Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks [2 ed.] 978-1-4614-7278-0, 978-1-4614-7279-7

Citation preview

International Series in Operations Research & Management Science

Thomas L. Saaty Luis G. Vargas

Decision Making with the Analytic Network Process Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks

Second Edition

International Series in Operations Research & Management Science Volume 195

Series Editor Frederick S. Hillier Stanford University, Stanford, CA, USA Special Editorial Consultant Camille C. Price Stephen F. Austin State University, Nacogdoches, TX, USA

For further volumes: http://www.springer.com/series/6161

Thomas L. Saaty Luis G. Vargas •

Decision Making with the Analytic Network Process Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks Second Edition

123

Thomas L. Saaty Katz Graduate School of Business and College of Business Administration University of Pittsburgh Pittsburgh, PA USA

ISSN 0884-8289 ISBN 978-1-4614-7278-0 DOI 10.1007/978-1-4614-7279-7

Luis G. Vargas Katz Graduate School of Business and College of Business Administration University of Pittsburgh Pittsburgh, PA USA

ISBN 978-1-4614-7279-7

(eBook)

Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2013935400  Springer Science+Business Media New York 2006, 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Applications of the Analytic Network Process (ANP) in decision making demonstrate to our considerable amazement, and by way of validation, that people as they experience life know far more about the world in which they live and more accurately than language alone allows them to express. Logic follows language in developing its analytical details. When we make decisions across the boundaries of different areas of information, we need a way to synthesize priorities in addition to using analysis and applying judgments in each area to create these priorities. It is synthesis that is needed to make good decisions. The network structures used in the context of benefits, opportunities, costs, and risks (BOCR) make it possible to identify, classify, and arrange all the factors and interests that influence the outcome of a decision. A decision is only as good as the framework we use to represent its clusters, their elements, and the connections we identify among them that depict the influences we perceive. Both the Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP) were conceived and their theoretical underpinnings were developed by T. L. Saaty, and there is now an international society on the subject that meets every two years under the name of ISAHP (International Symposium on the Analytic Hierarchy Process). The theory of the ANP was first introduced and simply illustrated in Chap. 8 of Saaty’s 1980 book Multicriteria Decision Making: The Analytic Hierarchy Process which was then followed in 1996 by Decision Making with Dependence and Feedback revised in 2001 to include BOCR and finally in 2005 to include negative priorities and different formulas for synthesis in Theory and Applications of the Analytic Network Process. As with our other co-authored book, Decision Making in: Economic, Political, Social, and Technological Environments with the Analytic Hierarchy Process, 2012, about applications of hierarchies in decision making; this book is about applying network structures with dependence and feedback in decisions. It is a collection of selected applications of the ANP to economic, social and political sciences, and technological design. Our friendship has often brought us together to carry out a project that would be onerous for one person to do alone. We enjoy thinking of the topics, motivating the works and performing the task of collecting and bringing together what appears to us to be of potential interest to readers and users of the Analytic Network Process worldwide. Most of these studies have been v

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edited and shortened but their essence preserved. We believe that the ANP is a general tool that is helpful in assisting the mind to organize its thoughts and experiences and to elicit judgments recorded in memory and quantify them in the form of priorities, and allow for representing diverse opinions after discussion and debate. The reader will notice that many of the chapters were developed by more than one person. We have observed that Co-authorship of the papers and reports is useful for debating judgments that may otherwise appear too subjective and idiosyncratic. Those authors often studied the literature to find out what the real actors in a problem thought and inferred their judgments from this knowledge. We have been particularly interested in three themes: economics, the social sciences and the linking of measurement with human values. The ANP offers economists a very different approach for dealing with economic problems than the usual mathematical models on which economics bases its quantitative thinking: utility theory (with its interval scales and its use of gambles or lotteries to elicit judgments from decision makers) and linear programming which can only work on elements that already have measurement scales. The variety of examples included here can perhaps stimulate some readers to try applying the ANP approach that is based on the much stronger, absolute scales used to represent pairwise comparison judgments in the context of dominance with respect to a property shared by the homogeneous elements being compared. How much or how many times more does A dominate B with respect to property P? Actually people are able to answer this question by using words to indicate intensity of dominance that all of us are equipped biologically to do all the time (equal, moderate, strong, very strong, and extreme) whose conversion to numbers, validation and extension to inhomogeneous elements form the foundation of the AHP/ANP. Priorities are then derived from the totality of the judgments. The second theme is concerned with the social sciences. The ANP offers psychologists, sociologists, and political scientists the methodology they have sought for some time to quantify and derive measurements for intangibles. We hope that the examples included in this book will entice them to study the theory. It should quickly become clear that the ANP is the kind of instrument they have been seeking. The third theme is concerned with providing people in the physical and engineering sciences with a quantitative method to link hard measurement to human values. In such a process one is able to interpret the true meaning of measurements made on a uniform scale using a unit. Measurements on such scales are only indicators of the state of the system; they often do not relate directly to the values of the human observers of the system. The variety in this book has been greatly enhanced by the availability of the SuperDecisions software (www.superdecisions.com), the personal computer implementation of the ANP that is now used fairly widely by decision makers, consultants, teachers and students in business and engineering schools.

Preface

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We would like to thank and acknowledge the contributions of the following individuals without whom this volume would not have been possible: Iwan Azis, Andrew R. Blair, Gershon Mandelker, and Rozann Whitaker (Chap. 2).

Acknowledgments

Michael P. Niemira (Chap. 3), Megan D. Farkasovsky and Anna Greda (Chap. 4), Justin Emanuel and Pete Cefalu (Chap. 5), Juan P. Alberio and Suri Mulani (Chap. 6), H. J. Zoffer (Chap. 7), Jose D. Figueroa and Daryl R. Wood (Chap. 8), Valorie Checque, Larry E. Nolph and Brian R. Patt (Chap. 9), Wiktor Adamus (Chap. 10), Wen-Lin Kung, Min-Hung Lu and Hsiao-Chi Liu (Chap. 11), Jeff Freund, Hang-Jun Kang and Sang Soo Lee (Chap. 12), Kirti Peniwati (Chap. 13), Jennifer S. Shang (Chap. 14), Jerrold H. May, Jennifer S. Shang and Tammy Tjader (Chap. 15). Some of the chapters in this volume were reports prepared for graduate courses taught by the first author (Chaps. 4–6, 8, 9, and 11) or the results of collaborations of the first author (Chaps. 2, 3, 7 and 14) and the second author (Chap. 15) with colleagues. We are grateful to these authors for permission to include their edited materials in the book. The excellent collection of articles included here has been made possible because of their contributions.

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1

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The Analytic Network Process . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 World Chess Championship Outcome Validation of Measurement in a Hierarchy: Karpov-Korchnoi Match . . . . . . . . . . . . . . . . . . 2 The Analytic Network Process (ANP) . . . . . . . . . . . . . 3 The Supermatrix of a Feedback System (Saaty 2001a, b, 2005). . . . . . . . . . . . . . . . . . . . . . . . 4 The Control Hierarchy and What Question to Ask . . . . 5 The Benefits, Costs, Opportunities and Risks and Their Merit Ratings. . . . . . . . . . . . . . . . . . . . . . . 6 Priorities in the Supermatrix. . . . . . . . . . . . . . . . . . . . 7 On the Limit Supermatrix and its Cesaro Sum . . . . . . . 8 Rating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Two Examples of Estimating Market Share . . . . . . . . . 9.1 Airline Example (2005) . . . . . . . . . . . . . . . . . . 9.2 Wine Example (2005) . . . . . . . . . . . . . . . . . . . 10 Group Decision Making. . . . . . . . . . . . . . . . . . . . . . . 10.1 How to Aggregate Individual Judgments . . . . . . 10.2 On the Construction of Group Choice from Individual Choices . . . . . . . . . . . . . . . . . . 10.3 Cardinal Preference Relations . . . . . . . . . . . . . . 10.4 Absolute Cardinal Preference Relations . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Forecasting the Resurgence of the U. S. Economy in 2001: An Expert Judgment Approach . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 On the Role of Judgment in Economic Forecasting . . . . . 3 The Setting: An Economic Slowdown After Years of Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A Holarchy Approach . . . . . . . . . . . . . 4.1 Decomposition of the Problem . . 4.2 Pairwise Comparison . . . . . . . . . 5 Producing the Forecast of the Recovery. 6 An ANP Approach . . . . . . . . . . . . . . . 6.1 ANP Structures . . . . . . . . . . . . . 6.2 Predictions . . . . . . . . . . . . . . . . 6.3 Analysis . . . . . . . . . . . . . . . . . . 7 Conclusion . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . 3

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An Analytic Network Process Model for Financial-Crisis Forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The ANP Financial Crisis Model Structure . . . . . . . . . 3 Building the ANP Financial Crisis Model . . . . . . . . . . 4 The 1991 U. S. Banking Crisis . . . . . . . . . . . . . . . . . . 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Outsourcing a Firm’s Application Development Group 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 BOCR Priorities . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 6 Where to Outsource . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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ANWR: Artic National Wildlife Refuge an ANP Validation Example . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 BOCR Model for ANWR. . . . . . . . . . . . . . . 3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusion and Sensitivity Analyses . . . . . . .

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The Ford Explorer Case . . . . 1 Introduction . . . . . . . . . . 2 Creating the Model . . . . . 2.1 Alternatives . . . . . 2.2 Cluster Definitions. 2.3 Procedure . . . . . . .

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Benefits Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Economic Benefits Clusters, Links and Judgments. 3.2 Social Benefits Clusters, Links and Judgments . . . 3.3 Synthesis of Judgments in the Benefits Model . . . 4 Costs Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Economic Costs Clusters, Links and Judgments . . 4.2 Political Costs Clusters, Links and Judgments . . . . 4.3 Social Costs Clusters, Links and Judgments . . . . . 4.4 Synthesis of Judgments in the Costs Model . . . . . 5 Risks Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Economic Risks Clusters, Links and Judgments . . 5.2 Social Risks Clusters, Links and Judgments . . . . . 5.3 Synthesis of Judgments in the Risks Model . . . . . 6 Ratings and Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . 7 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

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Synthesis of Complex Criteria Decision Making: A Case Towards a Consensus Agreement for a Middle East Conflict Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Structuring the ANP Model for the Middle East Conflict Resolution . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Merits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Benefits Subnet. . . . . . . . . . . . . . . . . . . . 4.3 The Costs Subnet . . . . . . . . . . . . . . . . . . . . . 4.4 The Opportunities Subnet . . . . . . . . . . . . . . . . 4.5 The Risk Subnet . . . . . . . . . . . . . . . . . . . . . . 4.6 Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . 5 Prioritization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Strategic Criteria and Their Priorities . . . . . . . . 5.2 BOCR Merits and Their Priorities . . . . . . . . . . 5.3 Decision Networks. . . . . . . . . . . . . . . . . . . . . 6 Synthesis of the BOCR Merits . . . . . . . . . . . . . . . . . 7 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . U. S. Energy Security . . . . . 1 Introduction . . . . . . . . . 2 ANP Model Description. 2.1 BOCR Model . . .

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2.2 Strategic Rating Model. . . . . . . . . . . . . 2.3 Alternatives Model . . . . . . . . . . . . . . . 3 Benefits, Opportunities, Costs and Risks Model 3.1 Benefits Model . . . . . . . . . . . . . . . . . . 3.2 Opportunities Model . . . . . . . . . . . . . . 3.3 Costs Model . . . . . . . . . . . . . . . . . . . . 3.4 Risks Model . . . . . . . . . . . . . . . . . . . . 4 BOCR/Alternative Analysis . . . . . . . . . . . . . . 5 Model Results. . . . . . . . . . . . . . . . . . . . . . . . 6 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . 6.1 Benefits . . . . . . . . . . . . . . . . . . . . . . . 6.2 Opportunities . . . . . . . . . . . . . . . . . . . 6.3 Costs . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Risks . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Stabilizing Social Security for the Long-Term . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 2 Strategic Criteria. . . . . . . . . . . . . . . . . . . . 3 Alternatives . . . . . . . . . . . . . . . . . . . . . . . 4 Benefits/Opportunities/Costs/Risk . . . . . . . . 5 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Sensitivity Analysis . . . . . . . . . . . . . . . . . . 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . Appendix Schedules . . . . . . . . . . . . . . . . . . . . . Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . .

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11 The Conflict Between China and Taiwan. . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Possible Alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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10 When Shall Poland Enter the Euro Zone?. . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Conditions for Euro Zone Membership: Convergence Criteria Defined by the Maastricht Treaty . . . . . . . . . . . . 3 Poland’s Economic Position Relative to Other Euro Zone Countries and Those Aspiring to Join the European Union. 4 Prioritization of ANP Model Control Criteria for Poland’s Entry into the Euro Zone . . . . . . . . . . . . . . . . . . . . . . . . 5 Decision Subnet Analysis for Each Selected Control Criterion BOCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Final Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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12 U. S. Response to North Korean Nuclear Threat . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 2 Alternative Courses of Action. . . . . . . . . . . . . 3 Benefits, Opportunities, Costs and Risks . . . . . 3.1 Benefits Subnet . . . . . . . . . . . . . . . . . . 3.2 Opportunities Subnet . . . . . . . . . . . . . . 3.3 Costs and Risks Subnets. . . . . . . . . . . . 4 Rating Benefits, Opportunities, Costs and Risks 5 Results and Sensitivity Analysis . . . . . . . . . . . 6 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . 7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . .

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13 Criteria for Evaluating Group Decision-Making Methods . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Criteria for Group Decision Making Methods. . . . . . . . . . 2.1 Group Maintenance: Leadership Effectiveness . . . . 2.2 Group Maintenance: Learning . . . . . . . . . . . . . . . . 2.3 Problem Abstraction: Scope . . . . . . . . . . . . . . . . . 2.4 Problem Abstraction: Development of Alternatives . 2.5 Structure: Breadth . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Structure: Depth . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Analysis: Faithfulness of Judgments. . . . . . . . . . . . 2.8 Analysis: Breadth and Depth of Analysis (What If) . 2.9 Fairness: Cardinal Separation of Alternatives . . . . . 2.10 Fairness: Prioritizing of Group Members . . . . . . . . 2.11 Fairness: Consideration of Other Actors and Stakeholders . . . . . . . . . . . . . . . . . . . . . . . . . 2.12 Scientific and Mathematical Generality . . . . . . . . . 2.13 Applicability to Intangibles. . . . . . . . . . . . . . . . . . 2.14 Psychophysical Applicability. . . . . . . . . . . . . . . . . 2.15 Applicability to Conflict Resolution. . . . . . . . . . . . 2.16 Validity of the Outcome (Prediction) . . . . . . . . . . .

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4 5 6

BOCR Model . . . . . . . . . . . 3.1 Strategic Criteria . . . . 3.2 Control Criteria . . . . . 3.3 Benefits . . . . . . . . . . 3.4 Opportunities . . . . . . 3.5 Costs . . . . . . . . . . . . 3.6 Risks . . . . . . . . . . . . Overall Synthesized Results . Sensitivity Analysis . . . . . . . Conclusions . . . . . . . . . . . .

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xvi

Contents

3

Group Decision Making Methods . . . . . . . . . . . . . . . . . 3.1 Structuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Ordering and Ranking . . . . . . . . . . . . . . . . . . . . 3.3 Structuring and Measuring . . . . . . . . . . . . . . . . . 4 Evaluation of the Methods on the Criteria . . . . . . . . . . . 4.1 Group Maintenance: Leadership Effectiveness . . . 4.2 Group Maintenance: Learning . . . . . . . . . . . . . . . 4.3 Problem Abstraction: Scope . . . . . . . . . . . . . . . . 4.4 Problem Abstraction: Development of Alternatives 4.5 Structure: Breadth . . . . . . . . . . . . . . . . . . . . . . . 4.6 Structure: Depth . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Analysis: Faithfulness of Judgments. . . . . . . . . . . 4.8 Breadth and Depth of Analysis (Analysis) . . . . . . 4.9 Fairness: Cardinal Separation of Alternatives . . . . 4.10 Fairness: Prioritizing Group Members . . . . . . . . . 4.11 Fairness: Consideration of Other Actors and Stakeholders . . . . . . . . . . . . . . . . . . . . . . . . 4.12 Scientific and Mathematical Generality . . . . . . . . 4.13 Applicability to Intangibles. . . . . . . . . . . . . . . . . 4.14 Psychophysical Applicability. . . . . . . . . . . . . . . . 4.15 Applicability to Conflict Resolution. . . . . . . . . . . 4.16 Validity of the Outcome (What If). . . . . . . . . . . . 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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327 328 329 332

14 An Innovative Orders-of-Magnitude Approach to AHP-Based Multicriteria Decision Making: Prioritizing Divergent Intangible Humane Acts . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Decision Making Using the New Orders-of-Magnitude AHP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 A New AHP Model for Comparing Heterogeneous Elements. . . . . . . . . . . . . . . . . . . . . . 3 The Importance of Valuing Activities Contributed by People . 3.1 Need Rating Intangible Contribution to Improve Life Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 On Quantifying the Relative Value of Altruistic Acts . 3.3 Non-monetary Units Already Used in Parts of Our World . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Identifying Criteria and Alternatives for the Proposed AHP Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The Evaluation Criteria . . . . . . . . . . . . . . . . . . . . . . 4.2 Categorization of Clusters. . . . . . . . . . . . . . . . . . . . . 4.3 Altruistic Alternatives . . . . . . . . . . . . . . . . . . . . . . .

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5

Applying the New AHP Model. . . . . . . 5.1 Pairwise Comparison . . . . . . . . . 5.2 Results: The Value of Benevolent 6 Conclusions . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . .

xvii

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15 Sensitivity Analysis in the Analytic Hierarchy Process . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Sensitivity Analysis of Judgments . . . . . . . . . 2.2 Sensitivity Analysis of Priorities . . . . . . . . . . 3 Problem Complexity . . . . . . . . . . . . . . . . . . . . . . . 4 Stability of the ANP Solution . . . . . . . . . . . . . . . . . 4.1 Binary Classification . . . . . . . . . . . . . . . . . . 4.2 Core Stability . . . . . . . . . . . . . . . . . . . . . . . 4.3 Solution Stability. . . . . . . . . . . . . . . . . . . . . 5 An Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions and Further Research. . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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345 345 346 346 347 347 348 349 351 352 354 358 359

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

361

Chapter 1

The Analytic Network Process

1 Introduction Analysis to break down a problem into its constituent components to study their behavior has been the major tool of scientific inquiry to test hypotheses and solve problems. It has proven to be extremely successful in dealing with the world of matter and energy. It has enabled man to land on the moon, to harness the energy of the atom, to master global communication, to invent the computer and to produce tens of thousands of useful and not so useful things. But it has not been so effective in the world of man. Transportation is a socio-technical problem and not a purely technical one as the moon journey was. How clean should the environment be depends on our expectations and on the limited resources we have. But our expectations have no limits imposed on them. Socio-technical problems are not ‘‘solved’’ in the strict sense that purely technical problems are. Solution here means that a reasonable compromise among various requirements is reached. The best solution may not be the best technical, or best economic, or best political or social even though it must consider all of them. Thus, analysis that partitions a problem into its components cannot forge the proper compromise solution to socio-technical questions. What is needed is a method of synthesis, to form the whole from the parts. It must enable one to deal with the different values and objectives, prioritizing their relative importance by looking ahead to forge a best compromise answer according to the different parties and influences involved and the values they have. Synthesis is the subject of the theory of this chapter supported by numerous applications in the rest of the book (Zandi 1975). There are two known ways to analyze causal influences and their effects. One is by using traditional deductive logic beginning with assumptions and carefully deducing an outcome from them. This is a linear and piecemeal approach in which several separate conclusions may be obtained and the problem is to piece them together in some coherent way which needs imagination and experience as logic tells us little or nothing about how to bring the different conclusions into an integrated outcome.

T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_1,  Springer Science+Business Media New York 2013

1

2

1 The Analytic Network Process

The other is a holistic approach in which all the factors and criteria involved are laid out in advance in a hierarchy or in a network system that allows for dependencies. All possible outcomes that can be thought of are joined together in these structures and then both judgment and logic are used to estimate the relative influence from which the overall answer is derived. This approach requires knowledge and experience with the subject, and is not totally dependent on the ability to reason logically which most people cannot do well anyway and which is not guaranteed to discover the truth because the assumptions may be poor, and the reasoning faulty. Feelings and intuition play at least as important a role in deciding the outcome as the ability to reason precisely and deduce unerringly. It may be that some matter of low importance that is determined with logical certainty is found to be cumulatively influential because of its indirect relationship with other important factors. This approach generally leads to a sound overall outcome about the real world. People who work in decision making have been concerned for a long time with the measurement of both physical and psychological events. By physical we mean the realm of what is known as tangibles in so far as they constitute some kind of objective reality outside the individual conducting the measurement. By contrast, the psychological to which judgments used in decision making belong, is the realm of the intangibles, comprising the subjective ideas, feelings, and beliefs of an individual, of a group working together, and more generally of society as a whole. The question is whether there is a coherent theory that can deal with both these worlds of reality without compromising either. The Analytic Hierarchy Process (AHP) is a method that can be used to establish measures in both the physical and social domains. The AHP is a general theory of measurement (Saaty 2000). It is used to derive relative priorities on absolute scales (invariant under the identity transformation) from both discrete and continuous paired comparisons in multilevel hierarchic structures. These comparisons may be taken from actual measurements or from a fundamental scale that reflects the relative strength of preferences and feelings. The AHP has a special concern with departure from consistency and the measurement of this departure, and with dependence within and between the groups of elements of its structure. It has found its widest applications in multicriteria decision making (Saaty and Alexander 1989) in planning (Saaty and Kearns 1985) and resource allocation (Saaty 2001a, b, 2005), and in conflict resolution. In its general form, the AHP is a nonlinear framework for carrying out both deductive and inductive thinking without use of the syllogism. This is made possible by taking several factors into consideration simultaneously, allowing for dependence and for feedback, and making numerical tradeoffs to arrive at a synthesis or conclusion. In using the AHP or its generalization to feedback networks, the Analytic Network Process (ANP) to model a problem, one needs a hierarchic or a network structure to represent that problem, as well as pairwise comparisons to establish relations within the structure. Paired comparison judgments in the AHP/ANP are applied to pairs of homogeneous elements. In all the examples in this book, the judgments used to perform

1 Introduction

3

Table 1 The fundamental scale of absolute numbers Explanation Intensity of Definition Importance 1

Equal importance

2 3

Weak Moderate importance

4 5

Moderate plus Strong importance

6 7

Strong plus Very strong or demonstrated importance

8 9

Very, very strong Extreme importance

Reciprocals If activity i has one of the above of above nonzero numbers assigned to it when compared with activity j, then j has the reciprocal value when compared with i Rationals Ratios arising from the scale

Two activities contribute equally to the objective Experience and judgment slightly favor one activity over another Experience and judgment strongly favor one activity over another An activity is favored very strongly over another; its dominance demonstrated in practice The evidence favoring one activity over another is of the highest possible order of affirmation A reasonable assumption

If consistency were to be forced by obtaining n numerical values to span the matrix

the comparisons are not purely the preferences of the authors, but are frequently tantamount to expert judgments. They represent their best understanding of the influences involved from the different parties’ points of view, as surmised from the literature, the parties’ points of view expressed in the media and occasionally, when possible, by consulting the parties themselves. Sensitivity analysis is used to analyze the effects of variations in judgments on the stability of the final outcome. The fundamental scale of values to represent the intensities of judgments is shown in Table 1. This scale has been derived through stimulus response theory and validated for effectiveness, not only in many applications by a number of people, but also through theoretical justification of what scale one must use in the comparison of homogeneous elements. There are many situations where elements are equal or almost equal in measurement and the comparison must be made not to determine how many times one is larger than the other, but what fraction it is larger than the other. In other words there are comparisons to be made between 1 and 2, and what we want is to estimate verbally the values such as 1.1, 1.2,…, 1.9. There is no problem in making the comparisons by directly estimating the numbers. Our proposal is to continue the verbal scale to make these distinctions so that 1.1 is a ‘‘tad’’, 1.3 indicates moderately more, 1.5 strongly more, 1.7 very strongly more and 1.9

4

1 The Analytic Network Process

Table 2 Relative consumption of drinks

Which Drink is Consumed More in the U.S.? An Example of Estimation Using Judgments

Drink Consumption Coffee Wine in the U.S.

Tea

Beer

Sodas

Milk

Water

Coffee

1

9

5

2

1

1

1/2

Wine

1/9

1

1/3

1/9

1/9

1/9

1/9

Tea

1/5

2

1

1/3

1/4

1/3

1/9

Beer

1/2

9

3

1

1/2

1

1/3

Sodas

1

9

4

2

1

2

1/2

Milk

1

9

3

1

1/2

1

1/3

Water

2

9

9

3

2

3

1

The derived scale based on the judgments in the matrix is: Coffee Wine Tea Beer Sodas Milk Water .177 .019 .042 .116 .190 .129 .327 with a consistency ratio of .022. The actual consumption (from statistical sources) is: .180 .010 .040 .120 .180 .140 .330

extremely more. This type of refinement can be used in any of the intervals from 1 to 9 and for further refinements if one needs them, for example, between 1.1 and 1.2 and so on. An important aspect of paired comparisons is the reciprocal property. When one element is determined to be x times more dominant than another with respect to a given property, the lesser one is used as the unit and the larger is estimated to be some multiple of that unit. The inverse comparison is made by assigning the lesser element the reciprocal value 1/x. Validity of the outcome of decisions using the scale is illustrated by practical examples where actual measurements are known. Table 2 shows how an audience of about 30 people used consensus to combine each group judgment instead of the mathematically proven geometric mean. They provided judgments in verbal form to estimate the dominance of the consumption of drinks in the United States by answering the question: Which drink on the left (e.g., coffee) is consumed more in the US over the drink on the top (e.g., wine) and how much more than another drink? The derived vector of relative consumption and the actual vector, obtained by normalizing the consumption given in official statistical data sources, are at the bottom of the table. When we have several criteria to perform prioritization and obtain synthesis, we need to also compare the importance of the criteria with respect to higher level criteria or with respect to a goal to determine their priorities, and as above, derive priorities for the alternatives with respect to each criterion. Finally, to obtain an overall ranking of the alternatives we multiply the normalized priorities of the alternatives by the corresponding normalized priorities of the criteria and add. This

1 Introduction

5

we also do for the criteria by using the priorities of higher level criteria (which in general we do in the same way by normalizing). This is called the distributive mode of the AHP. In it we assume, as often happens in practice, that an alternative depends on the number and quality of other alternatives with which it is compared. It is also used when the criteria also depend on the alternatives as in the ANP described below. If we wish to require for convenience in practice that the priorities of the alternatives should not be influenced by the number or quality of other alternatives, or if the criteria are not attributes directly related to the alternatives, then we use the ideal mode in which for each criterion we divide the priorities of the alternatives by the largest value among them and then multiply by the corresponding normalized priority of that criterion and add over the criteria. This is known as the ideal mode of the AHP. The ideal mode is also used in the ANP for each control criterion described below because the control criteria are needed to make paired comparisons and are not attributes of the alternatives whose priorities depend on the alternatives directly as in the ANP or indirectly (by comparing them with respect to a higher criterion or goal influenced by any existing or ideal alternative) as in the AHP.

1.1 World Chess Championship Outcome Validation of Measurement in a Hierarchy: Karpov-Korchnoi Match The following criteria (Table 3) and hierarchy (Fig. 1) were used to predict the outcome of world chess championship matches using judgments of ten grandmasters in the then Soviet Union and in the United States who responded to questionnaires they were mailed. The predicted outcomes that included the number of games played, drawn and won by each player either was exactly as they turned out to be or adequately close to predict the winner. The outcome of this exercise was officially notarized before the match took place. The notarized statement was later mailed to the editor of the Journal of Behavioral Sciences along with the paper (Saaty and Vargas 1991). The prediction was that Karpov would win by 6 to 5 games over Korchnoi, which he did.

