prioritizations are combined so that a group interval model is built. Therefore, the members of the group continue the analysis by trying to minimize the disagreements related to the range of preferences and reduce the preference intervals until an alternative is chosen. Kim and Ahn (1997) highlight the fact that finding pairwise dominance between alternatives through linear programming when information of all group members is considered becomes intractable due to the nonlinear form that the weight space may get. Therefore, the authors propose a way of aggregating DMs’ results based on group members’ preference strengths, based on the construction of a group aggregation function considering the relative importance of each DM (Kim and Ahn 1997, 1999). Kim et al. (1998) propose interactive procedures for solving multicriteria group decision-making problems with partial information based on the analysis of two utility ranges: total utility range, defined by the union of the utility value ranges of all DMs; and the agreed range, which is the intersection of the utility value ranges of all DMs, which may even be empty in some cases of strongly disagreement between the actors. Baucells and Sarin (2003) present an approach for constructing a group utility function, by aggregating individual utility functions, by presenting three elicitation methods for doing that: compromise on the willingness to pay; compromise on attribute weights; and compromise on attribute evaluation functions. Dias and Clımaco (2005) propose an adaptation on the VIP analysis methodology for dealing with group decision situations. The original VIP analysis software (Dias and Clímaco 2000) deals with additive aggregation of preferences under incomplete information provided by a DM, and the extension for group decision-making is made based on a GDSS that help the group to find a democratic solution, based on decision rules and/or consensus. Contreras and Mármol (2007) address the MCGDM problem under partial information by proposing a lexicographical method to minimize the maximum disagreement between DMs and therefore find compromising weights for evaluating alternatives. Keeney (2009) focus on collaborative group decisions, which does not embrace negotiations, risk-sharing arrangements, or voting procedures. In collaborative group decisions, DMs must interact to select alternatives. Aggregation of individual utility functions is also applied for building a group utility function. This chapter does not explicitly deals with partial information, but since key important issues related to aggregation of DMs are addressed, we decided to include in our assessment. Similarly, Adla et al. (2011) do not mention partial information specifically, but they present an interesting toolkit for guiding group decision support systems facilitators, which could perfectly be applied for aiding situations under partial information as well. The authors present a framework for supporting facilitators who are inexperienced to aid group decision-making processes. The work emphasizes how the facilitation process should be conducted, by considering several activities of the pre-meeting, meeting, and post-meeting phases. Different

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approaches for evaluation alternatives by DMs are considered, such as: direct rating of alternatives; holistic ranking of alternatives; voting tools; and also multicriteria evaluation with the same criteria weights for all DMs. Hinojosa and Mármol (2011) approach the group decision-making problem under partial information as a situation in which the DMs do not agree on the criteria weights, and therefore each DM establishes his own vector of weights and the decision has to be made by considering the information given by all members of the group. The authors propose different decision rules for dealing with such situations. Ackerman et al. (2013) brings out a different approach for considering partial information within the context of voting situations, stating that voters’ preferences information may not always be a ranking of all alternatives, but a partially ordered ranking instead. Chen et al. (2012) present a group decision support system for sorting alternatives in multicriteria decision problems based on decision rules for preferences aggregation based on DRSA (dominance-based rough set approach) and Dempster–Shafer rule. Jiménez-Martín et al. (2017) deal with partial information provided by DMs regarding alternatives’ consequences and attributes’ weights using the so-called dominance intensity methods, which lead to a ranking of the alternatives for each DM. In order to aggregate those rankings, the authors used the order explicit algorithm (OEA). Sarabando et al. (2019) consider partial information about DMs’ weights, attributes’ weights, and alternatives’ values to seek for optimal (or quasi-optimal) alternatives for a group of DMs in an MCDM problem. Other approaches considering partial information situations in group decisionmaking processes can also be found in the literature. A simulation study was conducted by Vetschera et al. (2014) in order to investigate the possible effects of different forms of partial information in group decision-making. The next section presents a new approach for dealing with preference modeling with incomplete information based on a flexible and interactive elicitation procedure.

Flexible and Interactive Tradeoff for MCGDM Preference Modeling FITradeoff Method The Flexible and Interactive Tradeoff (FITradeoff) method is a partial information method originally developed by de Almeida et al. (2016) for solving multicriteria decision-making problems under partial information, but preserving the whole axiomatic structure of the traditional tradeoff procedure proposed by Keeney and Raiffa (1976). The classical tradeoff procedure (Keeney and Raiffa 1976) is the elicitation procedure with the strongest axiomatic foundation (Weber and Borcherding 1993); however, it is rarely used in practice due to the difficulty presented for DMs, which leads to a 67% rate of inconsistencies, according to

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behavioral studies (Borcherding et al. 1991). In the classical tradeoff procedure, the DM compares hypothetical alternatives, considering tradeoffs between criteria, trying to find the exact value of some criterion that makes him/her feel indifferent to the maximum level of another criterion. Based on these indifferent statements provided by the DM, an equation system is solved to find the values of these parameters. But the main issue related to this procedure is that it is not easy for DMs to provide these indifferent points in a consistent way, since this information is very cognitively demanding. In this context, the FITradeoff method was developed to improve the applicability of the traditional tradeoff procedure for DMs, keeping its whole axiomatic structure, but with an easier elicitation process. Indifferent statements are replaced by preference statements provided by DMs, which characterizes a partial information situation. Linear inequalities are obtained from these preference statements, and then the synthesis step is conducted by performing linear programming models. In order to better understand how the process works, let us consider two hypothetical alternatives as shown in Fig. 2. Criteria scaling constants are first ordered according to the DM’s preferences (3). k1 > k2 > k3 > . . . > kn

ð3Þ

Then, the DM starts answering preference questions, in which he/she compares hypothetical alternatives similar to those in Fig. 2, considering tradeoffs among adjacent criteria. wi represents the worst possible outcome of criterion i, bi represents the best possible outcome of criterion i, and x represents some intermediate value between best and worst. Let us consider that the value of Criterion 2 which is indifferent to the best value of Criterion 3 is xI2. Therefore, if the value of x in Hypothetical Alternative A1 is set to x20, A1 will be preferred to A2, so that the global value of A1 is greater than the global value of A2 and the inequality in (4) is obtained. On the other hand, if the

Fig. 2 Hypothetical alternatives compared in FITradeoff

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value of x in Hypothetical Alternative A1 is set to x200, A2 will be preferred to A1, so that the global value of A2 is greater than the global value of A1 and the inequality in (5) is obtained. k 2 v2 ðx2 0 Þ > k 3

ð4Þ

k2 v2 ðx2 00 Þ < k3

ð5Þ

The FITradeoff elicitation process is interactive, so at each interaction the DM answers a new preference question comparing two hypothetical alternatives, and more inequalities similar to (4) and (5) are obtained. These inequalities form a space Φ a weights, inside which the performances of the alternatives are evaluated through linear programming problems so as to build a recommendation for the DM. It should be noticed here that, in FITradeoff, the DM does not have to specify the exact indifference value xI2, as required by the traditional tradeoff procedure. He/she just have to answer preference questions, which is cognitively easier and therefore the inconsistencies rate is expected to be reduced. Based on the weight space that is obtained, a recommendation for the DM may be given considering two different analyses depending on the goal of the decision maker: potential optimality analysis, when the DM wants to choose one alternative (de Almeida et al. 2016); and dominance analysis, when the goal is to build a ranking of the alternatives (Frej et al. 2019).

Choice Problematic: Potential Optimality Analysis Choice problematic situations in FITradeoff are dealt based on the analysis of the potential optimality of each alternative, at each interaction. According to de Almeida et al. (2016), an alternative is potentially optimal if its global value is greater than the global value of all other alternatives for at least one vector of weights within the weights space Φ. This condition can be verified by solving the LPP model (6, 7, 8, 9, 10, 11, and 12) below, for each alternative aj in a set of m alternatives:
 Xn
 Max v a j ¼ kv x i¼1 i i ij

ð6Þ

s:t: : k1 > k2 > . . . > kn
 ki vi x0i > kiþ1 i ¼ 1, . . . , n: ki vi ðx00 i Þ < kiþ1 i ¼ 1, . . . , n: Xn
 Xn kv x
k v ðx Þ j ¼ 1, . . . , m; z ¼ 1, . . . , m; j 6¼ z: i¼1 i i ij i¼1 i i iz Xn

k i¼1 i

¼1

ki
0 i ¼ 1, . . . , n:

ð7Þ ð8Þ ð9Þ ð10Þ ð11Þ ð12Þ

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The criteria scaling constants ki are the decision variables. The objective function (6) maximizes the global value of alternative aj. The constraint in (7) reflects the criteria scaling constants order previously established by the DM. The constraints in (8) and (9) are obtained based on strict preferences statements given by the DM when answering tradeoff questions (similar to those shown in Fig. 2). The constraints in (10) are the so-called potential optimality constraints, which aim to guarantee that the global value of alternative aj is greater than the global value of alternative each alternative az, j 6¼ z for at least one vector of weights. Normalization of weights and non-negativity are guaranteed by (11, 12), respectively. If the LPP model (6, 7, 8, 9, 10, 11, and 12) has viable solution, then aj is a potentially optimal alternative for the problem; i.e., it can be better than all the other alternatives for at least one vector of weights within the weight space. Otherwise, if this LPP model does not have a viable solution, then aj cannot be the optimal alternative of this problem, and therefore it is eliminated from the analysis. The choice recommendation for the DM is given when a unique alternative is found to be potentially optimal – it is the final optimal alternative for the MCDM problem. However, the flexibility of FITradeoff system allows the DM to visualize partial results at each step, after each interaction, in such a way that the current set of potentially optimal alternatives can be analyzed by the DM, who may choose to stop the process even before the end of the elicitation, if the partial results are already enough for his/her purposes.

Ranking Problematic: Pairwise Dominance Analysis The potential optimality analysis presented in the previous topic is an efficient way for dealing with choice problematic situations because it works based on a reduction of the alternatives set, by eliminating the ones that cannot be optimal for the problem. For ranking problematic situations, however, this approach is no longer useful for conducting the analysis. In order to be able to build a ranking with partial information provided, which is even more challenging than solving choice problems, the concept of pairwise dominance can be applied. According to Frej et al. (2019), an alternative aj dominates another alternative az if and only if the global value of az cannot be greater than the global value of for any vector of weights within the weight space Φ. Therefore, pairwise dominance relations are verified, at each interaction, for each pair of alternatives aj, az, based on LPP (13 - 18).
 Xn
 Xn Max D a j , az ¼ kv x  k v ðx Þ i¼1 i i ij i¼1 i i iz

ð13Þ

s:t: : k1 > k2 > . . . > kn

ð14Þ

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 ki vi x0i > kiþ1 i ¼ 1, . . . , n:

ð15Þ

ki vi ðx00 i Þ < kiþ1 i ¼ 1, . . . , n: Xn k ¼1 i¼1 i

ð16Þ

ki
0 i ¼ 1, . . . , n:

ð18Þ

ð17Þ

The decision variables are, again, the criteria scaling constants ki. The objective function (13) maximizes the difference between the global values of alternatives aj and az. The constraints (14, 15, 16, 17, and 18) characterize the weight space and are identical to the potential optimality model, except for the potential optimality constraints (10) which are no longer present in the current model. Frej et al. (2019) developed an algorithm for building a ranking of alternatives based on the dominance relations found. The ranking may be partial or complete, depending of the level of information obtained. At each interaction, more preferential information is obtained from the DM in such a way that the weight space gets tightened and the ranking is progressively refined. The process finishes when a complete order of the alternatives is obtained, or the DM can stop the elicitation process before the end if the partial ranking obtained is enough for him/her.

Group Decision Process Based on Flexible and Interactive Elicitation The flexible and interactive elicitation process is also useful for aiding group decision-making processes. The process is conducted through a decision support system (DSS) and it should be guided by an analyst with well background of the FITradeoff method. The process starts with the input data of the problem, which is composed by the consequences matrix, with the performance of the decision alternatives in each criterion, and the criteria order for each DM. Then, the question-answering process of FITradeoff starts. Each DM answers specific elicitation questions that are put for him/her by the FITradeoff DSS, according to the criteria order established by them. Based on the information given by each DM, both potential optimality and dominance analysis are performed by the FITradeoff system, for each DM. For instance, let us consider a problem with four criteria, four alternatives, and three DMs (DM1, 2, and 3), and alternatives are scored from 0 to 100 in each criterion. Figure 3 shows an example of a question made for DM, in which he has to specify his preferences between a hypothetical alternative with the worst outcome in criteria 2, 3, and 4 and a score of 90 in criterion 1 (which he considered as the most important criterion, according to his evaluation) and another hypothetical alternative with the worst outcome in criteria 1, 3, and 4 and the best outcome (score 100) in criterion 2. He can choose between consequence A, consequence B, indifference between the two consequences or even “no answer,” which is the case where the DM does not want to answer the question because he is

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Fig. 3 Elicitation question made by FITradeoff DSS

not sure about what he prefers; in such case, the system automatically computes another question, without loss of information. Another option for the DM is to choose the option “inconsistency,” if he thinks that some previous judgment given by him has to be changed. Still in Fig. 3, it is possible to see, in the top of the right side of the screen, how many questions this DM has already answer in the process (2, in this case) and also how many potentially optimal alternatives remain in his evaluation and how many ranking levels were achieved based on the partial information given until that point. By clicking on the button “show current results” (right side of Fig. 3), the DMs will be able to visualize the partial results obtained until that point for each DM, as can be seen in Fig. 4. The first table shows the potentially optimal alternatives for each DM; in this case, DMs 1 and 2 already found a unique optimal alternative in their evaluation, and DM 3 has still two potentially optimal alternatives. The second table in Fig. 4 shows the partial ranking obtained for each DM based on the dominance analysis explained in the previous topic; in this case, DMs 1 and 3 achieved three ranking levels, and DM 2 has two ranking levels. It should be highlighted that the number of ranking levels and potentially optimal alternatives is related to the amount of partial information gathered from each DM until the present moment. Another feature of the FITradeoff DSS is the possibility of having a graphical visualization of the partial results. On the top of Fig. 4, it is possible to see the labels “Bar Graph,” “Bubble Graph,” and “Radar Graph,” which are the three kinds of graphics available in the DSS. By clicking on the label “Bar Graph,” it is possible to visualize the graphic as in Fig. 5a; it shows the performance of the alternatives in each potentially optimal alternative in each criterion in a ratio 0–1 scale. The higher is the height of the bar,

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Fig. 4 Partial results for each DM in FITradeoff DSS

the better is the alternative in the respective criterion. This graphic is available for each DM, individually, and a collective graphic is also provided. Figure 5a illustrates the collective graphic, which shows, together, the potentially optimal alternatives for all DMs. Figure 5b and 5c shows, respectively, the collective bubble graphic and radar graphic, with the same information of the bar graphic in Fig. 5a, but in a different way, so that the DMs can choose the better visualization type according to their own preferences. It should be highlighted here that an analyst should be guiding the whole elicitation process, and he should also explain to the DMs how to interpret the questions, graphics, and other doubts that may happen during the process. The analyst should help the DMs to analyze the graphics and also their partial rankings, to see whether it is possible to achieve an agreement on which is the best solution for the group. The main idea of FITradeoff for group decision-making processes is to provide a flexible system for the group of DMs, with several tools that may help them to solve their problem. In some cases, however, the DMs may not be able to reach an agreement based on these analyses, and therefore it is necessary to apply different techniques to solve the MCGDM problem, such as decision rules, voting procedures, or even additive aggregation of DMs, as previously saw in this chapter. In case of performing an additive aggregation, issues related to DMs’ weights have to be carefully considered, since these parameters should not represent only the level of importance of the actors but also the consequence values related to each alternative chosen by each DM.

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Fig. 5 (a) Bar graphic – FITradeoff DSS. (b) Bubble Graphic – FITradeoff DSS. (c) Radar Graphic – FITradeoff DSS

Conclusions and Future Challenges A large number of MCDM/A methods are available in the literature to aid DMs when solving their problems, and the choice of the method should be made considering aspects regarding the DMs’ preference structure and rationality in the context of the decision-making problem (de Almeida et al. 2015). The increased amount of studies over years regarding MCDM/A methods with partial information confirms the relevance of this issue when dealing with complex problems. This chapter

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presented a brief overview of methods for preference modeling with partial information and classified them according to the framework for classification of partial information methods proposed by de Almeida et al. (2016). It can be noticed that all those approaches mentioned in section “Partial Information in Preference Modeling” have proposed innovated methodologies for solving MCDM/A and/or MCGDM/A problems, improving the applicability of traditional methods, and turning it possible to apply multicriteria techniques in real-life decisions, without much effort spent by DMs. Many of these papers present illustrative or even real-life applications in most various themes – such as supplier selection, job selection, selection of information systems and facility location, for instance – in order to show how their methods can be applied. This chapter does not consider methods with holistic judgments neither those methods with non-compensatory rationality, which should be considered in another study, since they have a completely different way of dealing with preference modeling. It can be argued that the most promising direction for future research on elicitation processes is toward requiring less information from the DM while maintaining the consistency of the result. Therefore, using partial information for preference modeling in MCDM/A methods may increase the potentiality and applicability of MCDM/A models in real situations. Regarding additional topics that should be explored in future researches, three major challenges can be highlighted. The first one concerns the problem of establishing weights for aggregation of decision makers. As previously discussed in this chapter, DMs’ weights should not reflect only the level of importance of each DM when an additive aggregation of DMs is performed, since these parameters should reflect the relative importance of the consequences related to the DMs’ results. Procedures for eliciting DMs’ weights should also be explored, as well as procedures for establishing criteria weights. The second challenge is related to the use of preference behavioral studies in order to modulate the decision methods and processes. Some initial studies have been done on this regard. For instance, Roselli et al. (2019) has applied decision neuroscience approach for improving the FITradeoff method, with recommendations for the design of its DSS and also improving the FITradeoff decision process with insights for the analyst and DM interaction. Another interesting future challenge is to deal with preference modeling in negotiation situations. Most of the negotiation support systems work based on direct rating of negotiation issues to build a utility/value function for each negotiator and therefore find an efficient frontier for both parts. However, in practice, establishing exact scores may not be truly meaningful for negotiators, which may lead to inconsistencies. Developing partial information approaches for preference modeling in negotiation situations appears itself as a high potential research field, since one of the most difficult tasks in negotiations is to model negotiators preferences in the prenegotiations phase.

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Cross-References ▶ Multicriteria Methods for Group Decision Processes: An Overview ▶ Multiple Criteria Decision Support ▶ Neuroscience Tools for Group Decision and Negotiation Acknowledgments This work had partial support from the Brazilian Research Council (CNPq).

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Group Decision Support Using the Analytic Hierarchy Process José María Moreno-Jiménez, Juan Aguarón, María Teresa Escobar, and Manuel Salvador

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AHP and Multi-actor Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Analytic Hierarchy Process (AHP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multi-actor Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AHP and Multi-actor Decision-Making (MACDM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contributions to Group Decision Support with AHP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AHP-Group Decision-Making Based on Consistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aggregation of Individual Preference Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Bayesian Approach in AHP-GDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A New Orientation in AHP-Multi-actor Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cognitive Multi-actor Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AHP-Cognitive Multi-actor Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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We provide a description of three significant and original contributions made by the Zaragoza Multicriteria Decision Making Group to the field of group decision and negotiation using the analytic hierarchy process. After beginning with a short overview of the AHP and its role in group decision support, we go on to include (i) a review of the importance of consistency in group decision-making and a profile of the proposal denominated as consistency consensus matrices; this is followed by (ii) an outline of the procedure that provides collective valuations of

J. M. Moreno-Jiménez (*) · J. Aguarón · M. T. Escobar · M. Salvador Grupo Decisión Multicriterio Zaragoza, Facultad de Economía y Empresa, Universidad de Zaragoza, Zaragoza, Spain e-mail: [email protected]; [email protected]; [email protected]; [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_51

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the alternatives in a group decision problem, known as the aggregation of individual preference structures,; and, finally, there is (iii) a brief examination of the Bayesian approach to group decision-making with the analytic hierarchy process and its relationship with prioritization, consistency, and compatibility. We conclude with an explanation and discussion of the cognitive orientation and its implementation in group decision-making. Keywords

Group decision and negotiation · Multiple criteria analysis · Cognition · Preferences · Decision support system · Group support · Multiple participantmultiple criteria · Negotiation process

Introduction The emergence of the Knowledge Society at the end of the twentieth century brought changes in philosophy (mechanistic reductionism to evolutionist holism), methodology (from the search for truth to the search for knowledge), and technology (communication networks and neurosciences). As a consequence, new analytical and computational decision tools have been developed and applied to new times and needs (Altuzarra et al. 2007, 2010; see chapter ▶ “Advances in Defining a Right Problem in Group Decision and Negotiation” by Shakun), including to the problem of group decision-making. More open and flexible scientific approaches to multi-actor decision-making (Moreno-Jiménez et al. 1999) must consider (i) the interdependences between factors, the interrelationships among actors, and the synergies derived from the holistic vision of reality; (ii) the integration of the rational and the emotional aspects in decision-making from a cognitive orientation, aimed at educating the actors involved in resolution processes (see chapter ▶ “Role of Emotion in Group Decision and Negotiation” by Martinovski); and (iii) the potential of information and communication technologies (ICTs) and neurosciences in the scientific resolution of problems, in particular, ITs to analyze big data and CTs to connect multiple actors and neuro and behavioral sciences for understanding perceptions and behavior (see chapter ▶ “Neuroscience Tools for Group Decision and Negotiation” by Almeida). One multicriterion methodology that responds well to the new times and needs is the analytic hierarchy process (AHP), developed by Thomas L. Saaty in the mid-1970s (Saaty 1980). AHP has become one of the most commonly employed approaches to the resolution of complex multi-actor problems for a variety of reasons (Moreno-Jiménez and Vargas 2018): (1) it is intuitive and realistic in scientific decision-making; (2) through hierarchies and clustering, it can integrate the large and the small; (3) it can combine tangible and intangible aspects of problems by means of absolute pairwise comparisons that yield relative ratio scales of priorities; (4) it has the flexibility to consider dependencies between

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levels in a hierarchy with the extension of the AHP known as the ANP (analytic network process); (5) it has a facility for incorporating into the formal models, in a deterministic or stochastic manner, the multi-actors’ visions of reality in the resolution of the problem; (6) in group decision-making, it allows decision-makers to construct group welfare functions that do not violate Arrow’s conditions; and (7) it is applicable to negotiations and learning/cognition (discussion, extraction, and dissemination of knowledge). After a brief review of AHP-based group decision support, this chapter comprises a summary of the three most significant contributions that the Zaragoza Multicriteria Decision-Making Group (GDMZ) has made to the field of multi-actor decisionmaking and the AHP in the last 15 years. Its structure is as follows: after this introduction, section “AHP and Multi-actor Decision-Making” presents the AHP and three situations (Escobar and Moreno-Jiménez 2007) associated with multi-actor decision-making (group decision-making, negotiated decision-making, and systemic decision-making); section “Contributions to Group Decision Support with AHP” outlines the basic ideas of the three contributions of the Zaragoza Multicriteria Decision Group to AHP-GDM that are included in this chapter: (i) a review of the seminal work on the use of consistency in group decision-making (consistency consensus matrix) and its extensions, (ii) an explanation of the aggregation of individual preference structures (AIPS) as a procedure to obtain the collective valuations of the alternatives in an uncertain and holistic context, and (iii) the Bayesian approach in AHP-group decision-making; finally, section “A New Orientation in AHP-Multi-actor Decision Making” introduces a potential line of research (cognitive orientation) for the AHP and, in general, for the future of the multicriteria decision-making (MCDM) field.

AHP and Multi-actor Decision-Making Multicriteria decision-making can be understood as the set of approximations, models, methods, and techniques that are followed in the resolution of complex problems that are characterized by the existence of multiple scenarios, actors, and both tangible and intangible criteria. The objectives are (i) to inculcate scientific rigor into the resolution process, complementing the rigor of classic science through the objective treatment of the subjective and by integrating reason and emotion; (ii) to help the decision-maker select the best and most realistic solutions, that is to say, the solutions that, simultaneously, are efficient (doing things correctly), efficacious (achieving goals), and effective (doing what is right to resolve the problem); and (iii) the continuous training (the value added by knowledge) of the actors implicated in the resolution of the problem in an essential aspect of the human being, the (scientific) decision-making. To achieve this, the arguments that support the different positions and decisions must be identified and disseminated (a cognitive orientation in decision-making – section “A New Orientation in AHP-Multi-actor Decision Making”).

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The Analytic Hierarchy Process (AHP) AHP is one of the most widely utilized multicriteria decision-making techniques. It is usually considered as a discrete multicriteria approach that uses a priori information on the preferences of the decision-maker (judgments emitted in pairwise comparisons), in which the priorities of the alternatives are obtained through the hierarchical aggregation of the values derived for the criteria or attributes that are considered. The methodology is based on four axioms (Saaty 1980), (i) reciprocity, (ii) homogeneity, (iii) inner and outer independence, and (iv) expectations, and consists of three phases: (a) modelling, (b) valuation, and (c) prioritization and synthesis. (a) The modelling of the problem is the construction of a hierarchy of different levels that represent the relevant aspects of the problem (scenarios, actors, criteria, alternatives). The mission or goal hangs on the highest level. The subsequent levels contain the criteria, the first-order sub-criteria, the second order, etc. This continues to the attributes (characteristics of the reality that are susceptible to be measured for the alternatives); the alternatives hang from the lowest sub-criteria level (attributes). The hierarchy must be complete, representative, nonredundant, and minimal. A dictionary of hierarchies can be seen in Saaty (Saaty and Forman 1993). There is an extension of the model, the analytic network process (ANP) which integrates dependencies in hierarchies (Saaty 1996). (b) Valuation involves the incorporation of the preferences of the decision-makers via pairwise comparisons of the elements (children) that hang from the nodes of the hierarchy in relation to the common (parent) node. Each judgment focuses on the comparison of two elements in respect of a single characteristic. The judgments reflect the relative importance of one element with respect to another with regard to the criterion that is considered. They are expressed in reciprocal pairwise comparison matrices. The judgments follow Saaty’s fundamental scale (Saaty 1980), which is an absolute scale (a quotient of ratio scales) of positive values {1/9,1/7,. . .,1/3,1/ 1,3/1,. . .,7/1,9/1} where 1 = equal; 3 = moderate; 5 = strong; 7 = very strong; and 9 = extreme. The intermediate values {2,4,6,8} and their reciprocals can be used to further specify the evaluations. The certainty of Saaty’s fundamental scale has been relaxed in posterior works in order to incorporate uncertainty through interval judgments (Moreno-Jiménez and Vargas 1993), reciprocal distributions (Escobar and Moreno-Jiménez 2000), and fuzzy numbers (Van Laarhoven and Pedrycz 1983). (c) Prioritization and synthesis determine the local, global, and total priorities. In general, priority can be understood as an abstract unit that is valid for any scale which integrates the preferences of the individual when comparing tangible and intangible aspects; it is used to order the alternatives and select the best one (Saaty 1980). Local priorities (priorities of the children with regard to the parent) are obtained from the pairwise comparison matrices in conjunction with any of the existing prioritization procedures. The eigenvector (EV) and the row geometric mean (RGM) are the two most commonly employed. Global priorities (the priorities of the elements of the hierarchy with regard to the mission) are obtained through the principle of hierarchical composition, while total priorities (the priorities of the

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alternatives with regard to the mission) are obtained by a multi-additive aggregation of the global priorities of each alternative. A multiplicative synthesis has also been contemplated but is rarely used. One of the outstanding virtues of the AHP is that it allows the relaxing of the restrictive hypotheses that impose traditional approaches on decision-making (utilitarian school); specifically, it does not demand the transitivity of the preferences. Human behavior is not always as rational as the school of rational choice assumes. In recent years, a new school of thought, based on psychology and economics, has emerged; it aims to demonstrate that transitivity does not always have to be satisfied in a rational decision. Kahneman and Tversky (1979) illustrated the many problems of expected utility theory as a descriptive theory of behavior that can lead to preference reversals; Tversky and Thaler (1990) provided plausible explanations as to how preference reversals may occur when people make decisions. The 2017 Nobel Prize winner for Economics, Richard Thaler, has demonstrated that human beings are afflicted by emotion and irrationality, which influences their decision-making on everything from retirement savings to health-care policy to professional sports. A theory of decision-making should allow for intransitivity if we wish to capture what Thaler (2017) calls predictably irrational behavior; and this is in complete agreement with the historical position of Saaty (Moreno-Jiménez and Vargas 2018). In addition, AHP allows for evaluation of the consistency of the decision-maker when eliciting judgments in the pairwise comparison matrices (PCMs). Saaty defined consistency in AHP as the cardinal transitivity of the judgments included in the PCMs, that is to say, the reciprocal pairwise comparison matrix Anxn = (aij) is consistent if 8i, j, k = 1, .., n satisfies aijajk = aik. Inconsistency is usually due to the limited capability of humans to understand the complexity of the problem, the lack of information, and the time available to make the decision. Two of the most widely used procedures in the AHP literature for evaluating inconsistency are Saaty’s consistency index (CI) (Saaty 1980) and the geometric consistency index (GCI) (Aguarón and Moreno-Jiménez 2003), used with the EV and the RGM prioritization methods, respectively. The expressions of these inconsistency measures are: CI ¼ GCI ¼

n  X  1 eij  1 nðn  1Þ i, j¼1

X 2 log 2 eij i 4, 8% when n = 4, and 5% when n = 3. The thresholds for the GCI can be found in Aguarón and Moreno-Jiménez (2003).

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When matrices exceed the permitted level of inconsistency, the decision-maker is asked to issue new judgments that meet the requirement. This requires tedious and expensive work. To mitigate these drawbacks, semiautomatic procedures with personal intervention have been suggested to modify the initial matrices until they achieve acceptable inconsistencies.

Multi-actor Decision-Making The consideration of multiple actors in decision-making has been motivated by the complexity of the problems, the relevance of the human factor, and the collaborative attitude toward the resolution of problems in the epoch of the Knowledge Society (KS), aided by the development of information and communication technologies (ICTs). Escobar and Moreno-Jiménez (2007) identified three multiple-actor decision-making situations: (1) group decision-making (GDM); (2) negotiated decisionmaking (NDM); and (3) systemic decision-making (SDM). Scientific literature usually includes these three situations under the name of group decision and negotiation. In this chapter, these situations will be maintained as detailed below. In GDM, individuals work together in pursuit of a common goal under the principle of consensus. Consensus refers to the approach, model, tools, and procedures for deriving the collective position or final group priority vector. NDM is based on the principle of agreement and the assumption that all the actors follow the same scientific approach. Each individual resolves the problem separately, the zones of agreement and disagreement between the actors are identified, and agreement paths (sometimes known as consensus paths) are constructed by changing, in a personal, semiautomatic, or automatic way, one or several judgments. SDM follows the principle of tolerance: each individual acts independently, and the individual preferences, expressed as probability distributions, are aggregated to form a collective one – the tolerance distribution. This new approach integrates all the preferences, even if they are encapsulated in different “individual theoretical models,” the only requirement is that they must be expressed as some kind of probability distribution. The systemic situation allows the capturing of the holistic vision of reality and the subjacent ideas of lateral thinking (de Bono 1970). The information provided by the tolerance distribution can be used to construct tolerance paths to produce a more democratic and representative final decision, in other words, a decision will be accepted by a greater number of actors or by a number of actors with greater weighting in the decisional process (Salvador et al. 2015; Moreno-Jiménez et al. 2016). The following section gives a brief explanation of the two techniques traditionally used in AHP-group decision-making: (i) the aggregation of individual judgments (AIJ) and (ii) the aggregation of individual priorities (AIP). This will provide a basis for the later description and development of the situations contemplated (GDM, NDM, SDM). However, it is first necessary to specify the notation that will be

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employed and to clarify the meaning of a series of terms that are often used without the necessary scientific rigor: Let D = {D[k], k!= 1, . . ., K} a group of K decision-makers with weightings P ½k β½k > 0 β ¼ 1 , A = {Ai, i = 1, . . ., n} a group of n alternatives, and C = {C‘, k

‘ = 1, . . ., m} a group of m criteria. For each criterion of the hierarchy C‘, the [k] decision-maker  D , k = 1,. . .,K, provides a positive and reciprocal square PCM ½‘,k ½‘,k ½‘,k ½‘,k AðnxnÞ ¼ aij with aij aji ¼ 1. In the case of a local or non-specified context, the superscript l is deleted for reasons of simplicity. At this point, it should be noted that in multi-actor decision-making, the terms consistency, compatibility, and consensus are often the cause of confusion. As they are commonly used, it is necessary to clarify their meaning, at least within the context of this present work and the expositions that follow. Consistency is associated with the (internal) coherence of the decision-makers when their judgments are considered in the PCMs (see section “The Analytic Hierarchy Process (AHP)”). Compatibility refers to the (internal) coherence of the group when selecting its priority vector (w[G] = (w1[G], . . ., wn[G])), that is to say, its representativeness in relation to the individual positions (w[k] = (w1[k], . . ., wn[k])). To evaluate the compatibility of an individual k(w[k]), k = 1, . . ., K, with the collective position or [G] group priority expression, taking  vector (w ), it issufficienttoadapt the previous  ½k ½G ½G ½k ½k ½G ½G eij ¼ aij = wj =wi or eij ¼ wi =wj = wj =wi . The concept of compatibility reflects the distance between the individual and collective positions and is calculated automatically, without the express intervention of the individual with the exception of the emission of the judgments of the PCMs. The geometric compatibility index (GCOMPI) is used in order to evaluate the compatibility of the individual positions with respect to the collective position provided by any of the existing procedures (Escobar et al. 2015; Aguarón et al. 2019). The expression of the GCOMPI for a decision-maker k in a local context (one criterion) is:

GCOMPI

½k,G

½G n1 X n X 2 ½k wj ¼ log 2 aij ½G ðn  1Þðn  2Þ i¼1 j¼iþ1 wi

! ð2Þ

and in a global context (hierarchy) by:

GCOMPI

½k,G

½G ½k  n1 X n X w wj 2 ¼ log 2 i½k ½G ðn  1Þðn  2Þ i¼1 j¼iþ1 wj wi

! ð3Þ

The GCOMPI for the group is given by: GCOMPI ½G ¼

X D½k  G

βðkÞ GCOMPI ½k,G

ð4Þ

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Finally, consensus refers to the situation in which the implicated individuals agree on the way to achieve a collective position. This agreement may concern the formation of collective judgments, the formation of collective priorities, or the acceptance of a procedure for attaining a collective priorities vector. Consensus is a fundamental concept in multi-actor decision-making (Moreno-Jiménez et al. 2005, 2008; Yu and Lai 2011), and this is especially true in the case of GDM. In this scientific literature, the term consensus is often used to reflect the idea of “personal” agreement or compatibility between individual and collective preferences (Dong et al. 2010; Wu and Xu 2012). The situation requires a personal intervention and acceptance of the collective position.

AHP and Multi-actor Decision-Making (MACDM) The following paragraphs detail some of the contributions that the GDMZ has made to three decision-making situations (GDM, NDM, and SDM) contemplated in AHP-MACDM. With AHP-GDM, all the actors seek the same goal in a coordinated manner; this supposes a common hierarchy when modelling the problem. There are a number of options for determining the priorities of the group (Saaty 1980; Iz and Gardiner 1993; Altuzarra et al. 2007). The two procedures conventionally employed in a determinist AHP-GDM context (Forman and Peniwati 1998) are AIJ and AIP. The first is used when the group works as a synergistic unit and the second when the group functions as a collective of individuals. Assuming a local context, with n alternatives {Ai, i = 1, . . ., n} and K decisionmakers {D[k], k = 1,. . ., K} whose relative importance in the group is   PK ½k ½k βk βk  0, k¼1 βk ¼ 1 , and denoted by A ¼ aij the pairwise comparison matrix of k-th decision-maker (i,j = 1,...,n), the priorities of the compared alternatives, in accordance with the AIJ and AIP, are obtained as follows: (i) Aggregation of individual judgments (AIJ): From the individual judgment matrices, A[k]k = 1, . . ., K, a group judgment matrix is constructed A½G ¼   ½G aij utilizing one of the individual judgment aggregation procedures (the geometric mean isthe most common); from this, the priorities of the alternatives    ½G=J  ½G=J  ¼ wi i ¼ 1, . . . , n are obtained by means of a prioritization w procedure. (ii) Aggregation of individual priorities (AIP): From the individual judgment matriare obtained by means of any of the ces A[k]k = 1, . . ., K, the individual  priorities  ½k 

prioritization procedures w½k ¼ wi

, k ¼ 1, . . . , K, and one of the aggrega-

tion of individual priorities is used to obtain the group priorities for  procedures  ½G=P

the alternatives w½G=P ¼ wi

.

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With regard to consistency in group decision-making with AHP, it has been demonstrated that with the weighted geometric mean method as the aggregation procedure, if the individual decision-makers show acceptable inconsistency, then so does the group; this is also true with both the eigenvector (Xu 2000) and the row geometric mean (Escobar et al. 2004) prioritization procedures. AHP (Turón et al. 2019) allows the application of most perspectives (determinist, stochastic, fuzzy, etc.) used in the scientific literature concerning the search for consensus (Herrera et al. 1996; Wu and Xu 2012; Zhang et al. 2014; see chapter ▶ “Multiple Criteria Decision Support” by Corrente). In addition to the two traditional (deterministic) approaches (AIJ, AIP), some more recent proposals in the stochastic context have been discussed by the GDMZ (Escobar et al. 2015). Altuzarra et al. (2007) presented a Bayesian prioritization procedure for AHPGDM that was more efficient than AIJ and AIP; Escobar and Moreno-Jiménez (2007) developed the aggregation of individual preference structures (AIPS) which captures the vision and uncertainty of decision-makers and the contextual interdependences of the alternatives (section “Aggregation of Individual Preference Structures”). Other AHP-GDM approaches include goal programming (Bryson and Joseph 1999); interval judgments (Arbel and Vargas 1993); stochastic preference modelling (Van den Honert 1998); fuzzy preference programming (Mikhailov 2004); and Dong et al. (2010) who suggested two new AHP consensus models that improve original inconsistency. Saaty and Peniwati (2008) compare different AHP-GDM methods. See also chapters ▶ “Multicriteria Methods for Group Decision Processes: An Overview” by Salo and ▶ “Multiple Criteria Decision Support” by Zarate. Using the consistency (section “AHP-Group Decision-Making Based on Consistency”), Moreno-Jiménez et al. (2005, 2008) devised a consensus searching decisional tool, the consistency consensus matrix (CCM), which has been recently extended (precise consistency consensus matrix – PCCM) in order to increase the number of entries considered in the CCM and the accuracy of the estimations (Escobar et al. 2015). Turón et al. (2019) described the algorithmic procedure for obtaining the PCCM and the accompanying graphic visualization tools. There are also a number of approaches to AHP-NDM: Gargallo et al. (2007) put forward a Bayesian procedure based on the use of mixtures; in cases with a large number of actors where a priori consensus is not required, they further developed graphic tools and clustering algorithms to identify homogeneous groups of actors with different patterns of behaviors for the priority rankings; Altuzarra et al. (2010), working in a local context with a small number of actors, introduced a semiautomatic procedure for the search for agreement/consensus that functions with complete and incomplete matrices; they use a hierarchical Bayesian regression linear model with log-normal errors and Monte Carlo Markov Chain (MCMC) methods to estimate the agreement priorities. In the same paper, they also suggest criteria for measuring the degree of agreement or compatibility between individual and collective priority vectors and use optimization procedures based on genetic algorithms for developing consensus paths among the actors.

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Other works dealing with the AHP-NDM context are Van den Honert and Lootsma (2000), who examined the relative strength of the negotiating position of each of the bargaining parties; Hämäläinen’s (2003) Decisionarium, a public site for interactive multicriteria decision support with tools for individual decision-making and group collaboration and negotiation; and Altuzarra et al. (2013) who have compiled a taxonomy for criteria, taking into account their influence and relevance in the final ranking of the alternatives. For analyzing negotiated processes, see chapter ▶ “Negotiation Process Modelling: From Soft and Tacit to Deliberate” by Szapiro. Moreno-Jiménez et al. (2016) discussed the third, and most original, situation in the AHP-MACDM context: AHP-SDM. It assumes that the actors independently elicit their judgments, and the individual preferences within a fixed set of alternatives are given a type of probability distribution that reflects the intensity of the preferences. Once the actors’ individual preferences are established, they look for a holistic decision, based on the principle of tolerance, which attempts to link multi-actor decision-making with one of the main ideas of lateral thinking (De Bono 1970).

Contributions to Group Decision Support with AHP AHP-Group Decision-Making Based on Consistency The relevance of the human factor in the resolution of the complex problems inherent in the Knowledge Society has made the consideration and collaboration of multiple actors in the decision-making processes essential. This is particularly true when incorporating the talent, imagination, and creativity of all the actors involved in decision-making. See also chapters ▶ “Looking Back on a Framework for Thinking About Group Support Systems” by Dörfler and ▶ “Group Support Systems: Past, Present, and Future” by Ackermann. In the case of the AHP-GDM, and using the RGM as the prioritization procedure, Moreno-Jiménez et al. (2005, 2008) proposed a new method for obtaining collective priorities, taking advantage of one of the characteristics (consistency) that distinguishes the methodology from other discrete multicriteria approaches. Assuming that the decision-makers would accept a collective position that was in their ambit of accepted inconsistency for the problem (usually CR 0 c0 τ τ½k ¼

1

σ ½k2

 n no s2o  Gamma o , for k ¼ 1, . . . , K 2 2

then, applying Bayes theorem:

ð9Þ

ð10Þ

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  1 μ½k j y½k  T n1 m½k , s½k2 ðX0 X þ c0 I n1 Þ , n0 þ J τ

½k

jy

½k

 n0 þ J ðn0 þ J Þs½k2 ,  Gamma 2 2

ð11Þ ð12Þ

0

n0 s2 þy½k ðI j XðX0 Xþc0 I n1 Þ1 X0 Þy½k with m[k] = (X0X + c0In  1)1(X'y[k]) and s½k2 ¼ 0 n0 þJ  0 ½k ½k ½k Þ ½k  where J ¼ nðn1 , y ¼ y , y , . . . :, y and X is the regression matrix (Jx(n-1)) 12 13 n1n 2

of Eq. (8). From Eq. (11), and using Monte Carlo methods, it is possible to calculate ½k  point and interval estimations of the priorities w½k ¼ vv½k0 and alpha (the most preferred alternative) and gamma (most preferred ranking) distributions. Using Eq. (12) it is possible to evaluate the consistency of the decision-maker. Bayesian treatment offers a natural framework for the inference processes of the parameters of the model and the model selection itself; it includes the associated uncertainty and makes exact inferences instead of asymptotic results of dubious validity in a context in which the number of observations is not usually very large (Bernardo and Smith 1994). In addition, it has enough flexibility to adapt to other techniques for providing information about the judgment matrices (Basak 1998; Hahn 2003). This obviously adds to the rigor and realism of the analysis and increases the robustness, accuracy, and consistency of the prioritization process (Altuzarra et al. 2007; Groselj and Stirn 2012). Furthermore, due to the appearance and development of Monte Carlo Markov Chain (MCMC) methods (Robert and Casella 2004), it has enough flexibility to integrate information external to data through prior distribution or by imposing constraints on the parameters or the variables of the problem by permitting the incorporation of incomplete/imprecise information through data augmentation techniques (Altuzarra et al. 2007). Finally, it facilitates the use of realistic discrepancy/incompatibility functions that enable measurement and analysis of the existing consensus/agreement in a group of decision-makers, and this increases the flexibility of AHP, obtaining more representative decisions and extracting knowledge from the decision process by enhancing the cognitive approach of the paradigm of multicriteria procedural rationality (MorenoJiménez and Vargas 2018; see chapter ▶ “Impact of Cognitive Style on Group Decision and Negotiation” by Adam-Ledunois). We now turn to some Bayesian GDM, NDM, and SDM methodological developments of the last 15 years which illustrate that which has been set out above. Some research lines are still open, and we hope to complete them in the near future. In a GDM scenario, Altuzarra et al. (2010) propose a consensus methodology which takes into account the weights {β[k]; k = 1, . . ., K}. They  suggest that ½k  ½k σ ½k2 ¼ λij σ 2 is taken in Eq. (8) where λ ¼ λij ; 1  i < j  n is a vector of individual attitude factors which allows the flexing of the opinions of each decision-maker in order to achieve consensus. Using these weights, the likelihood of the model is defined as:

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h  i YK h  iβ½k ½k ½G 2 ½k L y; μ½G , σ 2 ¼ f y jμ , σ , λ k¼1

ð13Þ

 0    0 0 where y ¼ y½1 , . . . , y½K , f y½k jμ½G , σ 2 , λ½k is the density of model Eq. (8), and, using a prior distribution similar to Eqs. (9–10), it is possible to estimate more et al. (2010) suggest discrepancy representative group priorities w[G]. Altuzarra  0 0 0 ½1 measures D(y, π consensus(λ)) where λ ¼ λ , . . . , λ½K  between the judgments y elicited by the decision-makers and the posterior distribution of (μG,σ 2) calculated using the Bayesian model Eqs. (9–10, 13) and to solve optimization problems given by: Minλ Dðy, π consensus ðλÞÞ subject to 1 

k p½max p½k ½k   λij  1 þ max 100 100

ð14Þ

k where 0 < p½max < 100; k = 1,. . .,K quantify the maximum degree of flexibility of each decision-maker. This procedure incorporates the negotiation attitudes of the decision-makers and allows the simulation of different scenarios where each decision-maker can soften or harden their original positions using the flexibility factors λ[k]. The optimum π consensus(λopt) would be used to take more representative decisions, trying to incorporate the diversity of opinions of the decision-makers. In NDM scenarios, consensus may not exist, especially if K is large. In this case, it would be interesting to identify partitions G ¼ G½1 , . . . , G½L of D (notice that the groups may be overlapping) of homogeneous P decision-makers. Gargallo et al.   (2007) advocate the use of mixtures μ½k  G ¼ L‘¼1 π ‘ N n1 μ‘G , Σ‘G and identify G using Bayesian nonparametric tools. Altuzarra et al. (2019) propose the use of the Bayesian selection of models to determine the number and composition of the groups in a local context but with K being small. It would be a good idea to extend these kinds of studies to multi-criteria problems with K being large. Hybrid grouping genetic algorithms similar to that proposed by Chen et al. (2011) could be an interesting line of future research. In SDM situations, the actors elicit their judgments independently, and the individual preferences within a fixed set of alternatives are given as a type of probability distribution that reflects the intensity of preferences. Once the actors’ individual preferences are established, they seek for a holistic decision, based on the principle of tolerance. The procedure attempts to link multi-actor decision-making with the parallel integration of the vision of reality of all the actors involved in the resolution process. Moreno-Jimenez et al. (2016) proposed a Bayesian framework for this process where it is assumed that the actors give their preferences through a set of posterior distributions {π k(w[k]| y[k]); k = 1, . . ., K} obtained from a set of different models used to describe the judgment elicitation process of each decisionmaker. The authors introduce the tolerance distribution as the probability distribution given by:

Group Decision Support Using the Analytic Hierarchy Process

i K β½k ½k   YK h  π tol w½G jfπ k ; k ¼ 1, . . . , K g 1 k¼1 π k w½G Σk¼1 β

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ð15Þ

which measures the degree of support of each priority vector w[G] as representative of the preferences of group members. Once πtol is determined, it is possible to select the best alternative or the k-best alternatives by means of Monte Carlo methods and to measure its compatibility with the preference of the actors (Salvador et al. 2015); this last chapter includes an algorithm for calculating a maximal group with a compatibility index larger than a fixed threshold and for calculating a tolerance distribution for imprecise information. In this way it is possible to know the existing opinions of the group in a very general framework where it is not necessary that the actors use the same criteria and the same methodology, and this therefore facilitates the development of multi-methodology methods in decision-making processes (Migers 2003). All the studies mentioned in this section assume a local context. The GDMZ is currently extending them to a global context with a hierarchy of criteria and subcriteria. A first step in this work was Altuzarra et al. (2013) which put forward a methodology of Bayesian prioritization. The authors assume that the judgment elicitation process of each criterion/sub-criterion can be described by a multiplicative model with log-normal errors. In this context, it is very difficult to calculate exact analytic expressions for the posterior distribution of global and total priorities, and Monte Carlo methods based on composition sampling should be used. The details can be seen in the above cited papers. The analysis of the influence of each criterion on the final decision makes it possible to extract knowledge on the decision process. To measure this influence, the authors suggest statistical cross-validation techniques that compare the posterior distribution of the total priorities when a criterion is included and excluded from the hierarchy. They also composed new measures to evaluate the discrepancy, discordance, or disagreement between both posterior distributions in such a way that the larger is the value, the larger is the influence exerted on the final result by the criterion being considered. Using these measures it is possible to identify the more relevant criteria by comparing the discrepancies between the posterior distributions of the total priorities and their partial priorities. A criterion will be relevant if there are no significant differences between the distributions in such a way that the final decision would have been the same if the criterion would have been the goal of the study. Altuzarra et al. (2013) assume only one decision-maker, but the results can be easily extended to GDM scenarios using AIJ or AIP procedures in the determination of local priorities and applying the results to the new decision-maker. The GDMZ is working on methods for the analysis of hierarchies in GDM, NDM, and SDM situations, and results will be published in due course. We are of the opinion that the Bayesian approach in AHP-MACDM offers more possibilities than the deterministic one when dealing with the uncertainty associated with the information

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provided by decision-makers. The use of hierarchical models and MCMC techniques can give enough flexibility to set up more realistic individual information elicitation processes (not necessarily based on the same approach) which incorporate individual and collective aspects (individual-negotiating attitude, perception of reality, moods, existence of various opinion groups, etc.) and analyze the consistency and compatibility of individuals’ opinions in order to achieve more consensual and representative decisions.

A New Orientation in AHP-Multi-actor Decision-Making In addition to improvements made in the decision tools developed by the GDMZ for AHP-MACDM and the identification of groups of actors with homogeneous preferences (Altuzarra et al. 2019), a new orientation in multicriteria decision-making and its implementation in the case of AHP-MACDM has been designed.

Cognitive Multi-actor Decision-Making The Knowledge Society (KS) can be understood as a space for the talent, imagination, and creativity of human beings. Aided by the development of information and communication technologies (ICTs), the Knowledge Society has three defining characteristics (Moreno-Jiménez and Vargas 2018): (i) interdependency between the factors and interrelationships between actors (a holistic vision of reality); (ii) improved education and training and the collaborative readiness of the actors (aptitude and attitude); and fundamentally, (iii) the importance of the human factor: the explicit consideration of the intangible, subjective, and emotional. The new scientific method must understand and reflect the fact that a key element of the KS is the human factor and its holistic perspective. The point of reference is the evolution of living systems characterized by three elements (Capra 1996): pattern, structure, and process: pattern is Maturana and Varela’s autopoiesis (selforganization); structure refers to Ilya Prigogine’s dissipative structures (order in disorder); and process corresponds to the vital process of living beings – the cognitive process founded on the plurality of opinions, the diversity of ideas, and personal selection. The process is able to foster the subsistence and evolution of humankind in a manner which is analogous to the process of genetic diversity and the natural selection of living systems that has functioned for thousands of years. Only species that learn and adapt to their context survive. It is clear that MACDM (and science in general) must have a cognitive orientation. It must be aimed at the continuous education of individuals (and the systems in which they are immersed) in that distinctive aspect of human beings – the ability to make decisions. The new methodology should add a further stage to the traditional stages included in the scientific resolution of problems: cognition, both individual and societal. It is not enough to reach the optimum decision (the product) or increase the knowledge and rigor of the resolution process; there must be an orientation

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toward improving the knowledge of people (Moreno-Jiménez and Vargas 2018; see chapters ▶ “Impact of Cognitive Style on Group Decision and Negotiation” and ▶ “Neuroscience Tools for Group Decision and Negotiation”).

AHP-Cognitive Multi-actor Decision-Making In the case of AHP-MACDM, the response to the challenges of cognitive orientation begins with the systematization of the cognitive exploitation of decisional processes (Moreno-Jiménez et al. 2014). The first step was multicriteria procedural rationality (MCPR) for the AHP-scientific resolution of problems (Moreno-Jiménez et al. 1999). MCPR seeks to improve the integral quality of the decision-making process by increasing knowledge of the problem and the procedures employed in its resolution. There are six phases: P1, formulation and description; P2, modelling; P3, valuation; P4, prioritization and synthesis; P5, uncertainty, robustness, and feedback; and P6, exploitation of the model: negotiation and learning. The new AHP methodology complements three traditional phases (P2, P3, and P4) with three original ones (P1, P5, and P6). P1 cognitively specifies the relevant aspects of the problem (the controllable and noncontrollable variables, the actors and their influences and confrontations, the criteria and their dependencies and conflicts, etc.). P5 analyzes the behavior of the system, including the validity of the approach, the robustness of the model, and the stability of the solution. P6 identifies the critical points, decision opportunities, and bottlenecks of the resolution process in order to determine modifications that favor the negotiation process among the actors involved in the decision-making process. The first stage of the cognitive orientation (MCPR) focuses on improving knowledge of the problem and the resolution process, but it does not, explicitly, consider the people or their continuous education. The educational process is facilitated by more fluid communication (mutual structural coupling) that is achieved by the inclusion of a discussion stage between the two rounds of voting (incorporation of preferences) and the diffusion of the knowledge extracted from the resolution process. Simply put, knowledge refers to the arguments that support the different opinions, positions, and decisions. There are three basic stages in the new AHP cognitive orientation: 1. Formulation – description and modelling, as previously described 2. Resolution – including two voting rounds with their respective stages of model exploitation that seek maximum knowledge and a discussion stage between the two voting rounds in which the actors provide text messages in support of their positions or criticize other positions 3. Cognition – the numerical information (priorities and preference structures) derived from the two voting rounds is combined with the text messages from the discussion stage in order to extract the knowledge (arguments that support decisions) derived from the scientific resolution of the problem. The knowledge must be shared to educate citizens and society in scientific decision-making. Visual graphic tools are some of the instruments employed in the sharing process.

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In addition, as a starting point for learning and continuing education, a fourth stage, accountability, is advisable. This is the evaluation of the efficiency (doing things correctly), the efficacy (achieving goals), and the effectiveness (doing what is right) of the resolution process. The discussion stage included in the process (Moreno-Jiménez and Vargas 2018) makes it possible to (i) take advantage of the talent and experience of actors; (ii) link the arguments with the preferences; (iii) incorporate quantitative information and qualitative knowledge; (iv) measure the individual importance and social relevance of the themes (messages and comments) as well as the individual confidence and social reputation of the participating actors; (v) evaluate the degree of compatibility between the individual and collective positions; (vi) determine the discrepancy thresholds which can be the basis for a new order in situations that are distant from the equilibrium (social dissipative structures); (vii) include social networks in the electronic participation (e-participation) processes; and (viii) guarantee the levels of security demanded by e-discussion and e-decision procedures. The exploitation of the mathematical model (AHP) and the information and knowledge generated by the discussion stage allow (cognition) (a) the measurement of the changes in collective and individual preferences; (b) the extraction of the arguments that support the opinions and decisions; (c) the identification of the social leaders and most significant themes; and, most importantly, (d) the measurement of the value added by the increase in individual and collective knowledge produced by the technique that is employed. This measurement can be used to determine the most suitable multiple criteria approach for each case: the approach that provides the greatest added value to the system (Moreno-Jiménez and Vargas 2018). In line with the evolution of living systems, this cognitive orientation of AHP/ ANP is based on the output and exploitation of decisional processes which can facilitate individual and social learning (cognitive orientation output). Nevertheless, a cognitive orientation can also be contemplated from the perspective of the input into the decisional processes. An outstanding issue in decisional science is the determination of the validity of an approach that is followed in scientific decision-making. Some of the characteristics that make the AHP/ANP school of thought particularly suitable for the consideration of human behavior and ideal for a cognitive orientation input are (i) the modelling of the hierarchy or network that allows linking the small with the large; (ii) the pairwise comparisons that evaluate the intangibles; (iii) the relaxation of consistency that allows slight intransitivity; (iv) the limitation of the number of alternatives (7  2) that allows the utilization of the power of the mind; and (v) the synthesis procedure that obtains the total priorities of the alternatives that reflect the behavior of the human brain. Similar arguments, using these ideas and the complementarity between quick answers (that capture experience and intuition) and slow responses (that capture analysis and logic) that are required by the temporal horizon of the problem, can be seen in Kanheman (2011), Thaler (2017), and Moreno-Jiménez and Vargas (2018).

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Cross-References ▶ A Group Multicriteria Approach ▶ Advances in Defining a Right Problem in Group Decision and Negotiation ▶ Behavioral Considerations in Group Support ▶ Group Decisions: Choosing Multiple Winners by Voting ▶ Group Support Systems: Concepts to Practice ▶ Group Support Systems: Past, Present, and Future ▶ Holistic Preferences and Prenegotiation Preparation ▶ Impact of Cognitive Style on Group Decision and Negotiation ▶ Methods to Analyze Negotiation Processes ▶ Multicriteria Methods for Group Decision Processes: An Overview ▶ Multiple Criteria Decision Support ▶ Negotiation Process Modelling: From Soft and Tacit to Deliberate ▶ Negotiation Processes: Empirical Insights ▶ Neuroscience Tools for Group Decision and Negotiation ▶ Role of Emotion in Group Decision and Negotiation

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Group Decisions with Intuitionistic Fuzzy Sets Peijia Ren, Zeshui Xu, and Janusz Kacprzyk

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Information Fusion with Intuitionistic Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Operations and Aggregations for Intuitionistic Fuzzy Information . . . . . . . . . . . . . . . . . . . . . . . . Measures and Clustering for Intuitionistic Fuzzy Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Decision-Making with Intuitionistic Fuzzy Preference Relations . . . . . . . . . . . . . . . . . . . . . . Consistency Checking and Improving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ranking Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Consensus Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple Attribute Group Decision-Making Methods with Intuitionistic Fuzzy Sets . . . . . . . . . Decision-Making Methods with Intuitionistic Fuzzy Aggregation Operators and Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intuitionistic Fuzzy Group Decision-Making Methods by Similarity to the Ideal Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intuitionistic Fuzzy Group Decision-Making Methods with Decision Characteristics . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions and Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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P. Ren School of Business Administration, South China University of Technology, Guangzhou, China e-mail: [email protected] Z. Xu (*) Business School, Sichuan University, Chengdu, Sichuan, China e-mail: [email protected] J. Kacprzyk Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_43

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Abstract

The intuitionistic fuzzy set has emerged as a powerful technique for presenting evaluations under uncertainty. It simultaneously describes an object from above and below, that is, by finding one description that includes the object and another that is included by it. Due to the increasing complexity of decision-making environments and the dynamic and uncertain characteristics of objects, the intuitionistic environment has proven valuable to support group decision-making over the past decades. To help decision makers interpret and apply intuitionistic fuzzy sets in group decision-making, an overview of intuitionistic fuzzy sets is analyzed from the perspectives of information fusion, intuitionistic fuzzy preference relation, and multi-attribute group decision. Intuitionistic fuzzy information (1) supports information fusion, the fundamental technique for processing decision information and the basis for attaining reasonable decisions, (2) facilitates fuzzy preference relations, enabling decision makers to express their evaluations and guaranteeing effective scientific decision-making, and (3) constitutes a significant tool for improving decision making and a direct means for reaching final decision results. To illustrate these ideas, the practical contributions of intuitionistic fuzzy sets are presented, including in the fields of supply chain management, healthcare, and risk assessment in hydropower station assessments and elsewhere. In addition, the prospects and challenges for future research are briefly pointed out. Keywords

Group decision · Context for group decision or context for negotiation · Fuzzy approaches · Intuitionistic fuzzy set · Information fusion · Intuitionistic fuzzy preference relation · Multiple attribute decision-making

Introduction As an increasingly complex society develops, group decision-making becomes ever more effective at solving the decision problems of everyday life, such as collaboration engineering (chapter ▶ “Collaboration Engineering for Group Decision and Negotiation”), voting activity (chapter ▶ “Group Decisions: Choosing a Winner by Voting”), etc. The intuitionistic fuzzy approach to decisions is scientific in that it comprehensively considers all decision-makers’ opinions and searches for appropriate adjustments when those opinions are significantly different. Properly conducted group decision-making helps to gather group intelligence and ensure reliable decisions. But increasing uncertainties in decision-making problems place increasing demands on the collective wisdom of decision-makers. Due to the increasing complexity and uncertainty of the social environment, people may lack knowledge in their cognition of things, giving decision-makers’ cognitive results the characteristics of ambiguity. Under such situations, decision-

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makers usually cannot give accurate numerical evaluations of objects and may therefore resort to vague descriptions. An intuitionistic fuzzy set (IFS) describes the degrees to which an object does or does not belong to a set using a membership function and a nonmembership function. This combination is a useful tool to depict decision-makers’ fuzziness in an uncertain environment. Mathematically, it is as introduced as (Atanassov 1986): Let X ¼ {x1, . . ., xn} be a fixed set. Then an Intuitionistic Fuzzy Set A in X is A ¼ fhx, μA ðxÞ, νA ðxÞijx  Xg, where μA(x) is the membership degree of x in A and νA(x) is the nonmembership degree of x in A. Note that 8x  X, μA(x), νA(x)  0, 0  μA(x) + νA(x)  1. Furthermore, the hesitancy or indeterminacy degree of x in A is defined as π A(x) ¼ 1  μA(x)  νA(x) (Szmidt and Kacprzyk 2000). The pair (μA(x), νA(x)) is also called an intuitionistic fuzzy number (IFN). For convenience, the IFN is denoted α ¼ (μα, να), where μα, να  0, μα + να  1 (Xu and Yager 2011). As the IFS can describe the initial evaluations of decision-makers from different angles, it provides a theoretical basis for scientific and rational group decisionmaking. Therefore, as group decision-making with intuitionistic fuzzy information has been discussed over the past decades, novel ideas for measuring the uncertainties of objects and making decisions under uncertainties have arisen. To enable readers to understand and effectively apply the IFS framework, we will review group decisionmaking methods with IFSs and their contribution to modeling and solving practical problems. The following ideas explain why our perspective proceeds from information fusion through preference relations to decision-making models. (1) Fusion techniques for intuitionistic fuzzy information will be reviewed, as information fusion facilitates collection and comparison of the opinions of the decision-makers and is therefore an essential step in group decision-making with IFSs. (2) The intuitionistic fuzzy preference relation (IFPR) will be introduced, as it has proven to be an indispensable tool for enabling decision-makers to judge the superiority or inferiority of one object to another, in the presence of fuzziness. (3) Ranking methods for alternatives with intuitionistic fuzzy information will be demonstrated, as it is straightforward and efficient to get the solution of group decision problems.

Information Fusion with Intuitionistic Fuzzy Numbers Information fusion is based on a systematic approach to synthesizing and extending modern information technology in a multidisciplinary context. With the rapid development of computer technology, information characteristics, such as diversity and size, have emerged. Meanwhile, increasing uncertainty and complexity has made modern information fusion techniques crucial to scientific decision. Therefore, the problem of how to effectively integrate information and utilize it to support decisions has become central.

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The growing interest on investigating the fusion theory of intuitionistic fuzzy information is generally classified into two categories: (1) operations and aggregations and (2) measures and clustering. In the following, we review both approaches to fusion theory and its applications.

Operations and Aggregations for Intuitionistic Fuzzy Information Generally, a group decision-making process must collect all decision-makers’ opinions, establish a suitable method for measuring them, obtain the final scores of all alternatives, and then rank them. For the purposes of group decision-making, we first present the operational laws for IFNs (Xu and Yager 2006; Xu 2007a): Let α ¼ (μ, ν), α1 ¼ (μ1, ν1), and α2 ¼ (μ2, ν2) be IFNs and let λ be a positive number. Then (1) (2) (3) (4) (5) (6) (7)

α ¼ ðν, μÞ; α1 \ α2 ¼ (min{μ1, μ2}, max {ν1, ν2}); α1 [ Lα2 ¼ (max{μ1, μ2}, min {ν1, ν2}); α1 N α2 ¼ (μ1 + μ2  μ1μ2, ν1ν2); α1 α2 ¼ (μ1μ2, ν1 + ν2  ν1ν2); λα ¼ (1  (1  μ)λ, νλ); αλ ¼ (μλ, 1  (1  ν)λ).

The following examples illustrate these operations: suppose that α1 ¼ (0.5, 0.2) and α2 ¼ (0.3, 0.4) are two IFNs L and set λ ¼ 2; then α1 ¼ ð0:2, N 0:5Þ, α1 \ α2 ¼ (0.3, 0.4), α1 [ α2 ¼ (0.5, 0.2), α1 α2 ¼ (0.65, 0.08), α1 α2 ¼ (0.15, 0.52), λα1 ¼ (0.75, 0.04), and α1λ ¼ (0.25, 0.36). To obtain group decision-making results, it is necessary to introduce aggregation techniques to collect decision-makers’ opinions and get the scores of alternatives. Currently, some operators have been introduced, such as an intuitionistic fuzzy weighted averaging (IFWA) operator (Xu 2007a), an intuitionistic fuzzy ordered weighted averaging (IFOWA) operator (Xu 2007a), an intuitionistic fuzzy hybrid averaging (IFHA) operator (Xu 2007a), an intuitionistic fuzzy weighted geometric (IFWG) operator (Xu and Yager 2006), an intuitionistic fuzzy ordered weighted geometric (IFOWG) operator (Xu and Yager 2006), and an intuitionistic fuzzy hybrid geometric (IFHG) operator (Xu and Yager 2006). Basically, for a set of IFNs αj ¼ (μj, νj)( j ¼ 1, . . ., n), if we let the IFWA and the IFWG: Ωn ! Ω, then the IFWA operator and the IFWG operator are respectively: IFWAðα1 , . . . , αn Þ ¼ w1 α1 IFWGðα1 , . . . , αn Þ ¼ α1 w1

M O

... ...

M O

wn αn α n wn

where w ¼ (w1, . . ., wn)T is the weight vector of αj for j ¼ 1, . . ., n. Note that, the IFOWA operator is an extension of the IFWA operator by positioning all IFNs in descending order, and the IFHA operator is a further extension of the IFOWA

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operator with both ordered weights and IFNs. In parallel, the IFOWG operator extends the IFWG operator by positioning all IFNs in descending order, and the IFHG operator is a further extension of the IFOWG operator with both ordered weights and IFNs. To obtain more general aggregation techniques, Zhao et al. (2010) developed a generalized intuitionistic fuzzy weighted averaging (GIFWA) operator, a generalized intuitionistic fuzzy ordered weighted averaging (GIFOWA) operator, and a generalized intuitionistic fuzzy hybrid averaging (GIFHA) operator. To take advantage of the Choquet integral to simultaneously reflect the importance degrees and correlations of the elements and the corresponding ordered positions, Xu (2010a) proposed an intuitionistic fuzzy correlated averaging (IFCA) operator and an intuitionistic fuzzy correlated geometric (IFCG) operator. In order to avoid the objective impacts on aggregation results of the weight vector and aggregation techniques, Xia and Xu (2010) introduced an intuitionistic fuzzy-dependent averaging (IFDA) operator and an intuitionistic fuzzy-dependent geometric (IFDG) operator. To depict the interrelationship between the collected IFNs in aggregation operators, Xu and Yager (2011) extended the Bonferroni mean into intuitionistic fuzzy environment and defined an intuitionistic fuzzy Bonferroni mean (IFBM) and a weighted intuitionistic fuzzy Bonferroni mean (WIFBM), which are shown next. For a set of IFNs αj ¼ (μj, νj) ( j ¼ 1, . . ., n), the IFBM and the WIFBM are mappings from Ωn to Ω. For p, q > 0, the IFBM operator and the WIFBM operator are 0

1 11pþq

0

B CC BM B 1 B n  p O q CC CC B IFBMp,q ðα1 , . . . , αn Þ ¼ B α α i j CC ; B nð n  1Þ B @ AA @ i, j¼1 i6¼j

0

1 11pþq

0

B CC BM O B 1 B n  q CC p C B B w jα j C ðwi αi Þ WIFBM ðα1 , . . . , αn Þ ¼ B CC , B @nðn  1Þ @ i, j¼1 AA p,q

i6¼j

where w ¼ (w1, . . ., wn)T is the weight vector of αj for j ¼ 1, . . ., n. Based on the aggregation results, comparison and ranking of alternatives is the final goal of all decision-making problems. To this end, Xu (2007a) introduced the comparative techniques as: Let s(α) ¼ μ  ν and h(α) ¼ μ + ν be the score function and accuracy function of an IFN α ¼ (μ, ν), respectively. If the scores and accuracy degrees of two IFNs α1 ¼ (μ1, ν1) and α2 ¼ (μ2, ν2) are calculated as s(α1), s(α2), h(α1), and h(α2), then (1) if s(α1) < s(α2), then α1 is smaller than α2, i.e., α1 < α2. (2) if s(α1) ¼ s(α2), then

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(i) if h(α1) < h(α2), then α1 is smaller than α2, i.e., α1 < α2. (ii) if h(α1) ¼ h(α2), then α1 is equal to α2, i.e., α1 ¼ α2.

Measures and Clustering for Intuitionistic Fuzzy Information In group decision-making, decision-makers usually have different kinds of expertise. For example, suppose workers in the business unit, financial department, personnel department, and other related departments need to participate in a project for an enterprise. In such a situation, these decision-makers may hold decision-making opinions with different perspectives. To make decision results more reasonable, it is a good idea to classify the opinions into clusters, make decisions in each cluster, and then finally gather together the results of all clusters. Because clustering is important for group decision-making with intuitionistic fuzzy information, we first review the basic techniques of clustering, i.e., distance and similarity measures for intuitionistic fuzzy information, and then present some recent research on clustering that applies in this context.

Distance and Similarity Measures Two commonly used distance measures for IFSs have been introduced: let d be the mapping d: (Φ(X))2 ! [0, 1] and X ¼ {x1, . . ., xn}, then the distance between A  Φ(X) and B  Φ(X) can be obtained by (Burillo and Bustince 1996): (1) The normalized Hamming distance: d1 ðA, BÞ ¼

n             1 X    μA x j  μB x j  þ νA x j  νB x j  þ π A x j  π B x j  : 2n j¼1

(2) The normalized Euclidean distance:

d 2 ðA, BÞ ¼

n   2     2     2  1 X    μA x j  μB x j þ νA x j  νB x j þ πA x j  πB x j 2n j¼1

!12

Correspondingly, similarity measures have been defined as (Szmidt and Kacprzyk 2004; Xu and Chen 2008): (1)

dðA, BÞ : s1 ðA, BÞ ¼  d A, B

(2) s2 ðA, BÞ ¼ 1 

dðA, BÞ  : d ðA, BÞ þ d A, B

:

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To integrate the normalized Hamming distance and the normalized Euclidean distance of IFSs, Xu (2007b) defined a distance measure of IFSs as: d 3 ðA, BÞ ¼

n   λ     λ     λ 1 X    μ x  μB x j  þ νA x j  νB x j  þ π A x j  π B x j  2n j¼1 A j

!1λ :

Based on the above work, some distance measures and similarity measures that consider weights and continuity have been investigated, such as the normalized Hamming distance based on the Hausdorff metric, the normalized Euclidean distance based on the Hausdorff metric, the weighted Hamming distance based on the Hausdorff metric, the weighted Euclidean distance based on the Hausdorff metric, similarity measures measuring the similarity or dissimilarity of objects (Szmidt and Kacprzyk 2004), and other similarity measures incorporating decision-makers’ risk preferences (Xu and Chen 2008; Xia and Xu 2010).

Clustering Clustering is an efficient way to analyze statistical data by dividing data into different categories according to the relationship between any pair of data items. The objective is to guarantee the rationality and precision of decision-making integrating different opinions. Before reviewing existing clustering algorithms for IFSs, we first show several different coefficient definitions of IFSs as follows: Let X ¼ {x1, . . ., xn} be a universe of discourse and A ¼ {hx, μA(x), νA(x)i| x  X}, B ¼ {hx, μB(x), νB(x)i|x  X} be two IFSs, A, B  Φ(X), then the association coefficients of A and B are: (1) if X ¼ {x1, . . ., xn}is a discrete universe of discourse, then (Xu et al. 2008) n P



c1 ðA, BÞ ¼ max

n  P

i¼1

ðμA ðxÞμB ðxÞ þ νA ðxÞνB ðxÞ þ π A ðxÞπ B ðxÞÞ

i¼1

n  P μ2A ðxÞ þ ν2A ðxÞ þ π 2A ðxÞ , ðμ2B ðxÞ þ ν2B ðxÞ þ π 2B ðxÞÞ

:

i¼1

(2) if X ¼ {x1, . . ., xn} is a continuous universe of discourse, then (Xu et al. 2008) Ðb c2 ðA, BÞ ¼

max

Ð  b

a ðμA ðxÞμB ðxÞ

2 a μ A ðxÞ

þ

ν2A ðxÞ

þ νA ðxÞνB ðxÞ þ π A ðxÞπ B ðxÞÞdx :  Ðb þ π 2A ðxÞ dx, a ðμ2B ðxÞ þ ν2B ðxÞ þ π 2B ðxÞÞdx

For m IFNs Aj( j ¼ 1, . . ., m), Xu et al. (2008) provided a procedure for establishing their association matrix by using the above equations to calculate the association coefficients between any two IFNs, where the element of ith row jth column in the association matrix is the association coefficient of IFNs Ai and Aj.

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Subsequently, a clustering algorithm was constructed by using λ-cutting matrix of the transformed form. Based on the fundamental measures of IFSs, such as Hamming, Euclidean, and other normalized distances, a hierarchical clustering algorithm was introduced for IFSs (Xu 2009a).

Applications The ability of IFSs to depict uncertainty and fuzziness has resulted in many practical applications. The idea of finding the smallest distance between the symptoms of a patient and the symptoms of possible illnesses is the basis of a decision-making method with IFSs that was developed to handle intelligent data analysis for medical diagnosis (Szmidt and Kacprzyk 2003a). Many of the above-referenced works on aggregation, similarity measures, and clustering algorithms for intuitionistic fuzzy information have been utilized to handle decision-making problems such as the emergency response and reconstruction plans for disasters, communication support, site selection, human resource management, etc.

Group Decision-Making with Intuitionistic Fuzzy Preference Relations Lack of information in group decision problems makes it difficult for decisionmakers to evaluate alternatives with respect to attributes directly; instead, decisionmakers may prefer to express their opinions in the context of pairwise comparisons of the alternatives. Since the process of comparing any two alternatives reflects decision-makers’ judgments and conforms to their thinking patterns, the construction of decision methods based on preference relations has become an important approach to address decision problems. Complexity and the limitations of human thinking abilities explain why preference relations with fuzzy information have become an important basis for modern decision-making. As described before, the intuitionistic information is a powerful tool to represent uncertainty and fuzziness. In this part, we review group decisionmaking with IFPRs from the perspectives of (1) decision-making models with IFPRs based on consistency checking and consistency improving, (2) ranking techniques based on IFPRs, and (3) group consensus models based on IFPRs.

Consistency Checking and Improving The concept of consistency is a measure of the rationality and effectiveness of decision-makers’ judgments. It is common for decision-makers’ comparative results on two pairs of alternatives to conflict. For example, if a decision-maker thinks that alternative A is superior to alternative B with degree 3, and that alternative B is

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superior to alternative C with degree 3, but sometimes the decision-maker may also feel that alternative A is superior to alternative C with degree 4. This situation is contradictory, and we know the degree of alternative A superior to alternative C must be 9 according to the transitivity. To avoid this conflict, the index for checking the consistency of the preference relation is very significant to be introduced to ensure the reasonability of decision results. Recently, there has been a surge of interest in the consistency of IFPRs. Firstly, the original definition of IFPR is presented as follows: Consider a set of alternatives X ¼ {x1, . . ., xn} and an IFPR B on X represented by a matrix B ¼ (bij)n  n  X  X, where bij ¼ (μij, νij) for all i, j ¼ 1, . . ., n are IFNs. Then μij is the certain degree to which xi is preferred to xj, and νijis the certain degree to which xi is non-preferred toxj, where (Xu 2007c): 0  μij þ νij  1, μij ¼ νji , νij ¼ μji , μii ¼ νii ¼ 0:5

for all

i, j ¼ 1, . . . , n:

Based on this definition, additively consistent and multiplicatively consistent IFPR have been investigated: For an IFPR B ¼ (bij)n  n  X  X, where bij ¼ (μij, νij), if w ¼ (w1, . . ., wn)T is n P the underlying weights of alternatives with 0  wi  1 and wi ¼ 1 , then a i¼1

consistent IFPR should satisfy: (1) Additive transitivity (Xu and Liao 2015; Xu 2007d; Wang 2013): (i) (bij  0.5) + (bjk  0.5) ¼ (bik  0.5) for all i, j, k ¼ 1, . . ., n. (ii) bij ¼ 0.5(wi  wj + 1) for all i, j ¼ 1, . . ., n. (iii) μij  0.5(wi  wj + 1)  1  νij for all i, j ¼ 1, . . ., n. (iv) μik + μjk + μki ¼ μki + μji + μik for all i, j, k ¼ 1, . . ., n. (2) Multiplicative transitivity (Tanino 1984; Xu 2007d; Xu et al. 2011; Liao and Xu 2014a): b b (i) bijji ¼ bbikki  bjkkj for all i, j, k ¼ 1, . . ., n. wi (ii) bij ¼ wi þw for all i, j ¼ 1, . . ., n. j wi (iii) μij  wi þw  1  νij for all i ¼ 1, . . ., n  1, j ¼ i + 1, . . ., n. j

(iv) μijμjkμ8 ki ¼ νijνjkνki for all i, j, k ¼ 1, . . ., n.   > 0, μik , μkj  fð0, 1Þ, ð1, 0Þg < μik μkj , otherwise, for all i  k  j. (v) μij ¼ > : μ μ þ ð1  μ Þ 1  μ  ik kj  ik kj  8 , ν 0, ν  ð 0, 1 Þ, ð 1, 0 Þ f g ik kj < νik νkj νij ¼   , otherwise, for all i  k  j. : νik νkj þ ð1  νik Þ 1  νkj

Because the consistency property of preference relations is difficult to satisfy, some research has been based on the concept of acceptable consistency. By measuring the distance between the original IFPR and its corresponding perfectly consistent IFPR, Xu and Liao (2013) and Xu and Xia (2014), respectively, proposed that B is called an acceptably consistent IFPR if

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  d B, B ¼

n X n  X      1 μij  μij  þ νij  νij  þ π ij  π ij   τ 2ðn  1Þðn  2Þ i¼1 k¼1

and   σ B, B ¼

n X n  X    1 μij  μij  þ νij  νij   τ  2nðn  1Þ i¼1 j¼1

where B is an IFPR, B is the corresponding perfectly consistent IFPR, and τ is a constant, which is the acceptable consistency threshold. Based on the consistency measure, the next step is to investigate how to repair inconsistent IFPRs into acceptable ones. To address this issue, different feedback algorithms were studied (Xu and Liao 2013; Xu and Xia 2014). In summary, these algorithms rely on procedures of consistency checking, adjusting the unacceptably inconsistent IFPR into an acceptably consistent one. The details of these algorithms can be briefly shown in Fig. 1. To enhance the applicability of IFPRs in group decision-making, the intuitionistic fuzzy analytic hierarchy process and the intuitionistic fuzzy analytic network process were further developed (Xu and Liao 2013; Liao et al. 2018). They commonly contain the following steps: (1) analyze the hierarchy or network structure of the group decision-making problem; (2) identify the individual IFPRs assigned by each decision-maker, making clusters and elements treatment for the intuitionistic fuzzy analytic network process; (3) check the consistency of each individual IFPR and repair the inconsistent one with the procedure in Fig. 1; (4) aggregate the individual IFPRs on criteria and alternatives into overall ones; (5) derive the local priorities of criteria and alternatives from the aggregated IFPRs; and (6) synthesize the global priorities of alternatives and ranking them.

Ranking Models As the final goal is to obtain a ranking of alternatives, ranking techniques based on IFPRs must be discussed. After defining IFPR, Xu (2007c) proposed to use intuitionistic fuzzy arithmetic averaging operator and intuitionistic fuzzy weighted START

Consistency definition of IFPR

The IFPR given by a decision maker

The perfectly consistent IFPR

Consistency index

Index < acceptable threshold

Yes

Output the IFPR

No Improving the consistency of IFPR by making it closer to its perfectly consistent IFPR

Fig. 1 Summarized procedure for obtaining an acceptably consistent IFPR

END

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arithmetic averaging operator to determine the final priority of each alternative. Even though these techniques provide a direct way to get the priorities of alternatives from IFPRs, they cannot ensure the reasonability of decision-making results as the consistency property of IFPR is ignored. With this consideration, some programming models were developed to address the rankings of alternatives based on the consistency definitions of IFPRs. Firstly, by constructing the score matrix of an IFPR, Xu (2007d) studied the additive consistency and multiplicative consistency of IFPR by linking the relationship between original IFPR and its corresponding score matrix. Then, to minimize the consistency existing in the IFPR, some linear programming models were established. Later on, applying the additive consistency criterion μij  0.5(wi  wj + 1)  1  νij, where B ¼ (bij)n  n is an IFPR and bij ¼ (μij, νij), a fundamental and simple programming model was constructed to generate the priorities from B, which can be shown as (Xu 2009b): Min

n1 X n  X i¼1



þ d ij þ d ij



j¼iþ1



s:t: 0:5 wi  w j þ 1 þ d  i ¼ 1, . . . , n  1; j ¼ i þ 1, . . . , n, ij  μij ,   þ 0:5 wi  w j þ 1  d ij  1  νij , i ¼ 1, . . . , n  1; j ¼ i þ 1, . . . , n, n X wi ¼ 1, wi  0, i ¼ 1, . . . , n, i¼1 þ d ij , d ij  0,

i ¼ 1, . . . , n  1; j ¼ i þ 1, . . . , n:

þ where d ij and d ij are nonnegative numbers. Furthermore, Liao and Xu (2014a) defined a novel concept of multiplicatively consistent IFPR by addressing its corresponding interval weights and then presented fractional programming models to get the priorities from an IFPR. Through building the preferred IFPR and the dual preferred IFPR of an IFPR and capturing the multiplicative transitivity of the combination matrix of the preferred IFPR and dual preferred IFPR, a definition for multiplicative consistency was introduced. Subsequently, 0–1 mixed programming models were established to determine priorities from the IFPR (Meng et al. 2017). By investigating the transitivity property of IFPR, Pȩkala et al. (2018) introduced an algorithm that generates weak transitivity for alternatives and further establishes a procedure for ranking alternatives in group decision-making in intuitionistic fuzzy environment. The above models present some techniques to derive priorities from individual IFPRs and are the fundamental core of group decision-making with IFPRs. Solutions involve addressing the individual IFPRs with these models and then aggregating the results.

Group Consensus Models Group decision-making is now the main process to deal with decision problems in practice. Actually, individual decision-makers usually provide different opinions,

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making it unclear how to measure the effectiveness of these opinions in high-quality decisions. Consensus, which can judge a decision-maker’s opinions are compatible with others’, is an important way to ensure the reasonability of the final decisions. Therefore, recent trends in decision theory have led to a proliferation of studies about group decision-making with consensus in an intuitionistic fuzzy environment. By defining the level of pairwise agreement between two IFPRs, Szmidt and Kacprzyk (2003b) presented the concept of α-level consensus and a way to measure the consensus degree among IFPRs. Based on defining the compatibility degree by comparing all pairs of decision information given by decision-makers, Xu (2013) presented a feedback algorithm for group decision-making with compatible IFPRs. Considering that the consistency of individual IFPRs is also a crucial factor for scientific decision-making, Liao et al. (2015) proposed a consensus-reaching procedure to find the optimal alternative after consistency checking for all individual IFPRs. Since existing consensus models may lose the judgments of the removed decision-maker(s) making the decision results biased, an enhanced consensus model for group decision-making under intuitionistic fuzzy environment was addressed (Liao et al. 2016). It reduces bias in decision results by removing the opinions of a decision-maker with large deviations from the overall opinions, rather than removing the decision-maker from the expert group. Similarly, to improve the effectiveness of decisions, Meng et al. (2017) developed a group decision-making process by establishing 0–1 mixed programming models to improve the consistency of all IFPRs, providing a consensus index for IFPRs and forming a procedure for group decision-making with inconsistent IFPRs. To sum up, the details of the algorithms/ procedures for group decision-making with consensus under intuitionistic fuzzy environment are briefly represented in Fig. 2.