2 The Analytic Network Process (ANP) Many decision problems cannot be structured hierarchically because they involve the interaction and dependence of higher-level elements on lower-level elements. Not only does the importance of the criteria determine the importance of the alternatives as in a hierarchy, but also the importance of the alternatives themselves determines the importance of the criteria. Two bridges, both strong, but the

6

1 The Analytic Network Process

Table 3 Definitions of chess factors T (1) Calculation (Q): The ability of a player to evaluate different alternatives or strategies in light of prevailing situations B (2) Ego (E): The image a player has of himself as to his general abilities and qualification and his desire to win T (3) Experience (EX): A composite of the versatility of opponents faced before, the strength of the tournaments participated in, and the time of exposure to a rich variety of chess players B (4) Gamesmanship (G): The capability of a player to influence his opponent’s game by destroying his concentration and self-confidence T (5) Good Health (GH): Physical and mental strength to withstand pressure and provide endurance B (6) Good Nerves and Will to Win (GN): The attitude of steadfastness that ensures a player’s health perspective while the going gets tough. He keeps in mind that the situation involves two people and that if he holds out the tide may go in his favor T (7) Imagination (IW): Ability to perceive and improvise good tactics and strategies T (8) Intuition (IN): Ability to guess the opponent’s intentions T (9) Game Aggressiveness (GA): The ability to exploit the opponent’s weaknesses and mistakes to one’s advantage. Occasionally referred to as ‘‘killer instinct’’ T (10) Long Range Planning (LRP): The ability of a player to foresee the outcome of a certain move, set up desired situations that are more favorable, and work to alter the outcome T (11) Memory (M): Ability to remember previous games B (12) Personality (P): Manners and emotional strength, and their effects on the opponent in playing the game and on the player in keeping his wits T (13) Preparation (PR): Study and review of previous games and ideas T (14) Quickness (Q): The ability of a player to see clearly the heart of a complex problem T (15) Relative Youth (RY): The vigor, aggressiveness, and daring to try new ideas and situations, a quality usually attributed to young age T (16) Seconds (S): The ability of other experts to help one to analyze strategies between games B (17) Stamina (ST): Physical and psychological ability of a player to endure fatigue and pressure T (18) Technique (T): Ability to use and respond to different openings, improvise middle game tactics, and steer the game to a familiar ground to one’s advantage

stronger is also uglier, would lead one to choose the strong but ugly one unless the criteria themselves are evaluated in terms of the bridges, and strength receives a smaller value and appearance a larger value because both bridges are strong. Feedback enables us to factor the future into the present to determine what we have to do to attain a desired future. Figures 2 and 3 below illustrate the difference between hierarchies and networks. A hierarchy is a linear top down structure. A network spreads out in all directions and involves cycles between clusters and loops within the same cluster (Saaty 2001, 2005).

2 The Analytic Network Process (ANP)

7

Fig. 1 Criteria and players in chess competition

Fig. 2 A three level hierarchy in detail

The feedback structure does not have the linear top-to-bottom form of a hierarchy but looks more like a network, with cycles connecting its components of elements, which we can no longer call levels, and with loops that connect a component to itself. It also has sources and sinks. A source node is an origin of paths of influence (importance) and never a destination of such paths. A sink node is a destination of paths of influence and never an origin of such paths. A full network can include source nodes; intermediate nodes that fall on paths from source nodes, lie on cycles, or fall on paths to sink nodes; and finally sink nodes. Some networks can contain only source and sink nodes. Still others can include only source and cycle nodes or cycle and sink nodes or only cycle nodes. A decision problem involving feedback arises often in practice. It can take on the form of any of the networks just described. The problem is to determine the priorities of the elements in the network and in particular the alternatives of the decision. Because feedback involves cycles, and cycling can be an infinite process, the operations needed to derive the priorities become more demanding than has been familiar with hierarchies. Unraveling their intricacies is challenging to the intellect and is essential for making the computations precise.

8

1 The Analytic Network Process

Loop in a component indicates an inner dependence of the elements in that component with respect to a common property.

Fig. 3 Structural difference between a linear and a nonlinear network

At present, in their effort to simplify and deal with complexity, people who work in decision making use mostly very simple hierarchic structures consisting of a goal, criteria, and alternatives. Yet, not only are decisions obtained from a simple hierarchy of three levels different from those obtained from a multilevel hierarchy, but also decisions obtained from a network can be significantly different from those obtained from a more complex hierarchy. We cannot collapse complexity artificially into a simplistic structure of two levels, criteria and alternatives, and hope to capture the outcome of interactions in the form of highly condensed judgments that correctly reflect all that goes on in the world. We must learn to decompose these judgments through more elaborate structures and organize our reasoning and calculations in sophisticated but simple ways to serve our understanding of the complexity around us. Experience indicates that it is not very difficult to do this although it takes more time and effort. Indeed, we must use feedback networks to arrive at the kind of decisions needed to cope with the future. To test for the mutual independence of elements such as the criteria, one proceeds as follows: Construct a zero–one matrix of criteria against criteria using the number one to signify dependence of one criterion on another, and zero otherwise. A criterion need not depend on itself as an industry, for example, may not use its own output. For each column of this matrix, construct a pairwise comparison matrix only for the dependent criteria, derive the priority vector, and augment it with zeros for the excluded criteria. If a column is all zeros, then assign a zero vector to represent the priorities. The question in the comparison would be: For a given criterion, which of two criteria depends more on that criterion with respect to the goal or with respect to a higher-order controlling criterion? In this chapter we lay out the theoretical foundations for the kinds of structures and matrices of derived scales associated with feedback networks from which we obtain the priorities for a decision. For numerous applications of the ANP the reader should consult the book called the Encyclicon (Saaty and Ozdemir 2005).

3 The Supermatrix of a Feedback System

9

3 The Supermatrix of a Feedback System (Saaty 2001a, b, 2005) Assume that we have a system of N components where the elements in each component interact or have an influence on some or all of the elements of another component with respect to a property governing the interactions of the entire system, such as energy or capital or political influence (see Fig. 4). In general, a network consists of components and elements in these components. But in creating structures to represent problems there may be larger parts to consider than components. According to size, we have a system that is made up of subsystems, with each subsystem made up of components, and each component made up of elements. We might consider that the whole need not be equal to the sum of its parts, but may, due to synergy, be larger or smaller in the sense of contributing to a goal. Sometimes we refer to a set of objects contained in a larger one as elements when in fact they may be components. The context would make this clear. Note that the network connecting the components of a decision system must always be connected. It cannot be divided into two or more disconnected parts, otherwise they cannot communicate with each other and it is pointless to ask for the influence of one part on another because there can never be any.

There are three kinds of components in Fig. 4. Those components which no arrow enters are source components such as C1 and C2. Those from which no arrow leaves are known as sink components such as C5; and finally those which arrows both enter and exit leave are known as transient components such as C3 and C4. In addition, C3 and C4 form a cycle of two components because they feed back and forth into each other. C2 and C4 have loops that connect them to themselves. They are inner dependent. All other

Intermediate component (Transient State)

Source Component

C1

C2

Outerdependence

Intermediate Component (Recurrent State)

Sink Component (Absorbing State)

C3

C5

Intermediate Component (Recurrent State) Inner dependence loop

C4 Fig. 4 Types of components in a network

10

1 The Analytic Network Process

connections represent dependence between components that are thus known to be outer dependent. An example of dependence between components is the input– output of materials among industries. The electric industry supplies electricity to other industries including itself. But it depends more on the coal industry than on its own electricity for operation and also more on the steel industry for its turbines. We denote a component of a decision network by Ch, h = 1,… m, and assume that it has nh elements, which we denote by eh1 ; eh2 ; . . .; ehmn . The influences of a given set of elements in a component on any element in the system are represented by a priority vector derived from paired comparisons in the usual way of the AHP. It is these derived vectors, how they are grouped and arranged, and then how to use the resulting structure which turns out to be a matrix, that interests us here. This matrix is thus used to represent the flow of influence from a component of elements to itself as in the loop that flows back to C4 above, or from a component from which an arrow is directed out to another component. Sometimes, as with hierarchies, one is concerned with the influence of the component at the end of an arrow on the component from which the arrow begins; one must decide on one or the other. The influence of elements in the network on other elements in that network can be represented in the following supermatrix: (Fig. 5) A typical entry Wij in the supermatrix, is called a block of the supermatrix. It is a matrix of the form 3 2 ðjnj Þ ðj1Þ ðj2Þ Wi1 Wi1    Wi1 7 6 ðjnj Þ 7 6 ðj1Þ ðj2Þ    Wi2 7 Wi2 6 Wi2 wij ¼ 6 .. 7 .. 7 6 .. 4 . . 5 .  jn ð jÞ ðj2Þ ðj1Þ Wini Wini Wini

Each column of Wij is a principal eigenvector of the influence (importance) of the elements in the ith component of the network on an element in the jth component. Some of its entries may be zero corresponding to those elements that have no influence. Thus we do not need to use all the elements in a component when we make the paired comparisons to derive the eigenvector, but only those that have a non-zero influence. Figures 6 and 7 and their accompanying supermatrices represent a hierarchy and a holarchy of m levels. As with any supermatrix, an entry in each of the foregoing two supermatrices is a block Wij positioned where the ith

Fig. 5 The supermatrix of a network

C1 e11e12 e C1 e11 12

C2 e1n

1

e21e22

CN e2n

2

eN1eN2

eNn

W11

W12

W1N

W21

W22

W2N

WN1

WN2

WNN

e1n

1

W=

C2

e21 e22

e2n

2

CN

eN1 eN2 eNn

N

N

3 The Supermatrix of a Feedback System

11

Fig. 6 The structure and supermatrix of a hierarchy

Fig. 7 The structure and supermatrix of a holarchy

• 0 0 • • 0 W 1,n ⎤ ⎡ 0 ⎢ • • • 0 0 0 0 ⎥⎥ W ⎢ 21 ⎢ 0 W 32 0 • • • 0 0⎥ ⎢ ⎥ W=⎢ • • • • • • • •⎥ ⎢ • • • • • • • •⎥ ⎢ ⎥ • • • • • • • W n-1, n-2 ⎢ ⎥ ⎢ 0 • W n,n-1 0 0 • • 0 ⎥⎦ ⎣

component or level is connected to and influences the jth level immediately above. The entry in the last row and column of the supermatrix of a hierarchy is the identity matrix I. It corresponds to a loop at the bottom level, used to show that each element depends only on itself. It is a necessary aspect of a hierarchy (or any sink) when viewed within the context of the supermatrix. The entry in the first row and last column of a holarchy is nonzero because the top level depends on the bottom level. A network may be generated from a hierarchy by increasing the hierarchy’s connections gradually so that pairs of components are connected as desired and some components have an inner dependence loop.

4 The Control Hierarchy and What Question to Ask For clarity and greater precision, the influence represented in all the derived eigenvectors of priorities entered in a supermatrix must be measured according to a single criterion, such as economic influence. Another supermatrix may represent social influence, and so on. We call such criteria with respect to which influence is represented in individual supermatrices control criteria. Because we need to combine all such influences obtained from the limits of the several supermatrices in order to obtain a measure of the priority of overall influence, we need to group the control criteria in a structure that allows us to derive priorities for them and use these priorities to weight the corresponding individual supermatrix limits and add. Such a structure of control criteria may itself be elaborate. For simplicity we call

12

1 The Analytic Network Process

the structure of control criteria a control hierarchy. Analysis of priorities in a system can be thought of in terms of a control hierarchy with dependence among its bottom-level alternatives arranged as a network (Fig. 6). Dependence can occur within the components and between them. A control hierarchy at the top may be replaced by a control network with dependence among its components. More generally, one can have a cascading set of control networks, the outcome of one used to synthesize the outcomes of what it controls. For obvious reasons relating to the complexity of exposition, apart from a control hierarchy, we will not discuss such complex control structures here. A control hierarchy can also be involved in the networks of its criteria with feedback involved. A component in the ANP is a collection of elements whose function derives from the synergy of their interaction and hence has a higher-order function not found in any single element. A component is like the audio or visual component of a television set or like an arm or a leg, consisting of muscle and bone, in the human body. A mechanical component has no synergy value but is simply an aggregate of elements and is not what we mean by a component. The components of a network should generally be synergistically different from the elements themselves. Otherwise they would be a mechanical collection with no intrinsic meaning. We make the observation that the criteria in the control hierarchy that are used for comparing the components are usually the major parent criteria whose subcriteria are used to compare the elements in the component. Thus the criteria for comparing the components need to be the same or more general than those of the elements because of the greater functional complexity of the components. There are two types of control criteria (subcriteria). A control criterion may be directly connected to the structure as the goal of a hierarchy if the structure is in fact a hierarchy. In this case the control criterion is called a comparison-‘‘linking’’ criterion. Otherwise, a control criterion does not connect directly to the structure but ‘‘induces’’ comparisons in a network and hence, it is called a comparison‘‘inducing’’ criterion. The generic question to be answered by making pairwise comparisons is: Given a control criterion (subcriterion), a component (element) of the network, and given a pair of components (elements), how much more does a given member of the pair influence that component (element) with respect to the control criterion (subcriterion) than the other member?

5 The Benefits, Costs, Opportunities and Risks and Their Merit Ratings Any decision has several favorable and unfavorable concerns to consider. Some of these are sure things, others are less certain and have a likelihood of materializing. The favorable sure concerns are called benefits while the unfavorable ones are called costs. The uncertain concerns of a decision are the positive opportunities

5 The Benefits, Costs, Opportunities and Risks and Their Merit Ratings

13

that the decision might create and the negative risks that it can entail. Each of these four concerns utilizes a separate structure for the decision, beginning with a benefits control structure and the network of interdependencies that belongs under each benefit control criterion, and ending with a risks control structure. We refer to the four concerns collectively as BOCR merits, having used the initials of the positive ones (benefits and opportunities) before the initials of the negative ones (costs and risks). Each of these concerns contributes to the merit of a decision and must be evaluated (rated) individually on a set of (prioritized) criteria that is used to also rate any other decision. We call these ratings merits and refer to the evaluation criteria to derive them as strategic criteria. Examples of strategic criteria are: satisfaction, happiness, convenience, fulfillment, order, harmony, peace, power, efficiency, social good, progress, wealth and so on. They must themselves be prioritized for frequent use in all decisions. In this manner we can synthesize the outcome of the alternatives for each of the BOCR structures, to obtain their overall synthesis. We note that for costs and risks one must ask which is more costly and which is more risky (not which is less costly and which is less risky) because in paired comparisons we can only estimate how much more the dominant member of a pair has a property as a multiple of how much the less dominant one has it and not the other way around. The priorities of the alternatives are now synthesized by using a marginal formula BO/CR and a total outcome or global one bB ? oO – cC - rR. The priorities b, o, c, and r are obtained by rating the B, O, C and R one at a time with respect to strategic criteria as the applications make clear. The rating is carried out by synthesizing the priorities of the alternatives (given in ideal form) with respect to each of the control criteria for which a network is constructed for each of the B, O, C and R merits, and using the top rated alternative in the rating of that merit (Saaty 2001a, b). Also note that the total outcome formula is related to the residual probabilities formula that always gives positive answers: bB ? oO ? c(1 - C) ? r(1 - R) = bB ? oO – cC - rR ? c ? r in which the costs and risks are subtracted from one and in the end it turns out that the same constant c ? r is added to the priority of every alternative. However, this last formula may be useful in situations involving BOCR that predict proportionate voting or other type of outcomes measured with positive numbers or statistics.

6 Priorities in the Supermatrix We are interested in deriving limit priorities of influence from the supermatrix. To obtain such priorities the supermatrix must first be transformed to a matrix each of whose columns sums to unity, known as a column stochastic or simply a stochastic matrix. If the matrix is stochastic, the limit priorities can be viewed in a way to depend on the concepts of reducibility, primitivity, and cyclicity of the matrix (the details not needed here are discussed in Saaty (2005) and Saaty (2001) in the text and in an appendix). Note that in applying the ideas, the reader will only

14

1 The Analytic Network Process

need to structure a decision problem and provide the necessary judgments as instructed or coached by the powerful software (SuperDecisions 2000) developed for this purpose. It is not mandatory to learn the details of the theory to apply it in practice. The question arises as to whether there is a natural way (a scientific on top of a mathematical justification) to transform a given supermatrix whose columns usually sum to more than one, to a stochastic matrix. The priority of an element in a component is an inadequate indicator of its priority in the entire set of components. The highest priority element in a component need not be the highest priority element in the set of components. This is obvious because each component has a highest ranked element and they cannot all be first in the system. Thus we need to compare the components themselves according to their influence on each component in the supermatrix with respect to a higher-order control criterion. The comparisons give rise to a derived vector of priorities of the influence of all the components (on the left of the supermatrix) on each component on top. This is done as many times as there are components. The resulting vectors are each used to weight the blocks of matrices that fall in the column under the given component. The first entry of the vector is multiplied by all the elements in the first block of that column, the second by all the elements in the second block of the column and so on. In this manner we weight the blocks in each column of the supermatrix. The result is known as the weighted supermatrix which is now stochastic. It is this stochastic matrix that we can work with to derive the desired priorities by transforming it to a limit matrix described below. This matrix yields the long-run or limit priority of influence of each element on every other element. Remark: By way of further elaboration on rendering the supermatrix stochastic we note that it may be that only some elements of a component have an influence on some elements of another component in which case zeros are entered where there is no influence. Or it may even be that no element of a component influences a given element of another (there would be zeros for all the priorities represented by that vector) or only some elements influence it (there would be zeros for the priorities of the elements that do not influence it in the priority vector). In the case where an entire vector, but not all vectors in that component, is zero, the weighted column of the supermatrix must be renormalized. It is appropriate to say here that if all the elements of a component have zero influence on all the elements of a second component, the priority of influence of the first component itself on the second must also be equal to zero. However, this is not true when some or all the elements of the first component have an influence on some or all of those of the second. That is why the renormalization of some columns is essential and natural in making the weighted supermatrix stochastic. We note that if the component of the alternatives of a decision is a sink of the network, and the other components do not depend on it, it need not be included in the supermatrix, and its priorities are used in the process of synthesis after limit priorities have been obtained for the relevant components of the supermatrix. This enables one to ensure rank preservation when desired by using the ideal mode of the AHP. If the component of alternatives is not a sink then it must be kept in the

6 Priorities in the Supermatrix

15

supermatrix whose priorities are analogous to the distributive mode and hence rank may legitimately be allowed to reverse.

7 On the Limit Supermatrix and its Cesaro Sum Why do we need to raise the supermatrix to powers? It is because we wish to capture the transmission of influence along all possible paths of the supermatrix. The entries of the weighted supermatrix itself give the direct influence of any element on any other element. But an element can influence a second element indirectly through its influence on some third element and then by the influence of that element on the second. There are potentially many third elements. One must consider every such possibility of a third element. All indirect influences of pairs of elements through an intermediate third element are obtained by squaring the weighted supermatrix. Again the influence of one element on another can occur by considering a third element that influences a fourth element, which in turn influences the second element. All such influences are obtained from the cubic power of the matrix, and so on. Thus we have an infinite sequence of influence matrices: the matrix itself, its square, its cube, etc., denoted by W k k = 1,2,…. If we take the limit of the average of a sequence of N of these powers of the supermatrix N P (known as the Cesaro sum), lim N1 W k , does the result converge and is the limit k!1

k¼1

unique? How do we compute this limit to obtain the desired priorities? It is known in mathematical analysis that if a sequence converges to a limit then its Cesaro sum converges to the same limit. Since the sequence is defined by the powers of the matrix, it is sufficient to find out what the limit of these powers is. It may well be that the sequence does not converge to a unique limit but its Cesaro sum averages out over the different limits of the sequence obtaining a unique limit. As we shall see, both these cases occur for our supermatrix when it is raised to powers. First we note from the Jordan Canonical Form of a stochastic matrix N P W that lim N1 W k generally exists. It is known that W is similar to its Jordan k!1

k¼1

matrix J if there is a nonsingular matrix P such the J = PWP-1. Thus raising W to limiting powers is equivalent to raising J to limiting powers. So what does J look like? With every square matrix is associated a unique Jordan matrix that has the following form: It consists of square blocks whose principal diagonals lie on its principal diagonal. All entries that lie outside these blocks are equal to zero. All entries that lie in a block are zero except for the principal diagonal all of whose entries are the same and are equal to an eigenvalue of W, and all entries in the diagonal immediately above the principal diagonal are equal to one. The matrix W is said to be the direct sum of its Jordan blocks. Without too much detail, it is N P clear that lim N1 W k exists if: (a) no eigenvalue of W has modulus greater than k!1

k¼1

16

1 The Analytic Network Process

one, (b) W has no eigenvalue of modulus one other than k ¼ 1, and if k ¼ 1 is an eigenvalue as it is with the stochastic matrix W, it has only 1-by-1 blocks in the Jordan Canonical Form. In fact one can define a limit in the sense of Cesaro when case (b) is not satisfied. To know that the limit exists and to derive that limit are different matters. We now derive this limit. According to J.J. Sylvester one can represent an entire function of a (diagonalizable) matrix W whose characteristic roots are distinct as: f ðW Þ ¼

n X

f ðki ÞZ ðki Þ;

i¼1

where Q

 kj I  W j6¼i  : Z ð ki Þ ¼ Q  kj  ki j6¼i

The Z(ki) can be shown to be complete orthogonal idempotent matrices of W; that is, they have the properties k X i¼1

  Z ðki Þ ¼ I; Z ðki ÞZ kj ¼ 0; i 6¼ j; Z 2 ðki Þ ¼ Z ðki Þ;

where I and 0 are the identity and null matrices, respectively. Thus for example if one raises a matrix to arbitrarily large powers, it is enough to raise its eigenvalues to these powers and form the above sum involving the sum of polynomials in W. Because the eigenvalues of a stochastic matrix are all less than one, when raised to powers they vanish except when they are equal to one or are complex conjugate roots of one. Because here the eigenvalues are assumed to be distinct, we have the simplest case to deal with, that is kmax ¼ 1 is a simple eigenvalue. Formally, because the right hand side is a polynomial in W multiplying both sides by W 1 each term on the right would be a constant multiplied by W 1 and the final outcome is also a constant multiplied by W 1 . Because we are only interested in the relative values of the entries in W 1 we can ignore the constant and simply raise W to very large powers which the computer program SuperDecisions (2000). Next we consider the case where kmax ¼ 1 is a multiple eigenvalue. For that case we have what is known as the confluent form of Sylvester’s theorem:   n Q ðk  ki Þ  k k mi 1 X X 1 d  f ðkÞðkI  W Þ1 i¼1 T ð ki Þ ¼ f ðWÞ ¼  n mi 1 ‘  ð m  1 Þ! dk i i¼1 j¼1 ð k  ki Þ   i¼miþ1 kk1

7 On the Limit Supermatrix and its Cesaro Sum

17

where k is the number of distinct roots and mi is the multiplicity of the root ki . However, as we show below, this too tells us that to obtain the limit priorities it is sufficient to raise W to arbitrarily large power to obtain a satisfactory decimal approximation to W 1 . The only possible nonzero survivors as we raise the matrix to powers are those k0 s that are equal to one or are roots of one. If the multiplicity of the largest real eigenvalue kmax ¼ 1 is n1 , then we have h i 1  dðn1 1Þ ðkI  WÞ DðkÞ  dkðn1 1Þ 1  W ¼ n1  ðn1 Þ D ðkÞ  k¼1

where one takes derivatives of the characteristic polynomial of the matrix W, and DðkÞ ¼ detðkI  WÞ ¼ kn þ p1 kn1 þ . . . þ pn : Also, ðkI  WÞ

1

¼ FðkÞ=DðkÞ and

FðkÞ ¼ W n1 þ ðk þ p1 ÞW n2 þ ðk2 þ pk1 þ p2 ÞW n3 þ    þ ðkn1 þ p1 kn2 þ    þ pn1 ÞI is the adjoint of ðkI  WÞ. Now the right side is a polynomial in W. Again, if we multiply both sides by W 1 , we would have on the right a constant multiplied by W 1 which means that we can obtain W 1 by raising W to large powers. For the cases of roots of one when kmax ¼ 1 is a simple or a multiple root, let us again formally see what happens to our polynomial expressions on the right in both of Sylvester’s formulas as we now multiply both on the left and on the right first by 1 ðW c Þ1 obtaining one equation and then again by ðW cþ1 Þ obtaining another and 1 so on c times, finally multiplying both sides by ðW cþc1 Þ . We then sum these equations and take their average on both sides. The left side of each of the equations reduces to W 1 and the average is given by 1c W 1 . On the right side the sum for each eigenvalue that is a root of unity is simply a constant times the sum 1 1 ðW c Þ1 þðW cþ1 Þ þ. . . þ ðW cþc1 Þ . Also, because this sum is common to all the eigenvalues, it factors out and their different constants sum to a new constant multiplied by (1/c). This is true whether one is a simple or a multiple eigenvalue because the same process applies to accumulating its constants. In the end we simply have 1 c



1

1

ðW c Þ1 þðW cþ1 Þ þ. . . þ ðW cþc1 Þ

¼ 1c ð1 þ W þ . . . þ W c1 ÞðW c Þ1 ; c  2

that amounts to averaging over a cycle of length c obtained in raising W to infinite power. The cyclicity c can be determined, among others, by noting the return of the form of the matrix of powers of W to the original form of blocks of zero in W. Caution: Some interesting things can happen in the limit supermatrix when kmax ¼ 1 is not a simple root. For example if we have multiple goals in a hierarchy that are not connected to a higher goal, that is if we have multiple sources, we may

18

1 The Analytic Network Process

have several limit vectors for the alternatives and these must be synthesized somehow to give a unique answer. To do that, the sources need to be connected to a higher goal and prioritized with respect to it. Otherwise, the outcome would not be unique and we would obtain nothing that is meaningful in a cooperative decision (but may be useful in a non-cooperative problem where the goals for example, are different ways of facing an opponent). It is significant to note that a hierarchy always has a single source node (the goal) and a single sink cluster (the alternatives), yet its supermatrix is reducible. Only when the supermatrix is irreducible (kmax ¼ 1 is a simple root) and thus its graph is strongly connected with a path from any node or cluster to any other node or cluster that the columns of the supermatrix would be identical. It is rare that the supermatrix of a decision problem is irreducible. If the source clusters do not have sufficient interaction to serve as a single source, one could take the average of the alternatives relating to the several sources as if they are equally important to obtain a single overall outcome.

8 Rating When one rates alternatives, they must be independent of one another. The presence or absence of an alternative must have no effect on how one rates any of the others. We call this kind of ranking of alternatives with respect to an ideal (which is an arbitrarily chosen fixed reference point) absolute measurement or rating. Absolute measurement is analogous to measuring something with a physical device; for example, measuring length with a yardstick. In order to rate alternatives with respect to an ideal, we need to create intensity levels or degrees of variation of quality on a criterion; for example, excellent, above average, average, below average and poor. We then pairwise compare them to establish priorities and normalize those priorities by dividing by the largest value among them, so that excellent would have a value of 1.000 and the others would be proportionately less. Idealizing the priorities by dividing by the largest assures that intensities belonging to large families do not receive small priorities simply because there are many of them. We then rate an alternative by selecting the appropriate intensity level for it on each criterion. Even when we use a numerical scale, say 1–100, to rate each alternative we must have an intuitive idea of how high or how low an alternative falls and in the process we subconsciously make comparisons among different levels on the scale. It is not the exact number chosen, but the level of intensity of feeling behind where it should fall, up or down, on the scale that matters. Because it compares the alternatives with respect to a standardized ideal, absolute measurement is normative not descriptive. The ratings approach is illustrated in the following example of choosing the best city to live in. Figure 8 shows the goal, criteria and their priorities obtained from paired comparisons, and the intensities for each criterion with their idealized values obtained by dividing by the largest value in the vector of priorities derived from their paired comparisons matrix.