Applications The introduction and development of processes for group decision-making with IFPRs have been utilized in actual decision-making cases. For example, the intuitionistic fuzzy analytic hierarchy process was applied to assess the performance of a venture capital guide fund (Gu et al. 2015) and to evaluate human settlement in

START

Aggregation of all IFPRs

Consensus definition

Consensus index

Index < acceptable threshold

Yes

Output all IFPRs

Make decision

No Adjusting the IFPRs according to the aggregated IFPR

END

Fig. 2 Summarized procedure for group decision-making with consensus under intuitionistic fuzzy environment

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Lhasa (Wang and Xu 2018), etc. Other applications have supported performance assessments of hydropower stations and brand management of the six golden flowers liquor, among others.

Multiple Attribute Group Decision-Making Methods with Intuitionistic Fuzzy Sets In a majority of practical group decision-making problems, decision-makers often need to evaluate the alternatives from multiple perspectives when they make decisions. Based on determining the attributes for decision-making problems, decisionmakers can clearly analyze the performance of alternatives with respect to each attribute and then adopt the proper methods to efficiently make decisions. The complexity and uncertainty in practice determine that IFS is one of the important tools to represent the fuzziness of objects and should be applied to deal with group decision-making problems. In this section, we aim to make retrospect about intuitionistic fuzzy decision-making methods for multiple attribute group decision-making (MAGDM) problems. The existing researches on group decision-making methods with intuitionistic fuzzy information can be generally classified into the following three categories: (1) decision-making methods with intuitionistic fuzzy aggregations and measures; (2) decision-making methods by similarity to the ideal solutions; and (3) decisionmaking methods with other decision characteristics.

Decision-Making Methods with Intuitionistic Fuzzy Aggregation Operators and Measures Aggregation operators provide fundamental techniques to solve group decisionmaking problems with IFSs. All intuitionistic fuzzy aggregation operators introduced in section “Operations and Aggregations for Intuitionistic Fuzzy Information” can be utilized to collect the decision-making results for different group decisionmaking problems under intuitionistic fuzzy environment. Additionally, some operators were provided to construct the group decision-making models with further combining the decision-making characteristics, like attribute weights and dynamic situations. For more details, based on establishing the score matrix of the aggregated decision matrix to determine the attribute weights, Xu (2007e) proposed to use the IFHG and IFWG operators given by Xu and Yager (2006) to respectively collect all decision-makers’ decision matrices and aggregate the final score for each alternative. To deal with the dynamic MAGDM problems, Xu and Yager (2008) defined the dynamic intuitionistic fuzzy weighted averaging (DIFWA) operator and the uncertain dynamic intuitionistic fuzzy weighted averaging (UDIFWA) operator and utilized them to establish some basic methods for determining the attribute weights, such as distribution method and exponential distribution method. Finally, the whole

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process for dynamic decision-making with intuitionistic fuzzy information was presented. In addition, there exist researches that establish the decision-making methods based on measures. To address the problem with unknown or partly known attribute weights, entropy and cross-entropy measures were introduced for intuitionistic fuzzy information, and then the decision-making procedures on the basis of the two measures were investigated (Xia and Xu 2012). Furthermore, Yu and Xu (2016) investigated the definite integrals of intuitionistic fuzzy information and correspondingly proposed a method for the multiple attribute decision-making (MADM) problem.

Intuitionistic Fuzzy Group Decision-Making Methods by Similarity to the Ideal Solutions This kind of methods is mainly to determine the optimal solution of the problem in a specific decision-making problem and find the solution that is closest to the ideal solution among all possible solutions as the best one. Some typical decision-making methods with this characteristic are TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) (Hwang and Yoon 1981), VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje) (Opricovic 1998), etc. There exist some studies focusing on constructing the methods for MAGDM problems with intuitionistic fuzzy information based on the idea of TOPSIS. For example, Zhang and Xu (2012) first gave the concept of L-similarity function as: LðαÞ ¼ 1 

d ðα, ð1, 0ÞÞ dðα, ð1, 0ÞÞ þ dðα, ð0, 1ÞÞ

where α ¼ (μα, να) is an IFN and d is the Hamming distance. Based on which, they investigated a ranking method to handle the group decision-making problems with IFNs. To overcome the drawbacks of the existing distance measures, Shen et al. (2018) redefined a distance measure and then used the proposed measure to build an extended TOPSIS method with IFSs. Based on the idea generated from other typical methods, the researches on the decision-making method based on the ideal solution have been developed. Aiming at the problems of incomplete attribute weights, Xu (2012) introduced the concept of satisfaction degrees of the alternatives based on the overall attribute ideal solution and the overall attribute negative ideal solution, then constructed an interactive method to deal with the problem through a multiobjective optimization model. Considering that some decision-making problems may be dynamic, based on the definitions of uncertain intuitionistic fuzzy ideal solution and uncertain intuitionistic fuzzy negative ideal solution, Xu and Yager (2008) introduced a procedure for solving the dynamic group decision-making problems with IFSs.

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Intuitionistic Fuzzy Group Decision-Making Methods with Decision Characteristics Besides the above two types of decision-making methods under intuitionistic fuzzy circumstance, there are some studies focusing on building the decision-making framework with different decision characteristics, such as the prior relationship, the distribution of decision information, the psychological state, etc. In the following, we make detailed expositions of them. (1) Methods for determining the attribute/expert weights. Based on the idea of the useful attribute weights, it is better to maximize the deviations between an alternative and other alternative toward attributes; Xu (2010b) introduced an optimization model for obtaining the attribute weights in the MAGDM problems with intuitionistic fuzzy information as: MaxmizeðwÞ ¼

m X n X  X  d bij , bik wi i¼1

s:t:

m X

j¼1 k6¼j

w2i ¼ 1, wi  0, i ¼ 1, . . . , m

i¼1

where bij is the overall decision value of ith alternative with respect to jth attribute and w ¼ (w1, . . ., wn)T is the attribute weight vector. Later on, Zhang and Xu (2014) introduced a mathematical model based on maximizing the group assessment consistency under intuitionistic fuzzy circumstance to address expert weights. (2) Methods with prior relationships. Since the decision-making problems aim at getting the ranking of alternatives, some researchers have made efforts on comparing each alternative and confirming their superiorities and inferiorities. By linking the relationship between each alternative and the ideal positive point, Chai et al. (2012) proposed to use the intuitionistic fuzzy superiority index and the intuitionistic fuzzy inferiority index to rank alternatives. The series of PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation) (Mareschal et al. 1984), ELECTRE (Elimination and Choice Expressing REality) (Roy 1996), and AHP (Analytic Hierarchy Process) (chapter ▶ “Group Decision Support Using the Analytic Hierarchy Process”), which are utilized to make decisions by sorting alternatives, have been extended to handle the intuitionistic fuzzy decision-making problems (Liao and Xu 2014b). With the outranking relation between any two IFSs, an outranking method was provided by Shen et al. (2016) for the MAGDM problems with IFSs. (3) Methods based on data characteristics. For the requirements of accurate decision-making, Ren et al. (2017) applied the concept of thermodynamic parameters into intuitionistic fuzzy environment to make decisions that simultaneously contains the numerical values and the data distributions of decision information. What’s more, Hao et al. (2017) constructed an intuitionistic fuzzy

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decision-making method not only addressing the overall performance of the alternatives but also emphasizing the contrast among the alternatives. (4) Methods with other characteristics descriptions. To deal with the risk decisionmaking, Liang et al. (2017) combined the rough set theory and investigated the three-way decision under intuitionistic fuzzy environment, which was built on the Bayesian decision theory. From the necessity of solving the problem of helping venture capitalists to select a promising enterprise, Tian et al. (2018) applied the prospect theory to depict the risk attitudes of decision-makers with regard to their opinions and proposed a decision-making method that considers the decision-makers’ psychological states.

Applications The above research results have been applied to various fields of economic management, engineering, healthcare, etc. For example, in the field of economic management, Shen et al. (2018) applied the extended intuitionistic fuzzy TOPSIS to assess the credit risk, and other intuitionistic fuzzy decision-making methods have been used to solve “one belt, one road” investment (Hao et al. 2017), venture capital (Tian et al. 2018), among other problems. Furthermore, based on determining the attributes of tiered diagnosis and treatment for lung diseases, Ren et al. (2017) utilized the intuitionistic fuzzy thermodynamic method to distribute patients into different levels of hospitals to relieve medical stress.

Conclusions and Challenges Because of the complexity and uncertainty of modern decision problems, group decision-making with intuitionistic fuzzy information has had a great deal of development. To make recent research on intuitionistic fuzzy group decision-making clear to readers, this chapter has reviewed the related theory based on information fusion with IFNs, group decision-making with IFPRs, and multi-attribute group decisionmaking models with IFSs. More specifically, these topics include (1) the operations, aggregations, distance/similarity measures, and clustering of intuitionistic fuzzy information; (2) consistency measures and consistency checking of IFPRs, their weights derivations from IFPRs, and the consensus models based on IFPRs; and (3) MAGDM methods with fusion techniques as a way to approach ideal solutions and find their decision characteristics. Furthermore, we have presented some applications based on existing works in the fields of emergency decision, site selection, healthcare, and venture capital, among others. The reviews presented in this chapter have summarized the fundamental techniques and various decision-making models for supporting group decision-making with IFSs, which give a clear framework for decision-making problems with uncertainty and list basic methods for practical problems. To further improve the theory

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and its prospects for application, future research may need to address the following challenges: (1) In the current era of information explosion, how to process, extract, and classify useful decision-making information has become very important for scientific decision-making. Since different clustering techniques can lead to different classifications, it is urgent to investigate the consequences of various clustering techniques using actual decision problems so that clustering techniques can be better understood and put into practice accurately. (2) Existing approaches to group decisions focus mainly on establishing consensus by iteratively revising decision-makers’ opinions or removing some that are incompatible, which may distort the original judgments. In actual problems, consensus is a process of interaction and cooperation, and no one is always willing to compromise. In such a case, explicit consideration of decisionmakers’ levels of willingness to modify their opinions should contribute to more realistic decision-making results. (3) It is indispensable to consider all decision-makers’ opinions in group decision problems. Currently, procedures for collecting decision-makers’ opinions pay attention mainly to reaching group consensus, which lacks generalizability. There must always exist some cases that are irreconcilable, such as the inability of one voter to change the mind of another. Thus, the theory of group decisionmaking with IFSs should be developed to include non-unanimous decision situations. (4) As humans may have bounded rationality when they make decisions (Simon 1947), intuitionistic fuzzy group decision-making methods based on bounded rationality have been proposed. However, this related work is still in its first steps, and study of more novel and precise methods may well make for more efficient decision-making patterns.

Cross-References ▶ A Group Multicriteria Approach ▶ Crowd-Scale Deliberation for Group Decision-Making ▶ Group Decision Support Using the Analytic Hierarchy Process ▶ Multiple Criteria Decision Support

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Group Decisions with Linguistic Information: A Survey Yue He and Zeshui Xu

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Novel Concepts of Linguistic Information Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HFLTS and Its Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PLTS and Its Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Novel Concepts of Linguistic Information Expressions and Comparisons . . . . . . . . . Techniques for Integrating and Modeling of Linguistic Information . . . . . . . . . . . . . . . . . . . . . . . . . Aggregation Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distance, Similarity, and Entropy of Linguistic Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GDM with the Linguistic Preference Relation and Its Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts of Linguistic Preference Relation and Its Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . Consistency of Linguistic Preference Relations and Its Improving Process . . . . . . . . . . . . . . Group Decisions with Linguistic Preference Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Group Decision-Making Methods with Linguistic Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . MADM with Linguistic Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dynamic Group Decision-Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications of Recent Decision-Making Methods with Linguistic Information . . . . . . . . . Conclusions and Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Linguistic terms and their extensions have been shown to be practical tools in group decision problems, mainly because they can express the preferences of decision makers directly. In recent years, with the growing complexity of information and decision environments, several novel linguistic information expressions have been proposed, such as hesitant fuzzy linguistic term sets, probabilistic

Y. He · Z. Xu (*) Business School, Sichuan University, Chengdu, Sichuan, China e-mail: [email protected]; [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_42

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linguistic term sets, and double-hierarchy hesitant fuzzy linguistic term sets. Based on these concepts, methodologies for information fusion, preference expression, and group decision-making have been introduced, and are compared and discussed in this chapter. For information fusion, new aggregation operators can be seen as a part of the foundation of group decision-making. Measures for linguistic information, including distance measures, similarity measures, and entropy, form another important part of this foundation. Decision makers often provide their preferences using various expressions for paired comparison. The consistency of linguistic preference relations and related methodologies is systematically introduced in this chapter. It is noteworthy that there remain many challenges in the development of group decision-making based on linguistic information, which deserves much attention because of both its theoretical and practical value. Keywords

Group decision · Context for group decision · Fuzzy approaches · Group decision-making · Hesitant fuzzy linguistic term set · Probabilistic linguistic term set · Linguistic preference relation

Introduction Due to the complexity and uncertainty of the real world, it is common to recruit group wisdom into decisions, in other words, to adopt group decision-making. It has been found that good results can be achieved by collecting evaluations from decision-makers, integrating their evaluations, and transferring them to information which can be input into the decision process (see chapters ▶ “Collaboration Engineering for Group Decision and Negotiation” and ▶ “A Group Multicriteria Approach”). Group decisions fuse the knowledge of experts from different fields, so collective decisions are more likely to be recognized by others. Group decision methods can be divided into two categories, multi-attribute decision-making (MADM) methods and dynamic decision methods. The former conducts decision process on the basis of different evaluations of alternatives, while the latter mainly considers changes in decision environments and decision-makers’ status. MADM methods can be further classified into aggregation-based methods, distance-based methods, and outranking-based methods. For dynamic decision-making methods, consensus reaching models and interactive decision methods are distinguished because they fully consider the status of decision-makers. Linguistic terms (Zadeh 1975) are a useful tool for expressing relations and are acceptable for group decision-makers because they are close to human thinking habits. Since the experience, cognitions, and knowledge backgrounds of decisionmakers are different, their evaluations may be difficult to compare, yet they may not be ignored. The concept of hesitant fuzzy linguistic term sets (HFLTSs) (Rodriguez et al. 2012) can express different linguistic evaluations, in which all possible

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linguistic terms are collected as hesitant fuzzy linguistic elements (HFLEs) and share the same position. However, in the real world, sometimes evaluations must be distinguished because their importance varies according to the different familiarities and specialty degrees of the decision-makers. Probabilistic linguistic term sets (PLTSs) (Pang et al. 2016) were put forward to express all possible linguistic evaluations with probabilities, representing the belief degrees or importance degrees of the evaluations. For example, suppose there are ten experts invited to evaluate the development of a company. They can use the linguistic term set {s0, s1, s2}, in which the elements represent slow, moderate, and fast, respectively. If three of the experts provide s0, two of them provide s1, and five of them provide s2, then the PLTS {s0(0.3), s1(0.2), s2(0.5)} can be used to express this situation. For group decisions, one important step is to integrate evaluations of different decision-makers or based on different attributes. Aggregation operators, distance measures, and similarity measures are commonly used tools to integrate or analyze linguistic information. The aggregation operator is usually applied to fuse evaluations provided by different decision-makers or to aggregate information based on different attributes, thus integrating the input information. Aggregation is also the most direct and simple process of group decisions; the aggregated information can be the basis for a final decision in many situations. Unlike fusion there is another approach to processing decision information, which is to measure deviations. Distance measures and similarity measures can represent the similarities of decisionmakers, attributes, or alternatives and act as the foundation for distance-based methods. When useful information related to the decision-making problem is scarce, decision-makers need to provide their evaluations based on their experience and preferences. Therefore, the linguistic preference relations (LPRs) can help decisionmakers to express their opinions toward alternatives by pairwise comparisons in a direct and intuitive way. With the development of the linguistic term set theory, LPR has been extended to hesitant fuzzy linguistic preference relation (HFLPR) (Zhu and Xu 2014) and probabilistic linguistic preference relation (PLPR) (Zhang et al. 2016); to ensure that linguistic preference relations are reasonable, processes to ensure consistency are applied. Decision-making with LPRs is not the same as MADM or dynamic decision-making; it obtains decision results by deriving priority vectors from the PRs. In this chapter, we provide a framework for GDM with linguistic information. The rest of the content is organized as follows: Section “Novel Concepts of Linguistic Information Expressions” introduces some novel concepts based on linguistic term sets, such as HFLTSs and PLTSs, and a comparative analysis of the extensions is conducted. Then techniques such as distance measures, similarity measures and entropy measures of HFLTSs and PLTSs are presented in section “Techniques for Integrating and Modeling of Linguistic Information.” In section “GDM with the Linguistic Preference Relation and Its Extensions,” we introduce the LPR and its extensions into hesitant fuzzy linguistic information and probabilistic linguistic information. Then we provide an overview of the consistency improving process and methods for the priority vectors. Section “Group Decision-Making Methods with

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Linguistic Information” introduces GDM methods with linguistic information based on the different categories. Some conclusions and future challenges are explained in section “Conclusions and Challenges.”

Novel Concepts of Linguistic Information Expressions In real situations, sometimes people get used to expressing their opinions by words instead of numbers, such as “good,” “bad,” and “perfect.” In order to express such information in a decision-making situation, Zadeh (1975) proposed the concept of linguistic variable, defined as “a variable whose values are not numbers but words or sentences in a natural or artificial language.” In the past few years, the concept of linguistic terms has been extended to adapt to the complexity of decision-making problems. In what follows, we will introduce several novel linguistic information expressions.

HFLTS and Its Extensions Due to the different cognitions, experience, and knowledge backgrounds of decision-makers, the evaluations provided by decision-makers may not be the same, and none of them should be ignored. Therefore, the concept of the hesitant fuzzy set (Torra 2010) was proposed which can include all the possible evaluations with the same importance degrees. The hesitant fuzzy set is used to express evaluations by fuzzy numbers. For the linguistic information, the concept of HFLTS was first proposed by Rodriguez et al. (2012), and it was motivated by the concept of the hesitant fuzzy set, shown as follows: Definition 1 (Rodriguez et al. 2012) Let S ¼ {s0, . . ., sτ} be a linguistic term set, a hesitant fuzzy linguistic term set (HFLTS), which is an ordered finite subset of the consecutive linguistic terms of S. To make it easier to understand and express in a decision-making problem, Liao et al. (2014) proposed the mathematical expression of a HFLTS, i.e., S ¼ {sα|α ¼  τ, . . ., 1, 0, 1, . . ., τ} be a linguistic term set. The HFLTS HS for a linguistic variable υ  V can then be represented mathematically as HS(υ). For convenience, H ¼ {HS(υ)|υ  V} is called a set of HFLTSs. Example 1 Suppose there are several experts invited to evaluate the development of a company. They can use the linguistic term set {s0, s1, s2}, in which the elements represent fast, moderate, and slow. Some of the experts believe the development of the company is fast, and others provide moderate. Their opinions are important and none of them can be ignored. So the evaluations can be expressed by the HFLTS, shown as

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H ¼ fs0 , s1 g According to the definition, the elements of a HFLTS should be consecutive. When the elements are discrete, linguistic information should be expressed by the extended hesitant fuzzy linguistic term set (EHFLTS) (Wang 2015) as follows: Given a LTS S ¼ {s0, s1, . . ., sτ}, an EHFLTS is an ordered finite subset of S, denoted as h_S ¼ fsα jsα  Sg. In order to depict the linguistic information more accurately, Gou et al. (2017a) proposed the concept of the double hierarchy linguistic term set, which is shown as follows: Definition 2 (Gou et al. 2017a) Let S ¼ {st|t ¼  τ, . . ., 1, 0, 1, . . ., τ} and O ¼ {ok|k ¼  ς, . . ., 1, 0, 1. . ., ς} be the first hierarchy and second hierarchy LTS, respectively, and they are fully independent. A double hierarchy linguistic term set (DHLTS), SO, is in the mathematical form of SO ¼ fst jt ¼ τ, . . . , 1, 0, 1, . . . , τ; k ¼ ς, . . . , 1, 0, 1, . . . , ςg where st is called the double hierarchy linguistic term (DHLT) and ok expresses the second hierarchy linguistic term when the first hierarchy linguistic term is st. Example 2 Suppose there are several experts invited to evaluate the development of a company. They can use the linguistic term set S ¼ {s-1, s0, s1} and O ¼ {o-1, o0, o1} in which the elements represent slow, moderate, fast, and a little, just right, much, respectively. Then, the linguistic expression “between a little moderate and just right moderate” can be expressed as: So ¼ fs0 , s0 g

PLTS and Its Extensions Sometimes, the importance of evaluations may be different and it should be distinguished. Therefore, Pang et al. (2016) proposed the concept of PLTS, in which each element is assigned with a probability representing the importance or the belief degree. The mathematical expression is shown as follows: Definition 3 (Pang et al. 2016) Let S ¼ {s0, s1, . . ., sτ} be a linguistic term set; a PLTS can be defined as: #L ðpÞ n
 X pðkÞ  1 LðpÞ ¼ LðkÞ pðkÞ LðkÞ  S, pðkÞ  0, k ¼ 1, 2, . . . , #LðpÞ, k¼1

)

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where L(k)( p(k)) is the linguistic term L(k) associated with the probability p(k) and #L( p) is the number of all different linguistic terms in L( p). Note that if

#L ðpÞ P

pðkÞ ¼ 1, then we have the complete information of probabilistic

k¼1

distribution of all possible linguistic terms. If

#L ðpÞ P

pðkÞ < 1, then partial ignorance

k¼1

exists because current knowledge is not enough to provide complete assessment information, which is not rare in practical group decision-making problems. Espe#L ðpÞ P cially, pðkÞ ¼ 0 means completely ignorance. Obviously, handling the ignorance k¼1

of L( p) is a crucial work for the use of PLTSs. For different decision-makers, they may have different understandings to the same set of linguistic terms. So Zhai et al. (2016) proposed the concept of probabilistic linguistic vector-term set to describe the change degrees of different linguistic terms for different decision-makers, which depicts the PLTS in a more accurate way, shown as follows: Definition 4 (Zhai et al. 2016) Let S1, S2,. . ., SN be a set of linguistic evaluation scales (LESs). A probabilistic linguistic vector-term set (PLVTS) can be defined as: !

S¼

¼

n



!o ! sðτÞ , pðτÞ jτ ¼ 1, 2, . . . , L S

n

! o ! ! $ αnðτÞ i þ $ r sn$αðτÞ j , pðτÞ jτ ¼ 1, 2, . . . , L S ; n ¼ 1, 2, . . . , N


! ! ! where ! sðτÞ , τ, L S , i , j , $ αnðτÞ , $ r sn$αðτÞ are defined as above and p(τ) is the !

probability of the τth linguistic evaluation term (LET) in S and satisfies 0  p(τ)  1,  ! L S
 P pðτÞ  1. For simplicity, s! ðτÞ , pðτÞ is called the probabilistic linguistic vectorτ¼1

term (PLVT).

Other Novel Concepts of Linguistic Information Expressions and Comparisons Because of the ubiquitous uncertainty in description of objects, some novel concepts of linguistic expressions are proposed in the past few years. For example, the virtual linguistic terms and the linguistic terms with hedges are introduced for different purposes in the process of expression. Traditional linguistic terms are discrete, and sometimes a single linguistic term cannot describe an object properly. The virtual linguistic terms (VLTs) (Xu and Wang 2017) provide a way to express an object in detail, and the concept of it is shown as follows:

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Definition 5 (Xu and Wang 2017) Let S ¼ {st|t ¼ 0, 1, . . ., τ} be a LTS with the semantics defined on the domain U. For any t  {0, 1, . . ., τ}, let 8 > < ½0, 0:5Þ, δ  ½0:5, 0, > : ½0:5, 0:5Þ,

t¼0 t¼τ else

and then the pair (t, δ) generates a VLT sα, with α ¼ t + δ. The set of VLTs is denoted by S ¼ {sα|α  [0, τ]}. When the decision-makers are uncertain about their provided linguistic term for an object, it is natural for them to use a hedge to modify the possible linguistic term, like “more or less bad.” For this situation, the concept of linguistic terms with weakened hedges (LTWHs) was introduced by Wang et al. (2018). At first, the weakened hedge set (WHS) is denoted as H(ς) ¼ {ht|t ¼ 1, 2, . . ., ς} such that hedge hj has more weakening force than hi if and only if i < j. Then the LTWHs can be defined as follows: Definition 6 (Wang et al. 2018) Given a LTS S(τ) and a weakened hedge set (WHS), a LTWH, denoted by a 2-tuple l ¼ hht, sαi, is generated by the following rule: hweakened hedgei≔ht , ht  HðςÞ ; hatomic termi≔sα , sα  SðτÞ ; hLTWH i≔hweakened hedgeihatomic termi Moreover, an atomic term sα can be seen as a special case of LTWHs if the hedge “definitely” is used because “definitely” has no weakening force. That is, sα ¼ hdefinitely, sαi for any sα  S(τ). To make the differences of these linguistic expressions clear, Table 1 is organized by the names, mathematical forms, and features, shown in Table 1: Moreover, these concepts are developed in a certain order, which means they are connected to each other, especially for HFLTSs and PLTSs and their extensions. The relationships among these linguistic information expressions are shown in Fig. 1.

Techniques for Integrating and Modeling of Linguistic Information In the decision-making process, the evaluations for an alternative are provided based on different attributes. Information fusion is a useful way to integrate the evaluations and makes them ready for decision-making. Aggregation operators are the most common tool for information fusion. Besides, distance measures, similarity measures, and entropy are also useful in the process of information integration,

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Table 1. Recent extensions of linguistic term sets HFLTS EHFLTS DHLTS PLTS

PLVTS

Mathematical forms H ¼ {HS(υ)|υ  V} h_S ¼ fsα jsα  Sg    t ¼ τ, . . . ,  1, 0, 1, . . . , τ; SO ¼ st  k ¼ ς, . . . ,  1, 0, 1, . . . , ς  8 9 ðkÞ  ðkÞ > > <   L  S, p  0, =  #L ðpÞ LðpÞ ¼ LðkÞ pðkÞ  P ðkÞ  > p  1> : ;  k ¼ 1, 2, . . . , #LðpÞ, k¼1 n

 o ! ! ! S¼ sðτÞ , pðτÞ jτ ¼ 1, 2, . . . , L S

VLT

S ¼ {sα|α  [0, τ]}

LTWH

l ¼ hht, sαi

Features Continuous evaluations Discrete evaluations Evaluations with two hierarchies Evaluations assigned with probabilities

Evaluations with probabilities and changing degrees Evaluations determined by two parameters Evaluations with modification degrees

Fig. 1 The relationships of linguistic information expressions

especially for the clustering algorithms. In what follows, we are going to introduce the concepts, methodologies, and applications of these integration tools based on linguistic information.

Aggregation Operators The aggregation operator is a direct way to integrate information. For linguistic information, it has been deeply investigated by worldwide researchers, and now it has become a mature tool for information fusion. So far, plenty of aggregation

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operators for linguistic information are introduced, like LWGA (Xu 2004), etc. Zhou and Chen (2012) introduced a large range of linguistic generalized power aggregation operators, such as GPOWA, WLGPA, LGPOWA, etc. Wang et al. (2014a) proposed the concept of cloud weighted arithmetic averaging (CWAA) operator and its extensions, in which the linguistic variables were first combined with cloud model. For intuitionistic linguistic information, Liu (2013) put forward several generalized dependent aggregation operators. In recent years, with the introduction of the HFLTS, the aggregation operators related to that concept have also been researched. Different aggregation operators were proposed based on different demands and decision-making situations, like IVHFLN (Wang et al. 2014b). Combined with the Bonferroni mean, Gou et al. (2017b) proposed the hesitant fuzzy linguistic Bonferroni mean (HFLBM) operator, expressed as: 1 1 11pþq BB B n C C B  q C 1 B CC C p p ,q 1 BB HFLB ðhS 1 , hS 2 , . . . , hS n Þ ¼ g BB B  ð hi Þ  hj C C C AA C A @@nðn  1Þ @ i,j ¼ 1 i 6¼ j 00

0

where hS1 , hS2 , . . . , hSn is a collection of hesitant fuzzy linguistic elements and p, q > 0. As for the EHFLTS, which can be seen as the extension of HFLTS, Wang et al. (2015) proposed a series of aggregation operators and defined an extension principle of aggregation operators, shown as follows: n

Definition 7 (Wang 2015) Let Θ be a function Θ : S ! S , where S ¼

 fsα jα  ½q, qg, H ¼ h1S , h2S , . . . , hnS be a set of EHFLTs on the reference set X. Then the extension of Θ on H is defined for each x in X by: ΘH ðxÞ ¼ [sα

1

,sα2 ,...,sαn  fh1S h2S ...hnS g fΘðsα1 , sα2 ,

. . . , sαn Þg

For the PLTS, two classic aggregation operators (Pang et al. 2016) are proposed to solve the MAGDM problem, which are PLWA ðL1 ðpÞ, L2 ðpÞ, . . . , Li ðpÞÞ ¼ w1 L1 ðpÞ  w2 L2 ðpÞ   wn Ln ðpÞ n o n o ðkÞ ðkÞ ðkÞ ðkÞ ¼ [LðkÞ  L ðpÞ w1 p1 L1  [LðkÞ  L ðpÞ w2 p2 L2   [LðkÞ  L 1

1

2

2

n

n n ðpÞ

wn pðnkÞ LðnkÞ

o

PLWGðL1 ðpÞ, L2 ðpÞ, . . . , Li ðpÞÞ ¼ ðL1 ðpÞÞw1  ðL2 ðpÞÞw2   ðLn ðpÞÞwn ( ) ( ) ( )
w1 pð1kÞ
w2 pð2kÞ
wn pðnkÞ ðkÞ ðkÞ ðk Þ  [LðkÞ  L ðpÞ L2   [LðkÞ  L ðpÞ Ln ¼ [LðkÞ  L ðpÞ L1 1

1

2

2

n

n

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Distance, Similarity, and Entropy of Linguistic Information The distance measure is a useful tool in GDM, which is usually applied to express the difference between the alternatives, attributes, or decision-makers. In general, the distance measures based on linguistic information should satisfy the following condition: Suppose that L1 and L2 are two linguistic elements, which may be any forms of linguistic information expressions, the distance measures between them should satisfy: 1. 0  d(L1, L2)  1. 2. d(L1, L2) ¼ 0 if and only if (L1, L2)1 ¼ (L1, L2)2. 3. d(L1, L2) ¼ d(L2, L1). The similarity measure is related to the distance measure and the meanings of similarity and distance are opposite. Similarity is used to express the closeness degree of two elements, and it can be calculated by S(L1, L2) ¼ 1  d(L1, L2). Therefore, the similarity measure should satisfy: 1. 0  S(L1, L2)  1. 2. S(L1, L2) ¼ 0 if and only if (L1, L2)1 ¼ (L1, L2)2. 3. S(L1, L2) ¼ S(L2, L1). According to the conditions, Liao et al. (2014) proposed a family of distance measures based on HFLTS in discrete and continuous cases separately, such as Hamming distance, Euclidean distance, Euclidean-Hausdorff distance, and their weighted forms. Considering the features of the similarity degree, it is used to measure the consensus degree in the consensus reaching models (Gou et al. 2018). Motivated by the idea of cosine similarity measures between fuzzy sets, Liao and Xu (2015) proposed the cosine distance measures and similarity measures for HFLTSs, expressed as: PN

1 Li



jδ1l ðxi Þj jδ2l ðxi Þj l¼1 2τþ1 2τþ1

P Li

i¼1   d2 H 1S , H2S ¼ 1 

PLi
δ1l ðxi Þ2 PN
1 PLi
δ2 ðxi Þ2 1=2 PN 1 l¼1 2τþ1 l¼1 2τþ1 i¼1 Li i¼1 Li

and PN

1 Li



jδ1l ðxi Þj jδ2l ðxi Þj l¼1 2τþ1 2τþ1

PLi

i¼1   ρ2 H 1S , H 2S ¼

PLi
δ1l ðxi Þ2 PN
1 PLi
δ2 ðxi Þ2 1=2 PN 1 l¼1 2τþ1 l¼1 2τþ1 i¼1 Li i¼1 Li

Like the distance measures and similarity measures, the entropy measure is another important tool for information integration. It is used to describe the complexity degree of the system and the information. For hesitant fuzzy linguistic

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environment, Gou et al. (2017c) proposed the concept of the entropy for HFLTSs, shown as follows: Definition 8 (Gou et al. 2017c) Let S ¼ {st|t ¼  τ, . . n ., 1, 0, 1, . . ., τ} beoa linguistic term set and hS ¼ {sσ(l )|l ¼ 1, . . ., #hS}, hS1 ¼ s1σ ðlÞ jl ¼ 1, . . . , #hS1 , n o and hS2 ¼ s2σðlÞ jl ¼ 1, . . . , #hS2 be three HFLEs (#hS,#hS1 , and #hS2 are the numbers of linguistic terms of these three HFLEs, respectively, and #hS¼#hS1 ¼#hS2 ¼ L). Let hS be the complementary set of hS. We call E an entropy measure for the HFLE hS if it satisfies: 1. 0  E(hS)  1. 2. E(hS) ¼ 0 if and only if g(hS) ¼ 0 or g(hS) ¼ 1. 3. E(hS) ¼ 1 if and only if
g(sσ(l g(sσ(L l + 1))
¼ 1,  for l ¼
1, 2, . . .,L.  )) +


4. EðhS1 Þ  EðhS2 Þ if g s1σ ðlÞ  g s2σðlÞ for g s2σðlÞ þ g s2σ ðLlþ1Þ  1 , or



 g s1σðlÞ  g s2σðlÞ for g s2σðlÞ þ g s2σðLlþ1Þ  1, l ¼ 1, 2, . . ., L.   5. EðhS Þ ¼ E hS Then, Farhadinia and Xu (2018) improved the existing entropy for HFLTSs and proposed some new hesitant fuzzy linguistic entropy and cross-entropy measures. Based on probabilistic linguistic information, Liu et al. (2018) put forward the entropy measures for PLTSs and introduced some properties and formulas about them. Besides the distance, similarity, and entropy, the correlation coefficient was also investigated for qualitative decision-making in hesitant fuzzy linguistic environment (Liao et al. 2015b).

GDM with the Linguistic Preference Relation and Its Extensions The preference relation, as a basic tool, is important content in the research of GDM theory and methods, which can make full use of the intellectual capital of decisionmakers in the process of group decision-making. In what follows, we are going to introduce the basic concepts of the linguistic preference relation and its extensions, the definitions, judgments and improvements of consistency of different linguistic preference expressions, and several kinds of GDM methods based on the linguistic preference information.

Concepts of Linguistic Preference Relation and Its Extensions The preference relation (Xu 2007a) is a useful tool for decision-makers to express their preference information. In the decision-making process, decision-makers may

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tend to express their preferences by pairwise comparisons, especially when they are faced with plenty of alternatives. In some circumstances, such as medical diagnosis and personnel appraisal, the preference information is provided by the linguistic expressions, which leads to the linguistic preference relation. Xu (2006) proposed the concept of uncertain additive linguistic preference relation, which is shown as follows: Definition 9 (Xu 2006) Let X ¼ {x1, x2, . . ., xn} be a finite set of alternatives and   r ij denotes the degree of let R~ ¼ e r ij nn be a linguistic preference relation, where e preference of the alternative xi over xj, given by the expert. If h i ~ r L  r U ¼ s0 , r L  r U ¼ s0 , for all i, j ¼ 1, 2, . . . , n e r ij ¼ r Lij , r U r ij  S, ij , e ij ji ji ij then R~ is called an uncertain additive linguistic preference relation. When the provided preferences are different from each other and none of them can be ignored, the hesitant fuzzy linguistic preference relation (HFLPR) (Zhu and Xu 2014) is used to express these information, and the concept is shown as follows: Definition 10 (Zhu and Xu 2014) HFLPR is presented by a matrix n A o  l B ¼ (bij)n  n X  X, where bij ¼ bij l ¼ 1, 2, . . . , #bij (#bij is the number of linguistic terms in bij) is a HFLTS, indicating the hesitant degrees to which xi is preferred to xj. For all i, j ¼ 1, 2, . . ., n, bij(i < j) should satisfy the following conditions: ρðlÞ

ρðlÞ

bij  bji ρðlÞ

where bij

ρðlÞ

¼ s0 , bii ¼ s0 , #bij ¼ #bji and bij

ρðlþ1Þ

< bij

ρðlþ1Þ

, bji

ρðlÞ

< bji

is the lth linguistic term in bij.

When evaluating the preferences by DHLTS, the double hierarchy hesitant fuzzy linguistic preference relation (DHHFLPR) was proposed by Gou et al. (2018), as follows:
 eSO ¼ hSO

A  A, where Definition 11 (Gou et al. 2018) A DHHFLPR H ij mm  n o  σ ðlÞ σ ð lÞ hSOij ¼ hSO l ¼ 1, 2, . . . , #hSOij (#hSOij is the number of DHLT in hSOij , hSO is the ij

ij

l-th DHLT in hSOij ) is a DHHFLE, indicating hesitant degrees to which Ai is preferred to Aj. For all i, j ¼ 1, 2, . . . , m, hSOij ði < jÞ satisfies the conditions: σ ðlÞ

σ ðlÞ

1. hSO þ hSO ¼ s0 , hSOii ¼ s0 , and #hSOij ¼ #hSOji . ij

σ ðlÞ

ji

σ ðlþ1Þ

2. hSO < hSO ij

ij

σ ðlÞ

σ ðlþ1Þ

and hSO > hSO ji

ji

.

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In hesitant fuzzy environment, the importance degrees of different evaluations cannot be shown. Therefore, the probabilistic linguistic preference relation (PLPR) was proposed by Zhang et al. (2016) to distinguish the importance degrees of linguistic preference information, as follows: Definition 12 (Zhang et al. 2016) A PLPR B on the set X is represented
a matrix  n by

B ¼ (Lij( p))n

 n

ðk Þ

X  X for all i, j ¼ 1, 2, . . ., n. Lij ¼ Lij

ðk Þ

pij

jk ¼

1, 2, . . . , #Lij :gði, j ¼ 1, 2, . . . , nÞ are PLTSs on the linguistic evaluation scale P#Lij ðpÞ ðkÞ ðkÞ S2 ¼ {sα|α ¼  τ, . . ., 1, 0, 1, . . ., τ}, where pij > 0 , k¼1 pij  1 , and #Lij( p) is the number of linguistic terms in Lij( p). Lij( p) indicates the preference degrees of the alternative xi over xi and satisfies the following characteristics:
 ðkÞ ðk Þ ðk Þ ðk Þ pij ¼ pji , Lij ¼ neg Lji , Lii ðpÞ ¼ fs0 ð1Þg ¼ fs0 g, #Lij ¼ #Lji ðkÞ ðkÞ

ðkþ1Þ ðkþ1Þ

ðkÞ ðkÞ

ðkþ1Þ ðkþ1Þ

ðk Þ

and Lij pij  Lij pij for i  j, Lij pij  Lij pij for i  j where Lij and ðk Þ pij are the kth linguistic term and the probability of the kth linguistic term, respectively, in Lij( p).

Consistency of Linguistic Preference Relations and Its Improving Process When decision-makers provide their evaluations with preference relations, there may be contradiction existing in the given preferences. The consistency is an important standard of the validity of the provided preference relations. The concept of consistency is defined by the transitivity, such as weak transitivity, max-max transitivity, max-min transitivity, additive transitivity, and multiplicative transitivity. Considering different decision-making environments and requirements, the consistency based on different linguistic preference relations is also in different forms, which we are going to introduce in this subsection. First of all, the concept of a consistent linguistic preference relation is introduced, as follows: Definition 13 (Zhu and Xu 2014) Let A ¼ (aij)n  n be a LPR; then A is called a consistent LPR; if aij ¼ aik  akj ði, j, k ¼ 1, 2, . . . , nÞ then A is consistent. In hesitant fuzzy linguistic information environment, because the HFLPR is expressed by multiple dimension of evaluations, the concept of its consistency should be different from the traditional LPR. Zhu and Xu (2014) defined the

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consistent HFLPR. At first, the normalized HFLPR is introduced before the definition of the consistent HFLPR. Definition 14 (Zhu and Xu 2014) Assume an HFLPR, B ¼ (bij)n  n, and an optimized parameter ς(0
 ς 1), using ς to add linguistic terms in bij(i < j); we can obtain a HFLPR, BN ¼ bNij

nn

, satisfying the condition that

n o #bNij ¼ max #bNij ji, j ¼ 1, 2, . . . , n ði, j ¼ 1, 2, . . . , n; i 6¼ jÞ
 where #bNij is the number of linguistic terms in bNij . We call BN ¼ bNij normalized hesitant fuzzy linguistic preference relation (NHFLPR) with ς.

nn

a

The concept of consistent HFLPR is shown as follows: Definition
15 (Zhu and Xu 2014) Given a HFLPR B ¼ (bij)n  n and its NHFLPR N with ς, if B ¼ bNij nn

 ρ
ρ bNij ¼ bNik  bNkj ði, j, k ¼ 1, 2, . . . , n; i 6¼ j 6¼ kÞ then B is a consistent HFLPR with ς. As for the PLPR, the elicitation and expression forms are the advanced version of the HFLPR, which contains more information than the HFLPR. Zhang et al. (2016) introduced the concept of consistent PLPR. Like consistent HFLPR, the normalized PLPR is defined before the introduction of the consistent PLPR. Given a PLTS with only one linguistic term B'
¼ (l
ij( pij))  n  n X  X, the NPLPR with one linguistic N N N term is denoted as B0 ¼ lij pij

X  X, where pNij ¼ 1 for 8i, j. In such nn

circumstances, the normalized PLPR is actually reduced to the general LPR, i.e., the LPR can be regarded as a special case of PLPR. And the consistent PLPR is shown as follows: ' Definition 16 (Zhang
et
al.2016) Let B ¼ (lij( pij))n  n be a PLPR with one be its normalized PLPR, then B is called an element and B0N ¼ lNij pNij

nn

additively consistent PLPR with one element if   lij p lij ¼ lie pðlie Þ  lei pðlei Þ, for any i, j, e ¼ 1, 2, . . . , n where p(lij) is the possibility of “event lij” (i.e.,pNij ), which is the normalized probability of lij.

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In real situations, strict consistency is too difficult to reach due to the complexity of the GDM environments. Acceptable consistency is proposed in order to solve the consistency reaching issues, and the LPRs can be seen as consistent LPRs when the acceptable consistency is reached in most situations. The consistency index (CI) is introduced to represent the consistency level of the overall preference relation, which is first proposed by Saaty (1977). With the development and extension of linguistic preference relation theories, the definition of the CI has been changed into different forms in order to accord with different environments and requirements of the group decision-making. For hesitant fuzzy linguistic preference information, assume a HFLPR B, an optimized parameter ς(0  ς  1), its NHFLPR BN, and its consistent NHFLPR N B ; a consistency index (CI) of B can be defined to measure the deviation between BN
 qffiffiffiffiffiffiffiffiffiffiffi P 2 n

N N N N 2 and B , which is denoted as CI ðBÞ ¼ d BN , B ¼ nðn1 d b , b , in ij ij Þ i 0

ð5Þ

where α, β are constants. The above hyperbolic discounting function is not robust to model increasing impatience of any degree (Bleichrodt et al. 2009). Bleichrodt et al. (2009) proposed a function shown in (6) that can model both increasing (δ < 0) and decreasing impatience (0 < δ < 1): 1δ

ϕðd Þ ¼ kerd , r > 0, δ < 1, k > 0

ð6Þ

where r, δ, k are constants. While (6) can be more robust, irrespective of the functional form, ϕ(d ) has to be obtained. The broad steps entailed in this are as follows: Step B1: Elicitation of user preferences by administering a time-preference elicitation (TPE) task Step B2: Calculation of indifference points from the user choices Step B3: Calculation of discount factors and plotting of discounting curve Step B4: Parameter estimation using curve fitting function and calculation of discount function φ(d) The TPE task presents the user with a set of questions between a “larger-sooner cost” and a “smaller-later cost” (note: the same can be readily adapted to rewards as well). The user answers the questions based on the outcomes and time delay. The questions are presented in a way that the user exhibits indifference between the available choices at a point of the task, known as the indifference point. The indifference points are normalized to get the utility points from which, for example, curve fitting can be used to obtain the parameters of the discount function. There are two approaches to Steps B1 and B2 above: choice and matching-based (Attema and Brouwer 2013) methods. A simple choice method is titration-based choice. Here, the participants make a choice between two options: delayed smaller price and immediate larger price. Such option questions are then systematically posed for a range of amount-delay combinations. In a simple version of the procedure, for example, for a given delay, a series

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of option-questions are posed by varying (i.e., titrating) the amounts, and then the indifference point is noted for this delay. This step is then repeated for various delayvalues.

Example 1: Choice Based Method Consider a user who has to choose between delivery tomorrow for $100 or a free delivery in 3 days. If the user chooses free delivery in 3 days, then the paid delivery price is decreased by some percentage, say, to $88, and a similar question is posed. If the user now chooses delivery tomorrow for $88, then indifference point is $94 (average of 88 and 100). On the other hand, if, in response to the original question, the user chooses delivery tomorrow for $100, then the paid delivery price is increased by some percentage, say, to $108, and then similar questions are posed until the indifference point is obtained. Then, the whole procedure is repeated for a different delay. The titration choice method tends to cover a range of amount-delay combinations and that can tend to reduce decision-biases on the part of the participant. It is, however, time consuming, so there are other methods, including other choicebased methods and the matching approaches given next. Matching task involves matching pairs of alternatives to indifference. Of the various types of matching methods, time-trade-off (TTO) method is an example (Attema et al. 2010). In the matching methods, the user has to fill in one of the attributes of one pair which makes it indifferent to other pair. This procedure gives information on the discount function without requiring assumptions about the shape of the discount function or the validity of the DU model. The TTO method entails a sequence t0, t1. . ., tn of time points such that there exist two outcomes β and γ with (t0: β)  (t1: γ) ( is symbol for indifference), (t1: β)  (t2: γ), . . .. . ..(tn-1: β)  (tn: γ); that is, each delay between two consecutive time points exactly offsets the same outcome improvement, and therefore makes both tuples indifferent.

Example 2: Matching Task Time-Trade-off Method Figure 5 illustrates this approach. As given in the top box, the user is asked how many days he/she is willing to wait for a lower delivery price of $50. Assume that the response is 3 days. This implies that, the user is indifferent between paying delivery price of INR 150 on day 0 to paying delivery price of INR 50 on day 3. This response is chained in the next question (box 2), and the procedure continues.

Appendix C: Integration of Time Preference Once the time-preference is characterized, it can be used to alter (Step 3 of section “Integration Exemplars”) the negotiation strategy (see also Krishnaswamy et al. 2016). Step (a) uses a strategy to determine the concession that must be offered,

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Fig. 5 Example for TTO task

giving bounds on the utility value that must be respected during offer generation (note: besides concessions, section 2 lists other negotiation principles as well). Step (b) gives the mechanism for generating multiple trade-off offers. a) The buyer fixes the utility Ut( p, d)for the current round t (t  {1, 2, . . .Tmax}) based on the concession level ut. Ut( p, d ) is given by: U t ðp, d Þ ¼ Ut1 ðp, dÞ  ut

ð7Þ

where the initial U0 ¼ 1.0 and ut is determined by using a concession tactic (Appendix A gives more details of one concession tactic to obtain round-utility). b) The ENS can then create an offer-tuple by choosing p-d values to satisfy (8) (round index t is dropped below):  U ðp, dÞ ¼

 pmax  p ϕð d Þ pmax  pmin

ð8Þ

That is, by choosing price from [pmin, pmax], we can determine the delivery time with (9); alternatively, for delivery time in [dmin, dmax] the price can be computed using (10):   U ðp, dÞ ½pmax  pmin  p ¼ pmax  , ϕð d Þ 1   U ðp, dÞ ½pmax  pmin 1δ 1 ln d¼ r ðpmax  pÞk

ð9Þ ð10Þ

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where ϕ(d) is a suitably chosen discounting function. This way the ENS can exploit price-time trade-offs and propose multiple offers, thereby reducing impasse and improving the possibility of integrative offers. If the seller accepts the offer or the negotiation deadline is reached, go to step (d). c) The seller proposes a set of counter-offer(s). If the buyer accepts the offer or the negotiation deadline is reached, go to step (d); else go to Step (a). d) Stop.

References Antoniou G, Harmelan F (2003) Handbook of ontologies. Springer Arunachalam V, Lytle A, Wall J (2001) An evaluation of two mediationtechniques, negotiator power, and culture in negotiation. J Appl Soc Psychol 31(5):951–980 Attema A, Brouwer W (2013) In search of a preferred preference elicitation method: a test of the internal consistency of choice and matching tasks. J Econ Psychol 39:126–140 Attema AE, Bleichrodt H, Rohde KIM, Wakker PP (2010) Time-tradeoff sequences for analyzing discounting and time inconsistency. Manag Sci 56(11):2015–2030 Axelrod R (1984) The evolution of cooperation. Basic Books, New York Benton AA, Druckman D (1973) Salient solutions and the bargaining behavior of representatives and nonrepresentatives. Int J Group Tensions 3:28–39 Bleichrodt H, Rohde KI, Wakker PP (2009) Non-hyperbolic time inconsistency. Games Econ Behav 66(1):27–38 Carnevale PJ, Lawler EJ (1986) Time pressure and the development of integrative agreements in bilateral negotiation. J Confl Resolut 30:636–659 Chan DK-S, Triandis H, Carnevale PJ, Tam A (1992) A cross-cultural comparison of negotiation: effects of collectivism, relationship between negotiators, and concession pattern on negotiation. Working paper University of Illinois De Dreu CK, Beersma B, Steinel W, Van Kleef GA (2007) The psychology of negotiation: principles and basic processes. In: Kruglanski AW, Higgins ET (eds) Social psychology: Handbook of basic principles, 2nd edn. Guilford, pp 608–629 Druckman D (1986). “Stages, turning points, and crises: Negotiating military base rights, Spain and the United States,” Journal of Conflict Resolution 30, 327–360 Druckman D, Ramberg B, Harris R (2002) Computer-assisted international negotiation: a tool for research and practice. Group Decis Negot 11(3):231–256 Ekman P, Friesen WV, Ellsworth P (1971) Emotion in the human face: guide-lines for research and an integration of findings: guidelines for research and an integration of findings. Pergamon, Elmsford Etezadi-Amoli J (2010) The adoption and use of negotiation systems. In: Handbook of group decision and negotiation. Springer, Dordrecht, pp 393–408 Faratin P, Sierra C, Jennings NR (1998) Negotiation decision functions for autonomous agents. Int J Robot Auton Syst 24(3–4):159–182 Filzmoser (2010) Springer book. Simulation of Automated Negotiation, 2010 Springer-Verlag/ Wien ISBN 978-3-7091-0132-2 Fredrick S, Loewenstein G, O’Donoghue T (2002) Time discounting and time preference: a critical review. J Econ Lit 40(2):351–401 Giebels E, Dreu CD, de Vliert EV (2000) Interdependence in negotiation: effects of exit options and social motive on distributive and integrative negotiation. Eur J Soc Psychol 30:255–272 Harnick F, De Dreu CKW (2004) Negotiating values or resources: the moderating impact of time pressure. Eur J Soc Psychol 34:595–612

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Petty RE, Cacioppo JT (1981) Attitudes and persuation: classic and contemporary approaches. William C. Brown, Dubuque Plutchik, R. (1980). A general psychoevolutionary theory of emotion. In R. Plutchik & H. Kellerman (Eds.), Emotion: Theory, research and experience, Theories of emotion (Vol. 1, pp. 3–33). New York: Academic Press. Pruitt D, Carnevale P (2011) Negotiation and social conflict. Open University Press, Maiden Head, Berkshire, UK. Roszkowska E, Wachowicz T (2015) Inaccuracy in defining preferences by the electronic negotiation system users. In: Kamiński B, Kersten GE, Szapiro T (eds) Outlooks and insights on group decision and negotiation. Springer International Publishing, Cham, pp 131–143 Samuelson P (1937) A Note on Measurement of Utility. Review of. EconomicStudies, 4(2):155–161 Schoop M (2010) Support of complex electronic negotiations. In: Handbook of group decision and negotiation. Springer, Dordrecht, pp 409–423 Schoop M, Jertila A, List T (2003) Negoisst: a negotiation support system for electronic businessto-business negotiations in e-commerce. Data Knowl Eng 47(3):371–401 Sormaz D, Sarkar A (2019) SIMPM – upper-level ontology for manufacturing process plan network generation. Robot Comput Integr Manuf 55:183–198 Stroebel M, Weinhardt C (2003) The Montreal taxonomy for electronic negotiations. Group Decis Negot 12:143–164 Sundarraj R, Mok W (2011) Models for human negotiation elements: validation, and implications for electronic procurement. IEEE Trans Eng Manag 58(3):412–430 Sundarraj and Mok (2012) Optimization-Based Methods for Improving the Accuracy and Outcome of Learning in Electronic Procurement Negotiations IEEE Transactions on Engineering Management 59(4):666–678 Sundarraj RP, Shi X (2012) Optimization-based methods for improving the accuracy and outcome of learning in electronic procurement negotiations. IEEE Trans Eng Manag 99:1–13 Sykora MD, Jackson T, O’Brien A, Elayan S (2013) Emotive ontology: extracting fine-grained emotions from terse, informal messages. IADIS Int J Comput Sci Inf Syst 8(2):1 06–11 8. ISSN: 1646–3692 Tamma V, Phelpsa S, Dickinson I, Wooldridge M (2005) Ontologies for supporting negotiation in ecommerce. Eng Appl Artif Intell 18:223–236 Trope Y, Liberman N (2003) Temporal construal theory of time-dependent preferences. Psychol Econ Decis 1:235–249 Van de Vliert E (1990) Positive effects of conflict: a field assessment. Int J Confl Manag I:69–80 Van Kleef GA (2009) How emotions regulate social life: the emotions as social information (EASI) model. Curr Dir Psychol Sci 18(3):184–188 Van Poucke D, Bulens M (2002) Predicting the outcome of a two-partyprice negotiation: contributions of reservation price, aspiration priceand opening offer. J Econ Psychol 23:67–76 Venkatesh V, Morris MG, Davis GB, Davis FD (2003) User acceptance of information technology: toward a unified view. MIS Q 27:425–478 Vetschera R, Koeszegi ST, Schoop M (2013) Electronic negotiation systems. In: Wiley encyclopedia of operations research and management science, pp 1–8 Vetschera R, Filzmoser M, Miterhofer R (2014) An analytical approach to offer generation in concession-based negotiation processes. Group Decis Negot 23:71–99 Walton RE, McKersie R (1965) A behavioral theory of labor negotiations: an analysis of a social interaction system. McGraw-Hill, New York Watrobski J, Jankowski J, Ziemba P, Karczmarczyk A (2019) Generalised framework for multicriteria method selection. Omega 86:107–124

Negotiation, Online Dispute Resolution, and Artificial Intelligence John Zeleznikow

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alternative Dispute Resolution (ADR) and Online Dispute Resolution (ODR) . . . . . . . . . . . . . . Negotiation Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Alternative Dispute Resolution (ADR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Earliest Forms of the Use of Information Technology to Support Negotiation . . . . . . . . . . Template-Based NSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rule-Based NSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Case-Based NSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Knowledge Discovery to Support the Construction of NSS . . . . . . . . . . . . . . . . . . . . . . . . Split-Up as a NSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Game Theory and Intelligent NSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NSS in Specific Domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NSS for International Conflicts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . NSS for Family Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The British Columbia Civil Resolution Tribunal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intelligent Online Dispute Resolution Systems During the Era of COVID-19 . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Artificial intelligence (AI) has been fundamental to the development of both online dispute resolution and negotiation support systems (NSS). The earliest NSS were settlement-oriented and template-based or rule-based. Then followed the development of case-based systems, which were an important extension on the use of rule-based reasoning in AI. Simultaneously, game theory was used as the basis of providing intelligent negotiation support, as shown in the Adjusted Winner, Family Winner, and Smartsettle Systems. In the early years of J. Zeleznikow (*) La Trobe University Law School, Bundoora, VIC, Australia e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_38

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negotiation support using AI, systems development was often ad hoc rather than systematic, with a focus more upon technology than user needs. The situation changed as intelligent NSS were proposed for use in a variety of domains such as family law and international disputes. We conclude with a discussion of the features that a truly helpful online dispute resolution system would provide, and with comments on how the COVID-19 pandemic has changed the need for online dispute resolution. Keywords

Negotiation · Electronic negotiations · Artificial intelligence · Online dispute resolution · Decision support systems · Game theory

Introduction The appropriate resolution of conflict is one of the earliest forms of human endeavor. For example, the Jewish Torah mentions the dialog (or negotiation) between Abraham and God regarding criteria for the destruction of Sodom and Gomorrah. God wanted to destroy these twin cities because of the licentiousness of its citizens. Abraham reached an agreement with God if he could find 50 “good” citizens living in these cities. Through a series of negotiations, the required number was reduced to 40, then 30, and 20, and finally 10. This negotiation was based on the principle that a few good people should not be punished for the sins of the majority. The principles of negotiation have a long history. How we can optimize (or at least improve) our outcomes in a dispute process has been a constant question in mathematics and philosophy and more recently in artificial intelligence (AI) and computer science. The development of artificial intelligence and computer systems that help people conduct negotiations have been further encouraged the development of processes to help disputants conduct negotiations. Examples of such theories include the differentiation between distributive and integrative negotiation, the development of principled negotiation and issues of reactive devaluation and readiness and ripeness for dispute resolution (Lewicki et al. 2020). One oft well-quoted example is that of a brother and sister haggling about an orange. Their mother’s original intention was to cut the orange in half and give each of the children half an orange. The mother was wise enough to ask both of the children why they wanted the orange. She found out that the brother was thirsty and wished to drink the juice of the orange while the daughter wanted to use the rind of the orange to bake a cake. By giving the son the juice and the daughter the rind, the mother was able to give both of the children 100% of what they wanted – truly a win–win situation and an example of integrative negotiation (Docherty 2004). As we will note in our discussion of the evolution of intelligent systems to support negotiation, there was no initial expectation that the computer systems would

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communicate with each other, nor be online. There are now separate theories of autonomous software agents (Hess et al. 2000) and of online dispute resolution (ODR) (Katsh and Rabinovich-Einy 2017). In this chapter, we review what techniques can be used to enhance human negotiation. In particular, we investigate how artificial intelligence can help such human decision-making. In some limited cases, the potential exists to automate negotiation processes. In the section “Alternative Dispute Resolution (ADR) and Online Dispute Resolution (ODR),” we discuss the development of the modern alternative dispute resolution and its technological child the online dispute resolution movement. In the section “The Earliest Forms of the Use of Information Technology to Support Negotiation,” we discuss the initial or first wave of the use of artificial intelligence for the development of computer software that supports negotiation. Initially, whether the systems used templates, rule-based reasoning, case-based reasoning, machine learning, or hybrids of these techniques, the systems were developed in an ad hoc manner and for a variety of diverse domains. The systems and research were rarely related to other work. In the section “Game Theory and Intelligent NSS,” we discuss the second wave of intelligent negotiation systems – both fully automated and decision support systems. The focus here is upon using game theory to provide intelligent advice. The section “NSS in Specific Domains” involves a discussion of intelligent negotiation support systems (NSS) in international conflicts, family disputes, and industrial relations. It concludes by examining two currently used systems, Rechtwijzer and the British Columbia Civil Resolution Tribunal, and briefly examining developments occurring due to the spread of the COVID-19 pandemic.

Alternative Dispute Resolution (ADR) and Online Dispute Resolution (ODR) Negotiation Principles Despite the concept of negotiation having a long and varied history, there is limited theory on what are good principles to use when conducting a negotiation. Those theories that do exist were invariably developed for specific domains. Such theories were initially developed in the 1960s, at the same time as the first development of AI systems such as Weizenbaum’s (1966) Eliza program. Likewise, until recently, general AI systems have not been developed. Rather the problems addressed by AI systems have, in general, been very specific. Walton and McKersie (1965) introduced the distinction between distributive and integrative bargaining in the domain of industrial conflicts. In distributive approaches, the problems are viewed as zero-sum and resources are imagined as fixed: divide the pie. In integrative approaches to negotiation, problems are

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considered as having more potential solutions than are immediately obvious and the goal is to expand the pie before dividing it. Parties attempt to accommodate as many interests of each of the parties as possible, leading to the so-called win-win or all gain approach. In the section “Game Theory and Intelligent NSS,” we shall focus upon using game theory to develop NSS that support integrative bargaining. There has been plentiful research in this domain. Mnookin and Kornhauser (1979) developed the notion of Bargaining in the Shadow of the Law in the domain of divorce law. They contended that the legal rights of each party can be understood as bargaining chips that can affect settlement outcomes. They argued that parties who negotiate the terms of a divorce in the shadow of matrimonial law rather than pursue their respective rights in the courtroom engage in a form of “private ordering.” Such a private ordering is desirable in the context of divorce settlements to minimize the financial cost and emotional pain of divorce litigation. Gross (2019) argues that Mnookin and Kornhauser’s article spawned a vast array of scholarship applying and extending the theme that negotiators engage in private ordering and proceed in the shadow of norms developed during courtroom processes. Bibas (2004) has claimed that some scholars (but not himself) treat pleabargaining1 as simply another case of bargaining in the shadow of a trial. He notes that “the conventional wisdom is that litigants bargain towards settlement in the shadow of expected trial outcomes. In this model, rational parties forecast the expected trial outcome and strike bargains that leave both sides better off by splitting the saved costs of trial. . . . This shadow of trial model now dominates the literature on civil settlements.” Expanding on the notion of integrative or interest-based negotiation, Fisher and Ury (1981) developed the practice of principled negotiation. Principled negotiation promotes deciding issues on their merits rather than through a haggling process focused on what each side says it will and will not do. Among the features of principled negotiation are: (a) (b) (c) (d)

Separating the people from the problem. Focusing upon interests rather than positions. Insisting upon objective criteria. Knowing your BATNA (Best Alternative To a Negotiated Agreement).

The reason you negotiate with someone is to produce better results than would otherwise occur. If you are unaware of what results you could obtain if the negotiations are unsuccessful, you run the risk of entering into an agreement that you would be better-off rejecting; or rejecting an agreement you would be better off entering into. 1

Plea bargaining is the process whereby the accused and the prosecutor in a criminal case workout a mutually satisfactory disposition of the case subject to court approval. It usually involves the defendant’s pleading guilty to a lesser offense or to only one or some of the counts of a multicount indictment in return for a lighter sentence.

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Alternative Dispute Resolution (ADR) While the topic of Artificial Intelligence and Negotiation may, on first consideration, require a wider discussion than merely looking at the application of Artificial Intelligence and Law, it is important to realize that all disputes are resolved in the shadow of the law. If disputants cannot resolve their conflicts, then the shadow of the appropriate law acts as a beacon for arriving at a resolution. Thus, it is not surprising that most intelligent NSS focus upon legal domains. The decade of the 1970s saw the rise of the modern alternative dispute resolution movement. Alternatives to litigation were heavily influenced by the National Conference on the Causes of Popular Dissatisfaction with the Administration of Justice, which took place in Minneapolis, Minnesota from April 7–9, 1976. At this conference, the then Chief Justice of the US Supreme Court, Warren Burger, encouraged the exploration and use of informal dispute resolution processes. Sander (1976) introduced the idea of the multidoor courthouse movement, and claimed it would be the technique for resolving disputes in the year 2000. In the following years, Fisher and Ury published their seminal work “Getting to Yes” (Fisher and Ury 1981) and Howard Raiffa published “The Art and Science of Negotiation” (Raiffa 1982). These three researchers worked at the Harvard Program on Negotiation, the world’s first teaching and research center dedicated to negotiation and dispute resolution. It was founded in 1983. The late 1970s and 1980s, which preceded the development of the world wide web, was an era in which stand-alone software was developed, that assisted with decision-making in specific legal and negotiation domains. In this era, we saw the development of (and hype about) futuristic legal expert systems to support decisionmaking. Researchers speculated that eventually such expert systems could change the nature of legal practice. Examples of such systems include TAXMAN (McCarty 1976) and the Latent Damage Advisor of Capper and Susskind (Susskind 1987). The decade of the 1990s saw the commercial development of the Internet and initial proposals for online dispute resolution (ODR). Much of this work came from legal academics rather than technology developers. They saw the potential of ODR to resolve disputes that originated on the internet. Lodder and Zeleznikow (2010) indicate, while there is no generally accepted definition of online dispute resolution, we can think of it as using the Internet to perform ADR. While this is a useful working definition, we need to note that one difficulty in providing a more precise and widely accepted definition of ODR is that the concept means many things, to many people. ODR has also been described as 1. Technology-assisted dispute resolution. 2. Technology-facilitated dispute resolution. 3. Technology-based dispute resolution. The one common factor in all these descriptions of ODR is the existence of a fourth party – namely the technology (chapter ▶ “Online Dispute Resolution Services: Justice, Concepts, and Challenges”).

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While the focus of negotiation has largely been on face-to-face processes, incorporating technology into negotiation processes has been commonplace for some time. The prime source has been the telephone (Thomson 2011) which allows people to meet who cannot or should not be together in the same room, whether due to geographical difficulties or to extremely vitriolic situations. As Internet technology has become widespread, much attention has been directed at using these tools for dispute resolution. In some ways, ODR is a natural evolution of convening over the telephone. Technology now offers parties different levels of immediacy, interactivity, and media richness to choose from. Through some platforms, parties can choose to communicate through text; through others, they can convene in real-time video, allowing them to see each other and often, a mediator. However, ODR is far more than a range of new communication platforms. ODR developers are seeking to create intelligent agents, and robust NSS. These systems aim to assist humans in achieving better outcomes then they would themselves, even when performing to the peak of their abilities. The decade of the 1990s saw the development of the Internet and initial proposals for ODR. Much of this work came from legal academics rather than technology developers. They saw the potential of ODR to resolve disputes that originated on the internet (Katsh 1995). The decade of the 2000s saw the development of ODR for Ecommerce; examples include its use by EBay and PayPal (Rule 2003). Over the past decade, we have finally seen the development of practical usable intelligent NSS such as Rechtwijzer in the Netherlands and UK (Smith 2016) and the Civil Resolution Tribunal in British Columbia, Canada (Salter and Thompson 2016). These systems are discussed in the section “NSS in Specific Domains.” Recently, ODR has moved beyond ecommerce. ODR is finally being used for nonfinancial disputes – see for instance the work of Ethan Katsh, and Orna Rabinovich-Einy (Katsh and Rabinovich-Einy 2017) and the access to justice work at Kent Law School.2

The Earliest Forms of the Use of Information Technology to Support Negotiation As we discussed in the section “Alternative Dispute Resolution (ADR) and Online Dispute Resolution (ODR),” the 1970s saw the development of two useful processes for developing negotiation decision support systems – the ADR movement and the use of personal computers.

2 See https://www.kentlaw.iit.edu/institutes-centers/center-for-access-to-justice-and-technology last viewed November 10, 2019

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Template-Based NSS Some of the earliest NSS were template-based, with little attention given to the role the system itself should play in negotiations and decision-making support. Such systems could in no ways be construed as using artificial intelligence. However, they did provide useful, at that time, advice and support. The main role of these systems was to demonstrate to users how close they were to a negotiated settlement. The systems did not specifically suggest solutions. Rather, by informing users of the issues in dispute and a measure of the level of the disagreement, they provided useful decision support for those involved in a negotiation. Eidelman (1993) discussed two template-based software systems that were available to assist lawyers during negotiations: Negotiator Pro and The Art of Negotiating. Negotiator Pro had three primary features: (a) a psychological profiling system; (b) a plan that assisted the disputant to both enter the negotiations better prepared to achieve her goals, and to recognize counter moves that the other side might attempt; and (c) an extensive glossary that drew upon more than 350 excerpts from then leading books on negotiation. The Art of Negotiation presented a menu to take the user through various submenus and questions in seven areas: (1) subject matter of the negotiations; (2) objectives: of each side and the ranking, by importance to each side, of the objectives; (3) issues and positions; (4) needs/gambits; (5) Climates – determining each party’s negotiating philosophy, major climate categories, choosing climates to create, and anticipating the other side’s climates; (6) Strategies; and (7) Agenda. The program performed (and asked the user about) some interesting comparisons. DEUS (Zeleznikow et al. 1995) was an Australian template-based system that displayed the level of disagreement, with respect to each item, between disputants. The goals of the parties (and their offers) are shown on the screen, side by side with each other. The model underpinning the program calculates the level of agreement and disagreement between the litigants’ goals at any given time. The disputants reached a negotiated settlement when the difference between the goals was nil. Using DEUS was beneficial for gaining an understanding of what issues were in dispute and the extent of the dispute over these issues. INSPIRE (Kersten 1997) was initially a template-based NSS that used utility functions to graph offers. It was the first system to enable disputants to negotiate through the Internet, making extensive use of email and web browser facilities. The system displayed previous and present offers, and used utility functions to evaluate proposals determined to be Pareto-optimal.3 Disputants communicated by exchanging offers and electronic mail, and could check the closeness of a package to their initial preferences through a utility graph function.

3

A Pareto-optimal outcome is defined by the property that any other outcome that makes one party better off makes at least one other party worse off.

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While each of these four systems provided support for negotiation decision support and this advice could be considered useful and perhaps intelligent, they undoubtedly did not involve the use of artificial intelligence.

Rule-Based NSS The first expert systems were developed in the mid-1960s and the first legal expert systems were created in the 1970s (Susskind 1986). A rule-based expert system is a collection of rules of the form: IF THEN . Rule-based systems include production rule systems, and some would argue logic-based systems as well. The earliest NSS that used artificial intelligence were developed by the Rand Corporation in the early 1980s to advise upon risk assessment in damages claims. Lift dispatching system (LDS) (Waterman and Peterson 1981) assisted legal experts in settling product liability cases. LDS’s knowledge consisted of legislation, case law, and, importantly, informal principles and strategies used by lawyers and claims adjustors in settling cases. SAL, the system for asbestos litigation (Waterman et al. 1986) helped insurance claims adjusters evaluate claims related to asbestos exposure. SAL used knowledge about damages, defendant liability, plaintiff responsibility, and case characteristics such as the type of litigants and skill of the opposing lawyers. These two systems represented the first steps in recognizing the virtue of settlement-oriented decision support systems. Schlobohm and Waterman (1987) developed estate planning system (EPS). It was a prototype expert system that performed testamentary estate planning by interacting directly with clients or paralegal professionals. The result of a consultation between a client and EPS is the client’s will, printed by a form generating program that EPS accesses. The system was written in ROSIE (an expert system shell). Estate planning is the process by which a person plans the accumulation, management, conservation, and disposition of his or her estate, so as to derive the maximum benefit and satisfaction during the person’s lifetime and also for his or her family after death. To develop a prototype, Schlobohm and Waterman initially limited EPS’ domain to testamentary estate planning, that is, the knowledge necessary to create a client’s will or revocable trust. NEGOPLAN (Matwin et al. 1989) was a rule-based system written in PROLOG. It addressed a complex, two-party negotiation problem containing the following characteristics: (a) the many negotiation issues that were elements of a negotiating party’s position; (b) the negotiation goals that could be reduced to unequivocal statements about the problem domain, and that represented negotiation issues; (c) the existence of a fluid negotiating environment characterized by changing issues and relations between them; and (d) the parties negotiated to achieve goals that may change. The NEGOPLAN method did not simulate the entire negotiation process. Rather, it gave one party a competitive advantage. The opposing party’s goals and subgoals

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were hidden from the side supported by NEGOPLAN. The opposing party revealed only those issues that were the subject of the bargaining. NEGOPLAN was used to advise upon industrial disputes in the Canadian paper industry. Several experiments were conducted to show the flexibility and expressive power of restructurable modeling and its computer implementation, the Negoplan system. The approach allowed for the stability analysis of alternative proposals and use of different prescriptive methods and descriptive models for a more comprehensive simulation and analysis of negotiation processes (Kersten 1995).

Case-Based NSS Case-based reasoning is the process of using previous experience to analyze or solve a new problem, explain why previous experiences are or are not similar to the present problem and adapting past solutions to meet the requirements of the present problem. In a later section on Artificial Intelligence in International Conflict Resolution, we will discuss the mediator system (Kolodner and Simpson 1989) which used casebased reasoning. PERSUADER (Sycara 1993) integrated case-based reasoning and game theory to provide decision support with regard to US labor disputes. One of the crucial characteristics of a NSS is that it is capable of improving its performance, both in terms of efficiency and solution quality, by employing machine learning techniques. The model integrated case-based reasoning and decision-theoretic techniques (multiattribute utilities) to provide enhanced conflict resolution and negotiation support for group problem-solving. In contrast to quantitative models or expert systems that solve each problem from scratch and discard the solution at the end of problemsolving, case-based reasoning retains the process and results of its computational decisions so that they can be reused, to solve future-related problems. Case-based reasoning is a powerful learning method since it enables a system not only to exploit previous successful decisions, thus short-cutting possibly long reasoning chains, but also to profit from previous failures by using them to recognize similar failures in advance so they can be avoided in the future.

Using Knowledge Discovery to Support the Construction of NSS Machine learning is that subsection of learning in which the artificial intelligence system attempts to learn automatically. Knowledge discovery from databases (KDD) is the “nontrivial extraction of implicit, previously unknown and potentially useful information from data” (Piatetsky-Shapiro and Frawley 1991). Data mining is a problem-solving methodology that finds a logical or mathematical description, eventually of a complex nature, of patterns and regularities in a set of data (Fayyad et al. 1996).

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KDD techniques can be grouped into five categories: (a) (b) (c) (d)

Classification: grouping data into predefined categories. Clustering: analyzing the data into groups of similar data. Series analysis: discovering sequences within the data. Association: discovering ways in which data elements are associated with each other. (e) Text mining: information retrieval methods for the automated generation of a document summary, the extraction of concepts such as case factors from judgments, the assignment of a document to a category, and other approaches that deal with large repositories of textual documents.

Split-Up as a NSS One of the first systems to provide support for negotiation using knowledge discovery was the split-up system (Stranieri and Zeleznikow 2006). The developers of this system wanted to show that knowledge discovery could be gainfully used in the domain of law. The Split-Up system provides advice on the distribution of property following divorce in Australia (Stranieri et al. 1999). In developing Split-Up, the designers consulted with domain experts at Victoria Legal Aid,4 to identify relevant factors in the distribution of property under Australian family law. They represented these factors as Toulmin Argument Structures.5 They then wanted to assemble a data set of values on these factors from past cases that can be fed to machine learning programs such as neural networks.6 Ninety-four variables were identified as relevant for a determination in consultation with experts. The way the factors combine was not elicited from experts as rules or complex formulas. Rather, values on the 94 variables were to be extracted from cases previously decided, so that a neural network could learn to mimic the way in which judges had combined variables.

4

https://www.legalaid.vic.gov.au/about-us last viewed July 19, 2020 Toulmin (1958) stated that all arguments, regardless of the domain, have a structure that consists of four basic invariants: claim, data, warrant, and backing. Every argument makes an assertion. The assertion of an argument stands as the claim of the argument. A mechanism is required to act as a justification for the claim, given the data. This justification is known as the warrant. The backing supports the warrant and in a legal argument is typically a reference to a statute or precedent case. 6 A neural network receives its name from the fact that it resembles a nervous system in the brain. It consists of many self-adjusting processing elements cooperating in a densely interconnected network. Each processing element generates a single output signal which is transmitted to the other processing elements. The output signal of a processing element depends on the inputs to the processing element: each input is gated by a weighting factor that determines the amount of influence that the input will have on the output. The strength of the weighting factors is adjusted autonomously by the processing element as data is processed. 5

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At the time of its development in the early 1990s, the Split-Up system was not designed to support negotiation. It was only when the system was shown to legal professionals that we realized that the system could easily support negotiation. We now show how Split-Up can be directly used to proffer advice redetermining each part’s BATNA. Deus, Split-Up, and Family-Winner (Bellucci and Zeleznikow 2005) all provide advice about the distribution of property in Australian Family Law. Let us consider the following example: Suppose the disputants’ goals are entered into the Split-Up system to determine the asset distributions for both the wife and husband. Split-Up first shows both the wife and husband what they would be expected to be awarded by a court if their relative claims were accepted. The litigants are able to have dialogs with the Split-Up system about hypothetical situations such as the one we are describing. Given the requirements of wife and husband in the hypothetical example, the split-up system provided the following answers as to the percentages of the distributable assets received by each partner (Table 1): Thus, we see that which place is the primary residency (also known as the custody) of the children is very significant in determining the husband’s property distribution. If he were unlikely to be awarded the primary residency of the children, the husband would be well advised to accept 40% of the common pool (otherwise he would also risk paying large legal fees and having ongoing conflict, which could be very damaging to the children). While Split-Up is a decision support system rather than a negotiation support system, it does provide disputants with their respective BATNAs and hence provides an important starting point for negotiations. Those involved in multiple-issue negotiations frequently select pareto-inferior agreements that “leave money on the table.” Oliver (1996) showed how a system of artificial adaptive agents, using a genetic algorithm-based learning technique, could learn strategies that enable it to effectively participate in stylized business negotiations. The negotiation policies learned were evaluated on several dimensions including (a) joint outcomes, (b) nearness to the efficient frontier, and (c) similarity to outcomes of human negotiations. The results were promising for integrating such agents into electronic commerce systems. They not only leave less money on the table but also enable new types of transactions to be negotiated cost-effectively. Katia Sycara and her colleagues have a chapter about agents and negotiation in this handbook (▶ “Agent Reasoning in AIPowered Negotiation”). Table 1 Split-up BATNAs for husband and wife Scenario Given one totally accepts wife’s requests Given one totally accepts husband’s requests Given one accepts husband’s requests but gives wife custody of children

Husband’s % 35 58 40

Wife’s % 65 42 60

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Game Theory and Intelligent NSS The mathematical theory of games was invented by von Neumann and Morgenstern (1947). It is a branch of applied mathematics that provides advice about the optimal distribution of resources. In the case of a negotiation, the goal of game theory is to develop the best outcome related to the choices each person has made. In a negotiation, each party to the negotiation is considered to be an agent. ▶ “Negotiation as a Cooperative Game” and ▶ “The Notion of Fair Division in Negotiations” chapters in this handbook about game theory-related ideas. Sycara (1998) notes that in developing real-world NSS one must assume bounded rationality and the presence of incomplete information. In such decision-making, we assume each agent has a utility. An agent’s utility refers to the amount of “welfare” an agent derives from an object or an event. By “welfare,” we refer to some normative index of relative well-being, justified by reference to some background framework. In game theory, the objective is to optimize utility functions. The term zero-sum describes a situation in which a participant’s gain or loss is exactly balanced by the losses or gains of the other participant(s). If the total gains and losses of the participants are summed, then the sum will be zero. Cutting a cake is zero-sum, because taking a larger piece reduces the amount of cake available for others. The zero-sum property (if one gains, another loses) means that any result of a zero-sum situation is Pareto optimal. Game theoretic techniques and decision theory were the basis for Adjusted Winner (Brams and Taylor 1996). It is a two-party point allocation procedure that distributes items or issues to people on the premise of whoever values the item or issue more. The two disputants are required to explicitly indicate how much they value each of the different issues by distributing 100 points across the range of issues in dispute. In this paradigm, it is assumed there are two or more discrete issues in dispute, each of which is divisible. Brams and Taylor claim the Adjusted Winner paradigm is a fair and equitable procedure because at the end of allocation, each party will have accrued the same number of points. Bellucci and Zeleznikow (2005) extended the principles developed by Brams and Taylor into their Family Winner system. They observed that an important way in which family mediators encourage disputants to resolve their conflicts is through the use of compromises and trade-offs. Once the trade-offs have been identified, other decision-making mechanisms must be employed to resolve the dispute. They noted that: • The more issues and subissues in dispute, the easier it is to form trade-offs and hence reach a negotiated agreement, and • They choose as the first issue to resolve the one on which the disputants are furthest apart – one party wants it greatly, the other considerably less so. In assisting the resolution of a dispute, Family_Winner asked the disputants to list the items in dispute and to attach importance values to indicate how significant it is that the disputants be awarded each of the items. The system uses this information to

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form trade-off rules. The trade-off rules are then used to allocate issues according to a “logrolling” strategy.7 Family_Winner accepts as input a list of issues and importance ratings that represent a concise evaluation of a disputant’s preferences. In forming these ratings, the system assumes that the disputants have conducted a comparison of the issues. As noted by Sycara (1993), bargainers are constantly asked if they prefer one set of outcomes to another. Thus, Sycara suggests considering two issues at a time, assuming all others are fixed. Family_Winner uses a similar strategy in which pair-wise comparisons are used to form trade-off strategies between two issues. The trade-offs pertaining to a disputant are graphically displayed through a series of trade-off maps (Zeleznikow and Bellucci 2003). Their incorporation into the system enables disputants to visually understand trade-off opportunities relevant to their side of the dispute. A trade-off is formed after the system conducts a comparison between the ratings of two issues. The value of a trade-off relationship is determined by analyzing the differences between the parties, as suggested by Mnookin et al. (2000). In his PhD thesis, Ernie Thiessen (1993) developed an efficient methodology to solve very complex negotiation problems. In Thiessen et al. (1998), he described the algorithms and results obtained using an interactive computer program developed to assist those involved in negotiating agreements among parties having conflicting objectives. This Interactive Computer-Assisted Negotiation Support System (ICANS) can be used during the negotiation process by opposing parties or by a professional mediator. On the basis of information provided to the program, in confidence, by each party, it can help all parties identify feasible alternatives, if any exist, that should be preferred to each party’s proposal. If such alternatives do not exist, the program can help parties develop counter-proposals. Through a series of iterations in which each party’s input data, assumptions, and preferences may change, ICANS can aid each party in their search for a mutually acceptable and preferred agreement. This paper describes the algorithms used for analyzing preferences and for generating alternative feasible agreements. Also presented are the results of some limited experiments involving water resource system development and use conflicts that illustrate the potential of programs such as ICANS. While game theory is not, in general, considered an artificial intelligence technique, it is an important and intelligent strategy for providing negotiation support. It can be combined with other AI techniques to provide significant hybrid ODR systems.

Logrolling is a process in which participants look collectively at multiple issues to find issues that one party considers more important than does the opposing party. Logrolling is successful if the parties concede issues to which they give low importance values. See (Pruitt 1981).

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NSS in Specific Domains There have been a number of NSS that offer advice in specific domains. For example, in the area of Industrial Relations, Negoplan (see the section “RuleBased NSS”) used rule-based reasoning to successfully model labor management negotiations in the Canadian paper industry. They based their example on a labor contract negotiation between the Canadian Paper workers Union and CIP Ltd. of Montreal. CIP is a major pulp and paper manufacturer. The negotiations took place in the May of 1987. Negoplan distinguished five major phases: preparation, stalemate, initial strike, full strike, and real bargaining. These phases seem to be typical in labor management negotiation, particularly when the union’s position is strong. Persuader (Sycara 1993) integrated case-based reasoning and decision-theoretic techniques to provide decision support for US industrial disputes.