8 Rating

19 GOAL Best City to Live in 1.000

Cultural 0.152

Family 0.454

Housing 0.072

Jobs 0.305

Extreme 1.000

750 mi

Rent>35% Sal. .056

.079

Transportation 0.038

Excellent 1.000 Above Avg .664 Average .306 Below Avg .126 Poor .065

Abundant .906 Considerable 1.000 Manageable .396 Negligible .120

Fig. 8 Most livable cities in the US

The pairwise comparisons for the Cultural criterion intensities and the resulting priorities are illustrated in Table 4. The values in the Idealized column are obtained by dividing each priority in the priorities column by the largest, 0.569. The prioritized intensities become the standards from which one selects the appropriate one to describe a particular city’s performance with respect to Cultural (interpret this as cultural opportunities). The prioritized intensities in essence become a standardized performance scale, something like a yardstick that can be used to rate a city on culture. Note that for this criterion of culture, judgment is still involved in deciding which intensity to pick. Actual data can also be used in establishing the priorities, usually involving some form of idealization where data is converted to priorities directly. A score is computed for a city by multiplying the priority of the selected intensity times the priority of the criterion and summing for all the criteria, shown in the Total Score column in Table 5. The Priorities column is obtained by Table 4 Deriving priorities for the cultural criterion categories Extreme Great Significant Moderate Tad

Priorities

Idealized

Extreme Great Significant Moderate Tad

0.569 0.234 0.107 0.06 0.03

1 0.411 0.188 0.106 0.052

1 1/5 1/6 1/8 1/9

5 1 1/4 1/5 1/7

6 4 1 1/3 1/5

8 5 3 1 1/4

9 7 5 4 1

20

1 The Analytic Network Process

Table 5 Verbal ratings of cities under each criterion Jobs Housing Alternatives Cultural Family 0.325 0.056 0.394 0.195 Pittsburgh Boston Bethesda Santa Fe

Signific. \100 mi Extreme 301–750 mi Great 101–300 mi Signific. [750 mi

Transport 0.03

Total Score

Priorities (Normal)

Own [ 35 % Average Manageable 0.562 Rent [ 35 % Above Abundant 0.512 Avg. Rent \ 35 % Excellent Considerable 0.650

0.294 0.267

Own [ 35 % Average

0.100

Negligible

0.191

0.339

Table 6 Priorities of ratings of cities under each criterion Transport Alternatives Cultural Family Housing Jobs 0.325 0.030 0.056 0.394 0.195

Total Score

Priorities (Normal)

Pittsburgh Boston Bethesda Santa Fe

0.562 0.512 0.650 0.191

0.294 0.267 0.339 0.100

0.188 1 0.411 0.188

1 0.179 0.521 0.079

0.363 0.056 0.17 0.363

0.306 0.664 1 0.306

0.396 0.906 1 0.120

normalizing the Total Score column by dividing by the sum of the values in it. The selected intensities for each alternative, the ratings, are shown in Table below. The priorities corresponding to the ratings are shown in Table 6.

9 Two Examples of Estimating Market Share The Appendix of Chap. 2 shows all the comparison judgment matrices that go with the application. In Chap. 4 cluster comparisons, unweighted, weighted, and limit supermatrix are illustrated and all the priorities shown. The material in this section shows how well the network approach works in making decisions subject to a single control criterion: market share. Similarly Chap. 2 deals with the prediction of the turn around date of the US economy (a single criterion of economic impacts) in 2001 and Chap. 3 deals with a single financial control concern. It is also in Chap. 4 and nearly all the remaining chapters that we deal with the BOCR merits and their control criteria and with strategic criteria to effect their synthesis into an overall final outcome.

9.1 Airline Example (2005) The first author’s graduate students Nalin Gupta and Uwaifo Aromose did the following study of the market share of four US airlines. Nowhere did they use numerical data, but only their knowledge of the airlines and how good each is

9 Two Examples of Estimating Market Share

21

Fig. 9 Airline model from the ANP super decisions software

Table 7 Actual and Predicted Relative Market Share of Airlines

BA AA UA CA

ANP market share

Actual market share

38.0 20.0 20.9 20.9

37 19 23 21

% % % %

% % % %

relative to the others on the factors mentioned below. Note that in four of the clusters there is an inner dependence loop which indicates that the elements in that cluster depend on each other with respect to market share. Figure 9 shows the model with the clusters and their inner and outer dependence connections. They write: We developed an Analytic Network Process model to find the business class market share of four airlines: British Airways, United Airlines, Continental Airlines and American Airlines. We grouped the criteria into four clusters which included service (leg room, food quality, digital entertainment and seat comfort), advertising (promotional, frequent flier program, frequency and global coverage), other (flight attendants hospitality, rapid rransit, connecting flights interval, reputation and price) and finally the alternatives (British Airways, United Airlines, Continental Airlines and American Airlines).

The results from the ANP model and the actual market share are shown in Table 7.

22

1 The Analytic Network Process

Fig. 10 Wine Model from the ANP super decisions software

Table 8 Wine market share results

Red White Blush a

Actuala

ANP model

40.5 % 40.4 % 19.1 %

43.3 % 37.4 % 19.3 %

www.wineinstitute.org

9.2 Wine Example (2005) Frank Bautti, also a student of the first author, did this example. He says, ‘‘I did my first model, a personal decision model, on types of wine grapes, so I will stick with the same theme and look at the market share of wine in U.S. food stores. There are basically three general categories for wine, red, white, and blush. I will give a prediction, build an ANP decision model to look at the results from it, and then compare those numbers to the 2004 wine market share statistics from the Wine Institute web site at www.wineinstitute.org under the 2004 sales link.’’ The wine market share model is shown in Fig. 10. The relative market share as derived in the ANP model and the actual market share are shown in Table 8.

10

Group Decision Making

23

10 Group Decision Making Here we consider two issues in group decision making. The first is how to aggregate individual judgments, and the second is how to construct a group choice from individual choices. The reciprocal property plays an important role in combining the judgments of several individuals to obtain a judgment for a group. Judgments must be combined so that the reciprocal of the synthesized judgments must be equal to the syntheses of the reciprocals of these judgments. It has been proved that the geometric mean is the unique way to do that. If the individuals are experts, they my not wish to combine their judgments but only their final outcome from a hierarchy. In that case one takes the geometric mean of the final outcomes. If the individuals have different priorities of importance, their judgments (final outcomes) are raised to the power of their priorities and then the geometric mean is formed.

10.1 How to Aggregate Individual Judgments Let the function f ðx1 ; . . .; xn Þ for synthesizing the judgments given by n judges, satisfy the 1. Separability condition (S): f ðx1 ; . . .; xn Þ ¼ gðx1 Þ. . .gðxn Þ, for all x1 ; . . .; xn in an interval P of positive numbers, where g is a function mapping P onto a proper interval J and is a continuous, associative and cancellative operation. [(S) means that the influences of the individual judgments can be separated as above.] 2. Unanimity condition (U): f ðx; . . .; xÞ ¼ x for all x in P. [(U) means that if all individuals give the same judgment x, that judgment should also be the synthesized judgment.] 3. Homogeneity condition (H): f ðux1 ; . . .; uxn Þ ¼ uf ðx1 ; . . .; xn Þwhere u [ 0 and xk ; uxk (k = 1,2,….,n) are all in P. [For ratio judgments (H) means that if all individuals judge a ratio u times as large as another ratio, then the synthesized judgment should also be u times as large.] 4. Power conditions (Pp): f ðxp1 ; . . .; xpn Þ ¼ f p ðx1 ; . . .; xn Þ. [(P2) for example means that if the kth individual judges the length of a side of a square to be xk , the synthesized judgment on the area of that square will be given by the square of the synthesized judgment on the length of its side.] Special case (R = P-1): fð

1 1 ; . . .; Þ ¼ 1=f ðx1 ; . . .; xn Þ: x1 xn

24

1 The Analytic Network Process

[(R) is of particular importance in ratio judgments. It means that the synthesized value of the reciprocal of the individual judgments should be the reciprocal of the synthesized value of the original judgments.] Aczel and Saaty (Saaty 2001a, b) proved the following theorem: Theorem 1 The general separable (S) synthesizing functions satisfying the unanimity (U) and homogeneity (H) conditions are the geometric mean and the rootmean-power. If moreover the reciprocal property (R) is assumed even for a single n-tuple ðx1 ; . . .; xn Þ of the judgments of n individuals, where not all xk are equal, then only the geometric mean satisfies all the above conditions. In any rational consensus, those who know more should, accordingly, influence the consensus more strongly than those who are less knowledgeable. Some people are clearly wiser and more sensible in such matters than others, others may be more powerful and their opinions should be given appropriately greater weight. For such unequal importance of voters not all g’s in (S) are the same function. In place of (S), the weighted separability property (WS) is now: f ðx1 ; . . .; xn Þ ¼ g1 ðx1 Þ. . .gn ðxn Þ [(WS) implies that not all judging individuals have the same weight when the judgments are synthesized and the different influences are reflected in the different functions ðg1 ; . . .; gn Þ.] In this situation, Aczel and Alsina (Saaty 2001a, b) proved the following theorem: Theorem 2 The general weighted-separable (WS) synthesizing functions with the unanimity (U) and homogeneity (H) properties are the weighted geometric mean q q f ðx1 ; x2 ; . . .; xn Þ ¼ x11 x22 . . . xqnn and the weighted root-mean- powers f ðx1 ; x2 ; ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p . . .; xn Þ ¼ c q1 xc1 þ q2 xc2 . . . þ qn xcn , where q1 þ . . . þ qn ¼ 1, qk [ 0; k ¼ 1; . . .; n, c [ 0, but otherwise q1 ; . . .; qn ; c are arbitrary constants. If f also has the reciprocal property (R) and for a single set of entries ðx1 ; . . .; xn Þ of judgments of n individuals, where not all xk are equal, then only the weighted geometric mean applies. We give the following theorem which is an explicit statement of the synthesis problem that follows from the previous results, and applies to the second and third cases of the deterministic approach: ðiÞ

ðiÞ

Theorem 3 If x1 ; . . .; xn i = 1,…, m are rankings of n alternatives by m independent judges and if ai is the importance of judge i developed m fromamhierarchy m P Q ai Q ai for evaluating the judges, and hence ai ¼ 1, then x1 ; . . .; xn are i¼1

i¼1

i¼1

the combined ranks of the alternatives for the m judges.

The power or priority of judge i is simply a replication of the judgment of that judge (as if there are as many other judges as indicated by his/her power ai), which implies multiplying his/her ratio by itself ai times, and the result follows. The first requires knowledge of the functions which the particular alternative performs and how well it compares with a standard or benchmark. The second requires comparison with the other alternatives to determine its importance.

10

Group Decision Making

25

10.2 On the Construction of Group Choice from Individual Choices A social welfare function is an aggregation of individual choice functions. According to Arrow, for a group to agree unanimously on a choice, their preferences must be the same as the preferences of one of the members of the group, the dictator. He assumes that people indicate their preferences by saying ‘‘I like a better than b or b better than a’’ without expressing the intensity or strength of those preferences, for example, ‘‘I like a much more than b.’’ Clearly, what ‘‘much more’’ means needs to be defined. In this context the preferences are ordinal. In an example at the end of the paper we illustrate that group decision making situations often require expressing the intensity of preferences. The social choice process is a two-stage one. In stage 1 the individual pairwise relations are mapped into a social pairwise relation. In stage 2 the social pairwise relation is used to generate a cardinal ranking of the members of X and this ranking is then used to select a particular member of X. Thus, to decide that alternative i is preferred to alternative j we need to derive a cardinal preference relation from the reciprocal pairwise relations. Let A ¼ fAi gni¼1 denote a finite set consisting of at least three alternatives or outcomes, and let M be a set of m individuals whose ordinal preferences (e.g., a preferred to b but not by how much) on A form a weak order. Let F denote the set of mappings from A  A to the set of positive real numbers Rþ . When a pairwise relation P is applied on a set of elements (alternatives), e.g., PðAi ; Aj Þ, it is referred to as a pairwise comparison or judgment in which the (pairwise) dominance of Ai over Aj or Aj over Ai is expressed numerically on an absolute scale. A reciprocal pairwise relation P over A  A is an element of F that satisfies the following conditions: 1. For all Ai 2 A, PðAi ; Ai Þ ¼ 1. 2. For all Ai ; Aj 2 A, i 6¼ j, PðAi ; Aj ÞPðAj ; Ai Þ ¼ 1, i.e., PðAj ; Ai Þ ¼ 1=PðAi ; Aj Þ.

Definition A reciprocal pairwise relation P is said to be consistent if and only if for all i, j and s the relationship PðAi ; Aj ÞPðAj ; As Þ ¼ PðAi ; As Þ holds. Definition The reciprocal pairwise relation P is said to satisfy pairwise preference of alternative Ai over alternative Aj if and only if PðAi ; Aj Þ [ 1. Let P be the set of all reciprocal pairwise preference relations. There are n(n-1)/2 paired comparisons PðAi ; Aj Þ of n elements that define these relations. Denote by Pk the reciprocal pairwise relation associated with the kth member of a group M of m members. A reciprocal pairwise profile is given by the sets of reciprocal pairwise preference relations P ¼ ðP1 ; P2 ; . . .; Pm Þ 2 Pm . In general, two members of the group would have different judgments, i.e., for any two alternatives i and j, Ph ðAi ; Aj Þ 6¼ Pk ðAi ; Aj Þ for h 6¼ k. A procedure for aggregating

26

1 The Analytic Network Process

or synthesizing pairwise preference relations is by definition a mapping f from a subset of the m-fold Cartesian product Pm toP, i.e., f ðPÞ ¼ f ðP1 ; . . .; Pm Þ ¼ P. We denote P|A as the restriction of the reciprocal pairwise profile P to a subset A of A. For reciprocal pairwise profiles not all aggregation procedures are valid. We would like the aggregation procedure to preserve the reciprocal property. Aczel and Saaty (1983) proved that the only aggregation procedure f that satisfies: 1. 2. 3. 4.

separability: f ðx1 ; . . .; xm Þ ¼ gðx1 Þ      gðxm Þ, unanimity: f ðx; . . .; xÞ ¼ x, homogeneity: f ðkx1 ; . . .; kxm Þ ¼ kf ðx1 ; . . .; xm Þ; k [ 0, and the reciprocal property: f ð1=x1 ; . . .; 1=xm Þ ¼ 1=f ðx1 ; . . .; xm Þ, is the geometric mean. The geometric mean is given by

f ðPÞðAi ; Aj Þ ¼

"

m Y

#m1

Pk ðAi ; Aj Þ :

k¼1

We can now introduce Arrow’s conditions for pairwise comparisons. Unrestricted Domain: A pairwise preference aggregation procedure is said to satisfy the condition of unrestricted domain if its domain is all of Pm . Pareto Principle: A pairwise preference aggregation procedure f : Pm ! P satisfies pairwise unanimity if and only if for some pair Ai and Aj of A and any reciprocal pairwise profile P, Pk ðAi ; Aj Þ [ 1 for all k 2 M, implies PðAi ; Aj Þ [ 1, where P ¼ f ðPÞ. Pairwise Cardinal Independence from Irrelevant Alternatives: A pairwise aggregation procedure f is said to satisfy pairwise cardinal independence from irrelevant alternatives (PCIIA) if for any subset A of A with three elements and for any two reciprocal pairwise profiles P and Q such that P|A = Q|A then f(P)|A = f(Q)|A. Not all aggregation procedures satisfy PCIIA. For example, map each individual weak order Rk on A generated by Pk ðAi ; Aj Þ into a utility representation, such that Ai  Aj if and only if uk ðAi Þ [ uk ðAj Þ, and then set uk ¼ uðRk Þ, P uk ðAi Þ

P . This procedure violates PCIIA. PðAi ; Aj Þ ¼ k2M u ðA Þ k

j

k2M

Non-Dictatorship: A pairwise aggregation procedure f is said to be pairwise cardinally non-dictatorial if there is no group member d 2 M such that for all P 2 Pm , f ðPÞ ¼ Pd . Theorem 4 The geometric mean aggregation procedure f : Pm ! P satisfies (a) unrestricted domain, (b) pairwise unanimity, (c) pairwise cardinal independence from irrelevant alternatives and (d) pairwise cardinal non-dictatorship. Thus, the geometric mean gives rise to an aggregate (social) reciprocal pairwise relation that satisfies all four of Arrow’s conditions. Here we assumed that all

10

Group Decision Making

27

members of the group have the same importance. However, when the individuals have different importance, Aczel and Alsina (1986) extended the foregoing Aczel and Saaty (1983) result. Using paired comparisons to represent intensity of preference has not been used very often in social choice. Barrett et al. (1992) used ordinal pairwise fuzzy relations as representations of intensity of preference, and they concluded that under several alternative transitivity conditions the power of the group is restricted to a coalition or the group is indecisive. A transitivity condition they explore is known as quasitransitivity. In terms of our reciprocal pairwise comparisons it would be written as follows: if for all Ai ; Aj ; As 2 A, PðAi ; Aj Þ [ 1 [ PðAj ; Ai Þ and PðAj ; As Þ [ 1 [ PðAs ; Aj Þ then PðAi ; As Þ [ 1 [ PðAs ; Ai Þ. This condition holds if the reciprocal pairwise comparisons are consistent, i.e., PðAi ; Ak Þ ¼ PðAi ; Aj Þ PðAj ; Ak Þ; for all i and j. Consistency implies quasitransitivity , but the converse is not true. To make group decisions it is not enough to only use pairwise comparisons, because the order implied by Ai  Aj if and only if (the geometric mean) e

f ðPÞðAi ; Aj Þ  1 may not be acyclic. That is, the utility representation w generated by f ðPÞðAi ; Aj Þ may be such that Ai  Aj because f ðPÞðAi ; Aj Þ [ 1, but wðAj Þ [ wðAi Þ. Thus, to decide that Ai  Aj , we need to derive a cardinal preference relation from the reciprocal pairwise relations.

10.3 Cardinal Preference Relations To define cardinal preference relations we need to introduce the concept of a scale. A scale is a triple ðA; R; wÞ where A is a set of objects, R is a set of numbers and w is a mapping from the objects to the numbers, w : A ! R, that must be invariant under transformation (Krantz et al. 1971; Roberts 1979). The type of transformation defines the type of scale. Ordinal, interval, ratio and absolute scales are invariant under monotone, affine (positive linear), similarity (multiplication by a positive constant) and identity transformations, respectively. There are many other scales of which a well-known one, that is too weak to be useful in this study, is the nominal scale that is invariant under one-to-one correspondence. Let C denote the set of all possible functions from A to the set of real numbers R; C ¼ fwjw : A ! Rg. In the economics literature a cardinal preference relation over A is a subset W of C of utility functions such that if f belongs to W then so does a þ bf for every real number a and every positive real number b, and if f and g both belong to W there is some real number a and some positive real number b such that g ¼ a þ bf . This definition can be easily extended to a set of transformations T such that if f belongs to W then so does /ðf Þ for every / in T, and for any two members f and g of W there is some / in T such that g ¼ /ðf Þ. / is called an invariance transformation that defines the kind of scale used.

28

1 The Analytic Network Process

If / is any monotone transformation the scale is ordinal. Goodman and Markowitz (1952) assumed that preferences are expressed by means of a value function invariant under monotone transformations. They showed that if / is also linear, then no social welfare function is possible. However, if / is a positive similarity transformation then the only possible social welfare function is the product of the welfare functions of the individuals. If / is an affine transformation (i.e., a similarity transformation followed by a translation) then interval scales are used. Samuelson (1967) conjectured that Arrow’s impossibility theorem should hold when individuals and the group express their ‘‘cardinal’’ preferences by the von-Neumann-Morgenstern (v-NM) utility functions known to belong to an interval scale. Campbell (1973) made a convincing case for the possibility of using intensity of preference in the formulation of the impossibility theorem, but he did not specify the type of function to be used. Kalai and Schmeidler (1977) proved Samuelson’s conjecture: If the set of alternatives contains 4 or more elements, then an aggregation procedure is continuous, satisfies cardinal independence from irrelevant alternatives and also satisfies unanimity if and only if it is cardinally dictatorial. Later Hylland (1980) proved that the continuity condition is not necessary. If / is a similarity transformation then the scales involved are ratio scales. By assuming that individual utility functions belong to the same ratio scale, a restriction known as ratio scale full comparability (RSFC), Roberts (1980) showed that if a social welfare function satisfies the conditions of unrestricted domain, independence from irrelevant alternatives, the weak Pareto condition of strict preference, and invariance under positive similarity transformations, then there exists a social welfare function that preserves positive proportionality known as homothetic (i.e., f ðxÞ  f ðyÞ , f ðkxÞ  f ðkyÞ for all k [ 0) that is not dictatorial. The main theme emerging from these works is that in order for a non-dictatorial social function to exist, it must at least be invariant under similarity transformations, i.e., belong to a ratio scale. In the traditional social choice literature (Kalai and Schmeidler 1977; Keeney 1976) a procedure for aggregating cardinal preferences is by definition a function u from an m-fold Cartesian product of C to C, i.e., u : Cm ! C, a social welfare function. A cardinal profile is given by W ¼ ðW1 ; . . .; Wm Þ 2 Cm . For a nonempty subset A of A and W in C, W|A denotes the cardinal preferences induced by W in A. Arrow’s conditions can now be stated as follows. Unrestricted Domain: An aggregation procedure u is said to satisfy the condition of unrestricted domain if its domain is all of Cm . Pareto Principle: An aggregation procedure u : Cm ! C satisfies unanimity if and only if for any pair Ai and Aj of A and any cardinal profile W ¼ ðW1 ; . . .; Wm Þ 2 Cm , if Wk ðAi Þ  Wk ðAj Þ for all k 2 M then WðAi Þ  WðAj Þ, where W  uðW Þ: Note: Wk ðAi Þ  Wk ðAj Þ if and only if wk ðAi Þ  wk ðAj Þ for all wk 2 Wk . Independence from Irrelevant Alternatives: An aggregation procedure is said to satisfy cardinal independence from irrelevant alternatives (CIIA) if for any

10

Group Decision Making

29

subset A of A with three elements, and for any two cardinal profiles W and V: W|A = V|A implies uðW ÞjA ¼ uðV ÞjA : Non-Dictatorship: An aggregation procedure u is cardinally non-dictatorial if there does not exist a member of the group, d 2 M, such that for all the cardinal profiles W 2 Cm , uðW Þ ¼ Wd , i.e., u is the projection of W on the dth coordinate. We are interested in a very specific type of cardinal preference relations, absolute cardinal preference relations, because the unidimensional scale derived from the pairwise comparisons (i.e., the principal right eigenvector) is an absolute ratio scale, i.e., a ratio scale with 1 as multiplier.

10.4 Absolute Cardinal Preference Relations In this section we show that if the cardinal preferences of the individuals were to be represented by numbers from an absolute scale, and instead of just one comparison, several are considered, and each comparison by many individuals is aggregated by using the geometric mean from which then a group function is derived, then that function satisfies Arrow’s conditions, both when the judgments of each individual are consistent and when they are not consistent. We have seen in Sect. 3 that a cardinal preference relation is associated with some type of invariance transformation that defines the scale in which the intensity of preference is measured. If the invariance transformation is the identity, then the intensity of preference is measured on an absolute scale. Let W denote the set of all absolute cardinal preference relations over A. An absolute cardinal preference relation W over A is a subset of W such that: 1. W is nonempty; and 2. If w; v 2 Wthen for all Ai 2 A, vðAi Þ  wðAi Þ, i.e., W contains one element. Traditionally, the social choice literature has studied the aggregation of these individual cardinal preference functions, i.e., a social welfare function is a mapping from W m to W. We instead study the aggregation of judgments from which an Arrowvian social welfare function can be derived. Thus, we establish a mapping from the set of reciprocal pairwise profiles Pm to the set of absolute cardinal preference relations W through the set of reciprocal pairwise relations P, i.e., Pm ! P ! W. We distinguish between two cases, consistent and inconsistent reciprocal pairwise relations. Let PC and PI denote the sets of consistent and inconsistent reciprocal pairwise relations, respectively. Reciprocal pairwise relations can be represented using matrix notation. Let

30

1 The Analytic Network Process

2 x1

x1 x2 x2 x2

xn x1

xn x2

x1 6 xx21 6

A¼6. 4 ..

.. .

  .. . 

x1 xn x2 xn

3

7 7 .. 7 .5

xn xn

be a consistent pairwise relation. The entries of the matrix A satisfy the properties: aij ajk ¼ aik and aij aji ¼ 1 or aji ¼ a1 ij . The former is known as the consistency property (Saaty 1977) and the latter as the reciprocal property. Conversely, if the matrix A is consistent, then its coefficients have the form aij  xxij . Thus, by multiplying the matrix A of pairwise comparisons by the vector of measurements x ¼ ðx1 ; x2 ; . . .; xn ÞT we have Ax ¼ nx. Since Trace(A) = n, the Trace(A) is equal to the sum of the eigenvalues of A, and the rank(A) = 1, it follows that n is the only non-zero eigenvalue of A, and the vector x is its associated (principal) right eigenvector. Therefore, to recover the measurements from the matrix when it is consistent it is sufficient (but not necessary) to solve an eigenvalue problem. In this simple case, the principal right eigenvector is any column of A because an eigenvector is unique to within a multiplicative constant. We next show that it is both necessary and sufficient when the matrix is not consistent (inconsistent). If the vector of measurements x is unknown then the relative paired comparisons would have to be estimated. That is, when the exact value aij  xxij is not

 known, we obtain an approximation to it made by judgment as ^aij ¼ xxij eij . In that

 x case ^ aji ¼ xji eji where the eij ’s are perturbations that satisfy eij eji ¼ 1. A perturbation theorem (Saaty 1977) in matrix algebra assures us that to obtain an estimate ^ x of the vector x it is sufficient to solve the principal eigenvalue problem ^ x ¼ kmax ^ ^ is the n-by-n matrix of judgments ^aij (perturbations of the A^ x, where A aij ¼ xi =xj ) and kmax is its principal eigenvalue. It turns out that the principal eigenvector is also necessary because comparisons involve the concept of dominance which says how much one object is preferred over another. Transitivity requires considering paths of different lengths between the two objects and calculating the intensity of dominance along its arcs. Each of these lengths is given by the corresponding power of A. When A is consistent, Ak ¼ nk1 A, and thus, all order transitivity is obtained as a constant times A. That is not the case when A is inconsistent (i.e., reciprocal but not consistent). In that case one must consider all powers of A obtaining the vector of dominance from the normalized sum of its rows for each power of A. The average of these vectors in the limit coincides with the principal right eigenvector of A (Saaty 2001a, b). The absolute cardinal preference relation associated with a pairwise preference relation is the principal right eigenvector of the matrix of pairwise comparison judgments. Suppose that the purpose of collective choice is the selection of one of the objects from among the n objects according to a criterion. For example, the objects could be alternative health care policies, and the criterion could be the estimated

10

Group Decision Making

31

Reciprocal Pairwise Profiles P = ( P1 ,..., Pm ) ∈ ↓

Absolute Cardinal Profiles ω1 ⎯⎯→ ⎯⎯ σ σ P⎯⎯ →→ W

m

fP

W = (W1 ,..., Wm ) ∈ W m ↓ fW

ω2

P = {P ( Ai , A j )}∈

w∈W

⎯⎯→

Reciprocal Pairwise Relations

Fig. 11 Mapping of priority rP ¼ x2  fP and rW ¼ fW  x1

and

Absolute Cardinal Preference Relations

judgment

↓

P = {P ( Ai , Aj )} ∈ Reciprocal Pairwise Relations

social

welfare

functions

W = (W1 ,..., Wm ) ∈ W m

m

fP

The

Absolute Cardinal Profiles

Reciprocal Pairwise Profiles P = ( P1 ,..., Pm ) ∈

spaces.