NSS for International Conflicts In the domain of international conflict resolution, Mediator (Kolodner and Simpson 1989) used case retrieval and adaptation to propose solutions to international disputes. The MEDIATOR’s task domain is common-sense advice giving for the resolution of resource disputes. The MEDIATOR program is responsible for understanding a problem, generating a plan for its solution, evaluating feedback from the disputants, and recovering from reasoning failures. GENIE integrates rule-based reasoning and multiattribute analysis to advise upon international disputes (Wilkenfeld et al. 1995). It can aid crisis negotiators in identifying utility-maximizing goals and in developing strategies to achieve these goals. GENIE provides the user with a strong set of tools which aid in the search for utility-maximizing goals and strategies. However, in a complex negotiating situation, this identification alone does not guarantee that the individual will be able to be successful in achieving utility maximization. The actions of the other negotiators affect the ability of the decision support system supported negotiator to achieve his/ her goals. Despite this fact, the experimental results show that decision support system users generally achieved higher utility scores, and groups in which decision support system users participated achieved higher overall group scores. Kraus et al. (2008) and others present an automated agent that negotiates efficiently with human players in a simulated bilateral international crisis. The agent negotiates in a situation characterized by time constraints, deadlines, full information, and the possibility of opting out of negotiation. The specific scenario that they focused upon concerned a crisis between Spain and Canada over access to a fishery in the North Atlantic. Canada blamed Spain for overfishing near its territorial waters and thereby damaging the flatfish stock. There have been attempts to use game theory for computer modeling to resolve international disputes. For example, Denoon and Brams (1997) used the Adjusted Winner algorithm to advise upon the claims of China, Taiwan, and four members of the Association of Southeast Asian Nations (ASEAN): Vietnam, the Philippines,

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Malaysia, and Brunei to part or all of the land areas and surrounding waters of the Spratly Islands (a group of over 230 small islands and reefs in the South China Sea), which were believed to have major oil and gas deposits. Adjusted Winner was also applied to the Panama Canal treaty and Camp David Accords. Brams and Togman (1996) applied the Adjusted Winner procedure to the final status issues between Israel and the Palestinians. They argued that the actual agreement fairly closely matched the advice given by the Adjusted Winner procedure. Massoud (2000) used interest-based negotiation (namely, the Adjusted Winner algorithm) to propose a plausible solution to the final status issues between Israel and the Palestinians. His results show that when the issues of security and borders are kept separate, Israel is likely to have its demands met on the issues of security, East Jerusalem, normalization of relations, and water. The Palestinians will win on the issues of sovereignty, Israeli settlements in the West Bank, Israeli settlements in Gaza, and Palestinian refugees. Both sides will need to compromise on the issue of boundaries. If security and borders are lumped together as one issue, Israel and the Palestinians will share the territory of East Jerusalem. Also related to the Israeli–Palestinian dispute, Korobkin and Zasloff (2005) concluded that the failure of the parties to that date to reach an agreement based on the land-for-peace framework can be attributed to some combination of three common roadblocks to negotiation success: (a) the absence of a bargaining zone, such that no single set of agreement terms would be preferable to continued impasse for both parties; (b) internal division within one or both principal parties, such that an agent or a minority faction with the ability to block an agreement undermines a result that would benefit the party as a whole; and (c) mutual hard bargaining, such that both sides refuse to accept an agreement that would be preferable to impasse and instead hold out for an even more desirable agreement. They proposed that a plan should begin with the United States presenting a nonnegotiable set of terms to the two disputing parties that they could either take or leave but not bargain over, maximize the chance that the parties will accept those terms by both including side payments to the parties as part of the proposed deal and simultaneously threatening to withhold political and economic support if the deal is rejected, and take specific steps to work with the disputants and allies to limit the power of Palestinians and Israelis who are opposed to an agreement to stand in its way. Zeleznikow (2014) contrasted family mediation with the Israeli–Palestinian dispute in an effort to use the AssetDivider system to provide advice about the dispute. In his allocation, it is suggested that Israel recognize a Palestinian state, with East Jerusalem as its capital. The Israelis would also be asked to dismantle the current security fence and evacuate those smaller settlements that are not in close proximity to current Israeli borders. To make such an agreement acceptable to Israel, the Palestinians would need to recognize the state of Israel and encourage other Arab states to do likewise. Palestinians would have to forgo any right of return to Israel (for which they would be compensated) and do their utmost to ensure no antiIsrael activities emanated from Israeli territories. Further, the Palestinians would need to

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encourage Iran not to develop nuclear weapons and not to make belligerent statements against Israel. Interestingly enough, this proposed solution is similar to the results of the Camp David Accords between Israel and Egypt in 1978, where Israel returned certain territory for recognition and security. However, while the Camp David Accords have endured, the then Egyptian President Anwar Sadat, who signed the Accords, was assassinated by an Egyptian in 1981, and the Israeli Prime Minister Yitzhak Rabin, who signed the Oslo Accords in 1993, was assassinated by an Israeli in 1995. Clearly, any peace partner is at peril from dissidents on his own side. The fundamental reason for the ongoing 72-year conflict between Israel and the Palestinians is not the lack of an acceptable peace plan. There are plenty of those. Rather the reason for the conflict is a lack of trust between the parties. To help minimize tensions it would be wise to engage in small trust-building activities, such as giving Palestinians better access to Israeli hospitals, easing travel restrictions on Palestinians and decreasing terrorism by Palestinian activists. Prawer and Zeleznikow (2019) analyze the use of data mining to support international conflict resolution. They proceed from the postulate that an accurate analysis of the behavior of parties in international conflicts requires a comprehensive analysis of the decision-making of the parties on the basis of consideration of all the tools available to them, including power-based approaches. For the domain of international conflicts, war is the most common power-based approach. They argue that while interest-based focuses are the most common approach for resolving international conflicts, a failure to investigate armed conflict as a tool of international conflict resolution leads to a warped analysis of the effectiveness, and limitations, of nonviolent methods of resolving conflicts. They demonstrate that armed conflict is a major tool used by countries, and that it has a high degree of effectiveness. Their findings and conclusions are that international conflict resolution field largely excludes an analysis of armed conflict as a method of dispute resolution, and that the exclusion of armed conflict from the analysis of international conflict resolution methods is not justified conceptually and leads to a distorted analysis of party behaviors in conflict situations. This leads to a “blind spot” in the efficient, and accurate, analysis of decision-making in international conflict resolution. Druckman and Wagner contribute a chapter on international conflicts in this handbook (Chapter ▶ Just Negotiations, Stable Peace Agreements, and Durable Peace).

NSS for Family Law Previously we have discussed two systems which provide advice upon the distribution of property under Australian Family Law. Split-Up uses rule-based reasoning and machine learning, together with a sophisticated argumentation system to advise upon BATNAs. The Split-Up system is not a Negotiation Support System. Similar to the Split-Up system, Portable and the Legal Services Commission of South Australia

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designed and developed Amica,8 a digital solution for Australian separating couples. Amica includes a machine learning algorithm that provides a suggested division of a former couple's total assets. The family winner system provided advice to disputing parents on how they could best negotiate trade-offs. The disputing parties were asked to indicate how much they valued each item in dispute. Using logrolling, parties obtained what they desired much. Family-Winner uses game theory to perform trade-offs to support disputants to engage in win–win negotiations. Our Family Wizard (Lewis 2015; Barsky 2016) is an electronic posting service that is a tool that can provide verifiable evidence of how parental communication takes place. It supports separating parents to engage in appropriate and civil behavior while assisting with developing parenting planning and maintain a record of parent behavior. It also provides judges who are making decisions in family disputes, to examine the behavior of parents to each other. While this is a useful tool, it as well as most other current ODR systems provide limited support to help disputants resolve their conflicts. The Australian family court system has unofficially adopted an app designed to help separated families manage daily life and hold parents “accountable” for their children’s welfare. Stepfamilies Australia built the MyMob app 5 years ago after seeing the need for a communication tool that children could use as well as their parents. The app includes a shared calendar, a virtual “fridge” for children to post their certificates and artwork, as well as storage of key information such as Medicare numbers, shoe sizes, and birthday wish lists. Judges like the app because it encourages positive communication and includes a profanity filter that tells parents who try to use bad language to go and have a cup of tea instead.9 For example, Adieu Technologies offers family law advice and supports triaging and drafting plans.10 One of its agents Lumi is a bot with expertise in law, mediation, and counseling. After having a confidential conversation with a client, Lumi will create a step-by-step plan to help the client navigate the mediation. The Dutch platform Rechtwijzer11 (Roadmap to Justice) was designed for couples who are separating or divorcing. The aim of Rechtwijzer was “to empower citizens to solve their problems by themselves or together with his or her partner. If necessary, it refers people to the assistance of experts.” Couples pay €100 for access to Rechtwijzer, which starts by asking each partner for information such as their age, income, education, whether they want the children to live with only one parent or part time with each, then guides them through questions about their preferences.

8

https://www.amica.gov.au/ last viewed July 20, 2020. https://www.smh.com.au/technology/judges-mandate-app-for-separated-parents-20190906p52op7.html last viewed February 18, 2020. 10 See, generally, Adieu, “Complete Your Financial Disclosure in a Fraction of the Time” https:// www.adieu.ai/ last viewed July 27, 2020. 11 https://rechtwijzer.nl/ last viewed July 20, 2020. 9

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The platform had a diagnosis phase; an intake phase for the initiating party; and then invited the other to join and undertake the same intake process. Once intake was completed, the parties could start working on agreements on the topics that occur in every separation – such as future communication channels, children matters, housing, property issues (money and debts), and maintenance. The dispute resolution model was that of integrative (principled) negotiation. The process was based on interests rather than rights, but the parties were told of rules such as those for dividing property, child support, and standard arrangements for visiting rights so that they could agree on the basis of informed consent. Agreed agreements were reviewed by a neutral lawyer. The platform uses algorithms to find points of agreement, and then proposes solutions similar to Family-Winner. If the proposed solutions are not accepted, then couples can employ the system to request a mediator for an additional €360, or a binding decision by an adjudicator. Rechtwijzer is voluntary and nonbinding up until the point where the parties seek adjudication. Rechtwijzer had aimed to be self-financing through user contributions. This has not occurred.

The British Columbia Civil Resolution Tribunal The British Columbia Civil Resolution Tribunal (Salter and Thompson 2016) is the most significant current widely available ODR system that comes closest to providing a full suite of dispute resolution services. The process commences with solution explorer. It diagnoses the dispute and provides legal information and tools such as customized letter templates. The template is essentially a formal, legal looking, letter of demand. If this action does not resolve the dispute, one can then apply to the Civil Resolution Tribunal for dispute resolution. The system then directs the user to the appropriate application forms. Once the application is accepted, the user enters a secure and confidential negotiation platform, where the disputants can attempt (by themselves) to resolve their dispute. If the parties cannot resolve the dispute, a facilitator will assist. Agreements can be turned into enforceable orders. If negotiation or facilitation does not lead to a resolution, an independent member will make a determination about the dispute. Currently, the Civil Resolution Tribunal deals with the following categories of cases: (a) (b) (c) (d) (e)

Motor vehicle injury disputes up to $50,000. Small claims disputes up to $5000. Strata property (condominium or owners corporation) disputes of any amount. Societies and cooperative associations disputes of any amount. Shared accommodation and some housing disputes up to $5000.

For these five domains, potential litigants can only use the Civil Resolution Tribunal. No paper-based solutions are available. Digitally disadvantaged litigants

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are provided with assistance in accessing the internet. One of the major reasons that the Civil Resolution Tribunal has been so successful is that British Columbia residents are mandated to use the system when dealing with issues listed in sections a–e above.

Intelligent Online Dispute Resolution Systems During the Era of COVID-19 Sourdin and Zeleznikow (2020) discussed mediation in the age of COVID-19. In it they state that a truly helpful ODR system should provide the following six facilities: (1) case management; (2) triaging; (3) advisory tools for reality testing; (4) communication tools; (5) decision support tools; and (6) drafting software. These six facilities are of particular significance in current times. With citizens of many (if not all) communities forced into isolation due to COVID-19 restrictions, disputants are no longer meeting face to face. The authors note that the systems currently in use only offer two of the six essential facilities of the ODR model (case management and communication). Further, with regards to communication, videoconferencing tools such as Zoom and Skype have prioritized openness and commercial viability over privacy and security. Systems currently in use, such as Immediation,12 MODRON,13 and Our Family Wizard only offer two of the six essential facilities of Zeleznikow’s ODR model (i.e., case management and communication). There are alternative technologies that do fulfill other aspects of this model, but not all. There are also other technology platforms that exist across a number of jurisdictions that have supported apps, as well as more sophisticated chat robots. Some of these systems have emerged from the vast complaint handling sector, where there is a greater capacity to collect demographic and other information that can assist with the development of human-centered design. However, the wide variation in terms of capacity and use suggests that jurisdictional variability will continue to be a concern for courts, ADR providers and those using such services. Indeed, this concern is heightened amid the justice sector’s move to digitalization in response to COVID-19. The authors argue that this reality ultimately calls for an evaluation of the issues plaguing the use of technology in the justice sector.

12 See, generally, Immediation, “What Is Immediation?” https://www.immediation.com/ last viewed July 27, 2020. 13 See, generally, MODRON, “Resolve the World’s Disputes Whenever Wherever” https://www. modron.com/ last viewed July 27, 2020. MODRON is the provider favored by the Australian Resolution Institute: Resolution Institute, “Resolution Institute and MODRON Have Partnered to Bring Our Members Spaces” (2020) https://www.resolution.institute/resources/online-dispute-reso lution-platforms/modron last viewed July 27, 2020.

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Conclusion In this chapter, we have examined the historical development of intelligent negotiation support systems. We noted that the earliest ones (primarily in the 1980s) were settlement-oriented and were generally template-based or rule-based. This then led to the development of case-based systems. Game theory is not, in general, considered as a sub-branch of artificial intelligence. But it too has been the basis of providing intelligent negotiation support, as shown in the Adjusted Winner, Family_Winner, and Smartsettle Systems. We concluded by investigating many intelligent NSS. The most widely used intelligent online dispute resolution system is the British Columbia Civil Resolution Tribunal. We examined its operation in detail. With citizens of most communities forced into isolation due to COVID-19 restrictions, disputants are no longer meeting face to face. While videoconferencing is being widely used, communication tools such as Zoom and Skype have prioritized openness and commercial viability over privacy and security. We would have predicted the advent of COVID-19 leading to the more widespread use of virtual services. Yet many criminal law jurisdictions have adjourned jury trials due to deficiencies in technological innovations and their specific applicability to the criminal law landscape. Additional issues that relate to how “public” hearings can continue have also led to sluggish responses. With citizens being forced into isolation due to COVID-19 restrictions, the justice system needs to adapt to the new challenges faced by litigants. Deep-seeded and underlying issues associated with technologies’ infiltration in the justice sector need to be addressed. These issues include: a lack of innovation readiness and justice budget; security and confidentiality concerns; community and business responses; and issues with videoconferencing. In this respect, it is suggested that patchy and inconclusive innovations need to be replaced with technologies that are specifically appropriate for courts. We note the contemporary views of Hagan (2018), who has argued that it is impractical to develop legal technological innovations without human design as the central focus.

Cross-References ▶ Agent Reasoning in AI-Powered Negotiation ▶ Just Negotiations, Stable Peace Agreements, and Durable Peace ▶ Negotiation as a Cooperative Game ▶ Online Dispute Resolution Services: Justice, Concepts, and Challenges ▶ The Notion of Fair Division in Negotiations

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Negoisst: Complex Digital Negotiation Support Mareike Schoop

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Digital Negotiations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theoretical Foundations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Communication Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Document Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Decision Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Negoisst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preference Elicitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Composition of Messages Using Communication Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rating Offers Using Decision Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Digital Contracting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Negoisst in Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Negotiations are an essential part of business interactions. Digitalization has proven to be both an opportunity and a challenge for organizations. The digital transformation of business negotiations requires new digital processes, digital skills of the negotiators, and, most of all, dedicated system support to use the full potential that information and communication technology has to offer. Negotiation support systems (NSSs) enable digital negotiations. However, they differ considerably in the amount of negotiation support they provide; they range from simple chat systems to sophisticated negotiation systems supporting all of the negotiation processes. To support complex negotiation processes rather than M. Schoop (*) Information Systems Group, University of Hohenheim, Stuttgart, Germany e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_24

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processes with standardized goods with a low business value, NSSs must support at least the two main elements of negotiations, namely communication and decision-making. The NSS Negoisst offers the highest level of support of all current NSSs by integrating communication support, decision support, and contract management. Thus, Negoisst enables digital transformation of even the most complex types of business negotiations. Negoisst has been used for two decades around the world to teach digital negotiations, to provide international negotiation experiments and competitions, to train future negotiators, and to enhance the much needed digital negotiation skills of negotiators. Keywords

Negotiation · Electronic negotiations · Negotiation support system · Communication · Decision support · Media effects · Negotiation process · Negotiation software assistant

Introduction Business negotiations – be they intraorganizational or interorganizational – are conducted at various levels of an organization and with various means. For example, such negotiations can be found as budget and salary negotiations, in resource allocation processes, during procurement processes, as part of supply chain interactions, etc. While negotiations were traditionally conducted face-to-face, other synchronous media such as telephone, video conference systems, or web conference systems were used in more recent times. Asynchronous media have been often used in terms of email negotiations but technological advances mean that business negotiations can nowadays be conducted digitally by means of dedicated negotiation support systems (Schoop et al. 2003; Schoop 2010; Kersten and Noronha 1999; Kersten and Lai 2010; Thiessen and Soberg 2003). The term “digital negotiation” or its synonym “electronic negotiation” is used in different ways. Some understand the mere conduct of a negotiation via some digital media as a digital negotiation. In this paper, we define a digital negotiation as a negotiation that is conducted digitally; that provides the means for asynchronous and dislocated negotiations; that consists of digital support of communication and/or decision-making and/or document management; and that offers additional value beyond the mere digital conduct which is only possible through the application of information and communication technology (ICT) (cf. Ströbel and Weinhardt 2003; Schoop 2010). Looking at the process of (business) negotiations, digitalization can be performed on all aspects of negotiations. Digital decision support assesses one’s own and the negotiation partner’s offers based on a utility function that was automatically calculated and it supports decisions based on incomplete or missing information. Digital communication support compensates for the lack of cues in written interactions (such as mimics, gestures, and intonation) and it enables the automatic

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detection of emotions in negotiations. Digital document management automatically extracts the current contract versions from negotiation messages and enables the management of contract obligations.

Digital Negotiations Even though digitalization has shaped, innovated, and sometimes changed most business processes, dedicated digital negotiation support is still scarce. There are three main types of digital negotiation systems, namely auctions, agents, and negotiation support systems (NSSs). Auctions and agents automate parts or all of the negotiation processes (e.g., Jennings et al. 2001; Sycara and Dai 2010). They belong to the quantitative school of thought, aiming at an economic optimum. Agents and auctions presuppose the negotiation good (e.g., product or service) to be structured, standardized, and clearly describable. Negotiation support systems follow the support paradigm and reject the goal of automation. Rather, they aim to support human negotiators as much as is required while leaving the decision power with the negotiator (Schoop 2010; Kersten and Lai 2010). Document-centered NSSs manage the business contract as the most important document of a negotiation process and support the exchange of forms or structured documents. Contract management approaches and the negotiation support system Inspire are examples of this class of systems (Kersten and Mallory 1998; Kersten and Noronha 1999). Their disadvantage is that they provide the structured part of negotiations but do not document the reasons for decisions, for taking particular alternatives, etc. This is what communication-centered NSSs focus on. Their aim is to support the communication process. One example of a communication-oriented negotiation system is (Yuan et al. 1998). However, such systems only document the argumentation side of negotiations but have the disadvantage that the content is unstructured. Thus, there is no structured way of accessing messages or arguments. A negotiation system that supports all types of business negotiations faces two main challenges. Firstly, negotiation partners exchange a large amount of data, e.g., in the form of messages, documents, and numbers. In contrast to buy-side solutions (such as procurement systems) or sell-side solutions (such as electronic shops), there is no one party that can force the other partners to follow a particular approach (e.g., mode of negotiation, data exchange format, fees to be paid, etc.). In organizational settings, negotiations often take place in a business network or in a marketplace structure where all interested parties can come together to trade. The challenge is to enable data exchange between heterogeneous partners and to pose as few technical preconditions as possible to enable global trade with the best partner for a specific project. Even though semantic web approaches enable semantic search for goods, the best search engine can only find what is in the database. Complex goods are often not standardized and difficult to describe which results in incomplete information to be stored in the repository. Auctions and agents cannot deal with that type of setting. Negotiation support systems are equipped for negotiating about the context and

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thereby specifying the good(s) in question. This can be done through communicative enrichment enabling the parties to express in detail what is required or offered, to make the exchanges traceable, and to come to results accepted by all parties involved. However, this would need to involve an NSS with both a communicative and a document focus as the communicative enrichment must be documented to be traceable. Secondly, the digital trade of complex goods and/or goods with a low market value requires trust between the negotiation partners. Auctions are usually one-off interactions and thus not well suited to the need of a trusting relationship between the parties involved. Agents have clear goals they are expected to achieve. Trust is not a concept that plays an important role for software agents. NSSs can lower distrust by documenting all exchanges, by explicating commitments and by providing transparency of the negotiation process. However, the distinction between communication-focused and document-focused NSS is again one that would prevent the required holistic approach of integrating communication and structure. The above-mentioned paradigms (i.e., quantitative paradigm and support paradigm divided into document-centered and communication-centered paradigms) are not only distinct but also separate, yet each provides only a partial view on negotiations. The solution presented in this chapter is to provide an integrated processoriented approach to electronic negotiations. To this end, the negotiation support Negoisst has been developed (Schoop et al. 2003; Schoop 2010), and that will be the focus of this chapter. The next section discusses the theoretical background to this work.

Theoretical Foundations The integrated approach to digital negotiations introduces and combines communication management, document management, and decision support. We will now review the relevant areas.

Communication Theories There is no negotiation without communication. Offer and nonoffer communication are at the heart of each negotiation process (Tutzauer 1992). To provide communication support in digital negotiations, we need a thorough analysis of human communication and a solid theoretical foundation. To this end, several communication theories provide the basis for the communication management in Negoisst.

Speech Act Theory Speech act theory by John Searle (1969) argues that the minimal unit of an utterance is not a word or a sentence but a speech act. Each speech act consists of (1) the propositional content, i.e., what the utterance is about and (2) the illocutionary force, i.e., the mode of utterance. To illustrate these components, let us look at the following propositional content: “contract to be signed.” This utterance can be

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made as a question (“Is the contract to be signed?”) or as a declaration: “The contract is to be signed!.” These utterances have the identical propositional content but different illocutionary forces, i.e., question and declaration. Is it also possible to have different propositional contents with identical illocutionary forces? Compare the previous question with the question about signing the contract – mode is identical but content is different. Therefore, the same mode can concern different contents and the same contents can be uttered in different modes. Mutual understanding is achieved when both the propositional content and the illocutionary force are understood. Based on the illocutionary force, Searle introduces five classes of speech act. Assertives represent facts about the real world or shared experiences (e.g., statements, reports, and descriptions); commissives represent the speaker’s intention to perform the action described in the propositional content (e.g., promises and assurances); directives try to get the hearer to perform an action (e.g., requests and orders); expressives represent the speaker’s psychological states or feelings (e.g., wishes, apologies, congratulations, and anger); and declaratives create a new fact through their utterance (e.g., opening a meeting, appointments, promotions, and sentencing in a trial).

The Theory of Communicative Action Sharing the separation of content and mode with speech act theory, Jürgen Habermas (1981) extends the concept of mutual understanding. Habermas’ theory of communication action argues that there are four conditions that need to be fulfilled in order to achieve mutual understanding. These so-called validity claims are implicitly or explicitly raised with every utterance and they must be accepted by the hearer. First of all, an utterance must be comprehensible so that the hearer can understand the speaker. The claim to truth means that the hearer can share the speaker’s knowledge. An utterance must be truthful so that the hearer can trust the speaker. Finally, it must be appropriate given a normative context so that the hearer can agree with the speaker on the standards and norms in question. If any of these claims is not fulfilled, communication problems arise. Comprehensibility problems are solved by translations or explanations. Problems concerning the truth of an utterance are solved by providing more information. A speaker solves problems of truthfulness by acting consistently or by assuring the hearer of their sincerity. If appropriateness is problematic, then other unproblematic norms are cited or acknowledged authorities are referred to. Media Richness Theory As the focus in this chapter is on digital negotiation, media richness theory is also relevant. Daft and Lengel (1986) interrelate the complexity of a collaboration task and the richness of a medium which depends on the number of simultaneous communication channels, the possibility of direct feedback, and the level of personalization. A complex task requires a rich medium such as face-to-face interactions whereas a simple task can be dealt with using telephone or emails. If a complex task is dealt

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with using a medium with a low level of richness, then oversimplification takes place resulting in impersonal interactions with no feedback. If, on the other hand, a simple task is performed using a very rich medium, the result is overcomplication which can lead to ambiguities and much irrelevant information.

Document Management Communication is the rich and rather unstructured part of negotiations. Document management represents the structured part and deals with creation, storage, modification, and deletion of documents and thus concerns the whole document life cycle. There are five classes of document management systems (Kampffmeyer and Merkel 1999), namely (1) archiving systems (storing documents in a permanent way and preventing modification of documents); (2) enquiry systems allow the access to the documents stored in an efficient manner; (3) classical document management systems offer operations for the whole life cycle, i.e., documents can be stored, accessed, modified, and versioned; (4) groupware document management systems support teamwork and related activities such as sharing of resources and cooperative authoring through discussion boards, forums, shared workspaces, etc.; and (5) workflow systems automate routine document management processes and provide process support. Document management in electronic negotiations can range from simple exchanges of forms to complete electronic contracting activities. The latter view the contract and its versions during the negotiation phase as the central element of negotiation. Communication steps (e.g., to explain offers, to convince, and to argue) are of less importance.

Decision Support The first approaches to electronic negotiations were decision support systems (Jarke et al. 1987; Jelassi and Foroughi 1989). A decision theoretic perspective is thus an established basis for e-negotiation approaches. In this perspective, the focus is on individual or joint decisions taken by the negotiators and system support to choose the best alternative in decision situations (Vetschera 2013). Preferences are elicited and a utility function is computed that can then be used to rate each offer. During and after the negotiation, it is possible to measure the individual and joint performance and thus to learn about the effects of certain strategies, etc. Inspire is a well-known electronic negotiation support system firmly rooted in the decision support tradition. Negotiation is thus seen as “a form of decision-making with two or more actively involved agents who cannot make decisions independently, and therefore must make concessions to achieve a compromise” (Kersten et al. 1991; Kersten and Noronha 1999).

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There are different preference elicitation methods. The conjoint analysis is widely used. It follows a decompositional approach; that is, negotiators are asked to rate packages; based on this rating, the relative importance of individual attributes can be computed. The variant of a hybrid conjoint analysis is the basis for many negotiation support systems (such as Inspire and Negoisst). It combines a compositional part (rating of each attribute with its ranges) and a decompositional part (rating of packages based on the utility function computed from the compositional part).

Summary As discussed in the previous sections, a negotiation consists of message exchange (representing the fact that negotiation is a form of communication) of decisionmaking processes and of contract management. Communication in negotiations consists of facts, emotions, questions, answers, offers, descriptions, acceptance, rejection, ideas, etc. Negotiation communication is rich and there is no negotiation without communication. Therefore, communication support is vital for digital negotiations. It needs to provide support for mutual understanding and it needs to overcome the limitations of written media to convey the richness of negotiation communication. Document management is an important issue in electronic negotiations as the negotiations aim at reaching an agreement documented in a contract. Therefore, the possibility of joint authorship, version control (to represent the developments during a negotiation), and a link to the argumentative force of the message exchanged are required (Staskiewicz 2009). Finally, decision support is required for negotiators in digital negotiations to help find the solution that is best in the given context. The brief review in this section has shown that there is relevant previous work but no integration has been done to provide a negotiation support system that offers communication management (based on a solid theoretic foundation), decision support (to account for the fact that humans have a bounded rationality and limited cognitive abilities), and document management (to enable contract versions to be managed) (cf. Schoop et al. 2004; Staskiewicz 2009). Therefore, Negoisst has been developed to integrate these three areas and thus to enable the support of complex electronic negotiations.

Negoisst In this section, the negotiation support system Negoisst will be presented referring to the requirements of a holistic support and to the background described in the previous section. Negoisst has been used for digital business negotiations for the past two decades (Schoop et al. 2003; Schoop 2010). We will now introduce its functionalities and discuss its merits by presenting the digital negotiation process.

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Preference Elicitation At the beginning of a negotiation, the negotiation issues need to be established, i.e., those attributes that are under negotiation. Once the negotiation partners agree on the set of issues (perhaps negotiated using Negoisst itself), each negotiator goes through the phase of preference elicitation, cf. Fig. 1. Firstly, all issues are rated. The sum of the ratings is 100%. Rather than operating with numbers only, we have established in various experiments that negotiators often prefer a visual means of specifying the rating. Therefore, a slider can also be used to

Fig. 1 Preference elicitation

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specify the rating. As an alternative, pairwise comparison can be performed to establish the rating of issues (Lenz and Schoop 2019). Once the issues are rated, their range or their alternatives need to be elicited. Negotiation issues in Negoisst can be numeric or categorical. In Fig. 1, the contract signing bonus is numeric and can thus be any number within a range that the negotiator specifies with worst case and best case as its borders. The CD cover design in Fig. 1 is a categorical issue. Here, all possible alternatives must be explicitly specified and then rated. Once the preference elicitation is done, a utility function is then calculated and packages with their ratings are presented to the user. If the user wants to change these ratings, then the utility function will be recalculated. An important feature of the decision support in Negoisst is that it is dynamic, i.e., it enables the adjustment of previously established preferences dynamically during the negotiation and the addition, modification, or deletion of issues and/or values during the negotiation processes (Lenz and Schoop 2019). The set of negotiation issues makes up the negotiation agenda, that is, those attributes that are negotiable and that need a firm value before the negotiation can be terminated successfully with a contract.

Composition of Messages Using Communication Support As mentioned in the previous sections, electronic negotiation is a form of written communication. Communication does not only have a descriptive role but also a performative role (Habermas 1981; Schoop 2010). Therefore, communication can also be seen as action. Such messages are similar to email with additional functionalities. In a digital setting, mimics, gestures, tone of voice, visual images of the negotiation partner, etc., are no longer visible although they help to convey the meaning of utterances in the traditional negotiation setting. It is relatively easy to see whether an utterance is meant in an ironic way, whether the speaker is serious, and whether the speaker expects some kind of reply. The digital form of communication inherently carries the disadvantages of missing cues (Sproull and Kiesler 1986, 1991) due to its restriction to one media channel only, namely written communication (cf. Daft and Lengel 1986). On the other hand, the digitalization can also provide some important advantages. For example, there can be asynchronous as well as dislocated exchanges; partners have time before replying to a message sent by the partner; negotiators can liaise with other departments or colleagues during the negotiation process, etc. To compensate for the missing cues, there must be a way to transfer semantics and pragmatics to avoid unwanted ambiguities, misunderstandings, etc., in electronic settings. Semantics represents the relation between signs and objects and conveys the meaning of signs; pragmatics represents the relation between the signs and the ones using them and conveys the intentions of communicative acts. Negoisst provides semantic and pragmatic enrichment which will now be introduced. Negotiation in Negoisst is conducted via message exchange. Each message in Negoisst has a propositional content and an illocutionary force to aid interpretation

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Fig. 2 Message elements in Negoisst

in a written setting, cf. Fig. 2. The propositional content is the content of a negotiation message, i.e., what it is about; the illocutionary force represents the mode of the message, i.e., how it is meant. The negotiator writes the message in natural language. This message content represents the propositional content of the message (cf. Searle 1969; Habermas 1981). To reduce semantic misunderstandings (i.e., those problems based on different mental models) and to aid understanding of the message content, the natural language text is semantically enriched. Firstly, Negoisst was designed with semantic enrichment. To avoid misunderstanding about the negotiation issues themselves, a negotiation ontology is created. An ontology is a network of concepts. It formally defines each concept and then uses a reasoner to create the relations between the concepts automatically (Cuenca Grau et al. 2008; Horrocks and Patel-Schneider 2004). As the negotiation ontology consists of concepts rather than terms, a concept can have different terms attached, for example, in different languages or in different professional terminologies. In Negoisst, the negotiation agenda is based on an ontology with the negotiation issues and their semantics clearly defined. In turn this means that the negotiation issues have not only a clear but also a shared meaning. Negotiators no longer operate on the basis of terms which are highly context dependent and subjective but on the basis of concepts with a clear definition. Therefore, misunderstandings usually can be prevented. In creating semantic enrichment for Negoisst, we also wanted to ensure that structure is added to the rich natural language messages to prevent misinterpretation of those written utterances. In contrast to other systems (e.g., Kersten and Noronha 1999), we wanted to retain the richness and thus rejected the idea of forms to fill in. Furthermore, offer communication (i.e., statements regarding the negotiation issues)

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Fig. 3 Message composition in Negoisst

and nonoffer communication (i.e., arguments, explanations, threats, compliments, greetings, etc.) must be consistent. In some negotiation systems, it is possible to send a form with attribute values and to talk about different values in a message. We wanted to ensure consistency as well as retaining the overall goal of mutual understanding. To this end, items in the natural language message can be related to the negotiation agenda. That way, the flexibility of natural language can be used in message composition while providing the link to the issues that are themselves linked to the negotiation agenda. Therefore, misunderstandings are prevented as much as possible and joint understanding is enabled and maintained. Figure 3 shows the message composition in Negoisst. The message field contains the message written by the author. On the right-hand side, the agenda with the negotiation issues is shown. The author is currently writing about the contract signing bonus. They can directly insert each negotiation issue, in this case “Contract Signing Bonus.” In the paragraph above that sentence, the promotional concerts have been specified and the number 8 was specified as the value for the issue “Promotional Concerts.” That way,

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the structure is added while retaining the flow of a natural language message. Any time a value is changed in the agenda, there is an automatic update in the message that is currently authored. Therefore, there is a firm link between the natural language text in the message and the structured negotiation agenda based on an ontology. In addition to understanding what a negotiation message is about, mutual understanding also requires an understanding of how a negotiation is meant by the author. This illocutionary force represents the mode of the utterance and is made explicit to show the recipient how to interpret the utterance. In Negoisst, the illocutionary force is realized as a message type. There are two message types, namely request, offer, counteroffer, accept, and reject as formal message types, and question and clarification as informal message types. Each action type is classified into the five classes of speech acts (assertives, commissives, directives, expressives, and declaratives). The classification is used to deduce the obligations following the exchanges automatically. For example, if accepted, a request as a directive carries an obligation for the recipient (the seller) to provide the goods and for the author (the buyer) to pay for them; an offer carries an obligation for the author (the seller) to provide the goods and for the recipient (the buyer) to pay for them. Of course, there are more detailed obligations that Negoisst makes explicit. The author of a message chooses the appropriate message type and thus makes their intentions explicit. This in turn helps the recipient to interpret the message in the way it was intended. Such pragmatic enrichment counteracts the missing cues of mimics, gestures, and tone of voice. To establish which message type can be used at each step of the negotiation, a message protocol has been designed, see Fig. 4. A negotiation begins with a request or an offer by party A. Party B, i.e., the recipient, now has three possibilities. They can reject the request or offer and thereby end the negotiation; they can accept the request or offer and thereby end the negotiation; they can send a counteroffer and continue the negotiation. Party A now has the same three possibilities and so on. A negotiation ends successfully in state q4 which is reached when one of the parties makes a final acceptance; it ends unsuccessfully in state q3 which is reached when Fig. 4 Negotiation protocol of formal messages

A:counter A: request/offer

q0

B: counter

q1

q2 B: accept

A: accept

B: reject

A: reject

q3

q4

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Fig. 5 Message thread with formal and informal messages in Negoisst

one of the parties make a final rejection. The message protocol provides clear interaction rules and a structured role assignment (e.g., sender and recipient, seller and buyer). It is important to mention that the protocol shown in Fig. 4 is a strictly alternating protocol, i.e., a negotiator cannot reply to his or her own message but only to a message of the negotiation partner. Traditional negotiations have formal and informal settings. An informal setting is, for example, the coffee break. To show whether a message is a formal request or merely an informal inquiry, the level of formality must be indicated. This is realized in Negoisst by distinguishing between a formal negotiation area that follows the protocol shown in Fig. 4 and an informal area similar to a virtual coffee break in which the negotiators leave the negotiation arena for information exchanges. All exchanges are documented but only formal exchanges lead to commitments and are relevant for the contract. Figure 5 shows a message thread containing formal and informal messages. The formal messages are “Offer” and “Counteroffer” whereas the informal messages are “Question” and “Clarification.” The formal exchanges display a rating (which represents the computed utility, cf. section “Rating Offers Using Decision Support”) while the informal exchanges do not as they are not contractually relevant. Once the questions have been clarified or the information exchanges should end, the formal negotiation continues by replying to one of the previous formal messages sent by the partner.

Rating Offers Using Decision Support The preference elicitation has provided the basis for the utility function that is computed by Negoisst. When writing a message, values for the negotiation issues

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Fig. 6 History graph

are offered. The decision support designed in Negoisst is used to rate each formal message – one’s own offers and the negotiation partner’s counteroffers – based on one’s own preferences. While creating a message, the utility is displayed to show how it would be rated, were the message sent. The utility for each formal message is displayed in the message thread as shown in Fig. 5. Furthermore, the numeric utility values are displayed in the history graph, cf. Fig. 6. The black line displays the utilities of offers made by the negotiator whereas the orange line displays the utilities made by the negotiation partner, i.e., those received by the negotiator. The utilities are based on the negotiator’s utility function which means that the history graph will look different for the negotiation partners involved. The decision support is an asymmetrical support feature – it is only visible for the negotiator using it. The partner will not be able to access that graph or the preferences of the other party. One important difference to other systems is that Negoisst can deal with partial offers – offers in which not all attributes are specified. Our empirical research has shown that negotiators often start with incomplete offers and work towards specifying all attributes only during the process since the values also depend on the partner’s behavior (Reiser 2012). If such partial offers are sent, the utility is not a value but a range showing the interval of possible values that can be reached when all attributes are specified, cf. representation in Fig. 7. Figure 7 shows messages with incomplete information. Therefore, their utilities are not a number but a range. The range for each of the negotiator’s own offers is shown in grey; the range for the negotiation partner’s offers is shown in yellow. Once all issues have been given values, the utility will become one number, see Fig. 8. Figure 8 shows the first offer to be incomplete (grey range). The negotiation partner started their first (counter) offer with complete information (shown in orange). The next offer made by the negotiator specified all issue values and is thus a number. It is also possible to use a so-called negotiation dance graph which displays the utility of each message based on the preferences of both partners. The preferences

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Fig. 7 History graph with incomplete information

Fig. 8 History graph with incomplete and complete information

themselves are not disclosed but the valuation of the message is based on this previously undisclosed information. We found that the dance graph lacks acceptance (Gettinger et al. 2012) but it is available if all negotiators involved agree to use it.

Digital Contracting As we have shown, the structured side of negotiations in terms of analytical support and negotiation agenda and ontology is linked to the rich communicative side in terms of natural language message exchange. Quite often, it is necessary to write up a contract after the negotiation has ended. This process can involve negotiations about terms and conditions once again and can indeed change what was agreed upon during the negotiation process. To prevent this would lead to an increase in trust as no modifications are allowed. Therefore, digital contracting is implemented in Negoisst as follows.

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Each formal message leads to a contract version. The content of the contract is automatically deduced from the semantically enriched message content and the message type. The message type implies the roles of the partners and thus their obligations (e.g., delivery made by the seller; payment made by the buyer). The message content with its semantic enrichment provides the structure, the issues, and their values. Only formal messages lead to new contract versions. As no modification is possible, the contract versions are strictly based on the message exchanges. A contract is thus completely traceable and transparent. As each formal message is linked to a contract version, the link can be used in two ways. Firstly, the negotiator can view the contract version that was deduced from each formal message. This shows the structured result from the natural language content. Secondly, for each entry in each contract version the negotiator can view the message that discussed that particular issue with that particular value. This shows the reason and arguments for a particular value. To enable reusability, Negoisst provides a contract library that can be used for contract templates so that a certain structure is already predefined. If negotiations are complex, the consequences of offers and actions are not always easy to anticipate. Therefore, it is possible to view obligations of an offer (and thus a message) before it is sent. Finally, all obligations of all negotiators are displayed so that it is clear who is responsible for what. Digital contract management is a symmetrical feature of Negoisst, that is, its usage is identical by all the negotiators and the displayed information is similar for all as the contract (and its versions) and the obligations are relevant and transparent for all parties involved.

Negoisst in Use Having introduced Negoisst, it is now obvious that it can support complex digital negotiations by following an integrated approach of novel communication management, decision support, and extended contract management. Negoisst has been used in real-life negotiations and in many laboratory experiments with students from all over the world. To train business negotiators, Negoisst has been used by them using particularly difficult negotiation cases to try out different strategies and approaches. The student experiments are conducted as bilateral international business negotiations. All negotiators are briefed on the system and its features (Melzer and Schoop 2016) and start a business negotiation with international partners. The case is a business negotiation case (such as a merger, a complex sale of goods, and a contract of products and services combined) containing public case information (“the story”) and private information (“individual goals”). The research questions that we address with these negotiations influence the case and the Negoisst features that are accessible to the negotiators. For example, we wanted to test the merits of decision support and provided one group with Negoisst decision support while the other group had no dedicated decision support. Selected experimental results can be found in (Schoop 2010).

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Conclusion Negoisst is a web-based negotiation support system enabling digital negotiations. It is firmly rooted in communication theories (Habermas 1981; Searle 1969) and distinguishes between the content of a speech act and the mode of expression (i.e., the intention). This is realized through semantic and pragmatic enrichment, thereby enabling structured yet rich and unambiguous digital negotiations. The message protocol provides a list of message types that can be used in a particular negotiation scenario depending on the role of the negotiator, the phase of the negotiation, and the previous message. Formal and informal message types are distinguished to represent the fact that not all exchanges should be binding and should lead to contractual obligations. For example, a negotiation can start with an informal exchange of questions and clarifications or such informal interactions can take place at any time during the negotiation process if one or both partners feel the need for it. We call this possibility to leave the formal arena a virtual coffee break representing the informal chats over coffee (or tea) that are important for any negotiation scenario. The formal action types are automatically classified in the five classes of speech act proposed by Searle. This is used to deduce obligations following each exchange. For example, an offer leads to a commitment to do as promised if the partner accepts. The validity claims introduced by Habermas are implicitly implemented through the possibility of rich exchanges and discussions. The goal of mutual understanding is supported by providing structure to help interpret an utterance and by providing the message type to show in which mode a message is meant by the negotiator who sent that message. The shared ontology further clarifies meanings of terms by using concepts and their definitions, thereby creating a shared communicative background for all negotiation partners. In terms of media richness theory (Daft and Lengel 1986), the communication support provides the ideal communication medium for the complex task of electronic negotiations. To support negotiators making the best possible decisions, digital decision support is offered. It is support rather than automation which means that the decision power remains with the human negotiators. The decision support in Negoisst can deal with incomplete and missing information in message composition and is based on different approaches of preference elicitation and preference modification (Lenz and Schoop 2019). Each formal message leads to a new contract version which is automatically deduced from the message. Therefore, no manipulation of the contract is possible. All exchanges are documented, leading to complete traceability. As all exchanges are transparent, these mechanisms can be seen as enhancing trust between the negotiation partners, thereby fulfilling one of the main challenges in electronic negotiation research. Negoisst does not require any specific software. It is completely web based and only requires a web browser and internet access. It is not limited to specific industries, countries, or products so many buyers and many sellers can interact, fulfilling the challenge of enabling market-like exchanges.

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Negoisst has been used in teaching negotiations and in international negotiation experiments by students from around the world for the past two decades. It has helped to train thousands of future negotiators and to enhance their digital skills conducting negotiations in the twenty-first century.

Cross-References ▶ Communication Media and Negotiation: A Review ▶ Context and Environment in Negotiation ▶ E-Negotiations: Foundations, Systems, and Processes ▶ Methods to Analyze Negotiation Processes ▶ Negotiation Processes: Empirical Insights ▶ Role of Emotion in Group Decision and Negotiation

References Bichler M, Kersten G, Strecker S (2003) Towards a structured design of electronic negotiations. Group Decis Negot 12(4):311–335 Cuenca Grau B, Horrocks I, Motik B, Parsia B, Patel-Schneider P, Sattler U (2008) OWL 2: the next step for OWL. J Web Semant 6(4):309–322 Daft RL, Lengel R (1986) Organizational information requirements, media richness and structural design. Manag Sci 32(5):554–571 Gettinger J, Koeszegi S, Schoop M (2012) Shall we dance? – the effect of information presentations on negotiation processes and outcomes. Decis Support Syst 53(1):161–174 Habermas J (1981) Theorie des kommunikativen Handelns. Suhrkamp Verlag, Frankfurt am Main Horrocks I, Patel-Schneider PF (2004) A proposal for an OWL rules language. In: Proceedings of the thirteenth international World Wide Web conference (WWW 2004). pp 723–731 Jarke M, Jelassi MT, Shakun MF (1987) MEDIATOR: towards a negotiation support system. Eur J Oper Res 31(3):314–334 Jelassi MT, Foroughi A (1989) Negotiation support systems: an overview of design issues and existing software. Decis Support Syst 5:167–181 Jennings NR, Faratin P, Lomuscio AR, Parsons S, Sierra C, Wooldridge M (2001) Automated negotiation: prospects, methods and challenges. Group Decis Negot 10(2):199–215 Kampffmeyer U, Merkel B (1999) Dokumentenmanagement. Grundlagen und Zukunft, Project Consult Kersten G, Lai H (2010) Electronic negotiations: foundations, systems, and processes. In: Kilgour, Eden (2010):361–392 Kersten GE, Mallory GR (1998) Rational inefficient compromises in negotiation. Research report INR04/98. http://ideas.repec.org/p/wop/iasawp/ir98024.html Kersten GE, Noronha SJ (1999) WWW-based negotiation support: design, implementation and use. Decis Support Syst 25:135–154 Kersten G, Michalowski W, Szpakowicz S, Koperczak Z (1991) Restructurable representations of negotiation. Manag Sci 37(10):1269–1290 Kilgour D, Eden C (2010) Handbook of group decision and negotiation. Springer Dordrecht. Lenz A, Schoop M (2019) Assessment of multi-criteria preference measurement methods for a dynamic environment. In: Proceedings of the 52nd Hawaii international conference on system sciences, Scholar Space: 1–10

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Melzer P, Schoop M (2016) The effects of personalised negotiation training on learning and performance in electronic negotiations. Group Decis Negot 25(6):1189–1210 Reiser A (2012) Entscheidungsunterstützung in elektronischen Verhandlungen: Eine Analyse unter besonderer Berücksichtigung von unvollständigen Informationen. Springer Gabler Verlag Wiesbaden Schoop M (2010) Support of complex electronic negotiation. In: Kilgour and Eden: 409–423 Schoop M, Jertila A, List T (2003) Negoisst: a negotiation support system for electronic businessto-business negotiations in E-commerce. Data Knowl Eng 47(3):371–401 Schoop M, Koehne F, Staskiewicz D (2004) An integrated decision and communication perspective on electronic negotiation support systems: challenges and solutions. J Decis Syst 13(4):375–398 Searle JR (1969) Speech acts – an essay in the philosophy of language. Cambridge University Press, Cambridge Sproull L, Kiesler S (1986) Reducing social context cues: electronic mail in organizational communication. Manag Sci 32(11):492–1512 Sproull L, Kiesler S (1991) Connections: new ways of working in the networked organization. MIT Press, Cambridge Staskiewicz D (2009) Document-centred electronic negotiations. Dr Hut München Ströbel M, Weinhardt C (2003) The Montreal taxonomy for electronic negotiations. Group Decis Negot 12:143–164 Sycara K, Dai T (2010) Agent reasoning in negotiation. In: Kilgour, Eden (2010):437–451 Thiessen E, Soberg A (2003) SmartSettle described with the Montreal taxonomy. Group Decis Negot 12(2):165–170 Tutzauer F (1992) The communication of offers in dyadic bargaining. In: Putnam L, Roloff M (eds) Communication and negotiation. Sage, Newbury Park, pp 67–82 Vetschera R (2013) Negotiation processes: an integrated perspective. EURO J Decis Process 1:135–164 Yuan Y, Rose JB, Suarga S, Archer NP (1998) A web-based negotiation support system. Int J Electron Mark 8(3):13–17

Online Dispute Resolution Services: Justice, Concepts, and Challenges Ofir Turel and Yufei Yuan

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . e-Disputes and e-Justice: The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Online Dispute Resolution Services: A Potential Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Big Picture: Online Dispute Resolution Services and Negotiation Support Systems . . . . Principle Matters: Principle-Based Dispute Resolution Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of Online Dispute Resolution Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Review of Existing Online Dispute Resolution Services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Key Challenge: The Adoption of ODR Services by Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Online dispute resolution (ODR) services are e-justice service conduits that utilize, implicitly or explicitly, electronic negotiation systems. They are a key mechanism that may provide a viable solution to the flood of e-disputes, and even for face-to-face disputes that can be resolved without being colocated (for instance, the social distance restriction of the COVID-19 epidemic forced court sessions to be conducted online). Justice is important in negotiation processes and in society. It is therefore suggested that ODR services are a viable means to serve justice on the web. We describe the state of e-justice and introduce the need for online dispute resolution services. We then present the concept of ODR, its different forms, and its association with negotiation support systems. To this end, we portray a classification of ODR services, give examples of different O. Turel (*) California State University, Fullerton, CA, USA e-mail: [email protected] Y. Yuan McMaster University, Hamilton, ON, Canada © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_25

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types of services, and specifically discuss one of the promising types, namely principle-based dispute resolution services. We conclude with an overview of the challenges associated with the introduction of ODR services, and specifically with their adoption by users, an issue that is also echoed in several other negotiation support studies. Keywords

Negotiation · Justice · Online dispute resolution · Argumentation · Negotiation location · Media effects · Multiple participant-multiple criteria · Negotiation process

Jim played the tuba as a senior in high school, more than three decades ago. When he decided to resume his old hobby, he searched eBay to find an instrument. He bid $510 on a tuba and won – only to find out that it was actually a baritone: a smaller, related instrument with a different tonal range. – Cara Cherry Lisco, Vice President, Dispute Resolution Services, SquareTrade, describes a typical online dispute, January 2005

Introduction While the phenomenal growth of online transactions may benefit nations (Swan 2017), firms (Zeng and Mackay 2019), and individuals (Pepper and Jackman 2019), it can also bring an increasing number of new types of commercial conflicts (Grimmelmann 2019). These conflicts can materialize due to the unique attributes of online markets, such as lack of trust building mechanisms (Etzioni 2019), globalization (Landry 2000; Moore et al. 1999; Watson et al. 1993), ease of committing fraudulent activities (Shah et al. 2019), and the conflict exacerbating nature of online text-based communications (Friedman and Currall 2003, 2003; Kiesler 1997). The latter type of conflicts may be further expended due to the increased use of online communications and web-based group support systems (group-support systems: past, present, and future, same-time different-place group support) for meetings and decision-making, all of which mostly rely on lean media for communication. In addition, in many consumer-to-consumer online marketplaces unique goods (e.g., art items) are sold by one user to another. In these cases, the product may not easily meet the expectations of the buyer. Furthermore, online buyers and sellers are not professional traders and accordingly, may lack experience in commercial practices. Overall, web-based commerce, and especially e-auctions, may involve one-time, “relationshipless” transactions that are based on lean communications, and therefore, harbor high potential for disputes. To exemplify the magnitude of the problem, one can look at a subset of these disputes – the ones that pertain to a single electronic market, namely, eBay, and got resolved via a single dispute resolution channel. SquareTrade, the alternative dispute resolution (ADR) service provider for eBay, reports on handling over two million

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dispute cases across 120 countries over the last 6 years. This means that the global number of e-disputes is much higher. While the likelihood for disputes is elevated in online environments, online consumers are more reluctant to act and solve these disputes. The reluctance stems partly from the global nature of the transactions, the time and cost associated with court litigation, and the lack of readily available ADR means. A large survey of online consumers revealed that 41% of auction participants have experienced commercial problems, such as late delivery of items, differences between actual items to promised ones, receiving damaged items, and never receiving the promised items (NCL 2001). The majority of users who experienced problems managed to solve them directly with the other party via email communications. The rest, however, had to use other means such as filing complaints with the auction site, credit card companies, insurance companies, and government agencies; or never took any action to solve their problem. So, has online justice been adequately served? Why is justice important? And, how can online merchants and trade-commissions promote online justice? It should be noted that such questions are no longer restricted to e-disputes. The unfolding of COVID-19 lockdowns has forced traditional justice systems (e.g., courts, mediation services) to move to online spaces. Thus, COVID-19 has forced institutions of justice to shift to ODR; for example, through meeting attorneys and judges via zoom (Puddister and Small 2020). Nevertheless, the focus of this chapter is on ODR for online transactions; future research can more closely look at how similar principles and online tools may apply to solving traditional, face-to-face disputes (i.e., disputes that do not pertain to online transactions).

e-Disputes and e-Justice: The Problem While justice is fundamental concept in exchange relations, and it can influence the negotiation process outcomes, and durability (just negotiations, stable peace agreements, and durable peace), e-Justice (i.e., justice on the Internet), so far, has not been adequately served. The IS and legal communities have offered many cyber-solutions for executing online transactions (trade platforms and protocols), but are yet to develop efficient and effective cyber-solutions for post-transaction dispute resolution. While attention has been given to preventing e-disputes, for example, through structured and secured trade mechanisms, disputes still occur. Thus, dispute resolution is often needed and merits some attention. The Internet has led to the confrontation of modern institutions with less effective information boundaries (Katsh 1994). Thus, online conflicts present new challenges in terms of potential resolution processes and legal actions. For instance, issues of jurisdiction, contract formation, contract validity, authentication, and integrity are among the topics that modern legal systems need to address (Pacini et al. 2002). Legislators adjust their systems to tackle these issues, but online markets evolve faster. Thus, the gap between the needed legislation to the applied one is growing, and justice deficiencies are formed (Turel and Yuan 2005, 2006).

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For example, imagine a Dutch person buying an item from an Australian person on a Canadian auction site that is hosted on a server based in India, and that the item is shipped to France. Who has legal jurisdiction if dispute arises? Different courts have developed dissimilar approaches, so jurisdiction determination can be inconclusive. International treaties have not solved these issues, nor have they solved the problem of enforcement of judgments across borders (Chen 2004). Thus, even when judgment is obtained in one country, it might be infeasible to enforce it on assets in another country. Moreover, in cross-national disputes there is an inevitable need to choose a jurisdiction and therefore impose specific values on the case. These values, especially when the object of dispute is religious or cultural, may differ from the values of those involved in the dispute (Jones 1999). Furthermore, even when jurisdiction is conclusive and other details of the e-conflict are clear, is it worth the cost of traveling across the globe for resolving disputes for low-cost, low-involvement items? On top of the legal issues associated with e-conflicts, disputes that arise in online markets may be inefficiently addressed by traditional (“brick-and-mortar”) court systems. Judicial procedures can be costly and time-consuming. On average, when using court litigation, completing a claim takes 600 days and the parties spend $50,700 on legal fees (DOJ 1992). Such times and expenditures may not be accepted by online consumers for most of their daily transactions. Fast and affordable relief is crucial in dispute resolution, as a former Chief Justice in the US Supreme Court commented “The notion that most people want black-robed judges, well-dressed lawyers, and fine paneled courtrooms as the setting to resolve their dispute is not correct. People with problems, like people with pains, want relief, and they want it as quickly and inexpensively as possible” (Burger 1977). Accordingly, many offline disputes shift from litigation systems to ADR. The latter term refers to any dispute resolution mechanism other than litigation in courts (e.g., mediation and arbitration). To exemplify this trend, the better business bureau (BBB) had handled almost half-million business-to-consumer disputes in the US in 2000 (Rule 2002). The main drivers to ADR and away from litigation are that it is faster, cheaper, confidential, and the parties can choose the decision maker. These attributes of ADR make it more applicable to most e-conflicts. As such, the US Federal Trade Commission as well as international organizations, such as the Organization for Economic Co-operation and Development, call for an alternative online means to resolve online disputes (Bergling 2000). The importance of a viable e-justice system (a combination of technology, people, institutions, and processes) stems from the fact that justice is an important component of our daily routines. Individuals, including online consumers, expect justice to be adequately served, and remedies to be offered to victims of mistreatments (e.g., illegal or unfair actions). An effective and efficient means for dealing with mistreatments is especially important in uncertain environments, such as the Internet. The mere fact that there is an impartial, quick, and affordable dispute resolution system in place can reduce the uncertainty associated with e-commerce and can enhance confidence in online markets and trade (Turel and Yuan 2007a). Particularly, such online justice systems can potentially increase institution-based trust in

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online merchants through the facilitation of structural assurances. These assurances are a salient determinant of Internet based services usage (Gefen et al. 2003). As such, it is reasonable to believe that the existence of affordable, efficient, and effective dispute resolution mechanisms on the Internet may promote trust in e-vendors, and foster electronic commerce.

Online Dispute Resolution Services: A Potential Solution Online Dispute Resolution (ODR) services are a key mechanism that may provide a viable solution to the flood of e-disputes. ODR services can cater to online (and potentially offline) consumers and can address many of the abovementioned problems of physical litigation systems. ODR services, also known as e-ADR services, are interactive, web-based services intended to support parties in dispute in reaching an agreement (Hornle 2003). Essentially, these services apply information technology and telecommunication via the Internet to ADR processes, such as negotiation, mediation, and arbitration. That is, electronic means, together with supporting individuals at times, are used for better serving e-Justice. The logic behind this concept is that consumers that transacted via electronic means are already accustomed to the Internet environment, and expect the same efficiency, time-wise and cost-wise, when it comes to resolving problems they have encountered online. Overall, it is believed that the use of ODR services is a potential solution to the current upsurge in online-based disputes, and the decaying ability of the judicial procedure to resolve such disagreements. Given the increasing demand and potential, many commercial ODR services have emerged, capitalizing on the capabilities of computerized environments (see a list at http://www.odr.info/providers.php). For example, SquareTrade provides online negotiation and mediation services for online shoppers (e.g., eBay users) as well as to offline consumers (e.g., clients of the California Association of Realtors). These services enable disputants to communicate directly with one another using electronic mail and then if needed (i.e., if settlement was not reached) use online chat facilities to communicate with a professional neutral (i.e., a mediator). Another example is CyberSettle that provides web-assisted claim resolution services using double-blind offers for insurance carriers and legal professionals. In this process, parties participate in several settlement rounds, in which they send their confidential offers electronically. The system decides when the offered amount from both sides is similar enough or identical, and determines this amount as the final settlement. A further illustration is given by the Internet Corporation for Assigned Names and Numbers (ICANN). This organization is responsible for the coordination of unique identifiers on the Internet (e.g., domain names). To deal with domain name copyright issues, abusive registrations of domain names, etc., they enforce mandatory ODR procedures on all domain name owners. The Uniform Domain-Name Dispute Resolution Policy (UDRP) ensures that all domain name registrars that have a claim submit it online to a selected dispute resolution provider. This provider appoints an “administrative panel” that arbitrates the case and makes a decision.

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The Big Picture: Online Dispute Resolution Services and Negotiation Support Systems ODR services use a special type of a broader set of systems, namely, negation support systems (NSS), or Electronic Negotiation Systems (ENS) (automatic negotiation). Nevertheless, due to the unique characteristics of ODR systems and services, they deserve special attention from the e-negotiation and the negotiation support systems (NSS) research communities. While in the last two decades information systems that support negotiators’ decisions and interactions (i.e., NSS) have attracted the attention of both researchers and practitioners (see, a review, in Kersten 2004), extant studies on such systems have been mostly technology focused, and have mainly dealt with the examination of system efficiency and effectiveness (e.g., Bichler et al. 2003; Kersten 2003). Indeed, a key challenge in the not so far past was the development of such systems. Finding efficient preference elicitation and decision optimization algorithms still remains a challenge that attracts a lot of research efforts. Nevertheless, many past studies have neglected to some extent relevant perceptional and behavioral aspects associated with the usage of such systems (Yuan and Turel 2007). It is important to address these issues, because even a perfect NSS system that is not “accepted” by users will be a cost-center and will fail to deliver the potential benefits to negotiators. Recognizing this issue, several behavioral e-negotiation studies have been published in recent years (Lai et al. 2006; Turel et al. 2008). However, ODR services, as a special case of these NSS, have not received much academic attention. ODR services deserve special academic attention for several reasons. First, the context of dispute resolution is different than this of new agreement formation, investigated in many NSS studies. There are two drivers for interacting in negotiations: “to create something new that neither party could do on his her own, or to resolve a problem or dispute between the parties” (Lewicki et al. 1999, p. 5). ODR services address the second type of negotiations. As such, the extant NSS literature, which focuses mostly on the first objective, may have limited relevancy to the specific ODR context. The reader should note that dispute resolution differs from agreement creation along various dimensions. For example, while in commercial negotiation for a new agreement there is typically a reasonable degree of trust and mutual interest between the parties; disputing parties typically do not have enough trust in one another. Moreover, in agreement negotiation emotional states tend to be positive (e.g., excitement), whereas in the case of dispute resolution, emotional states may be negative (e.g., anger). Such emotions can play an important role in facilitating negotiation processes and outcomes (role of emotion in group decision and negotiation). Thus, a NSS that is effective in forming new agreement may not be as effective for dispute resolution. Second, the existing NSS literature mostly focuses on the business-to-business (B2B) context (Schoop et al. 2003), although negotiations can also take place among individual consumers in online marketplaces (C2C context) and between online merchants and e-consumers (B2C context). As such, the examination of ODR

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systems and services may broaden the scope of NSS research such that it caters to various types of trade and online markets. Third, many of the existing NSS studies have examined systems with analytical support (decision support types of NSS (e.g., Thiessen et al. 1998; Thiessen and Soberg 2003)). Most of the commercial ODR services, however, utilize structured communications to resolve disputes (i.e., process support NSS), with no analytical support. One potential explanation for this across-the-board process support approach is that because conflicts may be complex, unstructured, and emotional, it is somewhat difficult to decompose them to utility dimensions, and elicit these dimensions into a rigid utility function. As such, the existing NSS literature may not be applicable for addressing many of the practical ODR problems. Overall, ODR services, as a subset of NSS, differ in focus and applications from the commonly studied NSS. Thus, application of sound methodology to study user interactions with process-support ODR services can lead to a more accurate depiction of users’ behavior in some electronic markets, and to a better understanding of these services. It can also expand the scope and breadth of NSS research, and integrate fairly discrete research streams such as justice, human–computer interaction, ADR, and technology adoption. This knowledge may be used by merchants and system developers for facilitating state-of-the-art, end-to-end, online markets, that support consumers from the prepurchase decision to postpurchase behaviors.

Principle Matters: Principle-Based Dispute Resolution Services Most current negotiation tools for ODR are based on utility theory (Hasan and Serguievskaia 2006). They try to attain an interest-based voluntary settlement agreement based on participant utility, but utility cannot be used to induce a rightbased and enforceable decision (Parlade 2006). Although some dispute cases can be resolved by utility theory according to the parties’ preferences or trade-offs, there are other cases in which we should first determine what is right and what is wrong, leading to a determination of who is liable or responsible. Thus, we must consider fairness and justice which is “the first virtue of social institutions” (Rawls 1999). The concept of justice can be traced back to Plato and Aristotle, who affirmed that justice may be either common to all human beings or an expression of the laws of the particular community (Vice 2006). Today, we normally view the concept of justice through the lens of our legal system: justice is the establishment or determination of rights according to the rules of law or equity (Merriam 2006). Law shapes the parties’ expectations and their strategies for dispute resolution (Katsh et al. 2000). It will also determine the parties’ bargaining positions. Therefore, ODR services should also make clear the types of rules, standards, or laws (such as legal provisions, equity, codes of conduct) that serve as the basis for the settlement or decision (European Commission 2001). Justice is dispensed on the basis of legal rights created by laws that are deemed to reflect publicly held values. The disputants should resolve their disputes under some fair and justified social norms or other agreed norms which may be more generous than the legal rules (Ramsay 1981). We

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refer to these norms as the principles for dispute resolution to achieve fairness and justice. We introduce the concept of principle-based dispute resolution and build architecture for principle-based dispute resolution systems. Principled negotiation or a strategy of negotiation on merit (also referred to as win-win negotiation) is a preferred alternative to positional bargaining (Fisher 1991). Principled negotiation seeks to modify certain behavioral proclivities of people that lead to positional bargaining, resting on four tenets that aim to “change the game”: (1) separate the people from the problem; (2) focus on interests and not positions; (3) invent options for mutual gain; and (4) insist on using objective criteria (Fisher et al. 1991). Principled negotiation has been widely used for almost all negotiation activities. It is a useful approach to negotiating in a wide variety of situations, valued for its simple model and its parsimonious arguments (Lewis and Spich 1996). In the case of consumer protection, the fourth tenet “objective criteria” is very important in order to get a fair resolution for disputes between companies and consumers. Based on objective criteria, disputes between consumers and companies can be justified and fairly resolved, even in a semiautomated fashion. In this chapter, we use a more specific term “principle-based dispute resolution” rather than the general term “principled negotiation.” Here, principle-based dispute resolution means that the disputing parties seek dispute resolution according to certain established principles such as legal rules, contract agreements, and consumer protection warranty plans. Although companies need to be protected from unreasonable requests from consumers in a dispute, in most cases a consumer seeking redress from a company typically finds him/herself engaged in a highly unequal contest (Maynes 1979). They cannot get a fair resolution to disputes without agreed objective criteria for the following reasons: (1) Resource imbalance. An individual consumer has much less resources available than a company. A company may absorb the cost of ignoring a consumer’s request and can usually fight an expensive lawsuit, but an individual usually cannot. (2) There is no power balance for setting rules. A company has more power to set up the contract and related rules in favor of their own interests instead of the consumer’s interests. (3) Imbalance in negotiation power, which can be defined as the ability of the negotiator to influence the behavior of another. Negotiating power is enhanced by legal support, personal knowledge, skill, resources, and hard work (Mediate 2006). A company usually has more negotiating power than a consumer does. To overcome this imbalance, government and industry regulation and third party intervention are needed. With third party help, negotiators can resolve a dispute by jointly developing objective criteria and standards of legitimacy, and then shaping proposed solutions so that they meet these joint standards (Fisher 1991). These may include appeals to principles of fairness and expert opinions (Maiese 2003). In this chapter, we refer to jointly developed and agreed objective criteria as “principles.” According to these principles, we can judge which party is liable for what penalty, and settlement details can then be negotiated between consumers and companies. This is the concept of principle-based dispute resolution, which can provide a fair and affordable dispute resolution service for consumer protection with the following advantages:

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First, principle-based dispute resolution makes access to justice affordable. Cost is perhaps the biggest determinant of access to justice, and most consumer disputes involve only trivial amounts of money (Schulze Suedhoff 2001). If legal action is necessary for redress from the company, the legal costs are very likely to exceed any gain from the correction of a complaint. As one type of ODR services, a principlebased dispute resolution system is less costly than traditional court and travel expenses, thus making access to justice affordable for most consumers. Second, principle-based dispute resolution enhances fairness and justice. According to Parlade (2006), for justice to be rendered, it is necessary (1) that each party be heard, (2) that there be no undue delay in the proceedings, and (3) that the judge be independent and impartial so that a decision will be based solely on the evidence presented. It is easy to see that the above three conditions can be satisfied by a principle-based dispute resolution system. Third, principle-based dispute resolution alleviates the impacts of unbalanced power between the parties. As pointed out by Parlade (2006), “A fair outcome usually is determined by the balance of power. Power is derived from many sources: it is frequently associated with wealth or position, but non-obvious sources of power can significantly affect the outcome. One party may possess superior knowledge or expertise about a particular matter affecting the dispute and use it to gain an unfair settlement. Nuisance power, or the ability to cause discomfort to a party, may compel a party to rush to a settlement. Personal power, or power drawn from personal attributes such as confidence and ability to articulate one’s views, or in some cases even race or gender, may magnify other sources of power. The original ODR has the inherent capability of neutralizing some sources of power since wealth, position and personal attributes of the parties are not readily apparent online. ODR may, in fact, reallocate power from a party who is articulate to one who is skilled in writing or from one who is at ease with face-to-face interaction to one who is at ease with technology.” In principle-based dispute resolution, only facts and claims are submitted to the system. This simplicity further reduces any differences that might exist between disputing parties with ease of using technology, another possible source of unbalanced power. So the system diminishes the effects of unbalance of power between the parties, and enhances the fairness of outcomes. Fourth, principle-based dispute resolution provides the basis for fair negotiation in the follow-up settlement. After disputants get a judgment complying with the stated principles, they can distinguish the liability and the liable party in advance of any successive negotiation. Then the settlement negotiation can proceed, based on different methods and strategies. Principle-based dispute resolution provides motivation to negotiating compensation. The verdict can help disputants to take a fair bargaining position, and leading to a fair solution. Finally, principle-based dispute resolution provides continuous improvement. Principles for dispute resolution can be extended and improved. First, we need to transform the principles into a set of rules. Then we can try to resolve disputes according to this set of rules, for real cases. Due to the variety and complexity of possible cases, reasoning may not always be successful, when rule sets are incomplete or in conflict. If we find there is a need to improve the principles and create new

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rules from these principles, these can be added to the rule set, and the “principle base” can also be updated. These cycles of improvement will upgrade the principlebased dispute resolution system continuously. For lawyers, solving a dispute means reconstructing what has happened, in order to determine who is right and who is wrong. With ODR, this raises many issues. Bonnet et al. (2002) pointed out that ODR must provide technical solutions which convince a dispute resolver of the authentic character of a piece of evidence. They analyzed the principle characteristics that an ODR system must fulfill, mapping the legal requirements to a structure of technical concepts. Xu and Yuan (2009) proposed the architecture of principle-based dispute resolution systems. They also described the steps of a principle-based dispute resolution process and illustrated the use of principle-based dispute resolution through a real case.

Classification of Online Dispute Resolution Services As demonstrated by the examples given in section “e-Disputes and e-Justice: The Problem,” there are many forms of ODR services and processes. Some of these simply mimic existing face-to-face dispute resolution procedures, and some apply technology in an innovative manner to better (faster, cheaper, with increased satisfaction and perceived fairness) serve online justice. These ODR services can be classified based on their level of support. This classification is provided in Table 1. According to this classification, ODR services can support the dispute resolution processes, the decision-making processes, or automate parts of or whole processes. While process support ODR services use electronic media for facilitating dispute resolution communications between parties, decision-support ODR services use electronic media for suggesting optional solutions in an attempt to improve the resolution. Dispute resolution automation is achieved by the interaction of software agents that represent the interests and preferences of the parties in dispute. Process-support ODR services focus on communication processes and use conflict resolution behavior and communication theories to improve the effectiveness of the dispute resolution procedure. Solution-support ODR services apply game theory, utility theory, and mathematical modeling for eliciting user preferences and suggest offers that may lead to optimal resolutions. Automated ODR services use agents that are programmed to represent certain interests and collect online information. These agents can use structured decision processes for achieving optimal resolutions. Agents can also support structured reasoning, interpretation, and explanation for justified argumentation. This approach can help to better serve justice because the argumentation is based on acceptable principles and logical arguments rather than on preferences. Overall, the three levels of support can be used for offering four primary forms of ADR: 1. Online negotiation services are the basic form of dispute resolution services. These services can facilitate online communications between parties in dispute,

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Table 1 ODR services by level of support Level of support Process support

Objective Improve efficiency

Solution support

Improve effectiveness

Automation

Automate dispute resolution process

Key functionality Facilitate structured process Facilitate multichannel communication Facilitate automatic documentation Facilitate integration with other ebusiness functions Preparation for dispute resolution sessions Real-time assessment of issues and preferences Search for better & optimal resolutions Automatic information gathering Automatic proposals and counterproposals Structured reasoning, interpretation and explanation Automatic decision making

Assumptions Human interaction is a key element in negotiation

Underlying concepts Conflict resolution and negotiation behaviors Communications

Human preferences can be elicited Mathematical modeling may be used for optimizing the decision making Users are utility seekers

Game theory Utility theory Mathematical modeling and optimization

Information is available online Humans Are slow Cannot process all relevant information May be biased

Artificial intelligence (AI) technologies Software agents

using either synchronous (e.g., instant messaging) or asynchronous (e.g., electronic mail) communications. Furthermore, some of these services offer analytical support for recommending optimal avenues of action to users, based on elicited profiles of user preferences; and some apply agent technologies for representing users. 2. Online mediation and arbitration services use online media to facilitate discussion between two parties and a neutral third party. These services transfer commonly used ADR process to the online environment. Mediation and arbitration sessions can be carried out in a joint chat-room, or in private chat rooms that serves a dyad of users at a time. While in mediation the neutral party helps the disputants to

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reach an agreement, but cannot force his or her resolution on them, in arbitration, the neutral third party offers a final and binding resolution. While it is not that common, decision-support systems and artificial intelligence can also support mediation and arbitration processes. Decision-support tools can aid the neutrals and the disputants to optimize the mutual utility of the final agreement. Artificial intelligence can be used for principled negotiation under the guidance of a third party. The online environment nicely supports mediation and arbitration processes because it enables real-time multi-party communication (text, voice, and video), allows the retrieval of online information in real time (e.g., transaction information), permits the exchange of documents (e.g., file transfers), and records the process such that users can easily monitor their progress. Most importantly, the parties do not have to be colocated to realize these benefits. Furthermore, the selection of the neutral third party can be more efficient and effective than in offline ADR. Users can browse and screen lists of potential neutrals by expertise, experience, success rates, language, time-zone, cost, etc. That is, users in one country can easily use the services of an expert from another country without having to bear high costs. Given the advantages of e-ADR and the relatively easy implementation, many offline legal firms started offering the services for extending their markets. Overall, accessibility to justice can be enhanced by online mediation and arbitration services. 3. Electronic settlements can use various computational mechanisms to settle disputes. These include, for example, double-blind offers and an e-jury of users. In the latter case, a panel of e-jurors is surveyed on a problem and offers a range of fair solutions. These suggestions are then averaged, and the average is taken as a binding resolution. These services use the Internet for offer exchanges, and then apply rule-based computations to determine the final judgment. Services based on double-blind offers gained some acceptance in the insurance sector, because they can accelerate the process of insurance claiming, and benefit insurance carriers and their clients. 4. The multiple-phase approach builds on the advantages of the above-mentioned approaches and offers flexible resolution processes. For example, users can try to negotiate online, and in case they fail to reach a resolution, turn to mediation. In case the mediation fails, they can turn to arbitration.

Review of Existing Online Dispute Resolution Services There is a small but growing number of ODR services emerging into the market in recent years. They provide a variety of ODR services ranging from online negotiation, mediation, to arbitration. Some services are standalone and some are associated with organizations for particular services (Table 2). While ODR is a promising concept, it does not provide a perfect solution for e-disputes, and still faces several challenges. ODR services fall short in terms of dealing with online cheating and resolution enforcement. In cases where the plaintiff

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Table 2 Summary of some existing online dispute resolution services Mediation Arbitration Resolution Services (MARS) http://www.resolvemydispute.com/ The MARS virtual ADR conference seeks to emulate, as closely as possible, the traditional mediation or arbitration conference. It provides a real-time video and audio environment to offer mediators, arbitrators, attorneys, and other legal practitioners the opportunity carry on mediation and arbitration conferences without the need for traveling Online Resolution http://www.onlineresolution.com/ Online Resolution was one of the first ODR providers in the United States. Onlineresolution.com provided three types of dispute resolution services including online negotiation, online mediation, and online arbitration. It also sold Resolution Room, a licensed secure online groupware, to dispute resolution professionals for their private practices. It ceased operations in 2003 SquareTrade http://www.squaretrade.com/ SquareTrade was allied with eBay to provide web-based tools for parties to resolve dispute in auction through direct online negotiation, mediation, or arbitration. In the last few years, SquareTrade has resolved millions of disputes across 120 countries in 5 different languages. SquareTrade has proven that processes such as online negotiation and online mediation can be efficient tools to resolve e-commerce disputes SmartSettle http://www.smartsettle.com SmartSettle is a secure negotiation support system using a patented optimization algorithm to produce fair and efficient solutions based on negotiator’s private preferences Nominet http://www.nominet.org.uk/ Nominet’s Dispute Resolution Service (DRS) offers an efficient and transparent method of resolving disputes in the .uk top-level domain. Through the DRS we seek to settle .uk domain name disputes through mediation, and where this is not possible, through an independent expert decision Family Relationships Online http://www.familyrelationships.gov.au/ Family Relationships Online, an Australia government initiative, provides all families (whether together or separated) with access to information about family relationship issues, ranging from building better relationships to dispute resolution. It also allows families to find out about a range of services that can assist them to manage relationship issues, including agreeing on appropriate arrangements for children after parents separate BBBOnline http://www.bbbonline.org/ The BBB, a nonprofit consumer watchdog group, implemented the BBBOnline to assist with online shopping disputes in the Internet’s unregulated business environment. The BBB provides three types of dispute resolution services (conciliation, mediation, or arbitration) for consumers who have had trouble with online merchants. Even though there is no regulation to internet commerce sites, the BBB serves a policing presence to keep the integrity and honesty of online merchants in check American Arbitration Association http://www.adr.org/drs The American Arbitration Association (AAA) is the nation’s largest full-service ADR provider, addressing disputes involving, but not limited to, employment, intellectual property, consumer, technology, health care, financial services, construction, and international trade conflicts. AAA dispute resolution services include case administration offered in conjunction with its dispute avoidance and early resolution rules and procedures and arbitration and mediation rules and procedures

uses a bogus identity and disappears, ODR service cannot help tracking down the person. Also, when a resolution is obtained, ODR services, similarly to offline litigation, cannot ensure the enforcement of the resolution. Other challenges include

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dealing with cross-cultural (mis)communications, and ensuring transaction security and privacy. The latter issues are especially important in disputes contexts. In these cases, the parties are typically conscious about not letting the dispute details leak to others.

A Key Challenge: The Adoption of ODR Services by Users While some websites, such as eBay,1 started offering ODR mechanisms through third party service providers (Bunnell and Luecke 2000; Gonzalez 2003; Katsh and Rifkin 2001), there are many other ODR services (listed on http://www.odr.info/ providers.php) that have not prevailed for various reasons. Given that the needed technology is, for the most part, in place (including typically simple secured communication spaces), the usage challenges pertain mostly to the commercialization of the technologies, and to user acceptance of these mechanisms and their corresponding intentions to use the technology (Turel 2006; Turel and Yuan 2005, 2006, 2007a, b, c; Turel et al. 2007, 2008). The fields of technology adoption and human–computer interaction deal with these issues in the broad fields of information systems and electronic commerce. Indeed, several recent studies have applied concepts and models from these fields to the realm of NSS technology adoption (e.g., Lim 2003; Lim et al. 2002), and even particularly to the issue of ODR service adoption and use (Turel 2006; Turel et al. 2008). In line with existing technology adoption studies, some of the NSS findings suggest that individual perceptions, such as perceived system usefulness and ease of use, as well as individual differences, such as playfulness, help shaping user decisions to utilize NSS (Lee et al. 2007). Nevertheless, the acceptance of NSS requires the agreement of two parties to the utilization of an agreed system. As such, Turel and Yuan (2007b) have included the perception regarding the intentions of the negotiation counterpart to engage in e-negotiations. Their findings suggest that the counterpart’s perceived intentions significantly and positively influence one’s decision to engage in web-based negotiation. Other models have also been developed for examining the adoption of NSS (e.g., Doong and Lai 2008; Vetschera et al. 2006), and statistical techniques for dealing with the unique statistical dependencies that arise in this line of research have been suggested (Turel 2009). Focusing specifically on ODR services, Turel et al. have shown that justice (fairness) and trust perception or focal considerations that drive the usage of ODR services. Thus, services that can demonstrate higher fairness, would be better at building trust with users, and ultimately will be more likely to be used (Turel et al. 2008). It has been further demonstrated that users decompose online mediation services into the human-mediator component and the system component, and use different attributions toward these components (Turel et al. 2007).

1

http://www.ebay.com/

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Overall, it is well recognized that the adoption of ODR services, and not necessarily the underlying technology, is a key challenge. While there are several studies that focus on the adoption of e-negotiation services, and particularly on the adoption of ODR services, much work is still left for understanding this topic and advancing the concept of ODR.

Summary In summary, e-transactions (and during pandemics, also face-to-face disputes) may need online mechanisms for better serving e-justice. Offline judicial procedures may be cumbersome, leading to delays, high costs, inaccessibility for certain market segments, and overall, to the miscarriage of justice. At the same time, the online environment can adequately facilitate ADR procedures in an efficient and effective fashion. Thus, ODR services should be researched, developed, and offered. These endeavors should involve e-commerce researchers, online vendors, consumer organizations, trade commissions, and other policy makers. Attention should be paid to technology adoption issues and human–computer interaction concerns, as these seem to be important stumbling points, which researchers and practitioners need to overcome.

Cross-References ▶ Context and Environment in Negotiation ▶ E-Negotiations: Foundations, Systems, and Processes ▶ Just Negotiations, Stable Peace Agreements, and Durable Peace ▶ Methods to Analyze Negotiation Processes ▶ Negotiation Processes: Empirical Insights ▶ Negotiation, Online Dispute Resolution, and Artificial Intelligence ▶ Sharing Profit and Risk in a Partnership ▶ The Notion of Fair Division in Negotiations

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Agent Reasoning in AI-Powered Negotiation Tinglong Dai, Katia Sycara, and Ronghuo Zheng

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formal Negotiation Research: Different Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A Framework for Negotiation Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Procedures for Multi-issue Negotiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Changing the Structure of the Negotiation Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Value Claiming and Value Creating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fair Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Persuasion for Conflict Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tactic Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Third-Party Mediation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Agents for Decision Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reasoning with Limit Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reasoning from a Machine-Learning Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Negotiation, a fast-developing application area of artificial intelligence, has been studied by social and mathematical scientists with starkly different goals. Whereas social scientists have sought to understand various factors and reasoning T. Dai Carey Business School, Johns Hopkins University, Baltimore, MD, USA e-mail: [email protected] K. Sycara (*) Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA e-mail: [email protected] R. Zheng McCombs School of Business, The University of Texas at Austin, Austin, TX, USA e-mail: [email protected] © Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6_26

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processes underlying human negotiation behavior, mathematical scientists have developed theoretic models that formalize various elements of negotiation. The focus of this chapter is on mathematical models of agent reasoning in a negotiation, which can be either analytical or computational by nature: Analytical models offer structural predictions of agent behavior and provide managerial insights into negotiation strategy, whereas computational models offer optimization algorithms and heuristics to function as building blocks of negotiation tools powered by artificial intelligence (AI). Together, mathematical models of negotiation can often be implemented in autonomous processes, referred to as negotiation agents, that can incorporate realistic negotiation factors and engage in negotiations in a decentralized manner. Such agent models promise to contribute to our understanding of human information processing in negotiation and can be used for decision support of human decision-makers. In the long run, they may even become substitutes for human negotiators. This chapter reviews the analytical and computational negotiation literature, reveals areas of differences and synergies, and provides pointers to open questions and future research. Keywords

Negotiation · Game theory · Artificial intelligence · Negotiation process · Operations research · Decision support system · Management science · Business analytics

Introduction Negotiation is a process among human beings and/or computational agents with the purpose of reaching an agreement that satisfies preferences and constraints of the concerned parties. As a process, negotiation has the following characteristics: (a) it is decentralized; (b) it involves communication among the parties; (c) it involves incomplete information (e.g., the utilities of the parties are private knowledge to each party); and (d) it encompasses possibly conflicting preferences over actions and outcomes. Additionally, the process of negotiation (except in its most simplified form) is not well structured, in the sense that there are no well-defined rules for creating “legal” sequences of communication actions. For example, an offer by party A may be followed by party B’s request for information to further clarify conditions of the offer, or by an argument to convey to A that the offer is unfair, or by a rejection, or by a counter-offer. AI-powered negotiation has been drawn from a vast and vibrant literature on negotiation emerging from economics, political science, sociology, psychology, organizational behavior, operations research, mathematics, and, more recently, computer science. In general, the goal of investigating negotiation in the social sciences is to understand the factors involved in negotiation among people, whereas the goal of the economics and mathematical sciences is to provide analytical formalizations of negotiation so that decision-making processes that lead to optimal negotiation

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outcomes could be discovered, and advice to decision-makers could be provided as to how to implement and utilize these formulations in practice (Turan et al. 2013). In this respect, the aim of the negotiation research in social sciences (see Klamler, ▶ “The Notion of Fair Division in Negotiations,” Sundarraj, ▶ “Electronic Negotiation and Behavioral Elements,” and De Vreede et al., ▶ “Collaboration Engineering for Group Decision and Negotiation” of this volume) is descriptive, whereas the aim of the mathematical science research is prescriptive. Within the mathematical sciences camp, we differentiate goals and approaches of economics and operations research (called thereafter for simplicity analytical approaches) on the one hand, and computer science on the other (computational approaches). The analytical approaches, dominated by game theory, have focused primarily on developing models that could be mathematically characterized and solved. Typically, the computational complexity of algorithms for achieving a solution has not been the main focus; neither have concerns for similarity of the analytical models to human reasoning. A notable exception has been at work by behavioral economists and decision scientists who have challenged game theoretic assumptions (see Rothkopf (1983) and Roth (1985)) and have developed models that are based on bounded rationality. Additionally, due to the desire to characterize ways to achieve optimal outcomes, analytical models simplify the negotiation process to sequences of offers and counter offers and focus on how optimal outcomes could be characterized. On the other hand, the focus of the computational literature has been on (a) computationally characterizing the complexity of negotiation, (b) finding computationally tractable algorithms, and (c) creating computational agents that embody reasoning that includes cognitive considerations. A distinction that has not received much attention in the literature is one of centralized vs. decentralized computation. The solution-finding procedures in the analytical models are centralized. This necessitates various fictitious devices, such as “simulation of the game” in game theory, the submission of simultaneous offers, and the invention of “signaling.” In other words, the calculation of the equilibria is done in a centralized way, and the execution is envisioned to be decentralized. Many computational models use centralized algorithms as well. However, one of the challenges is to embody the algorithms in separate autonomous computational agents that calculate the next step in the negotiation after observing the previous step. This poses interesting theoretical and computational issues since (a) the autonomous calculation is online and thus must be efficient, and (b) in multiparty interactions, there is an additional issue of how the order of interaction of the agents is determined. The analytical and computational approaches are synergistic. Analytical models provide certain guarantees of the solution concepts, although by necessity they cannot encompass the complexities of real negotiations or consider contextual or cognitive factors. The computational models, on the other hand, relying on approximate algorithms and heuristics have the flexibility to include cognitive considerations and features of human reasoning, thereby promising to contribute to our understanding of human information processing in negotiation. Additionally, such models could be used for decision support of human decision-makers, either as

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trusted third parties (mediators) or directly supporting their owner. In the long run, such models can even become substitutes for human mediators or negotiators. Mathematical models are currently oversimplified versions of reality. They generally make the assumption that the negotiation process is well structured where negotiation actions occur and result in agreement or opting out of the negotiation. In practice, however, the parties may take actions to change the structure of the negotiation itself, for example, adding or subtracting issues as the environment changes or as the parties try to “enlarge the pie” (cf., Shakun 1991; Kersten et al. 1991; Sebenius 1992). Research is very far from being able to model or derive automated ways to do such restructuring, but some initial attempts have been made (Sycara 1991). The basic elements of negotiation are the underlying interests and social motives of the participants, and their interactions, e.g., creating value or claiming value, which respectively characterize integrative vs. distributive negotiations. A critical area of interaction is persuasion, i.e., how one party can convince the other to accept a particular proposal or resolve some impasse. Various types of arguments and justifications can be offered to this end. Finally, these interactions become operationalized through observable communication actions, such as making proposals, counterproposals, asking for clarification, asking for the preferences of another party, etc. These observable actions along with an understanding of what activity sequences are coherent constitute the protocol of negotiation. What particular linguistic expressions to use during each of the communication actions in negotiation has been an area of considerable research (e.g., Lambert and Carberry 1992; Lochbaum 1998), but it is outside of the scope of the current chapter. In this chapter, we focus on work in the mathematical sciences. In particular, we discuss the similarities and differences of work on negotiation models in economics and operations research vis a vis work in computer science. Additionally, we present future beneficial synergies between the two research communities so that more effective prescriptive models as well as ways to provide advice and decision support to decision-makers can be constructed. The rest of the chapter is organized as follows. Section “Formal Negotiation Research: Different Perspectives” introduces different perspectives of formal negotiation research, highlighting the strengths and weaknesses of different approaches. We then propose a framework for negotiation reasoning in section “A Framework for Negotiation Reasoning,” which consists of seven types of reasoning, namely, reasoning about negotiation procedure, reasoning about problem structure, reasoning about claiming/creating value, reasoning about persuasion, tactical reasoning, reasoning with limit information, and reasoning from machine-learning perspectives. Sections “Procedures for Multi-Issue Negotiation,” “Changing the Structure of the Negotiation Problem,” “Value Claiming and Value Creating,” “Persuasion for Conflict Resolution,” “Tactic Reasoning,” “Reasoning with Limit Information,” and “Reasoning from a Machine-Learning Perspective” elaborate these seven different levels of reasoning, not only providing both overviews of existing research, but also pointing out ways to making negotiation modeling and analysis closer to real life. Section “Conclusions” concludes this chapter by reviewing different issues of reasoning in negotiation, and proposing new directions of negotiation research.