⎯⎯

σP

→

ω2 ⎯⎯→

w∈W Absolute Cardinal Preference Relations

Fig. 12 The social welfare mappingrP ¼ x2  fP

cost of implementing each of them. Each individual k in the group would provide a matrix of pairwise comparisons Ak and the objective is to combine them to produce a single pairwise comparison matrix that would represent the preferences of the group. From this matrix we derive a relative scale of priorities as its principal right eigenvector. This scale is the social welfare function. We can now approach the problem of constructing a social welfare function as depicted in the diagram given in Fig. 11. rP ¼ x2  fP is the synthesis of fP that first maps reciprocal pairwise profiles P to a reciprocal pairwise relation P, and x2 that maps a reciprocal pairwise relation P to a final cardinal preference relation w measured on an absolute scale. The traditional approach would be similar to the mapping rW ¼ fW  x1 that first maps each individual reciprocal pairwise relation Pk to its individual absolute cardinal preference relation Wk and then maps all the individual cardinal relations to a cardinal preference relation w which in our case would be measured on an absolute scale. The two mappings rP and rW yield the same result when the number of alternatives n is equal to three, or when they are restricted to consistent pairwise profiles, but for n  4 they may not coincide. The social welfare function is given by the principal right eigenvector of the matrix associated with the mapping rP ¼ x2  fP (Fig. 12). (Note here that in Fig. 12 we have intentionally left out the arrows between Pm and W m and between W m and W because there are no mappings.) Formally, this can be summarized as follows. Let fP be the geometric mean aggregation procedure from Pm to P, i.e., fP ðPÞ ¼ P. Let x2 be a mapping from P to W that assigns to each P in P the principal right eigenvector w of the corresponding matrix aij  PðAi ; Aj Þ , i.e. x2 ðPÞ  w. Let rP be the aggregation

32

1 The Analytic Network Process

procedure from Pm to W. rP assigns reciprocal pairwise profiles P to absolute cardinal relations w, i.e., rP ðPÞ ¼ ðx2  fP ÞðPÞ ¼ x2 ðfP ðPÞÞ ¼ x2 ðPÞ ¼ w. We define Arrow’s conditions for this mixed aggregation procedure as follows: Unrestricted Domain: An aggregation procedure rP is said to satisfy the condition of unrestricted domain if its domain is all of Pm . Pareto Principle: An aggregation procedure rP : Pm ! W satisfies unanimity if and only if for any pair Ai and Aj of A and any reciprocal pairwise profile P, Pk ðAi ; Aj Þ  1 for all k 2 M implies wðAi Þ  wðAj Þ, where w ¼ rP ðPÞ. Independence from Irrelevant Alternatives: An aggregation procedure rP is said to satisfy cardinal independence from irrelevant alternatives (CIIA) if for any subset A of A with three elements and for any two reciprocal pairwise profiles P and Q: P|A = Q|A implies w|A = v|A, where w ¼ rP ðPÞ and v ¼ rP ðQÞ. Non-Dictatorship: A pairwise aggregation procedure rP is said to be cardinally non-dictatorial if there is no group member d 2 M such that for allP 2 Pm , rP ðPÞ ¼ wd . We now show that this composite aggregation procedure rP ¼ x2  fP in fact satisfies Arrow’s conditions. We distinguish two mutually exclusive situations: m m m consistent (Pm C ) and inconsistent (P= ) pairwise profiles, i.e., P ¼ PC [ P= . 10.4.1 Consistent Profiles Theorem 5 The aggregation procedure rP : Pm C ! W defined on consistent pairwise profiles (Pm ) satisfies unanimity, cardinal independence from irrelevant C alternatives and it is non-dictatorial. rP defined on consistent profiles has the multiplicative form given by m T m Q Q 1=m 1=m wnk w1k ; . . .; . The social welfare functions developed by rW ðPÞ ¼ k¼1

k¼1

DeMeyer and Plott (1971) and Kaneko and Nakamura (1979) also have a multiplicative form. DeMeyer that for pairwise intensity of prefer and Plott showed  xk

ences given by ratios xik ; k ¼ 1; . . .; m , rather than perturbations of ratios of the j    k x k k i form ^ aij ¼ xk eij ; k ¼ 1; . . .; m as we assumed above, invariant under simij

larity transformations (i.e., multiplication by a positive constant), there exists a m Q ðxki ÞK , where K is a real non-dictatorial social welfare function of the form k¼1

number. DeMeyer and Plott’s social welfare function is an extension of Nash’s solution of the bargaining problem in which the welfare of a group is maximized by considering the payoffs resulting from the product of individual utilities (Nash 1950).

10

Group Decision Making

33

10.4.2 Inconsistent Profiles When rP is defined on inconsistent reciprocal pairwise profiles, unanimity and cardinal independence from irrelevant alternatives do not always hold. With consistency, if Pk ðAi ; Aj Þ  1 for all k, then wðAi Þ  wðAj Þ. However, with inconsistency unanimity may not be satisfied and we need to define conditions under which this also holds. One such condition is pairwise dominance. Pairwise Dominance: A pairwise relation Pk is said to satisfy pairwise dominance if for all pairs of alternatives i and j, the following condition holds: Pk ðAi ; Al Þ  Pk ðAj ; Al Þ, for all l or Pk ðAj ; Al Þ  Pk ðAi ; Al Þ, for all l. Pairwise dominance implies that given any

two rows of the matrix associated with the pairwise relation aijk  Pk ðAi ; Aj Þ , one row always dominates the other, i.e., ailk  ajlk , for all l, or ajlk  ailk , for all l. Pairwise dominance implies transitivity, for then if row i dominates row j and row j dominates row k, then row i dominates row k. Let Pk be a reciprocal pairwise relation that satisfies pairwise dominance. Let wk ¼ x2 ðPk Þ be the corresponding absolute cardinal relation. By construction, if for a pair of alternatives i and j, we have Pk ðAi ; Al Þ  Pk ðAj ; Al Þ for all l then the corresponding cardinal relation satisfies wk ðAi Þ  wk ðAj Þ. A reciprocal pairwise profile satisfies pairwise dominance if all its reciprocal pairwise relations satisfy pairwise dominance. This means that if alternative i is preferred to alternative j then alternative i is preferred to the other alternatives more than alternative j is preferred to them. Using this condition the Pareto principle can now be modified as follows. Pareto Principle with Pairwise Dominance: An aggregation procedure cP : Pm ! P satisfies strong unanimity if and only if for any pair Ai and Aj of A and any reciprocal pairwise profile P; Pk ðAi ; Al Þ  Pk ðAj ; Al Þ for all l and all k 2 M, implies PðAi ; Al Þ  PðAj ; Al Þ for all l, where cP ðPÞ ¼ P 2 P. Note that for pairwise profiles, strong unanimity implies unanimity. To see this, we substitute l = j in Pk ðAi ; Al Þ  Pk ðAj ; Al Þ, we have Pk ðAi ; Aj Þ  Pk ðAj ; Aj Þ ¼ 1 for all k, and PðAi ; Aj Þ  PðAj ; Aj Þ ¼ 1 follows. Let PD P be the set of reciprocal pairwise relations that satisfy pairwise m m dominance. Let rP jD : Pm = ! W be the restriction of rP to PD P= . Theorem 6 The geometric mean aggregation procedure cP restricted to Pm D Pm satisfies strong unanimity. = Theorem 7 The aggregation procedure rP jD : Pm = ! W satisfies unanimity, cardinal independence from irrelevant alternatives and it is non-dictatorial. Note that although the aggregation procedure is defined on the set of reciprocal pairwise relations that satisfy pairwise dominance, the condition of unrestricted domain is not violated. Consider three individuals and three alternatives, Ai ; i ¼ 1; 2; 3, whereby the first person has the ordering A1  A2  A3 ; the second

34

1 The Analytic Network Process

person the ordering A2  A3  A1 ; and the third person the ordering A3  A 1  A2 . We show below that the ordering A3  A2  A1 is possible.

Let aijk ; i; j; k ¼ 1; 2; 3 be their reciprocal pairwise preferences. To conform with these three different orderings along with pairwise dominance, these preferences must satisfy the following conditions:  A2  A3 implies that the entries of the matrix 0 Person 1: A1 1 1 a121 a131 1 @ a1 1 a231 A must satisfy a121 [ 1; a131 [ a231 , a1 and 121 121 [ a131 1 1 a131 a231 1 a231 [ 1, i.e., pairwise dominance.  A3  A1 implies that the entries of the matrix 0 Person 2: A2 1 1 a122 a132 1 1 @ a1 1 a232 A must satisfy a1 122 122 [ a132 ; a232 [ 1, a232 [ a122 and a132 \1. 1 1 a132 a232 1 Person 3: A3 1  A1  A2 implies that the entries of the matrix 0 1 a123 a133 @ a1 1 a233 A must satisfy a133 \1; a1 123 233 [ a123 , a133 [ a233 and a123 [ 1 . 1 1 a133 a233 1 The social reciprocal pairwise relation is given by the matrix of geometric means 1 0 3 3 Q Q 3 3 1 a a 12k 13k C B C B k¼1 k¼1 C BQ 3 3 Q C B a3 a312k 1 B 23k C C B k¼1 k¼1 C B 3 3 A @Q 3 Q a13k a323k 1 k¼1

k¼1

It is also known (Saaty 1980) that the principal right eigenvector of a 3-by-3 reciprocal matrix is given by the geometric mean of its rows. This is not true for higher-order matrices. The ordering A1 A2 A3 would be induced if the prin T cipal right eigenvector of the matrix of geometric means is the vector 13 ; 13 ; 13 .  3 3  3 3 3 3 Q 3 Q Q 3 Q 3 Thus, we must have a12k ¼ K, a3 a ¼ K and a 13k 12k 23k k¼1 k¼1 k¼1 k¼1  3 3 3 Q 3 Q ¼ K which upon normalization to unity would yield the a323k a13k k¼1 k¼1  3 3 3 1 1 1T Q 3 Q 3 vector a . Note that K = 1 because a ; ; 12k 23k 3 3 3 k¼1 k¼1  3   3 3 3 3 3 3 3 3 Q Q Q Q Q 3 Q 3 3 3 3 2 3 a23k a13k a23k a12k ¼K and a23k a13k k¼1 k¼1 k¼1 k¼1 k¼1 k¼1  3 3 3 Q 3 Q ¼ 1=K, and hence, we have K 2 ¼ 1=K or K 3 ¼ 1. Since a313k ¼ a12k k¼1

k¼1

10

Group Decision Making

K [ 0, we have K = 1 that yields

35 3 Q

k¼1

a3 12k ¼

3 Q

k¼1

a313k ¼

3 Q

k¼1

a3 23k ¼ a, a positive

constant. In sum, 1 the social pairwise preference relation is given by the matrix 0 1 a a1 @ a1 1 a A. This shows that the existence of such a social reciprocal 1 a a 1 pairwise relation and the ensuing absolute cardinal relation is not restricted by pairwise dominance. Of course, what is considered a three way tie in an ordinal setting need not be when cardinal intensity of preference is considered. For example, if the three people had the reciprocal pairwise relations given by Person 1 :

A1  A2  A3 A2  A3  A1 A3  A1  A2 1 0 1 1 0 1 1=6 1=5 1 2 4 1 5 1=2 C B C B 1 3 A ; Person 3 : B 1 3 A ; Person 2 : @ 6 @ 1=2 C B 1=5 1 1=6 C A @ 5 1=5 1 1=6 1=2 1 2 6 1 0

the social reciprocal pairwise relation would be given by 1 0 3 3 Q Q 0

1=3 3 3 a12k a13k C 10= B 1 1 C B B 6 k¼1 k¼1 C B

BQ 1=3 3 Q B 3 3 3 C B a 1 a23k C ¼ B 10=6 B 1 C @ B k¼1 12k k¼1

1=3 1=3 C B 3 3 A @Q 3 Q 4= 9= 10 6 1 a323k a13k k¼1

k¼1

1=3 1 4= 10

1=3 C C C 9= C 6 A 1



And the corresponding social absolute cardinal relation represented by the principal right eigenvector would be given by the vector ð0:3184; 0:3291; 0:3525ÞT which yields the ordering A3  A2  A1 , which is not an ordering of any of the group members.

10.4.3 Example To illustrate our approach we have selected the House Appropriations Subcommittee on Defense of the United States House of Representatives. The subcommittee not just ranked the different objectives, the troops’ well-being, weapon systems and fiscal responsibility, but made tradeoffs among them to produce the set of allocations given in the Fiscal Year 2009 Defense Appropriations Bill. Thus, to make the type of tradeoffs the Appropriations Subcommittee made we need to express preferences with a degree of intensity, e.g., ‘‘the troops’ well-being is moderately more important than weapons systems.’’ This type of comparison is known as a cardinal pairwise comparison or judgment. Let us assume that the Appropriations Subcommittee consists of five people and that they wish to distribute an additional budget amount of $99 billion among three ‘‘key investments’’ as they call them in (Juola 2008): Keeping our commitments to our troops and their families (Troops’ Well-Being), weapons programs (‘‘Weapons

36

1 The Analytic Network Process

Table 9 Individual judgments and geometric mean Goal[2]: ‘‘Strengthen our arm forces and the security of our great nation’’ Troops’ well-being Weapons systems Fiscal responsibility

Troops’ well-being

Weapons systems

Fiscal responsibility

1 (1/2,1/3,1/2,1/2,1/2) (1/5,1/5,1/2,1/4,1/4)

(2,3,2,2,2) 1 (1/2,1/3,1/3,1/3,1)

(5,5,2,4,4) (2,3,3,3,1) 1

Geometric mean

Troops’ well-being

Weapons systems

Fiscal responsibility

Priorities

Troops’ well-being Weapons systems Fiscal responsibility

1 1/2.1689 1/3.087

2.1689 1 1/2.2206

3.8073 2.2206 1

0.5742 0.2863 0.1395

Systems’’) and improving fiscal responsibility (‘‘Fiscal Responsibility’’). Each member of the subcommittee compares the three investments in pairs. In this case there are three pairs. For each pair, each member gives a judgment as to which investment is more important, and how much more important, in his/her opinion, to reach the goals mentioned above. For example, to attain the objectives, what is more important ‘‘Troops’ Well-Being’’ or ‘‘Weapons Systems’’ and how much more important? Judgments are translated into numerical values using the 1–9 scale. Using the summary of the 2009 appropriations subcommittee, in which they wrote (Juola 2008): The Defense Appropriations bill puts troops first, preparing them for whatever emergencies may arise, providing them with first class weapons and equipment, and ensuring that they and their families are well taken care of. The bill makes critical investments into the health, well-being and readiness of our forces. These recommendations address issues raised by troops, their families and Department of Defense officials in testimony before the Congress, and discovered through visits to military bases across the United States and overseas. At the same time, the bill realizes its obligation to meet the recent dependence on the use of contractors with increased support for their management and oversight. It likewise makes a commitment to fiscal responsibility.

we translated these writings (for illustrative purposes only) into judgments as given in Table 9. A pairwise comparison, for example, ‘‘Troops’ Well-Being’’ versus ‘‘Weapons Systems’’, for an individual consists in identifying the ‘‘key investment’’ he prefers less, say ‘‘Weapons Systems’’, and estimating numerically how many times more important the more preferred investment (‘‘Troops’ WellBeing’’) is than the less preferred one (‘‘Weapons Systems’’) using the scale in Fig. 3 (Saaty 1977). Assume that the five committee members provided the judgments (2, 3, 2, 2, 2), respectively. The less preferred investment is then assigned the reciprocal value when compared with the more preferred one (i.e., 1/ 2, 1/3, 1/2, 1/2, 1/2). The comparisons are arranged in a three by three matrix as given in Table 9, matrix 1. The individual judgments or pairwise comparisons are then synthesized by taking their geometric mean (Aczel and Saaty 1983) (see Table 9, matrix 2), and

10

Group Decision Making

37

Table 10 Group priorities

Funding Priorities Troops’ well-being Weapons systems Fiscal responsibility

Committee

Estimated

57.14 % 28.57 % 14.29 %

57.42 % 28.63 % 13.95 %

finally, a set of priorities is derived using the eigenvalue model (Saaty 1977) explained above. If all the decision makers agree on a numerical pairwise estimate, i.e., consensus is reached and there is no need for the geometric mean synthesis which of course if used, gives back the common value of the decision makers. Table 10 gives the committee’s and estimated relative funding priorities resulting from this exercise. The priorities derived induce a ranking on the alternatives that are compared. Most collective choice problems have multiple criteria. Thus, in addition to having to aggregate judgments under each criterion, we also need to aggregate social choice functions across criteria. The theory that pulls all this together, on which the concepts of this paper are based, is the Analytic Hierarchy Process (AHP) (Saaty 1977, 1980). It has been applied in a wide variety of settings (Saaty 2001a, b; Saaty and Vargas 2006).

Appendix Proof of Theorem 5: 1. The condition of unrestricted domain is automatically satisfied because the aggregation procedure is defined on all pairwise reciprocal profiles without restriction. 2. Given P 2 Pm such that for any pair Ai and Aj of A, Pk ðAi ; Aj Þ [ 1 for all k 2 M, then by definition, f ðPÞðAi ; Aj Þ ¼

"

m Y k¼1

#m1

Pk ðAi ; Aj Þ

[1

and f satisfies pairwise unanimity. 3. Let P and Q be two reciprocal pairwise profiles. Let aijk  Pk ðAi ; Aj Þ and bijk  Qk ðAi ; Aj Þ. Let A ¼ fAi ; Aj ; Al g A. If P|A = Q|A, then aijk ¼ bijk , ailk ¼ bilk and ajlk ¼ bjlk , for all k, and f(P)|A = f(Q)|A follows. 4. In general, the geometric mean of a set of (positive) numbers is not equal to any one of these numbers, and hence, it is non-dictatorial.

38

1 The Analytic Network Process

 Proof of Theorem 6: Let P ¼ Pk ðAi ; Aj Þ  wwikjk ; k ¼ 1; 2; . . .; m be a consistent pairwise profile. We have

0

m Q

1=m

B k¼1 rP ðPÞ ¼ ðx2  fP ÞðPÞ ¼ x2 ðPÞ ¼ x2 B m @PðAi ; Aj Þ ¼ Q ¼

m Y

1

C C A 1=m wjk . k¼1 !

1=m

wik ; i ¼ 1; . . .; n

k¼1

Also,

wik

¼ w:

rW ðPÞ ¼ ðfW  x1 ÞðPÞ ¼ fW ðx1 ðP1 Þ; . . .; x1 ðPm ÞÞ ¼ fW ðw1 ; . . .; wm Þ

where x1 ðPk Þ ¼ wk ¼ ðw1k ; . . .; wnk ÞT and we have rW ðPÞ ¼ m T m Q Q 1=m 1=m wnk w1k ; . . .; ¼ w and hence, rP ¼ rW on consistent pairwise profiles. k¼1

k¼1

In addition, because we have shown that the geometric mean satisfies Arrow’s conditions, it follows that rP ¼ rW also satisfies these conditions.

m Proof of Theorem 7: Let P ¼ ðP1 ; . . .; Pm Þ 2 Pm D P be a reciprocal pairwise profile that satisfies pairwise dominance. Then, for any pair of alternatives i and j,Pk ðAi ; Al Þ  Pk ðAj ; Al Þ, for all l and k, we have

fP ðPÞðAi ; Al Þ ¼

"

m Y

Pk ðAi ; Al Þ

k¼1

#m1



" m Y

#m1

Pk ðAj ; Al Þ ¼ fP ðPÞðAj ; Al Þ

k¼1

or PðAi ; Al Þ  PðAj ; Al Þ for all l and the geometric mean satisfies strong unanimity. Proof of Theorem 8: Let P ¼ ðP1 ; . . .; Pm Þ be a reciprocal cardinal profile. From Theorem 2, cP satisfies strong unanimity, i.e., for every pair of alternatives (i,j), fP ðPÞðAi ; Al Þ  fP ðPÞðAj ; Al Þ for all l, or ail ¼ PðAi ; Al Þ  PðAj ; Al Þ ¼ ajl for all l, n n P P and hence, by construction ajl wðAl Þ or wðAi Þ  wðAj Þ and rP jD ail wðAl Þ  l¼1

l¼1

satisfies unanimity. Let P and Q be two reciprocal pairwise profiles and let w and v the corresponding absolute cardinal relations, respectively. If for any subset A of A with three elements P|A = Q|A is true, then by Theorem 1 the geometric mean aggregation procedure satisfies pairwise independence from irrelevant alternatives and hence fP ðPÞjA ¼ fP ðQÞjA . Let fP ðPÞ ¼ P and fP ðQÞ ¼ Q, and let w ¼ x2 ðPÞ and v ¼ x2 ðQÞ. We have rP jD ðPÞjA ¼ ðx2  fP ÞðPÞjA ¼ x2 ðfP ðPÞjA Þ and thus wjA ¼ vjA . ð ¼ x2 ðfP ðQÞjA Þ ¼ ðx2  fP ÞðQÞjA ¼ rP jD ðQÞjA

10

Group Decision Making

39

m Let P ¼ ðP1 ; . . .; Pm Þ 2 Pm D and w ¼ rP ðPÞ 2 W. rP jD : P ! W is dictatorial if there is a member d of the group for which rP ðPÞ ¼ wd . For this to happen, the following must hold: rP ðPÞ ¼ x2 ðfP ðPÞÞ ¼ x2 ðPd Þ and wðAi Þ ¼ wd ðAi Þ for all i. But by Theorem 1, the geometric mean aggregation procedure fP is non-dictatorial, i.e.,fP ðPÞ 6¼ Pd , from which we have rP ðPÞ ¼ x2 ðfP ðPÞÞ 6¼ x2 ðPd Þ and hence, rP jD : Pm ! W is non-dictatorial.

References Aczel, J. and C. Alsina (1986). ‘‘On Synthesis of Judgments.’’ Socio-Economic Planning Sciences 20: 333–339. Aczel, J. and T. L. Saaty (1983). ‘‘Procedures for Synthesizing Ratio Judgments.’’ Journal of Mathematical Psychology 27: 93–102. Barrett, C. R., P. K. Pattanaik and M. Salles (1992). ‘‘Rationality and Aggregation of Preferences in an Ordinally Fuzzy Framework.’’ Fuzzy Sets and Systems 49: 9–13. Campbell, D. E. (1973). ‘‘Social Choice and Intensity of Preference.’’ Journal of Political Economy 81(1): 211–218. DeMeyer, F. and C. R. Plott (1971). ‘‘A Welfare Function Using ‘‘Relative Intensity’’ of Preference.’’ Quarterly Journal of Economics 85(1): 179–186. Goodman, L. A. and H. Markowitz (1952). ‘‘Social Welfare Functions Based on Individual Rankings.’’ American Journal of Sociology 58(3): 257–262. Hylland, A. (1980). ‘‘Aggregation procedure for cardinal preferences: A comment.’’ Econometrica 48(2): 539–542. Juola, P. (2008). Summary: FY09 Defense Appropriations Bill, U.S. House of Representatives: Committee on Appropriations. Kalai, E. and D. Schmeidler (1977). ‘‘Aggregation Procedure for Cardinal Preferences: A Formulation and Proof of Samuelson’s Impossibility Conjecture.’’ Econometrica 45(6): 1431–1438. Kaneko, M. and K. Nakamura (1979). ‘‘The Nash Social Welfare Function.’’ Econometrica 47(2): 423–436. Keeney, R. L. (1976). ‘‘A Group Preference Axiomatization with Cardinal Utility.’’ Management Science 23(2): 140–145. Krantz, D. H., R. D. Luce, P. Suppes and A. Tversky (1971). Foundations of Measurement Vol. I. New York, Academic Press. Nash, J. (1950). ‘‘The Bargaining Problem.’’ Econometrica 18: 155–162. Roberts, F. S. (1979). Measurement Theory with Applications to Decisionmaking, Utility and the Social Sciences. Encyclopedia of Mathematics and Its Applications, G.-C. Rota. Reading, MA, Addison-Wesley Publishing Company. Roberts, K. W. S. (1980). ‘‘Interpersonal Comparability and Social Choice Theory.’’ The Review of Economic Studies 27(2): 421–439. Saaty, T. L. (1977). ‘‘A Scaling Method for Priorities in Hierarchical Structures.’’ Journal of Mathematical Psychology 15: 234–281. Saaty, T. L. (1980). The Analytic Hierarchy Process. New York, McGraw Hill. Saaty, T. L. (2000). Fundamentals of Decision Making with the Analytic Hierarchy Process. Pittsburgh, PA, RWS Publications. Saaty, T. L. (2001). The Analytic Network Process. Pittsburgh, PA, RWS Publications. Saaty, T.L., Theory and Applications of the Analytic Network Process, 4922 Ellsworth Avenue, Pittsburgh, PA 15213, 2005.

40

1 The Analytic Network Process

Saaty, T.L., The Analytic Network Process (2nd version), 4922 Ellsworth Avenue, Pittsburgh, PA 15213, 2001. The first version appeared in 1996. Saaty, T.L., and M.S. Ozdemir, The Encyclicon, RWS Publications, 4922 Ellsworth Avenue, Pittsburgh, PA 15213, 2005. Saaty, T.L., and L. G. Vargas, Prediction, Projection and Forecasting, Kluwer Academic, Boston, 1991. Saaty, T.L., and J. Alexander, Conflict Resolution: The Analytic Hierarchy Process, Praeger, New York, 1989. Saaty, T.L., and K. Kearns, Analytical Planning; The Organization of Systems, Pergamon Press, Oxford, 1985. Translated to Russian. Paperback edition, RWS Publications, Pittsburgh, 1991. Saaty, T. L. and L. G. Vargas (2006). Decision Making with the Analytic Network Process. International Series in Operations Research and Management Science, F. E. Hillier, Springer. Samuelson, P. (1967). Arrow’s Mathematical Politics. Human Values and Economic Policy. S. Hook. New York, New Your University Press: 41–51. SuperDecisions: www.superdecisions.com/*saaty and download the SuperDecisions software. The installation file is the.exe file in the software folder. The serial number is located in the.doc file that is in the same folder. Zandi, I. (1975), The Technological Catch and Society, CUE, Chapter 1, 1975.

Chapter 2

Forecasting the Resurgence of the U. S. Economy in 2001: An Expert Judgment Approach

1 Introduction Building on work done earlier (Blair et al. 2001, 2002) this chapter illustrates our use of the Analytic Hierarchy/Network Process (Saaty 2005, 2006) to produce a December 2008 forecast of when the U.S. economy would begin to recover from the contraction that, according to an announcement dated December 1, 2008, from the Business Cycle Dating Committee of the National Bureau of Economic Research (NBER), began during the month of December, 2007 (NBER 2008). Here we illustrate two approaches. The first approach uses a holarchy (i.e., a hierarchy with an arc connecting the level of alternatives and the criteria level, thus creating a loop between the last level and the first level of the hierarchy), and the second one uses a traditional ANP model. Our earlier forecast of the economic recovery, produced in the year 2001 (Blair et al. 2002), was confirmed by the NBER in July 2003 (Hilsenrath 2003). As previously, we employed a conceptual framework grounded in modern macroeconomics and produced forecasts that relied upon expert judgment, without assistance from a conventional macroeconomic forecasting model.