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Formal Negotiation Research: Different Perspectives We have stated in the introduction that quantitative negotiation research can be divided into two sides: analytical and computational research. While the former group focuses on rigorous mathematical analysis, the latter seeks to create computationally tractable formal models, as well as, design and implementation of negotiation systems under various application scenarios. The connection between analytical and computational research is important: analytical models can provide valuable managerial insights and help choose a suitable bargaining protocol in the face of difficult tasks. Computational research is invaluable in (a) developing heuristic approximate solutions to analytical models of high computational complexity; (b) aiming to incorporate additional factors of realistic negotiations, such as argumentation, negotiation context, or culture; and (c) providing decision support systems and bargaining protocols in situations where analytical techniques cannot offer practical guidance. Both negotiation process and negotiation outcome must be addressed for realistic modeling. However, most of the existing research has focused on how to achieve outcomes with particular desirable properties, for example, Pareto optimality, or equilibrium behavior. Analytical negotiation research has focused on negotiation outcome rather than process due to the game-theoretical approaches they adopt: By assuming full rationality and various simplifying settings, bargaining game models can lead to highly stylized equilibrium analysis, which can be used to predict the outcome. Such approaches have been under increasing attack (e.g., Neelin et al. 1988; Ochs and Roth 1989; Sebenius 1992) for the rigidity and unrealistic assumptions of the game theoretic models. Even as early as the 1980s, there were spirited debates between game theorists (e.g., Harsanyi) and other scientists (e.g., Kadane, Larkey, Roth, and others) that adopted nonequilibrium game theory, bounded rationality, proclaimed the existence of subjective prior distributions on the behavior of other players, and urged the use of Bayesian decision-theoretic orientations (interested readers are referred to (Kadane and Larkey 1982a, b; Harsanyi 1982a, b; Kahan 1983; Roth and Schoumaker 1983; Rothkopf 1983; Shubik 1983). In contrast to research focusing on the generation of outcomes, other research has focused primarily on the negotiation process (e.g., Balakrishnan and Eliashberg 1995; Zeng and Sycara 1998; Bac 2001). The negotiation process refers to the events and interactions that occur between parties before the outcome and includes all verbal and nonverbal exchanges among parties, the enactment of bargaining strategies, and the external and situational events that influence the negotiation. Process analysis in bargaining has mainly focused on either the back-and-forth exchanges between the negotiators or on the broader phases of strategic activity over time. The most general categorization that comes from such analysis of negotiation outcomes and processes is the distinction between competitive and cooperative situations,1 which is also referred to as distributive vs. integrative or

1

The words cooperative and competitive here are not to be confused with the notions of cooperative and noncooperative game theory.

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hard vs. soft bargaining. In competitive negotiation, each party seeks to maximize his own gain or maximize the difference in gains between himself and the other parties. On the other hand, in cooperative negotiation, each party aims to increase joint gains (i.e., each party is both “self focused” and also “other focused”). Another view of distributive and integrative negotiations is that distributive negotiation can be regarded as a zero sum game where a fixed resource is simply divided, whereas in integrative negotiation, interests of both parties are satisfied although there may be concessions on both sides. Most recently, researchers (e.g., Weingart et al. 1993; Adair and Brett 2005) have postulated that negotiations and negotiators do not fit neatly into cooperative or utility maximizing types, but they are usually mixed-motive. In a mixedmotive interaction, parties use a mixture of competitive and cooperative strategies to pursue their interests which usually are competing and compatible at the same time. Additionally, it has been observed in the literature (e.g., Thompson 1996) that negotiating on a single issue typically leads to distributive negotiation, whereas in multi-issue negotiations, tradeoffs among the different issue values and the differential importance of issues to the parties enable integrative processes and outcomes. Negotiation with multiple issues is so complex that it defies rigorous modeling using noncooperative game theory. Therefore, a number of researchers (e.g., Luo et al. 2003) have studied multi-issue negotiations using issue by issue negotiation and analyze when this simplification is applicable. In cooperative game theory, Nash and others (Nash 1951, 1953; Luce and Raiffa 1989; Kalai and Smorodinsky 1975; Ponsati and Watson 1997) have focused on designing appropriate axioms that characterize the negotiation solution. Although game-theory has been the underlying fundamental theory behind many analytical models of negotiation, its explanatory and prescriptive merits have long been debated for the following reasons: First, standard assumptions in various game-theoretic models are incompatible with real-life situations. Among the restrictive reasons are (1) the rules of the games and beliefs of the players are “common knowledge,” (2) players have infinite reasoning and computational capacity to maximize their expected payoffs given their beliefs of others’ types, behaviors, and beliefs. Second, equilibrium analysis tends to focus on negotiation outcome, yet overlooks the negotiation process. Third, information disclosure mechanisms, i.e., who knows what under which conditions, which affect the negotiation process and outcomes in real-life situations, are difficult to model. Allowing partial information, instead of either complete information or no information, poses a daunting challenge for multiperiod game-theoretic analysis. This is still true even if agents have perfect reasoning powers. Fourth, most game-theoretic models assume that agents are fully rational, while in practice people are not, and they hence do not employ equilibrium strategies. Even if players are assumed to be perfectly rational, Alvin E. Roth and his colleagues (Roth and Malouf 1979; Roth et al. 1981; Roth and Keith Murnighan 1982) have shown in experiments with human subjects that subjective expectations of the players might influence the outcome, contrary to game theoretic assumptions.

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A Framework for Negotiation Reasoning In the following, we will concentrate on multi-issue negotiation since this is the most realistic and challenging. The elements of negotiations have been identified as negotiation parties, negotiation context, negotiation process, and negotiation outcomes (Agndal 2007). Such elements are viewed in a static way in most of the business negotiation research. We believe, however, the purpose of reasoning in negotiation is essentially managing such elements dynamically over time such that the negotiation process moves toward each party’s desired outcome. We proposed five types of reasoning based on the object being managed. The relationships between the different types of reasoning and negotiation elements are shown in Fig. 1. (a) Reasoning about negotiation procedures. While the negotiation procedures, i.e., what and how to negotiate, are usually given, it is sometimes determined by the negotiation parties either before or during the negotiation. This is especially true in the presence of multiple issues, incomplete information, and a changing environment. On the one hand, the negotiation procedures can be viewed as a strategic control variable from each negotiator’s point of view. On the other hand, each negotiator’s preference over different procedures indirectly conveys information about his social motives. (b) Reasoning about problem structure. The problem structure in a negotiation problem is defined as “negotiation goals and issues, relations and constraints among the variables and reservation prices that denote the minimum acceptable levels at which constraints can be satisfied” (Sycara 1991). To avoid deadlocks in a negotiation and make sure that agreements are reached, problem restructuring is an effective tool in managing the negotiation context as well as negotiating parties’ goals, beliefs, and relationships. In some sense, concession-

Fig. 1 A framework for reasoning in negotiation

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making during negotiation can be viewed as an embryonic form of problem restructuring. (c) Reasoning about claiming/creating value. While value creating is about how to make the pie bigger, value claiming is about how to get a larger proportion of the pie. How negotiators reason between claiming and creating value has much to do with their social motives, as well as the negotiation context, e.g., the deadline effect and the BATNA (Best alternative to a negotiated agreement). (d) Reasoning about persuasion. Negotiation is not just about proposal and counterproposal. In real-life negotiations, it is of crucial importance to be able to persuade others, i.e., to influence how other people reason about different alternatives. (e) Tactical reasoning about proposal/acceptance/counter-proposal/exit. Proposal, acceptance, counter-proposal, and exit constitute basic elements of the negotiation protocol. In addition to the above categories, drawn from the latest developments of AIpowered negotiation research, we will discuss in this chapter (f) reasoning with limit information, and (g) reasoning from a machine-learning perspective. It is worth pointing out that all of the above categories of reasoning stem from the negotiation parties’ internal variables, and they affect the negotiating parties as a consequence. Consider, for instance, that each party might have prior knowledge of its opponent’s belief structure, such understanding can be updated as the consequence of either his own learning through dealing with his opponent, or his opponent’s adopting of persuasion.

Procedures for Multi-issue Negotiation Faced with multiple issues, agents need to decide two concerns before the negotiation: one is the kind of negotiation procedure (agenda) they will take and the other is the type of agreement implementation. There usually exist three types of negotiation procedures: separate, simultaneous, and sequential (Inderst 2000; Gerding et al. 2000). Separate negotiation means agents negotiate each issue separately (independently and simultaneously as if there are no pairs of representatives for the two agents, and each pair independently negotiates one issue). Simultaneous negotiation means two agents negotiate a complete package on all issues simultaneously. Sequential negotiation is when two agents negotiate issue by issue sequentially, i.e., issue-by-issue negotiation. In issue-by-issue negotiation, agents also need to decide the order in which to negotiate each issue. There are two types of agreement implementations: sequential and simultaneous. Sequential implementation means the agreement on each issue is implemented once it is reached, while simultaneous implementation is that agreements are implemented together when all issues are settled.

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Research on issue-by-issue negotiation is mostly based on Rubinstein’s bargaining model (dividing a single pie) by introducing another issue (pie). The two issues may have different values and be differentially preferred by the agents. Besides, the two issues can either be simultaneously available or arrived at in a sequential order. Negotiating issues simultaneously is very challenging both for people and for automated models. The difficulties are due to bounded rationality: Simultaneously negotiating a complete package might be too complex for individual agents. However, this reason only provides an intuitive idea on issue-by-issue negotiation. More theoretical explanation or implication is needed. Next, we review theoretical work on why issue-by-issue negotiation may arise in two different contexts: incomplete information and complete information. Signaling is likely the first and only reason that researchers mention, why issueby-issue negotiation arises under incomplete information. Bac and Raff (1996) study a case with two simultaneous and identical pies where agents can either choose sequential negotiation with sequential implementation or simultaneous negotiation with simultaneous implementation. The authors show that in the context of complete information, agents will take simultaneous negotiation and reach an agreement without delay. But in the context of asymmetric information (assume two players A and B, A is informed, but B is uncertain of A’s time discount, which can take one of the values: δH with probability π and δL with 1 π), the authors argue that when B’s time discount is in some interval (not so strong and also not so weak), the “strong” type of the informed agent (A with δH) may make a single offer on one pie and leave it to the opponent (B) to make an offer on the second pie, while a “weak” type of informed player (A with δL) only makes a combined offer. So if issue-by-issue negotiation arises, it is because the “strong” and informed agent, by a single (signaling) offer, wants to let her opponent know she is strong and make the opponent concede. Busch and Horstmann (1999), similarly but more strictly, study the signaling factor with an incomplete information model that allows for different sized pies and each kind of agreement implementation. By setting some parameter configurations, they show that issue-by-issue negotiation may arise with signaling, and they prove under such configurations signaling does not arise if agents can only bargain a complete package. So the authors argue issue by issue negotiation arises purely because some favorable endogenous agenda for issue-by-issue bargaining is available. Besides, they also show that if issue-by-issue bargaining arises, agents will negotiate the “large” pie first. As mentioned above, under complete information, agents will negotiate a complete package if it is with simultaneous and identical pies. But when assumptions are changed, issue-by-issue negotiation could possibly arise under complete information. Busch and Horstmann (1999) study the difference between incomplete contract (issue-by-issue) and complete contract (simultaneous) negotiation with sequential pies on which agents have different preferences. From the equilibrium outcomes of the two procedures, it is shown that if agents are heterogeneous, they might have conflicting preferences on the two procedures, which means one prefers incomplete contract procedure but the other may prefer complete contract procedure. Further, Busch and Horstmann also show that when time is costless, agents will agree to negotiate a complete contract, while if time is very valuable, agents will negotiate an

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incomplete contract. From a different perspective, Lang and Rosenthal (2001) argue that joint concavity of two agents’ payoffs can eliminate the possibility of nonfullybundled (issue-by-issue) equilibrium offers, but in realistic settings, the property of joint concavity usually is not true so that a partial bundled offer on a subset of unsettled issues may be superior over a fully bundled offer. Additionally, the occurrence of breakdown can impact a multiattribute negotiation. Sometimes agents insisting on some issue may lead the whole negotiation to breakdown. Chen (2006) studied issue-by-issue negotiation taking into consideration the probability of breakdown. Chen applies a probability setting that a negotiation breaks down if a proposal on some issue is rejected. He assumes that agents’ utility functions are linear additive so that breakdown on one issue does not affect others. By comparing the equilibrium outcomes between issue-by-issue negotiation and simultaneous negotiation, Chen argues that when the probability of breakdown is low, agents prefer to negotiate a complete package because intuitively they know that the bargaining can last long enough so that agents can get to a “Win-Win” solution with inter-issue tradeoffs. However, when the breakdown probability is high, agents weakly prefer issue-by-issue negotiation. Chen also shows that if agents are sufficiently heterogeneous, issue-by-issue negotiation may also be superior over simultaneous negotiation. In and Serrano (2004) assume that the negotiation breakdown of one issue can make the whole negotiation fail, and agents are restricted to making an offer on only one of the remaining issues each round. They show that when the probability of breakdown goes to zero, there is a large multiplicity of equilibrium agreements and therefore inefficiency arises. But it does not happen for simultaneous negotiation. However, if agents are not restricted to making offers on only one issue at each round (i.e., agents can make partially or fully bundled offers), the outcome turns out to be Pareto-efficient (In and Serrano 2003). Thus, In and Serrano’s work indicates strict issue-by-issue negotiation may increase inefficiency. Inderst (2000) might be the only work that compares those three different negotiation procedures in one paper. On a set of unrelated issues, Inderst argues that if the issues are mutually beneficial, agents will prefer to bargain simultaneously over all issues. Besides the work above, Weingart, Bennett, and Brett (1993) study the multiattribute negotiation problem within a specific context allowing “Selective Acceptance.” In such a context, the offer initially needs to be a complete package including all issues, but agents can accept or reject the whole package as well as selectively accept part of the package on some issues. But, if agents accept a part on some issues, these issues cannot be reopened again. The author indicates that in some situations, this leads to good solutions. Weinberger shows “Selective Acceptance” can lead to inefficient equilibrium outcomes if some issues are indivisible or agents have opposing valuations on issues. For comparison, Weinberger shows that inefficient outcomes do not arise under the rule only to accept or reject the whole package. However, the equilibrium outcomes with “Selective Acceptance” are not dominated by the efficient outcome. It means there must be some agent who is better off by the rule of “Selective Acceptance” and will not agree on the efficient outcome. In the computational literature, Fatima et al. (2004a, b) propose an agendabased framework for multiattribute negotiation. In their framework, the agents can

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propose either a combined offer on multiple issues or a single offer on one issue. Different from the game theoretic models, their work focuses on computational tractability. They assume that the agents adopt a time-dependent strategy and the agents may make decisions on the issues independently faced with a combined offer. For example, if there are two issues in a combined offer, say x1 and x2, an agent may have two independent strategies S1 and S2 which are used to decide whether to accept x1 and x2. They make the assumption that the agents’ utility functions are given before the negotiation and they are linear additive. Pareto-optimality is not addressed.

Changing the Structure of the Negotiation Problem Problem structure refers to “characteristics of their feasible settlement spaces and efficient frontiers” (Mumpower 1991). As pointed out in Mumpower (1991), while some problem structures lead to agreements with efficient outcomes, others lead to inefficient outcomes, or deadlocks. Negotiation restructuring, therefore, seeks to understand the situation and perception of the negotiators and finds favorable directions to change the agents’ perceptions of the interaction, and hence the decisive factors of the negotiation. Negotiation restructuring is an effective tool for all sides in a negotiation so as to achieve joint gains by enlarging the pie. Very often, a third party mediator may be engaged to facilitate the negotiation and break deadlocks. A mediator can manage the negotiation environment so as to break or avoid deadlocks. Sycara (1991) proposed the concept of “problem restructuring,” i.e., to dynamically change the structure of the negotiation problem to achieve movement toward agreement. Under the context of her “PERSUADER” automated negotiation system, Sycara put forward four types of problem structuring: (Adair and Brett 2005) introduction of new goals, (Agndal 2007) goal substitution, (Amgoud et al. 2007) goal abandonment, and (Anderson and Shirako 2008) changing the reservation prices of the negotiating parties. Sycara also provides four methods to achieving the directions of problem restructuring, namely, (1) case-based reasoning (utilizing previous cases and experiences of dispute resolution), (2) situation assessment (representing and recognizing negotiation problems in terms of their abstract causal structure), (3) graphic search and control (Search for correlations among an agent’s goals in agents’ goal graphs), and (4) persuasive argumentation (generating various arguments, e.g., threats and promises). Shakun (1991) developed another framework of negotiation problem restructuring, namely, ESD (evolutionary systems design), which involves “evolution of the problem representation to an evolved structure that is not equivalent to the original one.” The authors implemented the ideas in various scenarios including labor relations and buyout in the airline industry. Kersten et al. (1991) introduced a rule-based restructurable negotiation model characterizing the hierarchy of each negotiating agent’s goals and proposed ways to restructuring the negotiation problem.

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Value Claiming and Value Creating Agents negotiate with certain motivations in mind. Many social science papers have adopted the somewhat rough distinction between selfish and prosocial motivation (see Weingart et al. 1993). Selfish motivation is characterized by competitive and individualistic goals, while prosocial motivation is characterized by cooperative and altruistic goals. Admittedly, in a realistic setting, a negotiator has mixed motives rather than behaves purely selfishly or purely prosocially. This framework, however crude it may be, has been well accepted in the social sciences community. The agents’ social motives give rise to different behaviors during negotiation. Referred to as “win-win,” “variable sum,” or “integrative” in various works, valuecreating is the process wherein the negotiating parties work together to resolve conflicts and achieve maximum joint benefits. By contrast, value-claiming behavior is often referred to as “win-lose,” “fixed sum,” or “distributive.” A value-claiming negotiating agent targets individual utility maximization without joint-gains improvement. In a typical model, an agent seeks to maximize its own utility. The utility function or preferences structure of negotiating parties for different interests and issues, i.e., how they trade-off or prioritize different issues, provides the ultimate driving force for the decision-making in a negotiation process. Given a set of issues, interests, and positions, a utility function or preference relation specifies how agents evaluate different alternatives. Most of the literature about negotiation provides a static and crisp definition of the utility function. In contrast, Fogelman-Soulie et al. (1983) develop an MDP model for the problem of bilateral two-issue negotiation. Instead of assuming bivariate utilities, the one-stage payoff is expressed as a payoff probability distribution representing the probability that a player obtains various amounts of each of the two variables. Kraus et al. (1995) discuss different forms of continuous utility functions over all possible outcomes, e.g., time-constant discount rates and constant cost of delay. Zlotkin and Rosenschein (1996) present an approach to the negotiation problem in noncooperative domains wherein agents’ preferences over different intermediate states are captured by “worth functions” by considering the probabilistic distance between intermediate states and final states. Rangaswamy and Richard Shell (1997) design a computer-aided negotiation support system, one part of which is to help negotiating parties disaggregate their own preferences and priorities in order to understand them better, utilizing several utility assessment techniques. Faratin et al. (2002) use a given linearly additive multiattribute utility function to represent agent preferences. Each agent is assumed to have a scoring function that gives the score it assigns to a value of each decision variable in the range of its acceptable values. Then the agent assigns a weight to each decision variable to represent its relative importance. A number of papers represent the trade-off between multiple issues using constraints instead of utility functions. As a representative example, Balakrishnan and Eliashberg (1995) propose a single-issue negotiation process model where the utilities are simply the negotiation outcome, and agents’ dynamic preferences are represented using a constraint with the left-hand side denoting agents’ “resistance forces,” and right-hand side “concession forces.”

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We identify, in general, three inherent driving forces behind negotiators’ tradingoff decisions between value-claiming and value-creation. First, different negotiators have different social motives. While some agents are selfish, others are prosocial. The inherent agent characteristics largely determine the nature of the negotiation. Second, there exists a so-called “deadline effect,” i.e., as the deadline of the negotiation approaches, agents make more efforts to create higher incremental value. This could be explained by the fact that agents could create more value at later negotiation rounds based on what has been achieved in the previous rounds (Zartman and Berman 1983). Bac (2001) builds a different analytical model and argues that deadline effect happens because the costs and benefits of negotiation efforts are not synchronized: While efforts are incurred in the negotiation rounds, the benefits are only realized after the final round. Third, the evolving BATNA (best alternative to negotiation agreement) is also behind agents’ trading-off behaviors. This is especially relevant in the presence of dynamic uncertain availability and quality of outside options. Li et al. (2006) build a bilateral negotiation model with the stochastic, dynamic outside options. The negotiation strategies are affected by outcome through their impact on the reservation price. Three modules with increased complexity, namely, single-threaded negotiations, synchronized multithreaded negotiations, and dynamic multithreaded negotiations, are studied. In the single-threaded negotiation model, optimal negotiation strategies are determined without specifically considering outside options. Then the synchronized multithreaded negotiation model addresses concurrently existing outside options. The dynamic multithreaded negotiation model further extends the synchronized multithreaded model by considering dynamic arrivirals of future outside options. Experimental studies show that the agent can achieve significant utility increase if she takes outside options into consideration, and the average utility is higher when her negotiation decisionmaking addresses not just the concurrent outside options, but foresees future options.

Fair Division2 The literature on multiattribute negotiations has examined the concept of “fairdivision” and developed division procedure using cooperative game theory. Usually, the goal of the procedure is to fairly divide a set of items between two agents, and it can consist of two steps: the first step ensures an efficient outcome and the second step establishes “fairness” through a redistribution of gains. This approach was first developed by Knaster and Steinhaus based on the idea of auctions (Raith 2000). The Knaster procedure is quite simple. In the first step, all items are assigned to the “winner” who totally values the items most, and then “fairness” is established through monetary transfers. The idea is two agents fairly share the excess. Knaster’s procedure focuses on fairly sharing of the excess between

Interested readers are referred to Klamler, ▶ “The Notion of Fair Division in Negotiations” in this volume for a comprehensive survey of various approaches to fair division.

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agents, but the “percent of estate” of the two agents is not “fair.” With such a consideration, Brams and Taylor (1996) introduced another fair-division procedure named “Adjusted Winner,” which implements an equitable outcome. In this procedure, each item (not all items as in Knaster’s procedure) is assigned to the agent who values it most in the first step, and then some money is transferred from the temporary winner to the temporary loser in the second step such that the “percent of estate” between agents is the same. Raith (2000) points out the outcome of “Adjusted Winner” might not be efficient. Thus, Raith designs another approach named “Adjusted Knaster” based on both of them, which marries Knaster’s efficient adjustment with the equitability condition of “Adjusted Winner.” Raith also compares the outcomes of “issue-by-issue” negotiation and “package deals” and indicates the former might not be efficient.

Persuasion for Conflict Resolution In a broad sense, negotiation can be viewed as “planning other agents’ plans” (Sycara 1989), i.e., to use persuasive argumentation to influence the other side’s belief structure. The purpose of using such argumentation is to influence the other party’s utility function, which derives from his belief structure, including goals, importance attached to different goals, and relations between goals. The associated reasoning involves not only the priorities of different issues and interests, but also the graphic structure, i.e., how one goal affects another. To put it simply, we can either change the opponent’s utility value of one objective, or change the relative importance he assigns to that objective. In a seminal work, Sycara (1990b) incorporates argumentation into negotiation and to illustrate the merit of argumentation-based reasoning in negotiation dialogues. Sycara also proposes a concrete framework in the light of a negotiation support system. Kraus et al. (1998) formalize the above argumentation tools and protocols in a set of logic models. They present a mental model representing agents’ beliefs, desires, intentions, and goals. Argumentation is modeled as an iterative process in the sense that it is initiated from agent exchanges and then changes the negotiation process, hopefully toward cooperation and agreements. Their logic models help specify argument formulation and evaluation. Other argumentation-based negotiation frameworks include Parsons and Jennings (1996) and Tohm (2002). Amgoud et al. (2007) point out that the inherent weakness of the above-mentioned frameworks lies in that they cannot explain when argumentations can be used in negotiation, and how they are dealt with by the agents who receive them. They establish a unified framework which formally analyzes the role of argumentation, and especially addresses how agents respond to arguments. Argumentation can also be combined with additional factors relevant to the negotiation process. Karunatillake et al. (2009) present a framework allowing agents to argue, negotiate, and resolve conflicts relating to their social influences within a multiagent society. Their framework can be used to devise a series of concrete algorithms that give agents a set of argumentation-generation strategies to argue

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and resolve conflicts in a multiagent task allocation scenario, especially when the social structure is complicated to analyze in other ways. They show that allowing agents to negotiate their social influences presents an effective and efficient method that enhances their performance within a society.

Tactic Reasoning In this section, we provide an overview of modeling efforts in externally observable behavior and characteristics such as strategies, tactics, and outcomes of negotiation. In the computational field, the existing work mainly focuses on automated negotiation frameworks and tractable heuristics. Sycara (1990a, b, 1991) uses a case-based reasoning approach for multiattribute negotiations where the agents make offers based on similarity of the negotiation context (including issues, opponents, and environment) to previous negotiations. Sycara also uses automatically generated persuasive argumentation as a mechanism for altering the utilities of agents, thus making them more prone to accept a proposal that otherwise they might reject. Most of the existing research focuses on agents’ optimal actions based on their reasoning strategies, and the efficiency compared to Pareto optimal solutions or human negotiation outcomes. Faratin et al. (2002) provide conditions for the convergence of optimal strategies, and negotiation outcomes for different scenarios with linear utility functions. Lai et al. (2008) propose a protocol where agents negotiate in a totally decentralized manner and have general nonlinear utility functions in multiissue negotiation aiming at reaching Pareto optimal outcomes. The agents have nonlinear and interdependent preferences and have no information about the opponent’s preference or strategy. The authors show that their model is computationally tractable and the outcomes are very close to Pareto equilibrium results. An important issue in multiattribute negotiation is the trade-off process between self-interested agents on different issues. Faratin et al. (2002) propose a novel idea to make the agents trade off on multiple issues. They suggest that the agents should apply similarity criteria to trade off the issues, i.e., make an offer on their indifference curve which is most similar to the offer made by the opponent in the last period. However, in this approach, to define and apply the similarity criteria, it is essential that the agents have some knowledge about the weights the opponent puts on the issues in the negotiation. A subsequent work (Coehoorn and Jennings 2004) proposes a method based on kernel density estimation to learn the weights. But, the performance still might be compromised if the agents have no or very little prior information about the real weights the opponent assigns on the issues. Moreover, it will be difficult to define and apply the similarity criteria if the agents’ utility functions are nonlinear and the issues are interdependent. Luo et al. (2003) develop a fuzzy constraint based framework for multiattribute negotiations. In this framework, an agent, say the buyer, first defines a set of fuzzy constraints and submits one of them by priority from the highest to lowest to the opponent, say a seller, during each round. The seller either makes an offer based on

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the constraints or lets the buyer relax the constraints if a satisfactory offer is not available. The buyer then makes the decision to accept or reject an offer, or to relax some constraints by priority from the lowest to highest, or to declare the failure of the negotiation. Li and Tesauro (2003) introduce a searching method based on Bayesian rules. It is assumed that the agents have some prior knowledge about the opponent’s utility function. When they concede, the agents apply depth-limited combinatorial searching based on their knowledge to find a most favorable offer. If the proposal is rejected, the agents update their knowledge by Bayesian rules. Their work assumes that the agents know partially about the opponent’s utility function and the work does not address Pareto-optimality. There also exists some research that addresses multiattribute negotiations on binary issues. For instance, Robu et al. (2005) propose an approach based on graph theory and probabilistic influence networks for the negotiations with multiple binary issues; Chevaleyre et al. (2005) address a categorization problem of the agents’ utility functions under which the social optimal allocation of a set of indivisible resources (binary issues) is achievable. Zeng and Sycara (1998) develop an automated negotiation model wherein agents are capable of reasoning based on experience and improve their negotiation strategies incrementally. They utilize the Bayesian framework to update an agent’s belief about its opponents. Lin et al. (2008) model an agent’s internal reasoning in terms of generating and accepting offers. When generating offers, an agent selects the best offer among the offers that the agent believes might be accepted. To be more specific, the agent selects the minimum value of (1) the agent’s own estimation of the offer, and (2) the agent’s estimation of its opponents’ acceptable offer, under the pessimistic assumption that the probability that an offer is accepted is based on the agent that favors the offer the least. In discussing the agent’s reasoning about accepting offers, they make the assumption that each offer is evaluated based on their relative values compared to the reservation price. We summarize the existing research as follows. First, almost all the models in the existing research are based on the assumption that the agents in a negotiation have explicit utility functions. Some also assume that the agents completely or partially know their opponent’s utility function. Second, the existing models either assume a simple utility function (two issues with linear additive utility functions) or focus on binary issue or cooperative negotiations. Finally, Pareto-optimality and tractability have not been considered simultaneously in most of the models.

Third-Party Mediation There are some papers that adopt a nonbiased mediator in the negotiation. Ehtamo et al. (1999) present a constraint proposal method to generate Pareto-frontier of a multiattribute negotiation. The mediator generates a constraint in each step and asks the agents to find their optimal solution under this constraint. If the feedback from the agents coincide, a Pareto-optimal solution of the negotiation is found; otherwise, the mediator updates the constraint based on the feedback, and the

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procedure continues. They show that their approach can generate the whole Paretofrontier efficiently. In their work, the negotiation agents do not have the ability to make self-interested decisions or have autonomous strategies, which limits its application in the negotiations with self-interested agents. Moreover, the approach relies on the assumption that the agents can solve multicriteria-decision-making (MCDM) problems efficiently, which is not always the case in practice. Klein et al. (2003) propose a mediating approach for negotiating complex contracts with more decision flexibility for the agents. Their approach focuses on the negotiations with binary valued issues (0 or 1). The nonbiased mediator generates an offer in each period and proposes to both agents. Then the agents vote whether to accept the offer based on their own strategies. If both agents vote to accept, the mediator mutates the offer (to change the values of some issues in the offer from 0 to 1, or reverse) and repeats the procedure. If at least one agent votes to reject the offer, the mediator mutates the last mutually acceptable offer and repeats the procedure. This approach is difficult to be applied to problems with continuously valued issues. Besides, a key assumption they make is that the mediator always can change the contract even if both agents have already voted to accept it, which might not be tractable in practice. Lai et al. (2006) present a model with incomplete information, decentralized selfinterested agents that are Pareto-optimal. Each agent not only does not know the utility function of the opponent but also does not know her own. The authors assume that given a limited number of offers, an agent, though not having an explicit model of her preference, can compare them, and she can decide whether an offer is acceptable or not. A nonbiased mediator is adopted in the model to help the players achieve Pareto-optimality and overcome the difficulty of absence of information about the preferences of the agents. The approach reduces the negotiation complexity by decomposing the original n-dimensional negotiation space into a sequence of negotiation base lines. Agents can negotiate upon a base line with simple strategies. The approach is shown to reach Pareto-optimal solutions asymptotically within logarithmically bounded computational time.

Agents for Decision Support Braun et al. (2006) summarize modeling approaches in decision-support negotiation literature, including (1) probabilistic decision theory, (2) probabilistic decision theory, (3) constraint-based reasoning, (4) heuristic search, (5) Bayesian learning, (6) probabilistic case-based reasoning, (7) Q-learning, and (8) evolutionary computing. This classification is based on specific computational methods used in computerized system design and can serve those readers who are interested in a complete review of operational analysis techniques in computational literature. There has been consistent evidence that using an intelligent agent to negotiate with a human counterpart achieves better outcomes than negotiation between two human beings (see Lin et al. (2008) and Kraus et al. (2008)). While the results are encouraging, several complexities restrict their significance: (1) Implementation of the computational model remains challenging to elicit human preferences on

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multiple issues. (2) Information exchange mechanism used by computational negotiation agents might not be able to exchange information as efficiently as human beings in situations where accurate representations are hard to achieve. (3) How “efficient” the negotiation outcome is ultimately depends on human affect and cultural factors, which have not been taken into account in the existing computational literature.

Reasoning with Limit Information Multiattribute negotiation often happens when two or more parties (or agents) with limited common knowledge about each others’ preferences try to arrive at an agreement on a set of issues over which they have possible conflicting preferences. Due to the potential conflicts of interests, agents can be reluctant to share information about their own preferences with each other. The presence of limited information makes it challenging to reach an agreement even when the zone of agreements is not empty. When the utility function is assumed to be linear and the information about the opponent’s utility function is known, a monotonic concession strategy and a Zeuthen strategy (Endriss 2006) have been proposed for negotiation. In the presence of incomplete information, Bayesian learning has been proposed in agents’ negotiation strategy (Li and Tesauro 2003; Buffett and Spencer 2005; Hindriks and Tykhonov 2008). Rational strategies that correspond to sequential equilibrium of a game have been proposed when each agent has probabilistic knowledge about its opponent (e.g., Fatima et al. 2004a). However, these strategies cannot be used if knowledge about opponents’ utility functions is absent and when the utility functions are nonlinear. Preference elicitation – before or through negotiation – has been studied where agents have no knowledge about opponents’ utilities (e.g., Chari and Agrawal 2007). However, preference elicitation is known to be a difficult and time-consuming procedure (Chen and Pu 2004), especially when the agents’ preferences are complex. Most crucially, preference elicitation does not guarantee that an agreement will be reached even when the zone of agreement is nonempty. Zheng et al. (2013, 2016) propose and analyze a distributed negotiation strategy for a multiagent, multiattribute negotiation in which the agents have no information about the utility functions of other agents. They analytically prove that, if the zone of agreement is nonempty and the agents concede up to their reservation utilities, agents generating offers using our offer-generation strategy, namely the sequential projection strategy, will converge to an agreement acceptable to all the agents; the convergence property does not depend on the specific concession strategy. In considering agents’ incentive to concede during the negotiation, they propose and analyze a reactive concession strategy. Through computational experiments, they demonstrate that the distributed negotiation strategy yields performance sufficiently close to the Nash bargaining solution and that our algorithms are robust to potential deviation strategies. Their result introduces a new analytical foundation for a broad class of computational group decision and negotiation problems.

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Sanchez-Anguix et al. (2019) adopt bottom-up approaches to achieve Paretooptimal agreements in group-negotiation process. The bottom-up approaches are necessary because information sharing only occurs within subgroups, whose members are more aligned and thus trust each other, but does not occur across subgroups. They first theoretically prove that an outcome that is Pareto-optimal for subgroups is also Pareto-optimal for the group as a whole. Then, they use real-life datasets to empirically analyze the appropriate conditions under which applying bottom-up approaches achieves Pareto-optimality under a wide variety of scenarios. The empirical results suggest the bottom-up approaches serve as a viable mechanism to achieve Pareto-optimality.

Reasoning from a Machine-Learning Perspective In the presence of incomplete information, while preference elicitation is known to be a difficult and time-consuming procedure (Chen and Pu 2004), recent development in machine-learning approaches continues to advance this stream of literature. Beam and Segev (1997) are among the first to introduce machine-learning methods applied by intelligent agents in negotiation, where they mainly discuss using genetic algorithms to learn an effective negotiation strategy. Li and Tesauro (2003), Buffett and Spencer (2005), and Hindriks and Tykhonov (2008) further propose Bayesian learning in agents’ negotiation strategy. More recently, Papaioannou et al. (2009) surveyed learning techniques based on neural networks to model the opponent’s behavior in both bilateral and multilateral negotiations. Chen and Pu (2004) survey preference elicitation methods for user modeling in decision-support systems, where the goal is to capture the user’s preferences. Similar to opponent modeling in automated negotiation, user modeling often uses some learning techniques such as pattern matching to estimate the user’s or opponent’s preferences. Recent studies have introduced more machine-learning techniques that improve preference elicitation methods for user or opponent modeling. Schatzmann et al. (2006) survey machine learning of dialogue-management strategies, which can be relevant for argumentation-based negotiation systems. Braziunas and Boutilier (2008) review direct preference elicitation methods, i.e., asking users to answer queries regarding their preferences and using this information to recommend a feasible and approximately optimal decision. Perrault and Boutilier (2019) develop and study a formal model of experiential elicitation (EE) that can be applied in household heating/cooling management. They propose the use of relative value queries and develop a Gaussian process-based approach for modeling user preferences in dynamic EE domains. Their empirical results suggest that their method accrues higher reward than several natural baselines. Another related area is the topic of machine-learning techniques in human-robot interaction and game playing. Rubin and Watson (2011) present a review of machine-learning algorithms and approaches in the area of computer poker. They argue, as in negotiation, opponent modeling can be essential for computer poker because maximizing the reward against an effectively exploitable opponent is

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potentially more beneficial than exhibiting optimal play. Doshi-Velez et al. (2012) use policy queries for active learning in partially observable Markov decision processes (POMDP) for human–robot interaction settings. They first propose an approximation method which is based on minimizing the immediate Bayes risk because the Bayes-risk criterion avoids the computational intractability of solving a POMDP with a multidimensional continuous state space. They then use policy queries – in which they ask an expert for the correct action – to infer the consequences of a potential pitfall without experiencing its effects. They show their method performs well in a variety of problems and settings.

Conclusions In this chapter, we presented a selective review of the analytical and computational research, organized as various modes of reasoning as they relate to AI-powered negotiation. We compared and contrasted the achievements of both of these strands of research. The analytical research in general creates elegant and simplified models that provide insights and often formal guarantees about optimality or model behavior. The computation research focuses on how to make analytical models computationally tractable, increase their flexibility, and make the algorithms decentralized. In addition, the computational literature aims to incorporate additional factors in the analytical models thus making them more realistic. A parallel and very important aim of the computational negotiation research is to incorporate negotiation models into decision support systems or into systems that negotiate with humans. The aims of the two literatures are synergistic, espousing the long-term goal of achieving analytical models with computational guarantees that incorporate elements of realistic negotiations. The economic models of bargaining that dominated the field in its nascent stages posit that the ultimate aim in negotiation is maximizing one’s own gain and the easiest and most efficient way to realize this aim is through integrative potential (Nash 1953). However, it is now well-documented that pure economic outcomes are poor indicators of not only what people value in negotiation but also of their behavioral manifestations. Research has shown that perceptions of self, relationship with the other party, or the desire to maintain a positive image may be as influential as, if not more than, economic gains. Issues such as self-efficacy, self-esteem, maintaining face, or maintaining social relationships with the other party may be of critical concern to the negotiators and subsequently influence processes and outcomes (Bandura 1977; Snyder and Higgins 1988; Anderson and Shirako 2008; McGinn and Keros 2002). A fertile area of bargaining research lies in understanding what negotiators value and how it influences their perceptions of the outcome. For example, Curhan et al. (2005) developed and validated a subjective value inventory (SVI) framework. The authors also find that the SVI is a more accurate predictor of future negotiation decisions than economic outcomes, which demonstrates again that what people value in negotiation cannot be fully or accurately predicted by profit-maximization models. Therefore a fertile area for future research would be to incorporate these subjective values into formal models. This will allow

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increased understanding, for example, of the conditions under which different subjective factors influence negotiations the most, different nonlinearities or tradeoffs among these subjective factors, etc. Another related issue is validation of analytical and computational models. If the formal models were able to incorporate representations and reasoning schemes of cognitive factors, then human experimental data could be used to validate the models. Another important future research direction is to study repeated interactions. Almost all of current research considers negotiation as a one-time event. However, in real life, negotiations are a repeated phenomenon, and very often they occur with the same individuals (e.g., in business negotiations). Currently, there is very limited research in repeated games and experience-based negotiation. We believe that analytical and computational models that incorporate repeated interactions and utilize machine learning techniques would be an important step in making negotiation less art and more science.

Cross-References ▶ Advances in Defining a Right Problem in Group Decision and Negotiation ▶ Collaboration Engineering for Group Decision and Negotiation ▶ Electronic Negotiation and Behavioral Elements ▶ The Notion of Fair Division in Negotiations Acknowledgments This chapter is an updated version of “Agent Reasoning in Negotiation,” a chapter of the first edition of the same handbook. The earlier version was made possible by the generous support from the ARO Multi University Research Initiative (Grant No.: W911-NF0810301).

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Turan N, Dai T, Sycara K, Weingart L (2013) Toward a unified negotiation framework: leveraging strengths in behavioral and computational communities. In: Models for intercultural collaboration and negotiation. Springer, Dordrecht, pp 53–65 Weingart LR, Bennett RJ, Brett JM (1993) The impact of consideration of issues and motivational orientation on group negotiation process and outcome. J Appl Psychol 78:504–517 Zartman IW, Berman MR (1983) The practical negotiator. Yale University Press, New Haven, CT Zeng D, Sycara K (1998) Bayesian learning in negotiation. Int J Hum-Comput Stud 48(1):125–141 Zheng R, Chakraborty N, Dai T, Sycara K, Lewis M (2013) Automated bilateral multi-issue negotiation with no information about opponent. In: Proceeding of the Hawaii international conference on systems science, Wailea, pp 520–527 Zheng R, Dai T, Sycara K, Chakraborty N (2016) Automated multilateral negotiation on multiple issues with private information. INFORMS J Comput 28(4):612–628 Zlotkin G, Rosenschein JS (1996) Mechanism design for automated negotiation, and its application to task oriented domains. Artif Intell 86(2):195–244

Further Reading Lai G, Sycara K (2009) A generic framework for automated multi-attribute negotiation. Group Decis Negot 18(2):169–187 Thompson LL (1991) Information exchange in negotiation. J Exp Soc Psychol 27(2):161–179

Index

A Actor network theory (ANT), 694 Actor-partner interdependence model (APIM), 44, 66 Adjusted winner (AW) procedure, 91–92, 1139 Agent, 139, 141, 363, 490, 1054, 1105, 1189 Aggregation of individual judgements, 952, 954 Aggregation of individual preference structures, 949, 955, 962–966 Aggregation of individual priorities (AIP), 952, 954 Aggregation operators, 1036, 1040 Aggression, 181–182 AHP, see Analytic hierarchy process Aichi design league, 382 AI-powered negotiation, 1054, 1188 AL procedure, 95–96 Alternating offers game, 562 Alternative dispute resolution (ADR), 1172, 1178 electronic settlements, 1180 multiple-phase approach, 1180 online mediation and arbitration services, 1179–1180 Amazon web services, 390 Amendment agenda, 424 American Arbitration Association, 1181 Analytic hierarchy process (AHP), 14, 257, 871–872, 948, 1012 group decision support with, 956–970 Analytic network process (ANP), 949, 950, 1013 Anonymous, 199, 457, 554, 560, 643, 687, 709, 796, 821, 1038, 1083 Anonymity, 554, 632, 643, 644 Anthropological constructivists theory of emotion, 164 Appraisal theory, 161, 169

Archiving systems, 1154 Argument, 13, 69, 142, 154, 159, 218, 234, 344, 358, 380, 487, 639, 693, 712, 839, 949, 971, 972, 1060, 1134, 1151, 1164, 1190 Argumentation, 13, 163–164 Arrow’s impossibility theorem, 431 Artificial intelligence (AI), 13, 15, 16, 39, 237, 840, 855–857, 1054, 1107, 1131, 1180 Aspiration point, 556 Aspire system, 1089 Assessment of the opponent, 221 Asymmetry , 25, 113, 129–132, 262, 279, 327, 550, 602, 1195 Asynchronous text-based electronic negotiation, 220 Attention restoration theory, 297 Attitude, 147, 161, 196, 223, 329, 408, 602, 784, 849, 952, 970 Author-based approaches, 362 Automated facilitation agent, 388 Autonomous negotiating agents, 16, 1195 Axiomatic approach, 236 Axioms, 84, 113, 236, 432, 532, 546, 865, 929, 950, 1101, 1192

B Ballots, 445–446 Bargaining problem, 547 Bargaining rules, 552 dictatorial rule, 560 Egalitarian rule, 557, 559 equal area rule, 561 Kalai-Smorodinsky rule, 555, 557 Nash rule, 553, 555 Perles-Maschler rule, 561 utilitarian rule, 560 Yu rule, 560, 561 Bargaining steps, 46

© Springer Nature Switzerland AG 2021 D. M. Kilgour, C. Eden (eds.), Handbook of Group Decision and Negotiation, https://doi.org/10.1007/978-3-030-49629-6

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1214 Barrier effect, 219 Bayesian AHP (B-AHP), 966–970 Bayesian prioritization procedure, 955 Behavioral mechanism, 240 Behavioral neuroscience, 319–320 Behavioral operational research (BOR), 882 Benevolence, 225 Best alternative to negotiated agreement (BATNA), 260, 1064, 1128, 1199 Better business bureau (BBB), 1172, 1181 Biases and beliefs, 403 Big data, 840, 855–857, 882, 948 Binary, 62, 139, 261, 419, 422, 425, 430, 574, 902, 1210 Bi-reference procedure, 245 Borda-efficiency, 87 Borda envy-freeness, 87 Borda maximinality, 87 Borda procedure, 448 Borda’s paradox, 417, 418 Boundary objects, 12, 13, 682, 710–711, 738, 783, 795, 838, 852 in group model building, 738 Brainstorming, 631, 634, 640, 762, 803, 821, 855, 1026, 1032 British Columbia Civil Resolution Tribunal, 1142–1143 BT procedure, 94–95 Bullet vote, 450 Business-to-business (B2B), 1174

C Causal mapping, 12, 683, 716, 718, 721–724, 794, 816 Central Bank policy, 242 Choquet integral methods, 1039 Classical document management systems, 1154 Client group, 736–738, 740 Climate change, 372, 404, 474, 884 Cloud based GSS, 12 Clustering tools, 1032 Coalition, 11, 588–589, 602, 784, 911, 1062 Coalition formation, 538 Cognition , 158, 195, 500, 711, 970 Cognitive diversity, 194, 198–199 Cognitive mapping, 8, 195, 203, 712 Cognitive multi-actor decision making, 970–972 Cognitive reasoning, 140 Cognitive revolution, 160 Cognitive semiotics, 142

Index Cognitive style, 7, 8, 195, 257 Cognitive Style Index, 196 Cold cognition, 853 Collaboration, 224, 522, 524, 708, 753, 865, 1025, 1027 Collaboration Engineering (CE), 13, 752, 755, 756 Collaboration process, 766 Collaboration support, 753 Collaborative tools, 1032, 1034, 1036–1041 Collagree Aichi Design League 2016, 384–386 discussion graphs, 378–381 facilitator support functions, 375 incentive mechanisms, 376–377 intelligent automated facilitators, 381 Nagoya City Planning, 382 Collective action, 12 crowdfunding and digital activism, 662 digitally enabled, 671–677 genres of, 677 from small group behavior to, 657–660 Common ground, 5, 138, 183, 215 Common reference frame (CRF), 508 Communicated affect, 221 Communication, 39, 61, 137, 157, 211, 291, 315, 505, 627, 1107, 1157 Communication theories media richness theory, 1153–1154 speech act theory, 1152–1153 theory of communication action, 1153 Communities of practice, 764, 854 Community conflicts, 9, 342 Comparative responsiveness, 23 Compatibility, 953 Competitive behavior, 64, 221 Competitive equilibrium from equal incomes, 106, 107 Complex digital negotiation support, 1083 Computational models, 1189 Computer-supported causal mapping, 794, 806 GDS workshops, 795 cooperative work, 629, 631, 633, 642, 643 CONAN software, 525 Concession curve, 47 Concessions, 220 Condorcet winner, 415, 418, 434, 436, 1032 Confidence-based mediation, 232 Conflict analysis multiple-participant-multiple criteria, 468–469 multiple-participant-single criteria, 470–474

Index relationships of formal approaches, 475–478 single-participant-multiple criteria, 468–470 Conformity pressures, 628, 631 Confrontation (dilemma) analysis options, positions and intentions, 509–511 preferences/doubts, 511–513 Confrontation Manager™ software, 526 Connectedness, 5, 138, 154 Consensus, 9, 199, 225, 343, 372, 391, 434–436, 632, 695, 710, 720, 734, 747, 761, 825, 876, 924, 949, 952–958, 984, 992, 1006, 1031, 1039–1041, 1055 Consensus tool, 1039–1041 Consistency, 949, 951, 953, 955, 956–962, 967, 970, 972 Consistency consensus matrix, 949, 955–957, 959, 960 Consistency index, 951, 1011 Consistency stability intervals, 957, 959, 961 Consultant-client relationship, 785–786 Content-based filtering, 362 Contested pile (CP) procedures, 94–100 Contracts, 787 Contraction independence, 554–556, 560 Convergence, 216 Conversation analysis (CA), 794, 798 Cooperative bargaining theory, 546 alternative agreement, 550 boundedness, 550 closedness, 550 convexity, 550 d-comprehensiveness, 550, 551 disagreement point, 550, 552 individually rational set, 551 ordinal bargaining, 564, 566 Pareto set, 551 Cooperative game theory models, 11, 541 Copeland rule, 419 COVID-19, 1143, 1171 Creativity, 629, 632, 643, 858–859 Credibility, 10, 221, 225, 486, 493, 499, 508, 902 Criteria and alternatives generation tool, 1038–1039 Cross-validation techniques, 969 Crowd-based filtering, 362 Crowd-based idea filtering algorithms, 360 Crowdfunding, 662 Crowd-scale decision support system, 375–381 Crowd-scale deliberation, 9, 356–357, 642 analytics, 361–362 consensus-making processes, 360

1215 idea filtering, 362–363 mapping, 361–362 task marketplace, 367 utility diagrams, 357 Crowd-scale group decisions, 9–10 Crowdsourcing, 696–697 Cumulative voting, 450 Cyber-physical discussion support, 386 CyberSettle, 1173

D D-agree automated facilitation agent, 388 experiment with Nagoya local government, 390–391 user interface, 388 Data augmentation techniques, 967 De-centring, 689 Decision conferencing, 638 Decision rule model, 904–905 Decision science, 233 Decision-support negotiation , 1203 Decision support system (DSS), 10, 11, 114, 159, 197, 208, 324, 343, 372, 464, 478–479, 570, 618, 629, 736, 866, 923, 938, 949, 1054, 1104, 1130, 1162, 1190, 1191 Decision validation, 140, 141 Deck of cards method, 909 Demand game, 562 Demystification, 695 Departure Game, 578 Depersonalization, 219 Descending demand, 90 Design, 758 Desire for future interaction, 224 Dialogue, 162, 164, 186 Dialogue mapping, 639 Dictatorial rule, 560 Diffuse reciprocity, 24 Digital activism crowdfunding and, 657 phase of, 670 stages of, 669 technology affordances and time in, 672 time and team membership in context of, 664 Digital contracting, 1163–1164 Digital negotiations, 1151–1152 Direct Entry procedure, 583 Direct preference declarations, 264 Direct rating, 257

1216 Disagreement point, 547, 549, 550, 552, 564 Discourse analysis, 159, 162, 166 Discourse interaction, 172 Dispersion of individual profits, 223 Dispute resolution services, 1053, 1074 Distributive justice, 6, 22, 834 considerations, 24 and stability, 26–29 Doctus, 844, 851 Document management, 1154, 1155 Dodgson’s method, 419, 420 Domain engineering, 1061–1063 Dominance intensity methods, 928 Double hierarchy hesitant fuzzy linguistic preference relation, 1008 Double hierarchy linguistic term set, 1001, 1004, 1008 Drama theory, 10, 471, 486, 506 Dual facilitation process, 816 with procedural justice, 829–832 treatment issues in, 832–834 working model, 817 Durable peace, 33–34 Dynamic intuitionistic fuzzy weighted averaging operator, 989

E eBay, 1170, 1182 EcommBuilder, 1074, 1075, 1077 Economic reference points, 220 E-disputes, 1171, 1173, 1180 Egalitarian bargaining rule, 557 Eigenvector, 950 E-justice, 1171–1173, 1183 ELECTRE, 264, 900–902, 1014 Electrocardiogram (EKG), 318 Electroencephalography (EEG), 318 Electronic media, 8 Electronic negotiation, 1053, 1104–1105, 1126, 1150, 1165 Elimination method, 469 Elmira 1 graph model, 575–576 Email, 216 E-markets, 1055 Emotion, 5, 7, 13, 39, 62, 138, 157–186, 219, 238, 297, 319, 486, 501, 643, 672, 716, 769, 781, 845, 874, 951, 1111, 1155, 1174 argumentation theory, 163–164 dimension, 72–73 face-to-face negotiation, 171–184 functional potential, 173

Index general affect, 167–169 virtual agent design and simulated negotiation, 169–171 Emotional commitment, 783–784, 852 Emotionally loaded imperative expressions, 154 Empathy, 147, 148, 150, 151 eNego system, 274 E-negotiation engineering domain engineering, 1061–1063 socio-technical system, 1059–1061 E-negotiation table, 1074–1077, 1105 E-negotiation, 5, 15, 166–167, 221, 346, 1059, 1113, 1182 Montreal taxonomy, 1063–1065 Enquiry systems, 1154 Envy-freeness, 85–91, 96, 99, 100, 102 Equal area rule, 561 Equality principle equal measures, 31 equal shares, 31 equal treatment, 31 Equitability, 87 Equivocality, 213 Ethnomethodology, 794, 798, 799, 882 Evolutionary systems design (ESD), 138, 1197 Experiential elicitation , 1205 Exponential utilities, 120–122, 130 Extended justified representation property, 458

F Face-to-face, 213 Facial electromyography, 318 Facilitation, 9, 752, 1026, 1033–1036 Facilitator, 736, 796, 799, 801, 804, 806–809 Facilitator-driven computer-supported GDSS, 842 Facilitator-mediated online discussion model, 373–375 Fair-division, 81–107, 1199–1200 Fair division procedures, indivisible items adjusted winner procedure, 91–92 bottom up rule, 104 contested pile procedures, 94–100 cut-and-choose, 106 descending demand, 90 iterated singles-doubles procedure, 101–103 picking procedures, 92–94 Fairness, 7, 25, 62, 82, 87, 93, 99, 106 Fair process effect, 820, 831 Family Relationships Online, 1181 Family winner system, 1141

Index Feasible payoff set, 547, 549–552, 556 First offers, 220 First-past-the-post rule, 415 Flexible and Interactive Tradeoff (FITradeoff) method, 929, 934–938 Formal negotiation research, 1190–1192 Forward and backward-looking outcomes, 29 Functional magnetic resonance imaging (fMRI), 318 Fundamental scale, 950, 960, 962 Fuzzy numbers, 950, 979–984, 1000 Fuzzy preferences, 608–616, 984, 1012

G Game-theoretic techniques, 1136 Game theory, 236, 471, 487, 506, 571, 591, 1133, 1192 common knowledge, 488 cooperative, 10, 11, 546 developments, 10–11 hypergames, 489–490 metagames, 490–494 modern formalization of, 487 non-cooperative, 11, 532 Gamification, 883 Gatekeeper, 737 Generalized Approval procedure, 452–454 Generalized decision protocols, 247 Generalized intuitionistic fuzzy hybrid averaging operator, 981 Generalized intuitionistic fuzzy ordered weighted averaging operator, 981 Generalized intuitionistic fuzzy weighted averaging operator, 981 General metarationality, 572, 579, 580, 584, 590 Geometric compatibility index, 953 Geometric consistency index, 951 Gibbard-Satterthwaite theorem, 432 Global priorities, 950 Grails framework, 1032 Grand coalition, 540, 541 Graph model for conflict resolution (GMCR), 11, 472, 573, 574, 577–578, 593, 599–602 behavioral, 618 decision support systems, 581 forward, 617–618 inverse analysis, 618–620 matrix formulation, 603–605 preference uncertainty, 605–616 Group behavior, 111, 627, 655, 709, 781, 797

1217 Group cause map, 712 Group collaboration processes, 752 Group decision, 9–10, 13–15, 158 connectedness, 141–154 right problem/solution, 138–141 Group decision and negotiation (GDN), 4–5, 787–788 context for, 7–8 crowd-scale group decisions, 9–10 electronic negotiations, 15–16 game theory developments, 10–11 group support systems, 11–13 justice and fairness, 6–7 multiple criteria analysis, 13–15 Group decision making (GDM), 214, 924, 949, 952, 956–962, 966–970 and cognitive styles, 195–198 IFPRs (see Intuitionistic fuzzy preference relations (IFPRs)) linguistic information (see Linguistic information) Group decision support (GDS) cognitive change, 782–783 emotional commitment, 783–785 as facilitating negotiation, 778–782 intervention, 795–797 political feasibility and consultant-client relationship, 785–787 Group decision support (GDS) practice impacts, 795, 799 in situ, 797, 799–806 live, 794, 797, 806 live recordings, 797–798 real, 795, 810 real-time, 795–797 Group decision support systems (GDSS), 629, 631–633, 637, 642, 1025, 1028–1029 approaches for considering success of, 839–842 decisions, 844–847 dimensions of analysis, 847–855 facilitator-driven computer-supported GDSS, 842 knowledge-based expert system, 844 metagame analysis, 843 virtual reality, 843 Group Explorer, 636–637, 642, 711–714, 722, 799, 818 Group facilitation, 778–782 Group model building, 12, 735–736 Group multi-criteria decision analysis, 1029–1031 GRoUP support (GRUS), 1031–1045

1218 Group support systems (GSSs), 11–14, 627, 655, 681, 709, 735, 753, 781, 797, 819, 841, 1031 Group systems, 630, 634, 635, 637, 640 Groupware document management systems, 1154 Group work, 752

H Hamming distance, 454, 982 Hesitant fuzzy linguistic Bonferroni mean operator, 1005 Hesitant fuzzy linguistic complex proportional assessment method, 1015 Hesitant fuzzy linguistic elements, 999, 1005, 1007, 1014 Hesitant fuzzy linguistic preference relation, 1008–1010 Hesitant fuzzy linguistic term sets, 14, 998– 1001, 1003–1008, 1014, 1015, 1018 Hessian matrix, 115 HFL-TOPSIS method, 1014 HFL-VIKOR method, 1014 Hit-and-run method, 913 Holistic importance, 962–966 Home field effect, 293–294 Homogeneity, 950 Horizontal model, 33 Hot cognition, 855

I Implementation, 759 Incentive mechanisms, 376–377 Incomplete information, 11, 14 Independence of irrelevant alternatives (IIA), 555 Indifference threshold, 1035 Indirect preference declarations, 266 Individually rational set, 548, 551, 560 Individual monotonicity, 556, 557 Individual profits, 222 Indivisible items, fair division procedures, 83 See also Fair division procedures, indivisible items Inducement, 496–498 Information fusion, with intuitionistic fuzzy numbers, 979–984 Information processing, 217, 318 Information transmission, 217 Inner and outer independence, 950 Instant messaging, 220

Index Integrative behavior, 16, 194 Integrative cognitive styles, 194, 201–202 enclaved configuration, 206 integrative cognitive profiles visual representation, 206 mercenaries configuration, 207 satellite configuration, 207 strategists configuration, 207 Intelligent online dispute resolution systems, 1143 INTERACT, 525 Interactive alignment, 148–153 Interactive Computer-Assisted Negotiation Support System (ICANS), 1137 Interactive evolutionary multiobjective optimization (IEMO) methods, 914 Interlocutors, 149 Internet, 212, 1171 Internet Corporation for Assigned Names and Numbers (ICANN), 1173 Interpersonal bonds, 219 Interval judgements, 950 Intuition, 140, 238, 844, 983 Intuitionistic fuzzy Bonferroni mean, 981 Intuitionistic fuzzy correlated averaging operator, 981 Intuitionistic fuzzy correlated geometric operator, 981 Intuitionistic fuzzy dependent averaging operator, 981 Intuitionistic fuzzy dependent geometric operator, 981 Intuitionistic fuzzy hybrid averaging operator, 980 Intuitionistic fuzzy hybrid geometric operator, 980, 981 Intuitionistic fuzzy information clustering, 983–984 distance and similarity measures, 982–983 operations and aggregations, 980–982 Intuitionistic fuzzy number, 979–981, 983, 985, 990, 992 Intuitionistic fuzzy ordered weighted averaging operator, 980 Intuitionistic fuzzy ordered weighted geometric operator, 980, 981 Intuitionistic fuzzy preference relations, 979 applications, 988–989 consistency checking and improving, 984–986 definition of, 985 group consensus models, 987–988 ranking models, 986–987

Index Intuitionistic fuzzy set, group decision making methods aggregation operators and measures, 989–990 applications, 992 decision characteristics, 991–992 ideal solutions, 990 Intuitionistic fuzzy weighted averaging operator, 980 Intuitionistic fuzzy weighted geometric operator, 980 Investment decision, 758 Iterated singles-doubles (ISD) procedure, 101–103

J Jazz history, 113 Joint improvement matrix, 604 Joint profit, 222 Journey making approach, 817 Justice, 5–7, 1171 and durable peace, 33–34 and negotiation processes, 23–25 See also Procedural Justice; Distributive justice; Negotiation processes

K Kalai-Smorodinsky rule, 116, 556 asymmetric, 130–132 exponential utilities, 121–122 power utilities, 123 Kemeny’s median rule, 435 Kirton Adaption Innovation, 196, 197 Knaster procedure, 1199 Knowledge-based expert system (KBS), 844 Knowledge discovery from databases, 1133 Knowledge Society (KS), 948, 952, 956, 970 Kolb Learning Style Inventory, 196

L Linguistic, 154, 344, 999 Linguistic evaluation scales, 1002 Linguistic evaluation term, 1002 Linguistic information aggregation operators, 1004–1006 business management, 1017 distance, similarity and entropy, 1006–1007 dynamic group decision making, 1015–1016 environment and energy evaluations, 1017

1219 HFLTS and extensions, 1000–1001 linguistic preference relation, 1007–1013 MADM, 1013–1015 medical diagnosis and systems, 1016–1017 PLTS and extensions, 1001–1002 social issues, 1017 Linguistic preference relations (LPRs), 999 consistency, 1009–1012 DHHFLPR, 1008 group decisions, 1012–1013 Linguistic terms with weakened hedges, 1003, 1004 Local priorities, 950 Location, 291, 1177 See also Context

M MACBETH, 263 Machine learning, 50, 1205–1206 Magnetoencephalography (MEG), 318 Management of meaning, 780, 783 MarketProwess, 1078–1080 MARS, 269–272 MARS virtual ADR conference, 1181 Mathematical models, 1190 Maximinality, 86, 87, 89, 100, 107 Maximin share, 106 Max-min procedure, 419 MCDA-assisted group process, phases of, 867–870 Media effects, 212, 1150, 1170 Media richness theory, 213–214, 1153–1154 Media synchronicity theory, 216–218 Meeting Works, 638 Metagames, 471, 473, 491, 843 analysis of options, 494–496 emotional decision-making, 498–499 Glaucon’s argument, 491–494 inducement, 496–498 models, 572 Minimax Procedure, 454 Minimax score, 443, 444 Minisum Procedure, 454 Miscommunication, 145 Mixed-motive tasks, 214 Modality, 684 Model-driven GDS, 808 Modeler/reflector, 737 Model integration, 409 Model of emotion in negotiation and decisiontaking, 168, 170, 171 Modified Satisfaction Approval, 451

1220 Moment of truth (MoT), 508 Moments, 694 Monotonic concession strategy , 1204 Monotonicity failure, 427, 436 Monte Carlo Markov chain (MCMC), 955, 967, 970 Montreal e-negotiation taxonomy, 1063–1065, 1091 Movement matrices, 603 MS-Azure cloud environment, 688 Multi-actor decision making, 952–956, 970–972 Multi-attribute decision making (MADM), 232, 316, 863, 893, 921, 977 Multi-attribute utility theory (MAUT), 236, 241, 263 Multi-attribute value theory (MAVT), 263, 870–871, 898–899 Multi-bilateral negotiation, 1067 Multicriteria decision analysis (MCDA) methods, 231, 257, 316, 444, 867–870, 897, 1028, 1043 behavioral issues and biases, 874–876 decision support process, guidelines for, 876–879 and multi-modeling, 873 partial/incomplete information, incorporation of, 872 portfolio decision analysis, 874 rationales for deployment, 865–866 spatial decision making, 873–874 Multi-Criteria Group Decision Making/ Aiding, 316 Multi-criteria process, 1045 Multidimensional scaling, 54 Multi-issue negotiation, 1194–1197 Multilateral bargaining, 536, 541 MULTIMOORA method, 1017 Multiple attribute group decision-making methods, with IFS, 989–992 Multiple criteria analysis, 13–15 Multiple criteria decision aiding (MCDA), 262, 895 choice, ranking and sorting problems, 896 decision rules, 904–905 developments and applications, 913–915 interaction between criteria, 905–908 multiple attribute value theory, 898–899 outranking methods, 900–904 robust ordinal regression, 910–911 stochastic multicriteria acceptability analysis, 912–913 Multiple criteria decision making/aid methods

Index alternative for, 937 application of, 922 decision rules, 928 framework, 929 group of DMs in, 934 information in, 922 methods for preference, 923 potentiality and applicability of, 942 problems, 925 tasks in, 922 Multiple criteria decision making (MCDM), 238, 344–346, 417, 468–470, 637–639, 949, 1028, 1203 Multiple criteria group decision making problem, 923, 925, 933, 940 Multiple objective linear programming (MOLP), 238 Multiple participant-multiple criteria decision making, 468–469 Multiple perspectives, 778, 780, 782, 783 Multi-stage negotiation, 1067 Multi-winner voting, 10, 444, 446–447 admissibility rules, 446, 447 approval ballots, 450–451 cardinal ballots, 449 characteristics, 440 excellence vs. diversity, 441–442 features, 440 ordinal ballots, 448–449 properties, 457 purposes, 440 voters’ ballots, 445 Mutuality, 146, 147 Myers-Briggs Type Indicator, 196, 200

N Nagoya City Planning, 382 Nash bargaining rule, 11, 113, 128–130, 533, 535, 541, 547, 548, 553 anonymity, 554 asymmetric formulation, 129–130 contraction independence, 554, 555 exponential utilities, 122–125 IIA, 555 normative, 547 Pareto optimal, 554 positive, 547 power utilities, 122–125 p-weighted, 555 scale invariance, 554, 555 symmetric, 554, 555 Nash demand game, 534

Index Nash equilibrium, 471, 533, 535, 571 Nash program, 549, 561, 562 Nash stability, 606 Natural language processing (NLP), 346, 347 Nature, 296 Negoisst, 1165 digital contracting, 1163–1164 message composition, communication support, 1157–1161 preference elicitation, 1156–1157 rating offers, decision support, 1161–1163 in use, 1164 Negotiated decision making, 949, 952 Negotiated social order, 852 Negotiating strategic priorities agreement and prioritization of key actions, 825–829 agreement of goals and aspirations, 821–825 group approach to interaction, 819–821 individual interviews and surveys, 818–819 pre workshop stage, 818 Negotiation agent-assisted, 1105 Negotiation outcome, 24, 62, 214, 300 Negotiation process, 22, 40, 61–75, 212, 231–252, 256, 294, 501, 546, 720, 867, 962, 1056, 1160, 1170, 1189 Negotiation process modeling artificial intelligence, 237 axiomatic approach, 236 behavioral mechanism, 238–242 decision making process, 238–244 future research, 251–252 game theory, 236 generic approaches, 232 group decision process, 235 methodological profiles, 233 systematic negotiation framework, 242–244 tacit knowledge impact, 247–251 Negotiation software agent, 1054, 1089, 1105 Negotiation software assistants, 1093 Negotiation style, 47 cooperative, 48 distributive, 47 Negotiation support, 1076–1081 Negotiation support systems (NSSs), 257, 1054, 1105, 1133, 1150, 1174–1175 communication-centered NSSs, 1151 document-centered NSSs, 1151 eNego, 274 family law, 1140–1142 Inspire, 273 for international conflicts, 1138–1140

1221 Mediator, 273 NegoCalc, 272 NegoManage, 273 online dispute resolution services, 1174–1175 SmartSettle, 272 Negotiation template, 260 design, 260 evaluation, 261, 266 Negotiator aspirations, 220 Negotiator protocol, 1069 Negotiator satisfaction, 223 Neural network, 1134 Neuron, 317 Neuroscience, 8, 882 decision making with, 321–331 foundations of, 317–319 modulate decision-making methods, 332–333 tools, 8, 318 variety of, 316 Nominet, 1181 Nonconvex bargaining problems, 549 Non-cooperative bargaining theory, equilibrium payoffs, 535 Non-cooperative game theory, 571 Non-cooperative models of bargaining, 534–536 Non-cooperative multilateral bargaining, 536–541 Non-verbal negotiation, 212 Normalized Euclidean distance, 982 Normalized Hamming distance, 982 Normalized hesitant fuzzy linguistic preference relation, 1010, 1011

O Offers, 7, 14, 40, 63, 257, 535 OLAP, 1044 One-person-one-vote system, 415 On-line, 391, 682, 1129, 1170 Online dispute resolution (ODR) services, 1173, 1180–1182 automated, 1178 challenge, 1182–1183 commercial, 1173 CyberSettle, 1173 decision support, 1178 electronic settlements, 1180 multiple-phase approach, 1180 NSS, 1174–1175

1222 Online dispute resolution (ODR) services (cont.) online mediation and arbitration services, 1179–1180 online negotiation services, 1178 principle-based dispute resolution services, 1175–1178 process support, 1178 solution support, 1178 SquareTrade, 1173 Online Resolution, 1181 Ontology, 1071 Opponent, 224 Optimal control, 126 Optimization models, 235 Option form, 473 Option-form entry, 582 Option prioritizing, 473, 583 Option weighting, 583 Ordinal, 11 Ordinal bargaining, 549, 564, 566 Ordinal environments, 564 Ordinal invariance, 560, 564 Organizational justice, 832 Organizational politics, 780 Organization development (OD), 779 Otherness communication, 147 empathy, 147 interactive alignment, 148, 149 reciprocal adaptation, 148 Outranking methods ELECTRE methods, 900–902 PROMETHEE methods, 902–904 vs. value functions, 900

P Parallelism, 218 Para-verbal negotiation, 212 Pareto optimality, 85, 91, 547, 548, 551, 554, 555, 557–559, 565 Pareto set, 548, 551, 552, 561, 564, 914 Partially observable Markov decision processes, 1206 Participatory modeling (PM), 9, 395–412 Partnerships, 112 Peace agreements, 6, 21 See also Durable peace Perles-Maschler rule, 561 Personal construct theory, 711 Personality traits, 194 Picking procedures, 92–94

Index Plea bargains, 142 Plexsys, 634 PL-ORESTE method, 1014 Plurality method, 415 Plurality runoff method, 415 Political feasibility, 780, 848–850 Portfolio decision analysis, 477 Positional procedure, 419 Positron emission tomography (PET), 318 Post-stability analysis, 582 Power utility functions, 122–125 Process coach, 737 Practitioner performance, 769 Practitioners, 756, 768 Precise consistency consensus matrix, 955, 957, 959–962, 965 Predictably irrational behavior, 951 Preference change, 498, 508 elicitation, 8, 1155–1157 matrices, 603 modelling and problem structuring methods, 343 tree method, 473 Prenegotiation preparation negotiation template, 259–262 software support of, 274 Principle-based dispute resolution services, 1175–1178 Principle of agreement, 952 Principle of consensus, 952 Principle of tolerance, 952, 956, 968 Principles of negotiation, 781–782 Prioritization, 950, 971 Priority, 950–953, 955, 961, 969 The Prisoner’s Dilemma, 523 Probabilistic linguistic preference relation, 1009–1011 Probabilistic linguistic term sets, 999, 1001–1005, 1007, 1009, 1010, 1014, 1017, 1018 Probabilistic linguistic vector-term, 1002 Probabilistic linguistic vector-term set, 1002, 1004 Problem finishing, 784 Problem – framing, right problem, structuring, 148, 158, 348, 356, 398, 464, 630, 682, 709, 867, 923, 948 Problem-solving, 34–35 Problem structuring methods (PSMs), 630, 636, 682, 683, 687 Procedural justice, 13, 22–24, 29–30, 710–711, 783–784, 819

Index dual facilitation process with, 829–832 narrow, 830 wide, 830 Procedural rationality, 778 Profit sharing, 112, 121 PROMETHEE methods, 902–904, 1014 Proportional Approval Voting, 454 Proportional-at-large, 455 Proportionality, 87 Proportionality property, 458 Proximity, 219 Psychological distance perspective, 219 Public choice theory, 343 Public conflicts description, 342 language use and communication, 346–348 multi-criteria decision-making, 344–346 preference modelling and problem structuring methods, 343 socio-economic modelling framework, 343 spatial decision support systems, 348–351 support systems, 344 Public-sector, 315, 351 PxC, 779, 785

Q QUALIFLEX, 1014

R Rank Ordered Centroid, 928 Rapport, 219, 221 Rationality, 139, 159, 487, 506 Rationalizability of bargaining rules, 549 Real-time on-line decision support system, 879 Reasoning, in negotiation, 1194 limit information, 1194, 1204–1205 machine-learning perspective, 1194, 1205–1206 negotiation procedures, 1193–1197 persuasion, 1194, 1200–1201 problem structure, 1193, 1197 tactic reasoning , 1201–1202 value claiming and value creating, 1194, 1197–1199 Rechtwijzer, 1141 Reciprocal adaptation, 148–152 Reciprocal distributions, 950, 963 Reciprocity, 23, 950 Recorder, 737 Rehearseability, 217 Reservation price, 534

1223 Restricted monotonicity, 557 Reviewability, 217 Reviseability, 217 Reweighted Range Voting, 449, 450 Right decision, 141 Right problem/solution agent, 141 group and larger society, 141 See also Problem Risk aversion, 121 Robust ordinal regression, 910–911 Robust Portfolio Modeling, 880 Row geometric mean, 950 Rubinstein model, 11, 536 RUC-APS, 1025, 1044 Rule based reasoning, 1132 Rule–based script, 762–763

S Satisfaction Approval, 451 SAW, 263 Scaffolding, 692 Scale invariance, 554–558, 564 Scoring system, 262 cardinal accuracy, 282 ordinal accuracy, 282 Selling GDN, 788 Semi-anonymous, 387 Sense of ownership, 852 Sequential algorithm (SA), 105–106 Sequential offers model, 540 Sequential Proportional Approval Voting, 451 Sequential stability, 607 Sequential Webster, 452 Serial dictatorial rule, 560 Shapley-Shubik rule, 565, 566 Sharing rule, 114 Signalled intentions (SI), 514–517 Simple Approval (AV), 451 Simpliciter, 420 Simulation experiments, 745 Simulation theory, 162 Simultaneous Webster, 454 Single nontransferable vote, 455 Single-participant-multiple criteria decision making, 468–470 Single process dimension, 63–69 Singles-doubles procedure, 100–101 Single-stage negotiation, 1067 Single transferable vote, 448 Single-winner voting, 10, 441 Skin conductance response, 318

1224 SMART, 263 SmartSettle, 1077, 1181 Social choice theory, 10, 82, 140, 417, 547 Social conduct, 33 Social context, 219 Social emotion, 219 Social influence, 219 Socially negotiated order, 852 Social media, 403 artificial intelligence, 405 Discussoo, 405 ‘rumors’ on, 406 Social skills, 721 Socio-economic modelling framework, 343 Sociomaterial activity, 695 Soft game theory, 500 Soft System Methodology, 698, 838 Software CONAN, 479, 525 Confrontation Manager, 479, 526 CyberSettle, 1172 D-agree, 388–391 Decision Conferencing, 637–638 Decision Explorer, 203, 527 DecisionMaker, 479 Dilemma Explorer, 479, 526 GMCR+, GMCR I, GMCR II, 479, 581–584 EcommBuilder, 1074–1076 eNego, 274 Group Explorer, 636, 637, 640, 642, 682–699, 711–714, 722, 799, 817–818, 831, 833 Group Systems, 630, 634–635, 640 GRUS, 637, 961, 1031–1045 Hi-View, 638 IBIS, 639 INTERACT, 479, 525 MACBETH, 263 MARS, 269–272 Meeting Works, 637–638 Negoisst, 1083, 1107, 1149–1166 NegoCalc, 272 Simply Voting, 644 Strategyfinder, 637 SOLAP, 1044 Spatial decision support systems, 348–351 Speech act theory, 1152–1153 Spiritual Evolutionary Design Framework, 139, 141, 144 Spirituality, 139 Spiritual rationality, 138, 140 Split-up system, 1134

Index Spoiler typologies, 35 Spontaneous moments, 694 SquareTrade, 1073, 1170, 1173, 1181 Standardized Interpolated Path Analysis (SIPA), 45 Stage management, 786–787 Stakeholders, 9, 24, 205, 259, 342, 357, 396, 400, 410, 634, 677, 734, 753, 820, 848, 864, 895, 1028, 1073, 1102 bias, 403, 404, 408 in democracy, 407 differences, 399 group think, 404 Status quo analysis, 532, 546, 572, 587–588, 600 Stochastic multicriteria acceptability analysis, 912–913 Strategic Choice Approach, 698 Strategic conflicts, 570–571 Strategic options and strategic analysis, 881 Strategic Options Development and Analysis (SODA), 636, 683, 684, 698, 711, 838 Strategy-proofness, 87 Subgame perfect equilibrium, 535, 537–540, 562 Subjective value inventory , 1206 Substantive dimension, 63–69 Suitability function, 1035 Supply chain management systems, 1055 Support systems, 257, 343, 372, 464, 570, 628–629, 681–703, 709–711, 735, 781, 799, 816, 837–858, 923, 942, 1053, 1107, 1130, 1150, 1170, 1191 See also Decision support systems; Group support systems; Negotiation support systems Symmetric metarationality (SMR), 572, 579, 580, 584, 586, 590 Synchronicity, 217 Synchronous text-based electronic negotiation, 220 System dynamics group model building, 736 Systemic decision making, 949, 952

T Tacit knowledge, 8, 234, 408, 854 Tactics, 6, 23, 39, 63, 152, 164, 219, 241, 512, 672, 965, 1058, 1102, 1201–1202 Tangibility, 219 Task analysis, 758 Task/media fit hypothesis, 213–214

Index Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), 258, 990, 992 Technology transition model, 635 Terminated decision process, 247 Theory of communication action, 1153 Theory of mind (ToM), 147, 149, 152 Theory of theory of mind (TToM), 147, 152, 159, 161, 167 ThinkLets, 13, 635–636, 642, 645, 759, 762–764 Third party mediation , 1202–1203 Thresholds, 1035 TIMES framework, 1092–1093 TODIM method, 1014 Total priorities, 950 TradeAccess, 1074, 1075 Training, 768 Transfer, 759 Transitional Object, 13, 783, 852–854 Translation invariance, 558 Transmission velocity, 217 Trial-and-error processes, 220 Trump rule, 103–104 Trust, 6, 25, 34–35, 53, 72, 221, 260, 300, 329, 346, 397, 489, 514, 717, 785, 833, 842, 866, 1064, 1103, 1140, 1152, 1174, 1190 U Unanimity, 435, 537 Uncertain dynamic intuitionistic fuzzy weighted averaging operator, 989 Uncertainty, 213, 950, 955, 962, 965–967, 969, 984, 998, 1044, 1172 Undercut procedure, 95, 97–100 Uniform Domain-Name Dispute Resolution Policy, 1173 UTASTAR, 266–269 Utilitarian rule, 559, 560 V Valuation, 950, 971 Values, 139 Verbalized simulation process, 151 Verbal negotiation, 212 Vertical model, 33 Veto threshold, 1035 Virtual linguistic terms, 1002–1004 Virtual reality, 8, 169, 185, 293, 299, 302, 303, 843

1225 Visual barrier, 53, 220 Visual cues, 219 Voice effect, 831 Vote tools, 1032 Voting, 9–10, 88, 350, 363, 413–437, 439–459, 477, 697, 709, 901, 932, 964, 978, 1032 method, 415 multitude of, 436 multi-winner (see Multi-winner voting) procedures, 422–423 regulations, 414 single-winner , 9–10 (see also Singlewinner voting) systems, evaluation of, 425–431

W Weakened hedge set, 1003 Weak Pareto optimality, 556, 558, 559 Weak Pareto set, 548, 551 Web-based commerce, 1170 Web-HIPRE MCDA tool, 873 WebNS system, 1081–1082 Weighted intuitionistic fuzzy Bonferroni mean, 981 Weighted Minimax, 455 Weighted Minisum, 455 Welfare reform, 740 Welfarism axiom, 549 Wilson’s model, 113–114 Win-win agreements, 67, 170, 220, 241, 357, 1077, 1128, 1176, 1198 Workflow, 1029, 1154 Working memory, 149 Workshop, 797 causal mapping, 795, 799, 800, 803, 807 facilitated modelling, 794, 799 GDS, 795, 808 strategy, 796

Y Yu rule, 560, 561

Z Zero normalisation, 539 Zero-sum, 1136 Zeuthen strategy , 1204