2 On the Role of Judgment in Economic Forecasting As stated in our earlier articles, conventional approaches to macroeconomic forecasting tend to be constrained by the estimated values of parameters and intercept terms. These are imbedded in the multi-equation models that are typically employed to produce ‘‘first-cut’’ forecasts of relevant endogenous variables. Additionally, the values of a large number of ‘‘exogenous’’ variables (relating to the future course of monetary and fiscal policy, the value of exports, etc.) must be subjectively estimated on the basis of available evidence and consensus judgment. Initial forecasts produced by the raw models are then typically adjusted by ‘‘add’’ or ‘‘fudge’’ factors, most commonly in the form of shifts in the values of T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_2,  Springer Science+Business Media New York 2013

41

42

2 Forecasting the Resurgence of the U. S. Economy in 2001

previously estimated intercept terms. This procedure is employed in order to produce forecasts that are consistent with recent values of key endogenous variables when it is evident that a shift of some kind has occurred in portions of the underlying model structure. Such exercises also provide ample opportunity for resetting the values of exogenous variables. Thus, and as stated in our earlier papers, this suggests that macroeconomic model builders/forecasters are well aware of the limitations of their underlying models and the need to incorporate subjective judgments. However, these judgmental adjustments are necessarily non-systematic and ad hoc in nature. Accordingly, here we again utilize an alternative, systematic approach—ANP—in order to remedy this deficiency. And while we have not illustrated this alternative by adapting a formal macroeconomic forecasting model, the conceptual framework, as noted above, is grounded in modern macroeconomics. Our alternative approach, moreover, could also be readily employed to enrich forecasting exercises based on formal models (e.g., generating\add factors more systematically and consistently; adjusting the values of exogenous variables). As stated in the earlier papers in this respect the two forecasting approaches can be seen to converge quite compatibly.

3 The Setting: An Economic Slowdown After Years of Expansion While in popular accounts it is conventional to view the U.S. economy as being in a recession if real Gross Domestic Product (GDP) has declined for two consecutive quarters, the National Bureau of Economic Research, utilizing a panel of experts (i.e., the above noted Business Cycle Dating Committee), has, by general consensus, been given the responsibility for dating the actual turning points in the U.S. economic cycle. This organization arrives at its assessments by utilizing a number of indicators of economic activity. It describes a recession as ‘‘a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in production, employment, real income, and other indicators’’ (NBER 2008). In its announcement, it notes that the committee views the payroll employment measure, which is based on a large survey of employers, as ‘‘the most reliable comprehensive estimate of employment’’ and observes that this series reached its peak in December 2007 and has declined every month since. It views the quarterly estimates of real Gross Domestic Product and real Gross Domestic Income as normally ‘‘the two most reliable comprehensive estimates of aggregate domestic production.’’ However, while the two measures are conceptually identical, measurement issues have produced a statistical discrepancy that has caused them to behave differently in recent quarters, with ambiguous implications for the dating of the peak of the most recent economic cycle. However, ‘‘Other series considered by the committee—including real personal

3 The Setting: An Economic Slowdown After Years of Expansion

43

income less transfer payments, real manufacturing and wholesale and retail sales, industrial production, and employment estimates based on the household survey— all reached peaks between November 2007 and June 2008.’’ This led the committee to conclude that ‘‘All evidence other than the ambiguous movements of the quarterly product-side measure of domestic production’’ confirmed that the contraction had begun at the end of 2007. Moreover, the NBER dates the trough of the previous cycle as having occurred in November of 2001, with the subsequent expansion hitting its peak, as we have now been informed, in December of 2007. This 73 month expansion was considerably shorter than the previous 120 month expansion that occurred between March 1991 and March 2001, the longest expansion in the post-world war II era, and was also shorter than two other postwar expansions (February 1961 to December 1969; November 1982 to July 1990) (NBER, no date). The most recent contraction has also been accompanied during 2008 by increasing turbulence in U.S. and global financial and equity markets (with its onset dating from the middle of 2007), reflecting, in turn, the fallout from the collapse of the housing market, the sub-prime mortgage market and related financial instruments such as mortgage-backed securities and credit default swaps. Additionally world oil prices rose very rapidly throughout much of 2008. For example, while the widely-quoted UK Brent Blend spot price of oil had been trending upward since the middle of 2004, it jumped to over $90 a barrel at the end of December 2007 and topped $140 a barrel in early July 2008. Since then, oil prices have fallen precipitously—to below 40 in December 2008—as the slowing of the global economy and the attendant diminished demand for oil have exerted their influence. For much of the year, the U.S. dollar was also under attack vis-à-vis the Euro and other major currencies, in a pattern that seemed, to some observers, to reflect a run-up in oil futures prices and the possibility that such futures were being used as a currency hedging vehicle, in addition to tracking underlying supply and demand factors in the oil market. The recent economic news has been dominated by the U.S. Treasury’s attempt to prop up the financial markets with an almost $350 billion infusion of support that was authorized by Congress as part of a total financial ‘‘bailout’’ package of $700 billion (the remainder of which is being reserved for the use of the incoming Obama administration). Various measures implemented by the Federal Reserve System resulted in the pumping of billions of dollars of reserves into the banking system and a steep reduction in the federal funds rate. Two prominent investment banks were permitted to be acquired by stronger financial firms (while the bankruptcy of still another prominent investment bank was allowed to take place without a rescue effort), and two other prominent investment banks were converted into bank holding companies that then came under Federal Reserve jurisdiction. Additionally, plans were being laid by the incoming administration for a major fiscal stimulus package to be implemented soon after taking office (with estimates being circulated on the order of $500 billion to $1 trillion). Finally, in December 2008, Congress failed to adopt a proposed package of loans to the three U.S. automobile companies, two of whom were confronting near-term serious cash flow

44

2 Forecasting the Resurgence of the U. S. Economy in 2001

problems. On December 19 the administration announced that $13.4 billion from the still unused ‘‘first tranche’’ of the financial bailout package would be deployed by the administration as a ‘‘bridge loan’’ to the two cash-strapped producers, so that fundamental issues surrounding the domestic industry could be addressed more directly by the incoming administration.

4 A Holarchy Approach This forecasting exercise employed a Holarchy to address the timing of the expected resurgence by seeking to answer the question ‘‘what is the most likely period in the future when the resurgence will occur?’’ By this term, we implicitly meant a recovery from the trough that will eventually be confirmed by the NBER, using the kinds of broad measures of the economy noted above. According to the NBER (NBER 2003), ‘‘the trough marks the end of the declining phase and the start of the rising phase of the business cycle. Economic activity is typically below normal in the early stages of an expansion, and it sometimes remains so well into the expansion.’’ Like typical forecasters, we were not precise with regard to the projected rate of the expansion.

4.1 Decomposition of the Problem Decomposing the problem hierarchically, the top level of the exercise consists of the primary factors believed by us to represent the forces or major influences driving the economy in the fall of 2008: ‘‘Aggregate Demand;’’ ‘‘Aggregate Supply;’’ and ‘‘the Current Global Financial Context.’’ Each of these primary categories was then decomposed into sub-factors represented in the second level. Under Aggregate Demand, we identified consumer spending, net exports (i.e., exports less imports), business capital investment, shifts in consumer and business investment confidence, fiscal policy, monetary policy, and expectations with regard to the future course of inflation (which, in turn, could reflect expectations concerning the future course of monetary policy and fiscal policy). As in the previous exercise, we make a distinction between shifts in consumer and business investment confidence and the formation of expectations regarding future economic developments. Under Aggregate Supply, we identified labor costs (which, in turn, are driven by changes in such underlying factors as labor productivity and real wages), natural resource costs (e.g., the price of oil and other energy costs), and expectations regarding such costs in the future. With regard to the Current Global Financial Context, we identified as the principal subfactors the likelihood of changes in major international political relationships (such as wars or other international conflicts), the high degree of global financial integration, a number of

4 A Holarchy Approach

45

issues surrounding the current mortgage markets crisis, expectations with regard to future oil prices, and the future value of the dollar. We decomposed the current mortgage markets crisis into five sub-factors: uncertainty about housing prices, uncertainty about the value of mortgage-backed securities, the role of credit default swaps, the role of government intervention in the financial markets, and the lack of confidence in the accuracy of financial reporting. With regard to the various sub-factors, we recognized that they are, in some instances, interdependent. This is especially evident with regard to the sub-factors listed under the mortgage markets crisis. The lowest level of the hierarchy consists of the alternate time periods in which the resurgence might occur as of December 5, 2008 (preliminary exercises had been conducted during October and November, 2008): within 0–6 months, within 6–12 months, within 12–24 months, or within 24–36 months. Because the primary factors and associated sub-factors are time-dependent, their relative importance had to be established in terms of each of the four alternative time periods. Thus, instead of establishing a single goal as one does for a conventional hierarchy, we used the bottom level time periods to compare the Primary factors at the top. This entailed the creation of a feedback hierarchy known as a ‘‘holarchy’’ in which the priorities of the elements at the top level are determined in terms of the elements at the bottom level, thus creating an interactive loop. Figure 1 provides a schematic representation of the holarchy we used to forecast the timing of the economic resurgence. There are five clusters, Primary Factors, Aggregate Demand Factors, Aggregate Supply Factors, Clobal Financial Context and Alternative Time Periods. The names of the Alternative Time Periods in Fig. 1 are abbreviated: 6 Months means 0–6 months, 12 Months means 6–12 months, 24 Months means 12–24 months, and 36 Months means 24–36 months.1

4.2 Pairwise Comparison After decomposing the problem hierarchically, the next step in the process was to pairwise-compare the relative importance of the primary factors (Aggregate Demand, Aggregate Supply, and the Global Financial Context) as they influence (1) the timing of the economic resurgence; (2) the relative importance of each of the sub-factors as drivers of the associated primary factor in the next level of the hierarchy; and (3) the relative importance of each of the subfactors under each primary factor as it influences the timing of the economic resurgence. These 1

The authors were asked by a reviewer why we did not include a fifth alternative time period (e.g., 36–48 months)? As part of our exercise, we had concluded that we would have no confidence in attempting to project that far out into the future. Moreover, some grounding for the shorter four alternatives chosen is that, according to the NBER, the longest post-World War II contractions were each 16 months (November 1973 to March 1975, and July 1981 to November 1982) (NBER no date).

46

2 Forecasting the Resurgence of the U. S. Economy in 2001

Primary Factors 1 Aggregate Demand 2 Aggregate Supply 3 Global Financial Context

1 Aggregate Demand Factors

3 Global Financial Context

1 Consumption 2 Net Exports 3 Investment 4 Confidence 5 Fiscal Policy

1 Major Int’l Political Relationships 2 Global Financial Integration 3 Mortgage Crisis Issues Uncertainty about Housing Prices Uncertainty about Mortgage Backed Securities Role of Credit-Default Swaps Gov’t Ownership and Intervention Lack of Confidence in Financial Reporting

Tax Policy Gov’t Expenditure

6 Monetary Policy 7 Expected Inflation

4 Expectations of Future Oil Prices 5 Future Value of the Dollar

2 Aggregate Supply Factors 1 Labor Costs 2 Natural Resource Costs 3 Expectations

Alternative Time Periods 1 Six months 2 Twelve months 3 Twenty four months 4 Thirty six months

Fig. 1 Overall view of the structure of the forecasting model

comparisons were carried out using the nine point fundamental scale of the AHP (Saaty 1996, 2006). The judgments with regard to identification of factors and sub-factors, as well as the comparisons of their relative impact and strength, were conducted by the authors, who assumed the role of representative ‘‘experts’’. Obviously, the outcomes are strongly dependent on the quality of those judgments. As noted, the final version of the exercise was conducted on December 5, 2008. Thirty sets of judgment matrices were generated in this exercise. The priorities that emerged from the exercise for the major factors, sub-factors and their relative importance with regard to the time frames for a possible turnaround, are shown in the tables in the Appendix. As explained below, a high-level overview of the priorities is shown in Table 1. At the beginning of the Appendix a brief explanation is given about how the questions were posed to elicit the judgments for each set of pairwise comparisons. A perusal of the Table 1 and the supporting tables in

0.067 0.104

0.005 0.006 0.030

0.029

7 Expected Inflation

0.072 0.059 0.073

0.011 0.004 0.003 0.004 0.003

0.423 0.167 0.107

3 Mortgage Crisis Issues 4 Expectations of Future Oil Prices 5 Future Value of the Dollar

0.031 0.063 0.095 0.128

0.251 0.044 0.076 0.097 0.200 0.300 0.403

3 Role of Credit Default Swaps 4 Gov't Ownership & Intervention 5 Lack of Confidence in Financial Reporting 1 Six months 2 Twelve months 3 Twenty four months 4 Thirty six months

1.000

0.073 0.073

0.000 0.001

0.248

2 Uncertainty about Mortgage-backed Sec.

0.000

0.000

0.000

0.000

0.073

0.003

0.380

1 Uncertainty about Housing Prices

0.072

0.000

0.055

0.007

0.055

0.001

0.271

0.057

0.033

0.029

0.249

3 Expectations

0.078

0.250

2 Global Financial Integration

0.069

0.594

2 Natural Resource Costs

0.190

0.000

0.090

0.078

1 Major International Political Relationships

0.018

0.157

1 Labor Costs

0.833

0.040

0.227

6 Monetary Policy

0.167

0.036

0.208

5 Fiscal Policy

2 Gov't Expenditure

0.018

0.104

4 Confidence

1 Tax Policy

0.090

0.009

0.053

3 Investment

0.083

0.004

0.025

2 Net Exports

0.051

0.000

0.062

0.026

0.083

3 Global Financial Context

0.000

0.000

0.355

0.116

0.364

2 Aggregate Supply 1 Consumption

0.175

0.553

1 Aggregate Demand

0.000

0.000

0.000

0.000

0.173 0.173

0.173

0.173

0.176

0.143

0.143

0.000

0.118

0.118

0.109

0.134

0.250

0.472

0.142

0.149

0.445

0.000

0.149

0.078

0.083

0.083

0.000

0.000

0.000

0.000

0.000

0.000

0.000

0.377 0.377

0.377

0.377

0.289

0.366

0.366

0.000

0.262

0.262

0.377

0.323

0.250

0.274

0.252

0.223

0.258

0.000

0.223

0.305

0.417

0.307

0.000

0.000

0.000

Local Priorities of Time Periods Compared with respect to 0 to 6 months 6 to 12 months 12 to 24 months

within each cluster sum to 1.000; ** When time periods are not directly linked from factors and compared with respect to them the priorities are shown as zeros

SUM OF GLOBAL PRIORITIES

31 Mortgage Crisis Subfactors

3 Global Financial Contexts

2 Aggregate Supply Factors

11 Fiscal Policy Subfactors

1 Aggregate Demand Factors

Global priority (entire model)

Local priority (within cluster*)

FACTORS

Table 1 High level summary of priorities in the model after final synthesis

4 A Holarchy Approach 47

48

2 Forecasting the Resurgence of the U. S. Economy in 2001

the Appendix reveal the following about the priorities derived from the pairwise comparison judgments. Prioritizing the Primary factors with respect to the four time periods, as shown in Table 7, resulted in Aggregate Demand factor dominating in the 0–6 month and 6–12 month forecasting periods with 79 % of the total. In the 12–24 and 24–36 month time periods Aggregate Supply becomes equally as important as Aggregate Demand so each has 45 % of the priority. With regard to attaining economic resurgence, the consumption, monetary policy, fiscal policy, and confidence sub-factors were assigned relative weights totaling 89 % of the Aggregate Demand primary factor. 1. Of the Aggregate Demand sub-factors, consumption, net exports, investment, and confidence were judged to be most influential in the 12–24 and 24–36 month forecasting horizons, whereas monetary and fiscal (especially government expenditure) policy exerted greater influence in a 6–12- or 12–24 month time frame. 2. Of the Aggregate Supply sub-factors, natural resource costs were dominant at almost 60 %, and this sub-factor assumed greater relative importance within the 24 and 36 month time horizons. 3. Of the Global Financial Context sub-factors, the mortgage crisis issues and the existence of global financial integration were dominant, totaling 69 % of relative importance, with mortgage crisis issues alone accounting for 42 %. The underlying mortgage issues sub-factors themselves were judged to be generally more amenable to solution within a 12–24 month or 24–36 month time horizon. Table 1 shows the final priorities of the factors in the model in two ways: their priority in the cluster they belong to (the priorities of all the factors in a cluster sum to 1.000) and their priority in the entire model (the priorities of all the factors in the model sum to 1.000). Read across the row for a given factor to see how the time periods were prioritized for that factor. Time periods are prioritized only for elements directly connected to them. For example, the time periods were not evaluated directly for Fiscal Policy, but rather for the subfactors of Fiscal Policy, Tax Policy and Gov’t Expenditure, hence the values are zero for the time periods for Fiscal Policy. As already noted, the detailed matrices of judgments that yield the priorities of the time periods in Table 1 are shown in the tables in the appendix. Table 7 in the Appendix is the starting supermatrix that contains the priorities from all the judgment matrices. The limit supermatrix Table 8 in the Appendix is the result of raising the supermatrix to large powers in which it converges to the final priorities of all the factors in the model. In this model, the powers of the supermatrix cycle, among several limit states, so the final limit supermatrix is obtained by summing these states. The priorities for the time periods appear in the last four rows of any column in the limit supermatrix in Table 8: 0.0307, 0.0634, 0.0953, and 0.1281. Normalizing these numbers gives the likelihood of the

4 A Holarchy Approach

49

Table 2 Computing the expected number of months until the turnaround of the economy Priority X Midpoint of time period Priorities Alternative time periods (span midpoint measured in months (normals) of time being considered) (1) Zero to six months (0–6) (2) Six to twelve months (6–12) (3) Twelve to twenty-four months (12–24) (4) Twenty-four to thirty-six months (24–36)

0.0968 0.1997 0.3001

3 9 18

0.2904 1.7973 5.4018

0.4034

30

12.1002

Sum

19.5897

turnaround occurring in 0–6 months (0.0968), in 6–12 months (0.1997), in 12–24 months (0.3001) and in 24–36 months (0.4034).

5 Producing the Forecast of the Recovery To determine the time until the economy turns around an expected value computation is carried out. The priority (or likelihood) of each time period is multiplied by the midpoint in months of the time period. To obtain the expected number of months from a starting point of zero in December 2008 until the recovery will occur these results were added (as one does when calculating expected values) as shown in Table 2. The value obtained shown as the sum above of 19.5897 means that the recovery is projected to occur sometime around late July or early August 2010; that is to say, toward the middle of the third quarter of 2010. Interestingly, as this paper was drafted in December 2008, a number of private and official forecasters were making projections that were more optimistic, believing that the trough of the cycle would be reached about a year earlier (Greenspan 2003; OECD 2008).

6 An ANP Approach Easy money and massive capital inflows from abroad fuelled a borrowing spree in the U.S., including the housing market. With the growing financial innovation and the wish to fulfill the ‘‘American dream,’’ subprime lending thrived since late 1990s. Believing that housing prices would always go north, such lending attracted mortgage companies, banks, homebuyers, and investors alike. Because banks sold off the underlying mortgages to investors, and the rating agencies assigned good rating to many of those debts, no one thought much about the risk. Risk was

50

2 Forecasting the Resurgence of the U. S. Economy in 2001

assumed to be shared and insured against by using credit default swap (cds), which essentially covered investors against losses from a default. When homeowners began to find it difficult to pay the mortgage, lenders got hit, and the complex web of trades started to disintegrate, creating multiple losses and logistical headaches for many parties. Like a house of cards, the shaky structure was blown apart by the negative financial forces. Since banks were also involved in mortgage debts, financial contagion kicked in. The entire financial market suffered from huge losses. The resulting liquidity crisis spread to consumption and investment credits, causing a major slowdown in the economy. As many firms went bust, insolvency problems set in. As in most crises and recessions, it is of interest to understand what the key factors are and how they play a role in the recovery process. The problem is that there is a great deal of uncertainty about almost everything associated with a financial meltdown of this epic proportion. The resulting policy conflicts cannot be more severe as the short-term objective (recovery) clashes with longer-term and more structural goals (governance, regulations, technology), making it even more difficult to predict the pace of recovery. Indeed, it is always tricky to predict crisis and recession, let alone to comprehend how a small segment of a financial market, i.e., subprime credit, could bring down the world’s largest economy into the worst recession since WWII. This paper predicts when the economy will recover by using the analytic network process (ANP) to model the macroeconomic and policy factors and their interactions and prioritize their effect on the time to recovery (Saaty 2001, 2005).

6.1 ANP Structures The structure of the relations among the factors is shown in Fig. 2. The clusters of elements and their connections fairly well describe the situation as agreed upon by the numerous participants in this study. The three main components (clusters) in the network are Aggregate Demand, Aggregate Supply, and External Factors. While most elements in the Aggregate Supply component are long-term in nature—unalterable in the short-run—those under the ‘External Factors’ have a more direct and immediate impact on the US economic turnaround. Without rising demand from abroad, the output of export products is unlikely to pick up. The recovery will need to rely on demand from other countries. Also, if the world economy continues to be in the doldrums and major countries are still suffering balance sheet recessions, external financing, expected to soften the impact of liquidity crunch in the US, will be hard to come by. Foreign investors’ perception and confidence in the US dollar also matter. A continued slide of the greenback can create a whole new story in terms of foreign investment flows in the US. It may put pressure on Treasury bonds, particularly the long-term 30 year maturities, presenting a risk that foreign creditors (most notably China) will cut back on their purchases.

6 An ANP Approach

51

Fig. 2 ANP structure showing the dependence and feedback among aggregate demand factors

As far as predicting the recovery is concerned, the Aggregate Demand component plays a far more determining role than the other two components. The subcomponents of aggregate demand are broken down into financial, housing and confidence sub-components. The importance of the financial sub component clearly stands out during the crisis. As discussed in [2], the episode has shown how the U.S financial market, world renowned for its size and strength, was weakened, causing production to fall and depressing labor markets across all sectors. The environment of easy money in the 2000s produced record levels of home equity borrowing and home sales, funded by ‘‘creative’’ financial companies operated like hedge funds.2 Their activities involved the asset-backed securities (ABS) or commercial paper used to finance mortgage firms, credit card companies, auto lenders, etc. At the beginning, many of the issuers of such commercial paper were real estate-related financial companies. They expanded the assets in the balance sheet by lending mortgages to future homeowners and sold these assets to investors by issuing the commercial paper (the essence of ABS is to sell commercial paper backed by such assets). As mortgage loans increased sharply since the mid 1990s, so did the ABS. Given such a critical role of ABS in the financial sector and the fact that the security market in general is the largest source of financing for US firms, the prospect of economic recovery is influenced by what

2

This led to borrowing-fueled speculative spree especially in the housing market, similar to the internet-stock mania in the 1990 s. The rules and regulations governing these financial companies were generally less restrictive than those for banks, mutual funds, and other financial institutions.

52

2 Forecasting the Resurgence of the U. S. Economy in 2001

Fig. 3 US financial sector’s investment in financial assets. Source authors’ calculation based on a series of U.S. flows-of-funds

happens with the securities market; hence, the node ‘Securities’ in the ‘Financial sub-component’ in Fig. 1. Lured by the prospect of huge profits during the housing boom period, investment banks jumped in. They operated beyond just performing as the underwriter for mortgage companies, by becoming directly involved in the mortgage loan scheme. Once they managed to lure home buyers to get the mortgages, the next and most important step was to sell securities backed by such mortgages (mortgage backed securities, MBS).3 As if the risks were not low enough, many investment banks also insured the MBSs and CDOs through a financial derivative known as credit default swap (CDS).4 When many mortgages went sour, these banks got hit. Thus, together with the ‘Securities’ market, ‘Banks’ appear as another critical node in the ‘Financial subcomponent’. Without their improvement, the recession would be prolonged. In the ‘Housing and Confidence sub-components,’ two nodes are identified: ‘Foreclosure’ and ‘Housing Price.’ An important motivation for investors to buy MBS was the strong perception that housing prices would always go north. The combination of wanting to fulfill the ‘‘American dream,’’ taking advantage of the low interest rates, and expecting that housing prices would continue to rise, allowed hundreds of thousands of Americans to buy homes they had believed they

3

Thus, these investment banks essentially transformed their role from being underwriters to becoming sellers of loans. In the process, they shared the risks of mortgage loans with other investors. At the same time they collected a large sum of ‘‘new loans’’ from those investors. Many of the buyers of the securities were wealthy and reputable individuals, as well as institutions including educational institutions, local governments, charitable organizations, and banks. 4 Practically non-existent until late in the 1990 s, CDS market grew very rapidly, reaching a staggering $62 trillion in 2008, more than 4 times the U.S GDP!.

6 An ANP Approach

53

could never afford. The number of risky portfolio holders surged. This meant more loans and more mortgages. As shown in Fig. 3, mortgage lending shot up since the mid-1990s, dominating the U.S. financial sector’s investment. When homeowners began to have difficulty with their payments, a wave of foreclosures, hangovers from a headier time, hit the housing market. One by one major financial institutions disclosed the problems they had associated with subprime lending and mortgage-backed assets.5 As some of these troubled institutions were forced to close down, insolvency set in. With millions of U.S households either on the brink or already in foreclosure and hundreds of subprime mortgage lenders already having gone belly up, the problem of over-supply in the housing market pushed housing prices down. The imploding home prices and rising foreclosures brought down the value of the insured mortgage pools. With lower asset values and falling incomes consumers’ spending declined. This led producers’ income and investment spending to fall, all of which stoked up the recession. Thus, unless the trend of rising foreclosures and the precipitous fall of housing prices can be halted, it will likely take a longer time than expected for the economy to recover. All of the above sub-components can be influenced by policy factors. Along with aggregate supply and external factors, policy factors influence the time to recovery by altering the priorities of aggregate demand sub-components. The specific policies are clustered separately from aggregate demand, and the clusters in the model shown in Fig. 1 are linked through what are considered important necessary conditions for recovery: i.e., the resumption of financial intermediation (the ‘Financial’ factor), the end of housing bust (the ‘Housing’ factor), and the restoration of market confidence (the ‘Confidence’ factor).6 As shown in Fig. 2, the important policy measures are: monetary (lowering the interest rates), liquidity injection (what the Fed has been adamantly forging ahead to do by buying private securities, essentially printing money), lowering taxes on both production and household income, rescuing some financial institutions (e.g., Bear Sterns, Freddie Mac & Freddie Mae), and increased spending for infrastructure through fiscal stimulus.7 These policy measures may or may not have helped slow the downturn. Even if they did it is hard to judge the relative effectiveness of those programs because any economy in recession will eventually recover. It is true that something had to be done because the effect of doing nothing would be even worse. But policy trade-offs that exist in virtually all policy measures used to revive an economy need to be considered. The ANP approach used in this analysis takes into account precisely the nature and intensity of such trade-offs.

5

The defining moment was really when holders of high-risk portfolios had to face a double whammy: investors demanding their money back, and lenders shutting the door in their face. 6 The importance of ‘Confidence’ in causing a crisis and influencing the pace of recovery is well discussed in Akerlof and Shiller (2009). 7 For more discussion about the policy response, see Azis (2009).

54

2 Forecasting the Resurgence of the U. S. Economy in 2001

Table 3 The time periods considered in the prediction model Time period Interpretation of what Midpoints of the time intervals name means (months) period intervals (in months from (months) 0)

Likelihood of turnaround during time period

0–18 18–30

9 24

0.099901 0.276769

36

0.490007

48

0.133323

30–42 42–54

From 0 to 18 months From more than 18 to 30 From more than 30 to 42 months From more than 42 to 54 months

6.2 Predictions We established a time line in months starting with December 2007 as the 0 point and ending 54 months later. Note that the start date was officially declared by the National Bureau of Economic Research (see NBER 2008b) as being when the recession began. We divided the time line into four intervals during which the turnaround might occur: ‘‘0–18 months, 18–30 months, 30–42 months, and 42–54 months’’. Priorities for the alternative time periods were derived by pairwise comparing elements in the model using the judgment of experts as to which is dominant and how dominant (in terms of importance, likelihood or preference) in the ANP structure. The priorities were then combined or synthesized throughout the entire model to derive the priority or likelihood of the turnaround occurring for each time period. The alternatives and the priorities derived for them are shown in Table 3 below. The time periods form a continuous time-line from 0 months all the way up to 54 months. The results of the decision model are priorities for the time periods that represent the likelihood of recovery occurring during that period. An expected value calculation was used to determine the expected number of months it would be until the economy recovers. The priorities that were obtained for the time periods from the ANP model are shown in the ‘‘Normals’’ column of Table 4. The priority for a time period may be

Table 4 Likelihoods or priorities derived from the ANP model

6 An ANP Approach

55

Table 5 Expected number of months until the turnaround Midpoints Priorities Time period intervals (names of intervals (Normals) as they appear in model in Fig. 1) (months)

Priority 9 Midpoint

(1) 0–18 (2) 18–30 (3) 30–42 (4) 42–54 Sum

0.8991 6.6432 17.64 6.3984 31.5807

0.0999 0.2768 0.49 0.1333

9 24 36 48

interpreted as the likelihood that the economy would turn around during that interval. The midpoint is the middle of an interval expressed in months from the zero point. For example, 36 is the midpoint of the interval ‘‘30–42 months’’ and as shown in Table 4 in the ‘‘Normals’’ column this interval received the highest likelihood (or priority) of 0.49. The expected number of months until recovery begins is obtained through the usual kind of computation for expected value in which the likelihood of each time period is multiplied by its midpoint and the results summed. Table 5 shows the expected value computations resulting in a prediction of 31.6 months until recovery starts. Since the starting point of the recession was December 2007, the recovery is expected to take place around July or August 2010.

6.3 Analysis The typical recession since World War II has lasted about one year, but this one is certainly more severe. The Federal Reserve, the Administration & Congress responded quickly and aggressively, repairing the damage to credit markets, albeit the effect of the repair is uncertain, making it more difficult to predict the pace of recovery. There is indeed a great deal of uncertainty about almost everything associated with a financial meltdown of this epic proportion, that the overall effects of many policies remain unknown. The resulting outcomes, however, are not all due to policy intervention. The market played its role too. The self-correcting market was evidenced by falling oil price (which affected spending), moderating

Table 6 Likelihood of a turnaround during a given time period Likelihood of a turnaround during Raw values (from the Time period time period (obtained by normalizing limit supermatrix) (months) the raw values to 1) 0–6 6–12 12–24 24–36

0.0307 0.0634 0.0953 0.1281

0.0967 0.1997 0.3001 0.4035

56

2 Forecasting the Resurgence of the U. S. Economy in 2001

wage increases (which influenced hiring), and a rising stock market (which affected household balance sheets, consumer confidence and spending). In recent months, market players and the media everywhere seem abuzz with talk of an impending recovery based on signs of improvement in the stock market, improvement in production in some sectors (e.g., automotive, partly due to the short-lived ‘‘cash-for-clinkers’’ program), and the slower pace of GDP decline. The Federal Reserve declared that the US economy has begun to be ‘‘leveling out’’ amid growing confidence in US markets that the country is heading for recovery. The Conference Board reported that its index of leading economic indicators started to increase. Although output is indeed no longer in free-fall, house prices are still falling and jobs are still being lost. Even if the bottom for output has already been reached, growth is still likely to be slow for some time. For sure, unemployment will continue to rise before it falls back to more normal levels. The number of US workers filing new claims for unemployment is still on the rise. Although the S&P/Case-Shiller index based on home prices in 20 cities ticked up slightly in May, more than one in every eight homeowners with a mortgage was behind on home loan payments. The percentage of loans that are in foreclosure continues to increase, and a glut of supply still weighs on prices due to a wave of repossessions.8 Housing expenditures account for more than one fifth of U.S GDP. When housing wealth and capital gains from home sales increase, consumers spend more. Interestingly, the housing sector tends to be strong no matter what happens with the stock market. If the stock market is strong (e.g., during a bubble), home prices receive a lift from investors’ decision to shift the stock gains into real estate. When stock values fall, home prices also receive a boost as investors pull money out of the stock market and put it into real estate in search of positive returns. According to Belsky and Prakken (2004), the effects of changes in housing and stock wealth on consumer spending are different in timing. It takes only about one year for spending from housing wealth to reach four fifths of a long-run effect, compared with several years for stock wealth. That is, the effect of housing wealth is more immediate. An important reason is that consumers are more cautious about changing their consumption behavior based on near-term movements in stock prices that can well prove unsustainable. While liquidation of home equity and realization of capital gains from home sales can add significantly to growth in consumer spending, the impacts are only temporary. Thus, an increase in home prices imparts more lasting benefits. This explains why historically the correlation between home prices and economic growth has been stronger.

8

Recent estimates show that seized properties account for almost one in four sales, and about a quarter of homes with mortgages are underwater. Deutsche Bank estimated that the negative equity will peak at 48 % of total homes by 2011.

7 Conclusion

57

7 Conclusion This exercise has once again demonstrated how the Analytic Network Process can serve as an additional tool for providing macroeconomic forecasts. We have based our forecast of the time period of the trough of the current economic cycle within the context of the macroeconomic conditions confronting the U.S. economy during late 2008, which had begun to experience a recession from its peak in December 2007 (Roubini and Menegatti 2007), after an expansion of 73 months. We have concluded that the recovery will begin during the third quarter of 2010, from a trough that will be reached some 20 months forward from the date of the December 2008 forecasting exercise (and some 32 months from the previous cyclical peak, which is considerably longer than all other post-World War II contractions). Other private and official forecasters are also forecasting a longer contraction than has been the case in previous postwar cycles, but our forecast is even less optimistic, and reflects our view that fundamental dislocations have occurred that will take additional time to overcome.

The Judgment Matrices, the Supermatrix and the Limit Supermatrix for the Holarchic Approach The pairwise comparison judgments and the priorities derived from them are given in Tables 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36 and 37. The caption of each table gives the parent element with respect to which the comparisons are being made; the derived priority is in the rightmost column of the table. The derived priorities are placed in their appropriate position in the supermatrix in the column labeled with the name of the parent element. The derived priorities in Tables 9–37 are used to form the supermatrix shown in three parts in Table 7. The supermatrix is raised to powers until it converges; that is, its values remain the same from one power to the next resulting in the limit supermatrix shown in Table 8.

Posing the Question When Comparing Criteria In this paper we use the terms criteria and factors interchangeably. The caption for Table 9 reads ‘‘Judgments for the importance of its subfactors to the main factor Aggregate Demand’’. The Aggregate Demand main factor is the parent element with respect to which its six subfactors in the Aggregate Demand cluster in Fig. 1 are compared. They are Consumption, Net Exports, Investment, Confidence, Fiscal Policy, Monetary Policy and Expected Inflation. The Fundamental Scale of the AHP is used to express the pairwise comparison judgments: [1-Equal, 3-Moderate,

2 Aggregate Supply

Factors

3 Investment

Factors

3 Expectations

4 Alternatives

3 Credit Def. Swaps

4Thirty six months

3Twenty four months

2Twelve months

1Six months

5 Financ'l Reporting

4 Gov't Owner. Inter.

2 Mortgage-bkd Sec.

Issues

1 Housing Prices

2 Gov't Expenditure

1 Tax Policy

5 Future Value of $

Crisis

31 Mortgage

Issues

11 Fiscal Pol.

3 Mortgage Crisis

Context

4 Expect. Oil Prices

2 Global Fnc'l Integ.

Financial

1 Major Int'l Polit.Rel.

Factors

3 Global

2 Natural Res. Costs

1 Labor Costs

7 Expected Inflation

6 Monetary Policy

5 Fiscal Policy

Supply

2 Aggregate

2 Net Exports

Demand

4 Confidence

1 Consumption

1 Aggregate

3 Global Fnc'l Con.

1 Aggregate Demand

0 Primary

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0.355

0.025

0.053

0.104

0.208

0.227

0.029

0.157

0.594

0.249

0

0

0

0

0

0

0 0 0 0 0 0 0 0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Finan'l

Supply

Demand

0

0

0

0

0

0

0

0

0

0

0

0.107

0.167

0.423

0.271

0.033

0

0

0

0

0

0

0

0

0

0

0

0

0

3Global

0Primary Factors 1Aggreg. 2Aggreg.

0.559

0.307

0.083

0.051

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

sump.

0.417

0.417

0.083

0.083

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Exports

0.538

0.305

0.078

0.078

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

ment

1Aggregate Demand Factors 1Con2Net 3Invest-

Table 7 Supermatrix that contains the weights derived from the pairwise comparison matrices

0.538

0.223

0.149

0.09

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

idence

4Conf-

0

0

0

0

0

0

0

0

0

0.833

0.167

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Policy

5Fiscal

0.108

0.258

0.445

0.19

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Policy

6Monetary

0.538

0.223

0.149

0.09

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Inflation

7Expected

0.25

0.25

0.25

0.25

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Costs

0.464

0.323

0.134

0.078

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Resource $

0.457

0.377

0.109

0.057

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

tations

2Aggregate Supply Factors 1Labor 2Natural 3Expec-

58 2 Forecasting the Resurgence of the U. S. Economy in 2001

0

0

0

5 Fiscal Policy

6 Monetary Policy

7 Expected Inflation

0.0553

0.1175

0.2622

0.5650

2Twelve months

3Twenty four months

4Thirty six months

0

5 Financ'l Reporting

1Six months

0

4 Gov't Owner. Inter.

4 Alternatives

0

3 Credit Def. Swaps

Issues

0

2 Mortgage-bkd Sec.

0

0

1 Housing Prices

2 Gov't Expenditure

0

0

5 Future Value of $

1 Tax Policy

Crisis

31 Mortgage

Issues

11 Fiscal Pol.

0

0

4 Expect. Oil Prices

Context

0

0

0

0

0

3 Mortgage Crisis

2 Global Fnc'l Integ.

Financial

1 Major Int'l Polit.Rel.

3 Expectations

Factors

3 Global

2 Natural Resource $

Supply

1 Labor Costs

0

2 Aggregate

0

3 Investment

4 Confidence

Factors

0

0

1 Consumption

2 Net Exports

Demand

0

3 Global Fnc'l Con.

1 Aggregate

0

2 Aggregate Supply

0

1 Aggregate Demand

0 Primary

Rel's

0.5650

0.2622

0.1175

0.0553

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Financ'l

0

0

0

0

0.0764

0.0444

0.2506

0.2482

0.3804

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Crisis

3Global Financial Contexts 1Int'l Pol. 2Global 3Mortgage

Factors

Table 7 (continued)

0.4188

0.3664

0.1429

0.0720

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Oil Prices

4Expect'ns

0.4188

0.3664

0.1429

0.0720

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Value $

5Future

0.5395

0.2523

0.1416

0.0666

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Policy

0.1498

0.2741

0.4717

0.1045

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Expend.

11Fiscal Pol. Issues 1Tax 2Gov't

0.4762

0.2888

0.1760

0.0591

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Housing $

0.3769

0.3769

0.1728

0.0734

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Mort. Sec.

31Mortgage Crisis Issues 1Uncertainty 2Uncertainty

0.3769

0.3769

0.1728

0.0734

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Swaps

3Cred. Def.

4Gov't

0.3769

0.3769

0.1728

0.0734

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Own.&Int.

5Financ'l

0.3769

0.3769

0.1728

0.0734

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Reporting

7 Conclusion 59

60

2 Forecasting the Resurgence of the U. S. Economy in 2001

Table 7 (continued) 4Alternatives 1Six 2Twelve

3Twenty four

4Thirty six

months

months

months

months 0.4545

0 Primary

1 Aggregate Demand

0.7854

0.7854

0.4545

Factors

2 Aggregate Supply

0.1488

0.1488

0.4545

0.4545

3 Global Fnc'l Con.

0.0658

0.0658

0.0909

0.0909

1 Aggregate

1 Consumption

0

0

0

0

Demand

2 Net Exports

0

0

0

0

Factors

3 Investment

0

0

0

0

4 Confidence

0

0

0

0

5 Fiscal Policy

0

0

0

0

6 Monetary Polic y

0

0

0

0

7 Expected Inflation

0

0

0

0

2 Aggregate

1 Labor Costs

0

0

0

0

Supply

2 Natural Resource $

0

0

0

0

Factors

3 Expectations

0

0

0

0

3 Global

1 Major Int'l Polit.Rel.

0

0

0

0

Financial

2 Global Fnc'l Integ.

0

0

0

0

Context

3 Mortgage Crisis

0

0

0

0

4 Expect. Oil Prices

0

0

0

0

5 Future Value of $

0

0

0

0

11 Fiscal Pol.

1 Tax Policy

0

0

0

0

Issues

2 Gov't Expenditure

0

0

0

0

31 Mortgage

1 Housing Prices

0

0

0

0

Crisis

2 Mortgage-bkd Sec.

0

0

0

0

Issues

3 Credit Def. Swaps

0

0

0

0

4 Gov't Owner. Inter.

0

0

0

0 0

4 Alternatives

5 Financ'l Reporting

0

0

0

1Six months

0

0

0

0

2Twelve months

0

0

0

0

3Twenty four months

0

0

0

0

4Thirty six months

0

0

0

0

5-Strong, 7-Very Strong, 9-Extreme; numbers in-between and decimals are also allowed]. The question posed is: ‘‘Which subfactor is more important in determining the time to recovery with respect to the Aggregate Demand main factor and how much more important?’’ The pair involved in a comparison is indicated by the (row, column) headings for the cell into which the judgment is placed. The judgment indicates how much more important the row element is than the column element in the opinion of the judge. For example, the value of 7 in the (Consumption, Exports) cell in Table 9 means Consumption is considered to be very strongly more important than Exports in determining the time to recovery. If instead the judgment was that Exports were very strongly more important than Consumption, the inverse value of 1/7 would be entered. An example of such an inverse value is the (Net Exports, Investment) judgment of 1/5 which means Investment is strongly more important than Net Exports in determining when the economy will turn around. The lower part of each matrix in a table has the reciprocal values of the entries of the transpose judgments in the upper part of the matrix.

0.0364

0.0398

0.0051

5 Fiscal Policy

6 Monetary Policy

7 Expected Inflation

0.0307

0.0634

0.0953

0.1281

2Twelve months

3Twenty four months

4Thirty six months

0.0009

5 Financ'l Reporting

1Six months

0.0005

4 Gov't Owner. Inter.

4 Alternatives

0.0028

3 Credit Def. Swaps

Issues

0.0028

2 Mortgage-bkd Sec.

0.0043

0.0303

1 Housing Prices

2 Gov't Expenditure

0.0028

0.0061

5 Future Value of $

1 Tax Policy

Crisis

31 Mortgage

Issues

11 Fiscal Pol.

0.0112

0.0044

4 Expect. Oil Prices

Context

0.0072

0.0009

0.0288

0.0686

0.0181

3 Mortgage Crisis

2 Global Fnc'l Integ.

Financial

1 Major Int'l Polit.Rel.

Factors

3 Global

2 Natural Resource $

3 Expectations

Supply

1 Labor Costs

0.0183

4 Confidence

2 Aggregate

0.0092

3 Investment

Factors

0.0044

2 Net Exports

Demand

0.0623

0.0265

1 Consumption

3 Global Fnc'l Con.

1 Aggregate

0.1155

2 Aggregate Supply

Factors

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Supply

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Finan'l

0.1755

Demand

1 Aggregate Demand

0 Primary

3Global

0Primary Factors 1Aggreg. 2Aggreg.

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

sump.

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Exports

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

ment

1Aggregate Demand Factors 1Con2Net 3Invest-

Table 8 Limit supermatrix; in this model all columns are the same

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

idence

4Conf-

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Policy

5Fiscal

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

tary Pol.

6Mone-

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Inflation

7Expected

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Costs

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Resource $

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

ations

2Aggregate Supply Factors 1Labor 2Natural 3Expect-

7 Conclusion 61

0.0364

0.0398

0.0051

5 Fiscal Policy

6 Monetary Policy

7 Expected Inflation

3 Expectations

Issues

0.0634

0.0953

0.1281

2Twelve months

3Twenty four months

4Thirty six months

0.0009

0.0307

5 Financ'l Reporting

1Six months

4 Gov't Owner. Inter.

4 Alternatives

0.0005

3 Credit Def. Swaps

0.0028

0.0028

2 Mortgage-bkd Sec.

Issues

0.0043

0.0303

1 Housing Prices

2 Gov't Expenditure

Crisis

31 Mortgage

0.0061

0.0028

5 Future Value of $

1 Tax Policy

0.0044

4 Expect. Oil Prices

11 Fiscal Pol.

0.0112

0.0072

2 Global Fnc'l Integ.

3 Mortgage Crisis

Financial

0.0009

0.0288

0.0686

0.0181

Context

1 Major Int'l Polit.Rel.

Factors

3 Global

2 Natural Resource $

Supply

1 Labor Costs

0.0183

4 Confidence

2 Aggregate

0.0092

3 Investment

Factors

0.0044

2 Net Exports

Demand

0.0623

1 Consumption

0.0265

3 Global Fnc'l Con.

1 Aggregate

0.1155

2 Aggregate Supply

0.1755

1 Aggregate Demand

0 Primary

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

3Global Financial Contexts 1 Int'l 2Global 3Mortgage Pol. Fnc'l Crisis Rel'ns Int.

Factors

Table 8 (continued)

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Value $

Oil Prices 0.1755

5Future

4Expect'ns

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Policy

1Tax

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Expend.

2Gov't

11Fiscal Policy Issues

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Housing $

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

Securities

31Mortgage Crisis Issues 2Mort. 1Uncertainty Bkd

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

3Role Credit Default Swps

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

0.1281

0.0953

0.0634

0.0307

0.0009

0.0005

0.0028

0.0028

0.0043

0.0303

0.0061

0.0028

0.0044

0.0112

0.0072

0.0009

0.0288

0.0686

0.0181

0.0051

0.0398

0.0364

0.0183

0.0092

0.0044

0.0623

0.0265

0.1155

0.1755

5Financ'l Reporting

4Gov't Own.&Int.

62 2 Forecasting the Resurgence of the U. S. Economy in 2001

7 Conclusion

63

Table 8 (continued) 4Alternatives 1Six

2Twelve

months

months

3Twenty four months

4Thirty six months

0 Primary

1 Aggregate Demand

0.1755

0.1755

0.1755

Factors

2 Aggregate Supply

0.1155

0.1155

0.1155

0.1755 0.1155

3 Global Fnc'l Con.

0.0265

0.0265

0.0265

0.0265

1 Aggregate

1 Consumption

0.0623

0.0623

0.0623

0.0623

Demand

2 Net Exports

0.0044

0.0044

0.0044

0.0044

Factors

3 Investment

0.0092

0.0092

0.0092

0.0092

4 Confidence

0.0183

0.0183

0.0183

0.0183

5 Fiscal Policy

0.0364

0.0364

0.0364

0.0364

6 Monetary Policy

0.0398

0.0398

0.0398

0.0398

7 Expected Inflation

0.0051

0.0051

0.0051

0.0051

1 Labor Costs

0.0181

0.0181

0.0181

0.0181

2 Aggregate Supply

2 Natural Resource $

0.0686

0.0686

0.0686

0.0686

Factors

3 Expectations

0.0288

0.0288

0.0288

0.0288

3 Global

1 Major Int'l Polit.Rel.

0.0009

0.0009

0.0009

0.0009

Financial

2 Global Fnc'l Integ.

0.0072

0.0072

0.0072

0.0072

Context

3 Mortgage Crisis

0.0112

0.0112

0.0112

0.0112

4 Expect. Oil Prices

0.0044

0.0044

0.0044

0.0044

11 Fiscal Pol. Issues

5 Future Value of $

0.0028

0.0028

0.0028

0.0028

1 Tax Policy

0.0061

0.0061

0.0061

0.0061

2 Gov't Expenditure

0.0303

0.0303

0.0303

0.0303

1 Housing Prices

0.0043

0.0043

0.0043

0.0043

Crisis

2 Mortgage-bkd Sec.

0.0028

0.0028

0.0028

0.0028

Issues

3 Credit Def. Swaps

0.0028

0.0028

0.0028

0.0028

4 Gov't Owner. Inter.

0.0005

0.0005

0.0005

0.0005

31 Mortgage

4 Alternatives

5 Financ'l Reporting

0.0009

0.0009

0.0009

0.0009

1Six months

0.0307

0.0307

0.0307

0.0307

2Twelve months

0.0634

0.0634

0.0634

0.0634

3Twenty four months

0.0953

0.0953

0.0953

0.0953

4Thirty six months

0.1281

0.1281

0.1281

0.1281

Entering the Derived Priorities in the Supermatrix The priorities in Table 9, determined by computing the principal eigenvector of the matrix of judgments, are: (0.355, 0.025, 0.053, 0.104, 0.208, 0.227, 0.029). The priorities may be interpreted as meaning that Consumption at .355 and Monetary Policy at .227 are the most important Aggregate Demand Factors. Put another way, Consumption is 35.5 % of what drives an economic recovery among aggregate demand factors while Net Exports is the least important at 2.5 %. These priorities are entered into the supermatrix in Table 9 under the Aggregate Demand column heading.

Posing the Question When Comparing Time Periods with Respect to Criteria The time periods are compared according to which is the more likely period for recovery due to the influence of the factor with respect to which the comparisons

Consumption Net exports Investment Confidence Fiscal policy Monetary Policy Expected inflation

1 1/7 1/7 1/5 1/3 1/2 1/7

Inconsistency ratio = 0.0739

(1) (2) (3) (4) (5) (6) (7)

7 1 5 7 8 7 1

7 1/5 1 3 5 6 1/2

5 1/7 1/3 1 4 4 1/6

Table 9 Judgements for the importance of its subfactors to the main factor aggregate demand (1) Consumption (2) Exports (3) Investment (4) Confidence 3 1/8 1/5 1/4 1 1 1/5

(5) Fiscal policy 2 1/7 1/6 1/4 1 1 1/7

(6) Monetary policy

7 1 2 6 5 7 1

(7) Expected inflation

0.35509 0.02481 0.05263 0.10406 0.20750 0.22665 0.02926

Weights

64 2 Forecasting the Resurgence of the U. S. Economy in 2001

7 Conclusion

65

are made. In Fig. 1 the Fiscal Policy criterion in the Aggregate Demand Factors cluster has the subfactors (or subcriteria): Tax Policy and Government Expenditure, so the time periods are pairwise compared with respect to each of these two subfactors rather than directly with respect to the factor Fiscal Policy. The time periods are compared directly with respect to the factors in the cluster that have no subfactors such as Consumption. The question posed would be: Is the 0–6 Months time period or the 6–12 Month time period more likely to be the turnaround time because of Consumption and how strongly more? Here 0–6 Months is not more likely than 6–12 Months; it is the other way around so a 1/3 is entered in Table 9 in the (0–6 Months, 6–12 Months) cell. In all the tables involving time periods the names are abbreviated as follows: 6 Months means 0–6 Months, 12 Months means 6–12 Months, 24 Months means 12–24 Months and 36 Months means 24–36 Months.

Posing the Question When Comparing the Primary Factors with Respect to Time Periods The final type of comparison arises because of the links back from the time periods to the primary factors. In this case the question posed is: For the turnaround to occur in the 6 Months time period which would have greater influence, and how strongly greater, the primary factor Aggregate Demand or Aggregate Supply? The judgment is that Aggregate Demand would be very strongly dominant over Aggregate Supply for the turnaround to occur in 6 months, so a 7 is entered in the (Aggregate Demand, Aggregate Supply) cell in Table 34.

Computing the Limit Supermatrix Overall priorities for the alternative time periods are obtained by raising the supermatrix to powers until it converges to the limit supermatrix shown in Table 9. In the limit supermatrix all the columns are the same. The raw values for the alternative time periods are the same in every column of the limit supermatrix. These four values are shown in column 2 of Table 6 below. They are normalized by dividing each by their sum to obtain the priorities for the time periods shown in the third column. These priorities may be interpreted as the likelihood of a turnaround occurring during these time periods.

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Table 10 Judgments for the importance of its subfactors to the main factor aggregate supply Labor costs Natural resources Expectations Weights Labor costs Natural resources Expectations

1 3 2

1/3 1 1/3

1/2 3 1

0.15705 0.59365 0.24931

Inconsistency ratio = 0.0515

Table 11 Judgments for the importance of its context Major Global international financial political integration relationships Major international political relationships Global financial integration Mortgage crisis issues Expectations of future oil prices Future value of the dollar

subfactors to the main factor global financial Mortgage crisis issues

Expectations of future oil prices

Future Weights value of the dollar

1

1/7

1/7

1/6

1/6

0.03274

7

1

1

2

2

0.27118

7

1

1

5

5

0.42257

6

1/2

1/5

1

3

0.16671

6

1/2

1/5

1/3

1

0.10680

Table 12 Judgments for the likelihood of the alternatives with respect to consumption 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 3 5 7

1/3 1 7 7

1/5 1/7 1 3

1/7 1/7 1/3 1

0.05081 0.08306 0.30720 0.55893

Inconsistency ratio = 0.1219

Table 13 Judgments for the likelihood of the Alternatives with respect to net exports 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 1 5 5

Inconsistency ratio = 0.0000

1 1 5 5

1/5 1/5 1 1

1/5 1/5 1 1

0.08333 0.08333 0.41667 0.41667

7 Conclusion

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Table 14 Judgement for the likelihood of the alternatives with respect to Investment 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 1 5 5

1 1 5 5

1/5 1/5 1 1

1/5 1/5 1/3 1

0.0783 0.0783 0.3051 0.5383

Inconsistency ratio = 0.0579

Table 15 Judgement for the likelihood of the alternatives with respect to confidence 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 2 3 4

1/2 1 2 3

1/3 1/2 1 4

1/4 1/3 1/4 1

0.08985 0.14917 0.22271 0.53827

Inconsistency ratio = 0.0577

Table 16 Judgements for the importance of its subcriteria with respect to fiscal policy Tax policy Gov’t expenditures Weights Tax policy Gov’t expenditures

1 5

1/5 1

0.16667 0.83333

Inconsistency ratio = 0.0000

Table 17 Judgments for the likelihood of the Alternatives with respect to Tax Policy 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 3 4 5

1/3 1 3 3

1/4 1/3 1 4

1/5 1/3 1/4 1

0.06661 0.14161 0.25226 0.53952

Inconsistency ratio = 0.1030

Table 18 Judgments for the likelihood of the alternatives with respect to government expenditures 6 Months 12 Months 24 Months 36 Months Weights 6 Months 12Months 24 Months 36 Months

1 3 3 2

Inconsistency ratio = 0.0362

1/3 1 1/2 1/4

1/3 2 1 1/2

1/2 4 2 1

0.10445 0.47168 0.27408 0.14979

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Table 19 Judgments for the likelihood of the alternatives with respect to monetary policy 6 months 12 months 24 months 36 months Weights. 6 months 12 months 24 months 36 months

1 3 2 1/3

1/3 1 1/2 1/3

1/2 2 1 1/2

3 3 2 1

0.18595 0.44478 0.25806 0.10758

Inconsistency ratio = 0.0618

Table 20 Judgments for the likelihood of the Alternatives with respect to expected inflation 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 2 3 4

1/2 1 2 3

1/3 1/2 1 4

1/4 1/3 1/4 1

0.08985 0.14917 0.22271 0.53827

Inconsistency ratio = 0.0577

Table 21 Judgments for the likelihood of the alternatives with respect to labor costs 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 1 1 1

1 1 1 1

1 1 1 1

1 1 1 1

0.25000 0.25000 0.25000 0.25000

Inconsistency ratio = 0.0000

Table 22 Judgments for the likelihood of the alternatives with respect to natural resource costs 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 3 3.5 4

1/3 1 4 4

1/3.5 1/4 1 2

1/4 1/4 1/2 1

0.07848 0.13405 0.32337 0.46411

Inconsistency ratio = 0.0843

Table 23 Judgments for the likelihood of the alternatives with respect to expectations 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 3 5 7

Inconsistency ratio = 0.00460

1/3 1 4 6

1/5 1/4 1 1

1/7 1/6 1 1

0.05670 0.10906 0.37692 0.45733

7 Conclusion

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Table 24 Judgments for the likelihood of the alternatives with respect to major International Political Relationships 6 months 12 months 24 months 36 months Weiqhts 6 months 12 months 24 months 36 months

1 3 5 7

1/3 1 3 5

1/5 1/3 1 3

1/7 1/5 1/3 1

0.05528 0.11751 0.26220 0.56501

Inconsistency ratio = 0.0438

Table 25 Judgments for the likelihood of the alternatives with respect to global financial integration 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 3 5 7

1/3 1 3 5

1/5 1/3 1 3

1/7 1/5 1/3 1

0.05528 0.11751 0.26220 0.56501

Inconsistency ratio = 0.0438

Table 26 Judgments for the importance of Uncertainty Uncertainty about about housing mortgageprices backed securities Uncertainty about housing prices Uncertainty about mortgagebacked securities Role of credit default swaps Gov’t ownership and intervention Lack of Confidence in Financial Reporting

its subcriteria with respect to mortgage crisis issues Role of Gov’t Lack of Weights credit ownership confidence in default and financial swaps intervention reporting

1

2

2

5

5

0.38043

1/2

1

1

5

5

0.24819

1/2

1

1

7

4

0.25057

1/5

1/5

1/7

1

1/3

0.04442

1/5

1/5

1/4

1/3

1

0.07640

Inconsistency ratio = 0.0469

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Table 27 Judgments for the likelihood of the alternatives with respect to uncertainty about housing prices 6 Months 12 Months 24 Months 36 Months Weiqhts 6 months 12 months 24 months 36 months

1 4 5 6

1/4 1 2 3

1/5 1/2 1 2

1/6 1/3 1/2 1

0.05908 0.17595 0.28879 0.47619

Inconsistency ratio = 0.0246

Table 28 Judgments for the likelihood of the alternatives with respect to uncertainty about mortgage backed securities 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 4 4 4

1/4 1 3 3

1/4 1/3 1 1

1/4 1/3 1 1

0.07343 0.17277 0.37690 0.37690

Inconsistency ratio = 0.0579 Table 29 Judgments for the likelihood of the alternatives with respect to role of credit default swaps 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 2.354 5.1349 5.1349

1/2.354 1 2.1811 2.1811

1/5.1349 1/2.1811 1 1

1/5.1349 1/2.1811 1 1

0.07340 0.17280 0.37690 0.37690

Inconsistency ratio = 0.0000 Table 30 Judgments for the likelihood of the alternatives with respect to gov’t ownership & intervention 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 2.354 5.1349 5.1349

1/2.354 1 2.1811 2.1811

1/5.1349 1/2.1811 1 1

1/5.1349 1/2.1811 1 1

0.07340 0.17280 0.37690 0.37690

Inconsistency ratio = 0.0000

Computing the Expected Number of Months Until the Turnaround To compute the expected time to the turnaround, as is traditionally done in economics, multiply the mid-point of each time period by the likelihood of the turnaround occurring during that time period. For example, the 0–6 Month

7 Conclusion

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Table 31 Judgments for the likelihood of the alternatives with respect to lack of confidence in financial reporting 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 2.3540 5.1349 5.1349

1/2.354 1 2.1811 2.1811

1/5.1349 1/2.1811 1 1

1/5.1349 1/2.1811 1 1

0.07340 0.17280 0.37690 0.37690

Inconsistency ratio = 0.0000

Table 32 Judgments for the likelihood of the alternatives with respect to expectations of future oil prices 6 months 12 months 24 months 36 months Weights 6 months 12 months 24 months 36 months

1 3 4 5

1/3 1 3 4

1/4 1/3 1 1

1/5 1/4 1 1

0.07196 0.14288 0.36638 0.41879

Inconsistency ratio = 0.0369

Table 33 Judgments for the likelihood of the alternatives with respect to future value of the dollar 6 Months 12 Months 24 Months 36 Months Weights 6 months 12 months 24 months 36 months

1 3 4 5

1/3 1 3 4

1/4 1/3 1 1

1/5 1/4 1 1

0.07196 0.14288 0.36638 0.41879

Inconsistency ratio = 0.0369

Table 34 Judgments for the importance of the primary factors in the 6 month time period Aggregate demand Aggregate supply Global financial context Weights Aggregate demand 1 Aggregate supply 1/7 Geopolitical 1/9

7 1 1/3

9 3 1

0.78539 0.14882 0.06579

Inconsistency ratio = 0.0772

Table 35 Judgments for the importance of the primary factors in the 12 month time period Aggregate demand Aggregate supply Global financial context Weights Aggregate demand 1 Aggregate supply 1/7 Geopolitical 1/9 Inconsistency ratio = 0.0772

7 1 1/3

9 3 1

0.78539 0.14882 0.06579

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Table 36 Judgments for the importance of the primary factors in the 24 month time period Aggregate demand Aggregate supply Global financial context Weights Aggregate demand 1 Aggregate supply 1 Geopolitical 1/5

1 1 1/5

5 5 1

0.45455 0.45455 0.09091

Inconsistency ratio = 0.0000

Table 37 Judgments for the importance of the primary factors in the 36 month time period Aggregate demand Aggregate supply Global financial context Weights Aggregate demand 1 Aggregate supply 1 Geopolitical 1/5

1 1 1/5

5 5 1

0.45455 0.45455 0.09091

Inconsistency ratio = 0.0000

time period runs from 0 to 6 months so its midpoint is 3 months. The 6–12 Month time period runs from 6 to 12 months so its midpoint falls at 9 months; the 12–24 time period runs from 12 to 24 months, so its midpoint falls at 18 months, and the 24–36 Month time period runs from 24 to 36, so its midpoint is at 30. Using an expected value calculation, in months, from December 2008: Expected turnaround = 3 9 0.0967 ? 9 9 0.1997 ? 18 9 0.3001 ? 30 9 0.4035 = 19.5898 The exercise was done in early December 2008, so this means the turnaround is expected to occur around late July or early August 2010. The pairwise comparison matrices are shown in Tables 9–37. A set of priorities or weights is obtained from each pairwise comparison matrix as its principal eigenvector. These derived priorities are placed into the supermatrix in the appropriate column. For example Table 9 gives the priorities or weights for the main factor Aggregate Demand, so they are placed in the supermatrix in Table 7 in the first column under ‘‘Aggregate Demand’’ beginning in the fourth row.

References Akerlof, George and Robert Shiller (2009). Animal Spirits: How Human Psychology Drives the Economy, and Why It Matters for Global Capitalism, Princeton University Press. Azis, Iwan J (2009). Crisis, Complexity and Conflict, Emerald Group Publishing Limited. Belsky, E., & Prakken, J. (2004). Housing wealth effects: Housing’s impact on wealth accumulation, wealth distribution and consumer spending. Joint Center for Housing Studies’ Report of a study commissioned and supported by the National Association of Realtors, Harvard University (W04–13). Cambridge, MA: National Center for Real Estate Research. Blair, A.R., Nachtmann, R. and Saaty, T.L., ‘‘Incorporating Expert Judgment in Economic Forecasts: The Case of the U.S. Economy in 1992,’’ Chapter 12 in the book: Saaty, T.L. and L.G. Vargas, Models, Methods, Concepts and Applications of the Analytic Hierarchy Process, Kluwer Academic Publishers, London, 2001.

References

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Blair, A.R., Nachtmann, R., Saaty, T.L. and Whitaker, R., ‘‘Forecasting the Resurgence of the US Economy in 2001: An Expert Judgment Approach,’’ Socio-Economic Planning Sciences, Vol. 36, 2002, pp. 77–91, and also Chapter 2 in Saaty, T.L. and L.G. Vargas, Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks, Springer, New York, 2006. Greenspan, A. (2003, March 4). Remarks at the annual convention of the Independent Community Bankers of America, Orlando, Florida (via satellite). Hilsenrath, Jon E., ‘‘Despite Job Losses, the Recession is Finally Declared Officially Over,’’ The Wall Street Journal, July 18, 2003. National Bureau of Economic Research, Business Cycle Dating Committee, ‘‘Determination of the December 2007 Peak in Economic Activity,’’ Dec. 1, 2008, NBER web site (www.nber.org). National Bureau of Economic Research, ‘‘Business Cycle Expansions and Contractions,’’ NBER web site (www.nber.org). National Bureau of Economic Research, no title, link ‘‘announcement of business cycle trough/ end of last recession,’’ July 17, 2003, NBER web site (www.nber.org). NBER (2008b). Determination of the December 2007 Peak in Economic Activity, in http:// www.nber.org/cycles/dec2008.html. Organization for Economic Cooperation and Development, ‘‘Economic Outlook No. 84,’’ November 2008, web site (www.oecd.org). Roubini, N., & Menegatti, C. (2007, March). The US housing recession is still far from bottoming out. RGE Monitor, pp. 1–22. Saaty, T. L. (1996). Fundamentals of decision making and priority theory with the Analytic Hierarchy Process. Pittsburgh, PA: RWS Publication. Saaty, T.L. (2001). Decision making with dependence and feedback: The Analytic Network Process. Pittsburgh: RWS Publication. Saaty, T.L., Theory and Applications of the Analytic Network Process: Decision Making with Benefits, Opportunities, Costs and Risks, RWS Publications, Pittsburgh, PA, 2005. Saaty, T.L., Fundamentals of Decision Making and Priority Theory with the Analytic Hierarchy Process, RWS Publications, Pittsburgh, PA, 2006.

Chapter 3

An Analytic Network Process Model for Financial-Crisis Forecasting

1 Introduction William Stanley Jevons (1835–1882) was a highly respected and influential economist and statistician of his time. Jevons argued in his book, Investigations in Currency and Finance, the economy underwent a series of ‘‘commercial crises,’’ which he traced back to the eighteenth century. Jevons’ view of the trade or business cycle as a sequence of crises was embraced broadly throughout the economics profession until the 1920s. Then as more economic and financial data were compiled and newer statistical techniques were crafted to analyze them, Wesley Mitchell’s ‘‘statistical cycles’’ replaced the event-driven concept of the business cycle. Statistical time-series cycles continue to underlie modern business cycle research. Today, cyclical composite index models, probit models, hidden Markov models (HMM) and threshold autoregressive (TAR) models are some typical methodologies used to forecast turning points in statistical cycles. However, over the last 10 years, the literature on financial crises rediscovered the traditional Jevons view of the cycle, where a turning point is triggered by some economic and/or political event. Financial crises are sudden events that may and often do occur after a growth cycle slowdown begins or classical business cycle recession ensues. Crises are predicated on some development, such as a collapse of a financial or non-financial institution or the recognition of a major imbalance in the financial sector, such as heavy debt holdings or too much dependence on foreign capital. In modern crisis theory of the business cycle, three types of financial crises are identified: fiscal, banking and currency (Sachs 1998). A fiscal crisis occurs when a government cannot roll over foreign debt and/or attract new loans. A currency crisis occurs when investors shift demand to foreign-denominated assets and away from domestic assets. A banking crisis occurs when a bank cannot attract enough new deposits to meet sudden withdrawal of reserves. Each of these crises can exist independently or in conjunction with one or more other crisis. Statistical data needed to track and to forecast a potential financial-crisis point can be somewhat illusive from country to country. Data limitations exist especially T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_3,  Springer Science+Business Media New York 2013

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3 An Analytic Network Process Model for Financial-Crisis Forecasting

in some emerging market economies that have undergone major structural change. In those countries, historical data are no longer consistent with the present institutions and, as such, are insufficient to signal a financial crisis before it occurs. Even when data exist, judgmental variables play a role in statistical models, as witnessed by the ‘‘freedom from corruption’’ qualitative variable in the probit model by Radelet and Sachs (1998). For these reasons, we propose a flexible and comprehensive framework to simultaneously model and forecast the three types of financial crisis using an Analytic Hierarchy Process (AHP) with feedback, which is known as the Analytic Network Process (ANP) as developed and implemented by Saaty (1996). The Analytic Network Process also provides a structure that potentially can reduce judgmental forecast error through improved ‘‘reliability of information processing.’’ The modeling application in this chapter extends the ANP recession forecasting model by Blair et al. (2002) to capture key economic concepts specified in the financial-crisis econometric model by Kaminsky and Reinhart (1999), the contagion econometric model by Lowell et al. (1998), as well as the studies by Aziz et al. (2000), Burns (1969), Glick and Moreno (1999), IMF (1998), Kindleberger (1996) and Wolfson (1994). Our ANP financial crisis model’s determinants are directly specified using quantitative and qualitative variables and empirically tested using an ‘‘expert system’’ approach instead of a true ‘‘expert opinion’’ approach—as the Blair study did—to allow for an historical back test.

2 The ANP Financial Crisis Model Structure The Analytic Network Process provides the mathematical framework for our model to forecast a financial-crisis probability using heuristics. Conceptually, the financialcrisis model can be described as a system of n components (which may be part of a cluster of components) that forms a network where every component (Cn) can interact or have an influence on itself or some or all of the other components of the system. The network, N = {C, L}, where C = {Ca, Cb, Cc, …, Cn} and L = {{Ca, Ca},{Ca, Cb},{Ca, Cc}, …,{Cn, Cn}} such that L represents the set of pairwise linkage within or between components of the network. The ANP-based crisis-forecasting model provides a formal scheme for mapping the component evaluations to an aggregate judgmental probability of a crisis (Saaty 1990, 1994, 1996). This multicriteria decision-making/forecasting model derives priorities or weights for each of the ‘‘n’’ criteria or components, Cn, of the model based on their judged (by the forecaster or a consensus of forecaster opinion) relative importance to the overall goal—which in this application is the likelihood that it will contribute to a financial crisis in a given period of time for a given forecast horizon. Not surprisingly, this process shares a common conceptual foundation with the derivation of component contributions from regression-based, time-series and/or cyclical-indicator composite index methodologies (Zarnowitz and Boschan 1975). However, the derivation of

2 The ANP Financial Crisis Model Structure

77

the ANP priority weights, which use pairwise assessment based on statistical or judgmental relevance, is quite different from those more traditional methods (Frei and Harker 1999; Niemira 2001). The Analytic Network Process framework is based on the following basic definitions and axioms: (a) A priority or weight, which is an absolute number, belongs to the closed interval [0,1] and is a measure of relative dominance; (b) A reciprocal condition exists that posits the ratio comparison between components is possible such that an evaluation of the pairwise couplet (CA,CB) equals 1/(CB,CA); (c) Homogeneity exists, which is the motivation for the Saaty 1-9 evaluation scale whereby the upper limit of 9 on that scale is due to the requirement of homogeneity to maintain the stability of the eigenvector to perturbation from consistency, and also to the requirement that only a small number of elements should be compared (an eigenvector with a small number of components considered.); and (d) A dependence condition is assumed that the system can be decomposed into component parts. Both the scale and the number of elements compared can be extended indefinitely. This is done by creating clusters with a small number of homogeneous elements in each and using a pivot element from cluster to the next (the largest in one is the smallest in the other) and applying the scale 1–9 to compare the elements in each, dividing by the priority of the pivot in the second cluster and multiplying the resulting priorities by the priority of the pivot in the first cluster and then combining the two clusters. Moreover, the Analytic Network Process extends the AHP method to incorporate component dependence and feedback by using a supermatrix approach (Saaty 1996). A supermatrix, W, is a complete system matrix of components, {Ca, Cb, Cc, …, Cn}, and their linkages or system weights, Wij, where Ci = {ei1, ei2, …, ein} is the sub-component elements of the criterion component ‘‘i.’’ ANP allows interaction and feedback within clusters, Ci, which is known as inner dependence, and between clusters, which is known as outer dependence. To make this more concrete, if there is no linkage between, say component Cb and Cc, then Wbc would be zero. However, if there is some relationship, then the entry would be non-zero, suggesting an outer dependence. An inner dependence would exist if there is a linkage within the components of a cluster, {ei1, ei2, …, ein}. Finally, the actual elements making up the columns (Wij) of the supermatrix are the eigenvector solutions within the clusters (such that each column sums to one). This supermatrix represents the impact of all model elements relative to the complete element set. The final priority weights—which account for component (element) interactions—are derived by multiplying the supermatrix by itself until the columns stabilize, which occurs when the supermatrix entries become identical across each row and this is known as the limiting matrix. The final priority weights are extracted from this limiting matrix. In essence, this solution algorithm derives weights that account for component interaction, which is a clear benefit of the dynamic ANP model over static models.

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3 Building the ANP Financial Crisis Model Our objective is to demonstrate that an ANP model structure incorporating a majority of variables from prior studies can be used to predict the likelihood that an economy would be in ‘‘financial crisis,’’ of any form, within 6 months. Explicitly, the model must account for banking, currency and fiscal crises as well as contagion effects on the domestic economy from other countries experiencing one of more of those crises. Moreover, it would be useful to include a conceptual range of ‘‘all possible’’ indicators of financial crisis into this model, even if some rarely occur and might not show up as statistically significant in econometric models. One of the advantages of the ANP framework is that it is not constrained by some statistical problems, such as multicollinearity, which might be encountered in econometric modeling of the same process. In this way, the ANP model shares a common conceptual foundation with traditional composite indicator methods, which also attempt to select indicators across a wide spectrum of economic processes. Diversification of the criteria used to trigger a forecast decision is important, but one should not give too much weight to trivial indicators, even if the variable is included for completeness. Arguably, the greatest advantage of the ANP model is that it can handle data limitations and intangibles (or qualitative variables—such as political or war risk) based on individual or collective judgment of the situation. As such, the measurement of intangibles is the main concern of the mathematics of the AHP/ANP approach. Often even if there are no recent statistical data or no time series at all for such intangibles, there may be a qualitative sense of the importance of the factor (that might be gleaned through news reports, for example), which can be accounted for and incorporated into the ANP forecasting model. Our model, which is dubbed the imbalance-crisis-turning-point model, incorporates the following features: (1) contagion effects, (2) fiscal crises, (3) banking crises, (4) currency crises, (5) the role of real-sector changes (6) monetary policy, (7) fiscal or tax policy and (8) external shocks, which include oil prices, food prices and technological or productivity changes (this block also might include other exogenous influences, including legal restrictions on capital flows, political instability, social unrest, etc.). The imbalance-crisis turning point ANP model is specified by clusters of criteria, their elements and the connection between them and judgmental evaluations are made with a forecast horizon of up to 6 months. The control cluster, in our model, is diagramed in Fig. 1. The arrows indicate direction of causal impact with the looped arrow indicating feedback effects. For example, in the exogenous-shocks block, it is assumed that an impact from oil prices will impact productivity shocks. The domestic imbalance criteria incorporate typical theoretical concepts and empirical evidence, but can be customized for a specific country’s economy. As we have modeled the process, the domestic imbalance block includes evaluations of capacity utilization rates (too low or too high could be problems), the ratio of cashflow-to-investment (ability to afford the investment), the consumer debt burden (an over-leveraged consumer could pose

3 Building the ANP Financial Crisis Model

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Fig. 1 Overview: the ANP-network financial crisis model’s control hierarchy

problems for the economy), foreign debt reliance (capital or current account deficit problem), labor shortages (implications for wages or immigration policy) and profit margins (ability to sustain business). The policy actions block includes evaluations of tax policy and monetary policy. The sources-of-financial-crisis block includes evaluations on banking, currency, fiscal deficits and crisis contagion. The exogenous block includes evaluations on oil price shocks, food price shocks and productivity shocks (which encompass numerous factors from strikes to technological impacts). Finally, the financial crisis chance block includes two elements—crisis or no crisis. Although these elements are generic enough to cover most economies, there would be a need to customize the sub-criteria for a specific type of economy. For example, the consumer debt burden sub-criterion, which is a component of domestic imbalance in some developed countries, would not apply to every economy since some local customs or banking system infrastructures would not result in heavy consumer borrowing. Similarly, labor shortages may be a problem in developed countries, but not in emerging markets. Once the characteristics of the model have been specified, then the forecaster must provide judgments on the relative importance of those various factors in the model as they relate to the system’s alternatives (in this case, financial crisis or not). The process to solve the ANP forecasting model is as follows: Step 1: Determine the Main Cluster Weights. The main or control cluster weights for {Ca, Cb, Cc, …, Cn} are determined based on: (1) whether there is feedback in the cluster (if not, the matrix entry is zero), and (2) the intensity of the relationship between the cluster and other clusters using the nine-point scale (see Table 1, p. 3). Instead of assigning two numbers wi and wj and forming the ratio wi/wj, we assign a single number drawn from the fundamental 1–9 scale of absolute numbers to represent the ratio (wi/wj)/1. It is a nearest integer

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Table 1 Formulating the control matrix

approximation to the ratio wi/wj. The derived scale will reveal what the wi and wj are. This is a central fact about the relative measurement approach used within ANP and the need for a fundamental scale. However, it should be noted that the 1–9 evaluation scale, in principle, has an unlimited range given the homogeneity and clustering that are used to extend the fundamental scale gradually from cluster to adjacent cluster, eventually enlarging the scale from 1–9 to 1–?.

3 Building the ANP Financial Crisis Model

81

To illustrate the development of the main cluster weights in our model, first observe that the exogenous-shock and financial-crisis-risk clusters do not include feedback (Fig. 1). Consequently, the entries for both clusters in the control matrix are zero. On the other hand, the policy actions, imbalances, and sources of financial crisis clusters are modeled with feedback given that those actions, events or activities can spiral upon themselves. This means a full forecast period effect must be assessed/forecasted akin to using the ‘‘dynamic multiplier’’ in stochastic modeling and cutting off the cumulative effect at the end of the forecast horizon. The crisis model’s forecast horizon is specified as 6 months. The pairwise comparisons and normalized weights for the five components of the main cluster are derived as paired comparisons of intensities, based on the 9-point scale. The development of the main-cluster priority weights is shown in Table 1 for a hypothetical developed economy. With respect to domestic imbalances, for example, a pairwise comparison of the sources-of-crisis criterion compared with the financial-crisis chance might be assigned a score in the control matrix of ‘‘8’’, which would mean that the sourcesof-crisis component has a very high likelihood of impacting domestic imbalances relative to the financial-crisis chance. These ratings—demonstrated here as judgmental scores—incorporate ‘‘existing knowledge’’ about the economic landscape from various informational sources. Each score encompasses two aspects of the forecasting process into one evaluation measure: (a) the significance of the cluster or economic process relative to the overall stated objective, and (b) the current importance of that factor. Although the former aspect may be relatively invariant over time, the latter evaluation criterion will clearly change. Step 2: Determine the Pairwise Comparisons for the Model Elements. The model weights within each cluster, {ei1, ei2, …, ein}, also are derived using the standard application of AHP. Again, pairwise comparisons are used to establish the element relationships within each cluster; the principal right eigenvector of observable pairwise-comparison matrix, A, from the system of homogeneous linear equations, Aw = nw, provides the element weights at this level, which will be used in the supermatrix. As an aside, the formulation of this problem shows that the scale for the weights, in the original units, can be recovered from the matrix of ratios by solving the problem Aw = nw or (A - nI)w = 0, which provides further assurance that the weights are mathematically related to the unobserved vector, w—that is with judicious pairwise judgment the derived weights should closely mirror the actual weights if they are available for checking. To demonstrate the process, consider an evaluation of paired comparison within the domestic imbalances block of the ANP model. The matrix of paired comparisons in this example might look as demonstrated in Table 2 for an evaluation of the elements within the domestic imbalance block with respect to the likelihood of a banking crisis for a hypothetical developed economy. The diagonal of this matrix will be all one, which implies that any component cannot be more or less likely than itself. Next, consider the entry in the cell for the comparison of the cashflow-toinvestment ratio on the left and capacity utilization rates with a banking crisis at the top of the matrix. Under the current circumstances, the cashflow of businesses would

82

3 An Analytic Network Process Model for Financial-Crisis Forecasting

greatly influence the likelihood of a banking crisis and hence the couplet is assigned the score of ‘‘5’’ on the 1–9 scale. By design, the comparison of capacity utilization and cashflow (row 1, column 2) will be equal to the reciprocal of the cashflow and capacity utilization evaluation (row 2, column 1), that is, 1/5 or 0.20. Similarly, paired comparison is used to build up the full matrix. Finally, the principal eigenvector provides the solution weights, which are shown in right-most column of Table 2. The degree of logical inconsistency is also checked. The value of the inconsistency index is 0.047 or a modest 4.7 % for this matrix of paired comparison, well below the 10 % practical threshold above which the evaluations are reassigned. Of course, a consistent evaluation is not necessarily a correct evaluation of the risks. Priority weights are computed for the other 15 matrices in this model, using a comparable approach, and each matrix is checked for its degree of inconsistency. Step 3: Construct and Solve the Supermatrix. The weights derived from steps 1 and 2 are used to populate the columns of the supermatrix. Each column of a supermatrix is either a normalized eigenvector with possibly some zero entries or all of its block entries are zero. The unweighted supermatrix, which is illustrated in the first panel of Table 3, is then multiplied by the priority weights from the clusters (which were determined in step 1), yielding the weighted supermatrix (second panel of Table 3). This is done because the resulting matrix must be column stochastic, that is its columns must add to one, for a limit that is not zero to exist. Finally, the system solution is derived by multiplying the weighted supermatrix of model variables by itself, which accounts for variable interaction, until a stable result is obtained. When the matrix is irreducible, the powers of the matrix converge to a matrix whose columns are all the same. This ‘‘power method’’ process yields the limiting matrix, which provides the relative importance weights for every factor in the model. In our example, those weights are reported in the bottom panel of Table 3. Now that the system weights have been determined, a financial-crisis turning point forecast could be derived using zero (0 %) and one (100 %) to represent no crisis or crisis (similar to the Radelet and Sachs model). This structured-judgmental forecast would be computed as Forecast Risk = 0.3841 9 (Financial Crisis) ? 0.6159 9 (No Financial Crisis) = 0.3841 9 100 % = 38.4 % chance of a financial crisis within 6 months. Although the forecast probability is a ‘‘snapshot’’ at a point in time for a specific economy, it demonstrates the process of constructing a financial-crisis turning point forecast model using ANP. Historical simulations based on rules for interpreting incoming information or expert-system rules could be used to back test the model for accuracy and to construct a time-dependent supermatrix (Saaty 1994), if historical time series data exist. Moreover, sensitivity analysis—as demonstrated in Saaty (2001)—of the individual model components provides the user with bounds on how significant changes must be in order to impact a forecast (crisis or no crisis, in this case).

Capacity utilization Cashf low toinvestment Consumer debt burden Foreign debt reliance Inventory-to-sales ratio Labor shortage Profit margins Inconsistency index

1.000

0.333

1.000

0.333

5.000

1.000

3.000

1.000

1.000

3.000

1.000

3.000

1.000

Consumer debt burden

1.000 0.333 1.000 3.000 0.333 3.000 = 0.047 (desirable value to be less than 0.10)

0.200

Cashllow-toinvestment

1.000

Capacity utilization

Table 2 Comparisons for domestic imbalances Comparisons for Domestic Imbalances with respect to Banking Crisis

0.500 2.000

1.000

1.000

0.333

1.000

0.333

Foreign debt reliance

1.000 3.000

1.000

1.000

1.000

3.000

1.000

Inventory-tosales ratio

1.000 1.000

1.000

2.000

1.000

3.000

1.000

Labor shortage

1.000 1.000

0.333

0.500

0.333

3.000

0.333

Profit margins

0.09672 0.19593

0.09085

0.17439

0.07511

0.29725

0.06975

Normalized weights

3 Building the ANP Financial Crisis Model 83

0.33333

0.23034 0.17885 0.49339 0.09743

0.5

0.4 0.2 0.2 0.2

Capacity utilization Cashflow-to-investment

0.02375 0.07223

0 0.66667 0.33333 0.66667

0 0.16667 0.83333 0.5

0.02733 0.08511

0

0.13593

0.11842

0

0.05652

0.10936

0.148

0.31232

0.14116

0

0.11506

0.15973

0

0.17473

0.20587

0.19936

0.05744

0.0661

Weighted supermatrix

Capacity utilization Cashflowtoinvestment Consumer debt burden Foreign debt reliance Inventoryto-sales ratio Labor shortage Profit margins Food prices Oil prices Productivity Financial No financial Monetary policy Tax policy Banking Contagion Currency Fiscal

Capacity Cashflowutilization toinvestment

Unweighted supermatrix

0.0436 0.1067

0.495 0.165 0.19958 0.14042

0.25

0 0.75 0.25 0.75

0

0

0.15252

0.13625

0.08147

0.10859

0.15762

0.25809

0.10546

0.04028 0.0813

0.09366 0.36975 0.40259 0.134

0.5

0 0.875 0.125 0.5

0

0

0.02545 0.05405

0.25 0.25 0.25 0.25

0.5

0 0.5 0.5 0.5

0

0

0.14706 0.15826

0.09115 0.09628

0.09115 0.09552

0.26877 0.36021

0.10777 0.09742

0.19666 0.13073

0.02802 0.05863

0.2 0.2 0.4 0.2

0.25

0 0.66667 0.33333 0.75

0

0

0.16324

0.14182

0.05085

0.31847

0.11603

0.14182

0.06777

Food prices

Oil prices

0.10863

0.10433 0.07751 0.132

0.02779 0.10958

0.38905 0.1724 0.31704 0.12151

0.25

0 0.66667 0.33333 0.75

0

0

0.16295 0.05432

0.24627 0.24627 0.29788 0.20959

0

0 0 0 0

0

0

0.01943 0.06537

0.38905 0.1724 0.31704 0.12151

0

1 0 0 0

0

0

0.04616 0.05024

0.2 0.4 0.2 0.2

0

0 0 0 0

0

0

0.17932 0.08496 0.19982 0.132

0.1319

0.08732 0.09233 0.06787 0.10863

0.16283 0.09233 0.12161 0.10863

0.10636 0.43324 0.27882 0.08421

0.26506 0.10049 0.1961

0.0207 0.04228

0.22572 0.13414 0.51664 0.1235

0.5

0 0 0 0.5

0

0

0.16839

0.11499

0.06501

0.33893

0.12373

0.12684

0.06211

0.0344 0.04451

0.46659 0.17134 0.17134 0.19073

0.2

0 0 0 0.8

0

0

0.14596

0.09868

0.26006

0.12799

0.13056

0.13354

0.10321

0.04319 0.05074

0.24626 0.2036 0.34654 0.2036

0

0 0.16667 0.83333 1

0

0

0.15507

0.14292

0.11583

0.17459

0.15479

0.13872

0.11808

0 0

0.53556 0.08434 0.32068 0.05942

1

0 0.16667 0.83333 0

0

0

0

0

0

0

0

0

0

Productivity Financial No Monetary Tax policy financial policy

0.06721 0.09233 0.05828 0.32589

Profit Inventory- Labor shortage margins to-sales ratio

0.09744 0.06157

Consumer Foreign debt debt reliance burden

Table 3 ANP supermatrices and limit matrix

0.0279 0.1189

0.54341 0.09057 0.31374 0.05229

0.2

0 0.66667 0.33333 0.8

0

0

0.19593

0.09672

0.09085

0.17439

0.07511

0.29725

0.06975

0.05324 0.05951

0.29626 0.10818 0.53567 0.05989

0.5

0 0.66667 0.33333 0.5

0

0

0.15413

0.11785

0.07901

0.23837

0.12875

0.14879

0.1331

0.05587 0.08201

0.51704 0.07097 0.36497 0.04701

0.75

0 0.25 0.75 0.25

0

0

0.18752

0.10342

0.11227

0.12672

0.12537

0.20503

0.13968

(continued)

0.02128 0.08435

0.51704 0.07097 0.36497 0.04701

0.33333

0 0.83333 0.16667 0.66667

0

0

0.20049

0.07374

0.06903

0.23329

0.15938

0.21086

0.0532

Banking Contagion Currency Fiscal

84 3 An Analytic Network Process Model for Financial-Crisis Forecasting

Capacity utilization Cashflow-to-investment Consumer debt burden Foreign debt reliance Inventory-to-sales ratio Labor shortage Profit margins Food prices Oil prices Productivity Financial No financial Monetary policy

Limiting supermatrix

Consumer debt burden Foreign debt reliance Inventory-to-sales ratio Labor shortage Profit margins Food prices Oil prices Productivity Financial No Financial Monetary Policy Tax Policy Banking Contagion Currency Fiscal

Weighted supermatrix

0.02337

0.0562

0.06119

0

0

0 0.04053 0.02026 0.1245 0.06225 0.07809 0.06064 0.16728 0.03303

0.04521

0.04896

0.08242

0

0

0 0.01013 0.05066 0.09337 0.09337 0.13562 0.06781 0.06781 0.06781

0.02375 0.07223 0.04757 0.12912 0.02337 0.0562 0.06119 0 0 0 0.04053 0.02026 0.1245

0.12912

0.05836

0.02733 0.08511 0.06604 0.05836 0.04521 0.04896 0.08242 0 0 0 0.01013 0.05066 0.09337

0.04757

0.06604

Table 3 (continued)

0.0436 0.1067 0.06516 0.04489 0.03368 0.05633 0.06306 0 0 0 0.04559 0.0152 0.14006

0 0.04559 0.0152 0.14006 0.04669 0.16783 0.05594 0.06767 0.04761

0

0

0.06306

0.05633

0.03368

0.04489

0.06516

0.04028 0.0813 0.04455 0.11111 0.03768 0.03768 0.0608 0 0 0 0.05319 0.0076 0.09337

0 0.05319 0.0076 0.09337 0.09337 0.03175 0.12536 0.1365 0.04543

0

0

0.0608

0.03768

0.03768

0.11111

0.04455

0.02545 0.05405 0.04028 0.14892 0.03949 0.03981 0.06543 0 0 0 0.0304 0.0304 0.09337

0 0.0304 0.0304 0.09337 0.09337 0.08476 0.08476 0.08476 0.08476

0

0

0.06543

0.03981

0.03949

0.14892

0.04028

0.02802 0.05863 0.04797 0.13166 0.02102 0.05863 0.06749 0 0 0 0.04053 0.02026 0.14006

0 0.04053 0.02026 0.14006 0.04669 0.06781 0.06781 0.13562 0.06781

0

0

0.06749

0.05863

0.02102

0.13166

0.04797

0.02779 0.10958 0.04397 0.06732 0.0361 0.05453 0.07413 0 0 0 0.04053 0.02026 0.14006

0 0.04053 0.02026 0.14006 0.04669 0.13191 0.05845 0.10749 0.0412

0

0

0.07413

0.05453

0.0361

0.06732

0.04397

0.04616 0.05024 0.21662 0.04616 0.04616 0.05217 0.04248 0 0 0 0 0 0

0 0 0 0 0 0.1 0.2 0.1 0.1

0

0

0.04248

0.05217

0.04616

0.04616

0.21662

0.01943 0.06537 0.09294 0.04054 0.02262 0.02584 0.06661 0 0 0.33333 0 0 0

0.33333 0 0 0 0 0.12968 0.05747 0.10568 0.0405

0

0

0.06661

0.02584

0.02262

0.04054

0.09294

0.16295 0.05432 0.0421 0.05432 0.05432 0.066 0.066 0 0 0 0 0 0

0 0 0 0 0 0.12313 0.12313 0.14894 0.10479

0

0

0.066

0.066

0.05432

0.05432

0.0421

0.0207 0.04228 0.04124 0.11298 0.02167 0.03833 0.05613 0 0 0 0 0 0.16667

0 0 0 0.16667 0.16667 0.07524 0.04471 0.17221 0.04117

0

0

0.05613

0.03833

0.02167

0.11298

0.04124

0.0344 0.04451 0.04352 0.04266 0.08669 0.03289 0.04865 0 0 0 0 0 0.26667

0 0 0 0.26667 0.06667 0.15553 0.05711 0.05711 0.06358

0

0

0.04865

0.03289

0.08669

0.04266

0.04352

0.04319 0.05074 0.05662 0.06386 0.04237 0.05228 0.05672 0 0 0 0.06191 0.30953 0.14318

0 0.06191 0.30953 0.14318 0 0.02945 0.02435 0.04145 0.02435

0

0

0.05672

0.05228

0.04237

0.06386

0.05662

0 0 0 0 0 0 0 0 0 0 0.09761 0.48804 0

0 0.09761 0.48804 0 0.22576 0.101 0.01591 0.06048 0.01121

0

0

0

0

0

0

0

0.0279 0.1189 0.03004 0.06976 0.03634 0.03869 0.07837 0 0 0 0.13333 0.06667 0.16

0 0.13333 0.06667 0.16 0.04 0.10868 0.01811 0.06275 0.01046

0

0

0.07837

0.03869

0.03634

0.06976

0.03004

0.05324 0.05951 0.0515 0.09535 0.0316 0.04714 0.06165 0 0 0 0.13333 0.06667 0.1

0 0.13333 0.06667 0.1 0.1 0.05925 0.02164 0.10713 0.01198

0

0

0.06165

0.04714

0.0316

0.09535

0.0515

0.05587 0.08201 0.05015 0.05069 0.04491 0.04137 0.07501 0 0 0 0.05 0.15 0.05

0 0.05 0.15 0.05 0.15 0.10341 0.01419 0.07299 0.0094

0

0

0.07501

0.04137

0.04491

0.05069

0.05015

(continued)

0.02128 0.08435 0.06375 0.09332 0.02761 0.0295 0.0802 0 0 0 0.16667 0.03333 0.13333

0 0.16667 0.03333 0.13333 0.06667 0.10341 0.01419 0.07299 0.0094

0

0

0.0802

0.0295

0.02761

0.09332

0.06375

3 Building the ANP Financial Crisis Model 85

Tax policy Banking Contagion Currency Fiscal

Limiting supermatrix

0.09337 0.13562 0.06781 0.06781 0.06781

Table 3 (continued)

0.06225 0.07809 0.06064 0.16728 0.03303

0.04669 0.16783 0.05594 0.06767 0.04761

0.09337 0.03175 0.12536 0.1365 0.04543

0.09337 0.08476 0.08476 0.08476 0.08476

0.04669 0.06781 0.06781 0.13562 0.06781

0.04669 0.13191 0.05845 0.10749 0.0412

0 0.1 0.2 0.1 0.1

0 0.12968 0.05747 0.10568 0.0405

0 0.12313 0.12313 0.14894 0.10479

0.16667 0.07524 0.04471 0.17221 0.04117

0.06667 0.15553 0.05711 0.05711 0.06358

0 0.02945 0.02435 0.04145 0.02435

0.22576 0.101 0.01591 0.06048 0.01121

0.04 0.10868 0.01811 0.06275 0.01046

0.1 0.05925 0.02164 0.10713 0.01198

0.06667 0.10341 0.01419 0.07299 0.0094

0.15 0.10341 0.01419 0.07299 0.0094

86 3 An Analytic Network Process Model for Financial-Crisis Forecasting

4 The 1991 U. S. Banking Crisis

87

4 The 1991 U. S. Banking Crisis Now that we have sketched out the structure and mechanics of the ANP model, the remaining question is: How good is this model empirically, even though it captures the essence of previous econometric and judgmental forecasting research? Obviously, one shortcoming of judgmental forecasting is determining historical accuracy. Notwithstanding, it should be clear that we offer the ANP framework as a method to structure one’s thinking about financial-crisis triggers or catalysts, especially when data do not exist or given numerous intangibles, such as an unstable political climate and changes to the legal or regulatory structure. The ANP method derives a judgmental forecast of the event risk given the evaluator’s knowledge of the current situation, institutions, structural and political changes, and the expectation of change. This framework is conceptually very different from econometric or time-series model forecasts of financial-crisis risk, which are based on ‘‘historical statistical experience.’’ These methods rarely are interchangeable, but they can be complementary (Stewart and Lusk 1994). It is impossible to fairly use a judgmental forecasting method, such as this ANP model, to back test how accurate the model ‘‘would have been’’ in signaling an event-driven financial crisis. Nonetheless, it is possible to test our model based on constructed decision rules, provided that historical data exist to derive them and largely ignoring purely judgmental information that may have been available at the time. Obviously, this test will compromise the true benefit of including pure intangibles, but it will test the validity of the model structure. Of course, nothing will replace real-time testing of a judgmental forecasting model, rule-based historical testing is a second-best solution, though Armstrong and Collopy (1998) observed that forecast rules can work well when trends are not persistent and there is good knowledge about the situation. Rules are used here as a proxy for judgmental decision making and they facilitate testing of the ANP model. Yet this relatively simplistic historical evaluation of the ANP model inputs using those rules can not prove the ANP model’s accuracy, only its validity. Our test of the ANP financial-crisis forecasting model is based on whether it signaled the January 1991 banking crisis in the U.S. economy as determined by Wolfson (1994). In lieu of human judgment, each indicator in the model was evaluated by the Goldstein et al. (2000) ‘‘signaling technique,’’ whereby an optimal threshold for each criterion was derived based on its histogram, and a threshold signal was marked off when the value of the indicator crossed a given percentile. Thresholds were determined based on the individual indicator’s distribution at 5, 10, 15, 20 and 25 %, if the lower bound was of interest, or when the upper bound in the distribution was of interest the threshold breakpoints were 75, 80, 85, 90 and 95 % where the indicator change signaled the crisis point. This approach assumes: (1) Observations falling in the lower or upper 25 % or less of the distribution are considered to be signals of increased risk (where the nature of the series determines whether the upper tail or lower tail is relevant), (2) The strength of those signals will be determined by how much of an outlier the actual

88

3 An Analytic Network Process Model for Financial-Crisis Forecasting

Table 4 Backtesting rule for assigning risk scores using the ‘‘signaling technique’’ evaluating incoming information on the saaty scale based on histogram Assigned Saaty Threshold for upper tail Threshold for lower tail score of distribution of distribution 1 3 5 7 8 9

Less than 75 % Equal to 75 % but Greater than 80 % 85 % Greater than 85 % 90 % Greater than 90 % 95 % Greater than 95 %

less than 80 % but less than but less than but less than

Greater than 25 % Equal to 25 % but greater than 20 % Less than 20 % but greater than 15 % Less than 15 % but greater than 10 % Less than 10 % but greater than 5 % Less than 5 %

value is relative to its histogram (or fitted distribution), which is a proxy for ‘‘perceived impact,’’ and (3) The signal rejection region (no crisis) is located in the remainder of the distribution. Our application of this threshold-search process was prompted by the successful use of it by Goldstein et al. (2000), in their determination of signals of financial vulnerability for emerging markets. To implement the mechanical ‘‘pseudo-judgmental’’ evaluation (so as to allow for reproducibility) of historical information based on the fundamental evaluation scale, risk scores were assigned to observations based on how extreme the values were in the historical distribution for each series. Depending on whether an ANP model factor’s lower tail or upper tail of the historical observations mattered (at least theoretically) for financial risk, the assigned risk scores and threshold points followed the rules shown in Table 4. For example, if the value of the current-account-deficit-to-GDP ratio (our empirical measure of foreign-debt reliance) was in the bottom 20 % of the distribution, it was assigned a score of ‘‘5’’, but if it was in the bottom 5 % of the distribution then it was assigned a score of ‘‘9’’ on the fundamental scale. Finally, a decision-making rule was applied as a backtesting simplification based on the two outcomes or alternatives: ‘‘crisis’’ (100 % chance) or ‘‘no crisis’’ (0 % chance). This rule mapped risk scores greater than ‘‘6’’ on the 1–9 scale (based on the maximum reading over the current and three previous month’s readings) to the crisis outcome and everything else to the no crisis scenario for the individual component under analysis. This procedure was applied to each component, as shown in Table 5, and for each period. Over the 1990–1992 period, the sequential model evaluation by those decision rules showed that the overall probability of a financial crisis rose from essentially zero earlier in 1990 to about 80 % by October 1990, which seemingly would have warned of some looming form of financial crisis. The more specific probability of a banking crisis, meanwhile, which was less than 20 % at the beginning of 1990 grew to over 60 % by mid 1990, then receded a bit and rose to a peak of over 70 % by March 1991. Wolfson’s research determined that the beginning of the banking crisis was January 1991. As such, the model captured the growing banking-crisis

0.6 % 0.2 % 2.1 % 0.0 pts. -0.33 % 0.801 % 0.7 % 5.7 % 82.1 % -0.8 % 0.0 pt. 62.6 pts. 8.8 % -1.39 % 5.5 % 2.7 %

Wholesale energy prices Wholesale food prices Productivity Profit margin Inventory/sales ratio Corp. financing ability Consumer debt Unemployment rate Capacity utilization rate Current account Monetary policy Tax policy Banking Fiscal Currency Contagion

Monthly percentage change Monthly percentage change Quarterly percentage change (AR) First difference Growth (TQSAR) Cashflow-to-investment ratio Monthly percentage change Level Level Current account to GDP ratio Change in fed funds rate Effective tax rates (corp. ? personal) Nonfin. corp. credit Mkt borrowing % Federal deficit/GDP ratio Trade-weighted dollar growth Change in export and import shares

Average

Table 5 Variables used to backtest ANP model Variable/concept Form 2.8 pp. 1.1 pp. 3.6 pp. 0.4 pts. 2.52 pp. 0.078 pp. 0.5 pp. 1. 58 pp. 3.52 pp. 1.4 pp. 0.6 pp. 12.1 pp. 3.8 pp. 2.0 pp. 6.86 pp. 7.3 pp.

Std. dev. 13.4 % 9.5 % 13.3 % 1.3 pts. 6.63 % 0.955 % 2.3 % 10.8 % 89.4 % 1.3 % 3.1 pts. 86.7 pts. 17.1 % 2.5 % 24.3 % 37.4 %

Max

-14.0 % -3.3 % -5.9 % -2.3 pts. -7.84 % 0.600 % -1.4 % 2.5 % 71.1 % -4.5 % -6.6 pts. 47.7 pts. -3.1 % -6.4 % -10.0 % -17.9 %

Max

4 The 1991 U. S. Banking Crisis 89

90

3 An Analytic Network Process Model for Financial-Crisis Forecasting

Fig. 2 Financial-crisis model backtesting exercise

risk during 1990, though its peak risk level occurred after the actual turning point date. The results are displayed in Fig. 2. Although this empirical test of the ANP crisis-forecasting model was very encouraging, we must underscore the point that it is only illustrative of capturing the crisis dynamic within an ANP framework. The full power of the ANP framework was compromised necessarily by this backtesting exercise. Nevertheless, as a test of the mathematical structure of this model and the logic embodied in it, these results using the imbalance-crisis-turning-point model were very encouraging.

5 Conclusion

91

5 Conclusion As a practical matter, Kahneman and Tversky (1973) observed that, ‘‘In making predictions and judgments under uncertainty, people do not appear to follow the calculus of chance or the statistical theory of prediction. Instead, they rely on a limited number of heuristics.’’ This especially may be true when data limitations make a timely statistical forecast impossible. However, ANP offers a judgmental forecasting structure to evaluate those heuristics in a consistent manner. The model was back tested for a period in the early 1990s when there was a banking crisis in the United States. It was not our intent to evaluate any individual forecaster’s ability or collective forecasting accuracy, per se, but to evaluate the potential robustness of the crisis forecasting model’s structure, which in turn might be used for real-time judgmental forecasting. We found that the ANP model approach indeed was a promising methodology to forecast the likelihood of event-driven cycles.

References Armstrong, J. S. & Collopy, F. (1998). Integration of Statistical Methods and Judgment for Time Series Forecasting: Principles from Empirical Research. Forecasting with Judgment. New York: Wiley, 269-293. Aziz, J., Caramazza, F. & Salgado, R. (2000). Currency Crises: In Search of Common Elements. IMF Working Paper No. 67. Washington, DC: International Monetary Fund. Blair, A. R., Nachtmann, R., Saaty, T. L., & Whitaker, R. (2002). Forecasting the Resurgence of the U.S. Economy in 2001: An Expert Judgment Approach. Soci-Economic Planning Sciences, 36 (June), 77-91. Burns, A. F. (1969). The Business Cycle in a Changing World. New York: National Bureau of Economic Research, Columbia University Press. Frei, F. X. & Harker, P. T. (1999). Measuring Aggregate Process Performance Using AHP. European Journal of Operational Research, 116, 436-442. Glick, R. & Moreno, R. (1999). Money and Credit, Competitiveness, and Currency Crises in Asia and Latin America. Working Paper PB99-01. San Francisco, CA: Federal Reserve Bank, Center for Pacific Basic Monetary and Economic Studies. Goldstein, M., Kaminsky, G. & Reinhart, C. (2000). Assessing Financial Vulnerability: An Early Warning System for Emerging Markets. Washington, DC: Institute for International Economics. International Monetary Fund (1998). Financial Crises: Characteristics and Indicators of Vulnerability. World Economic Outlook. Washington, DC: IMF, 74-97. Kahneman, D. & Tversky, A. (1973). On the Psychology of Prediction. Psychological Review, 80, 237-251. Kaminsky, G. & Reinhart, C. (1999). The Twin-Crises: The Causes of Banking and Balance-ofPayments Problems. American Economic Review, 89 (No. 3), 473-500. Kindleberger, C. (1996). Manias, Panics, and Crashes: A History of Financial Crises, Third Edition, New York: Wiley. Lowell, J., Neu, C. R., & Tong, D. (1998). Financial Crises and Contagion in Emerging Market Countries. Santa Monica, CA: RAND.

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Medda, F., & Nijkamp, P. (forthcoming). A Combinatorial Assessment Methodology for Complex Policy Analysis. Journal of Integrated Assessment. Niemira, M. P. (2001). An AHP-Based Composite Cyclical-Performance Index. Indian Economic Review, 36 (1), 241-250. Radelet, S. & Sachs, J. D. (1998). The East Asian Financial Crisis: Diagnosis, Remedies, Prospects. Brookings Papers on Economic Activity, 1, 1-90. Saaty, T. L. (2001). Decision Making with the Analytic Network Process (ANP) and its ‘SuperDecisions’ Software: The National Missile Defense (NMD) Example. Berne, Switzerland: ISAHP Conference Presentation. Saaty, T. L. (1996). Decision Making With Dependence and Feedback: The Analytic Network Process. Pittsburgh, PA: RWS Publications, 4922 Ellsworth Ave. Saaty, T. L. (1994). Fundamentals of Decision Making and Priority Theory. Pittsburgh, PA: RWS Publications, 4922 Ellsworth Ave. Saaty, T. L. (1990). Multicriteria Decision Making: The Analytic Hierarchy Process. Pittsburgh, PA: RWS Publications, 4922 Ellsworth Ave. Sachs, J. D. (1998). Alternative Approaches to Financial Crises in Emerging Markets. Capital Flows and Financial Crises (Miles Kahler, ed.). Itacha, NY: Cornell University Press, 247262. Stewart, T. R. & Lusk, C. M. (1994). Seven Components of Judgmental Forecasting Skill: Implications for Research and the Improvement of Forecasts. Journal of Forecasting, 13, 579599. Wolfson, M. H. (1994). Financial Crises: Understanding the Postwar U.S. Experience, Second Edition. Armonk, New York: M. E. Sharpe. Zarnowitz, V. & Boschan, C. (1975). Cyclical Indicators: An Evaluation of and New Leading Indexes. Business Conditions Digest. Washington, DC: U.S. Department of Commerce, Bureau of Economic Analysis, v-xxiv.

Chapter 4

Outsourcing a Firm’s Application Development Group

1 Introduction Outsourcing Information Technology (IT) functions is a growing trend in businesses looking for ways to reduce cost and hasten time-to-market of customerfacing and internal applications. The strategy of outsourcing functions, tasks, and activities to another company has existed for decades. During periods of recession, U.S. corporations cut costs by moving jobs that are of a repetitive nature to lowercost regions, typically ‘‘offshore’’ or in non-U.S. countries. For example, manufacturing companies have been leveraging offshore resources since the 1950s, while the off-shoring of IT started about 10–15 years ago with the movement of legacy system maintenance tasks to Ireland and Canada. According to Bart Perkins, Computer World, businesses are now looking towards outsourcing for three reasons: budget pressures, a view of IT as a ‘‘no win’’ function, and the existence of specialized service providers. Many firms continue to face budget constraints with budgets remaining flat and most firms looking to reduce costs. In some cases, the IT function is viewed as a utility that can and should be outsourced. With the rapid changes in technology, it is difficult for in-house developers to match the skill sets of outsourcers with specialized, targeted skills, making it more attractive to outsource development activities in order to keep up with improvements in technology. Given these views, many businesses are resurrecting the interest in outsourcing. IT outsourcing seems to be easier than ever to accomplish: telecommunications have improved drastically, enabling better productivity of a remote workforce; geographic distances are becoming more transparent with use of collaboration tools available today, such as online web meetings and improved video conferencing technology. And who can argue with the obvious personnel and IT asset cost reduction opportunities associated with this strategy? All of this, however, must be tempered with the soft costs and risks inherent in moving a firm’s codified business processes to a potentially insecure, unstable environment. The decision model network and judgments discussed below are based upon research, as cited in the References section of this chapter. T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_4,  Springer Science+Business Media New York 2013

93

94

4

Outsourcing a Firm’s Application Development Group

How should companies staff their application development functions?

Benefits

Opportunities

Costs

Risks

Fig. 1 BOCR model

2 The Model The objective or goal of this model is to address the question: ‘‘How should companies staff their application development function?’’ The model includes the benefits, opportunities, costs, and risks involved in making this decision. Further details appear below (Fig. 1). Alternatives: 1. Outsource all application development work 2. Outsource the design and programming phases 3. Do not outsource any application development work. Systems Development Life Cycle Alternative #1 - Outsource all application development work

Needs & Requirements Definition

Analysis & Design

Program/Code

Test

Move to Production

Alternative #2 - Outsource design and programming phases Alternative #3 - Do not outsource any application development work

Merits The merits and elements used in the model are described below and shown in the following table (Table 1). Benefits Economic and Technological benefits were identified for this portion of the model (Fig. 2).

2 The Model

95

Table 1 Clusters in the decision networks and elements in the clusters BOCR Benefits

Control criteria Economic

Clusters

Elements in clusters

Financial Operational

(1) IT assets, (2) Personnel, (3) Legal (1) Time to finish project/job, (2) Use oF project management, (3) Knowledge transfer during requirements def, (4) Control/influence over human resources, (5) Fast time-to-market (1) Leverage solutions from prev. business problems, (2) Newest technology available (1) Knowledge of latest technologies, (2) Immediately available (1) Grow into other countries, (2) Customer retention (1) Agile, quick response to customer requests. (2) New features/functionality (1) Expansion into foreign countries, (2) Expand product line (1) Make investments. (2) Reduce debt (1) Focus—quality assurance of software, (2) Focus—firm’s core cap abilities, (3) Focus— software alignment with business. (4) Productivity (1) IT assets, (2) Personnel, (3) Legal (1) Time to finish project/job, (2) Use of project management. (3) Knowledge transfer during requirements def, (4) Control / influence over human resources, (5) Time- to-market (1) Knowledge of latest technologies, (2) Immediately available (1) Company shareholders perception, (2) Media criticism, (3) Company executives/managers perception. (4) Company employees perception (1) US unemployment, (2) Employee morale, (3) Control/influence over human resources, (4) Productivity (1) Legal costs (1) Business process knowledge. (2) Business continuity. (3) Quality assurance (1) Physical. (2) Intellectual property. (3) Geopolitical environment—stability (1) Geographic distance, (2) Communication tool availability—email voice mail. (3) H-1B and L-1 visa availability, (4) Language differences (1) Employee morale, (2) Productivity, (3) US unemployment (1) Company shareholders perception, (2) Media criticism. (3) Company executives f managers perception, (4) Company employees perception (1) Outsource all application development work, (2) Outsource the design and programming phases. (3) Do not outsource any application development work

Technological Technology Resources Opportunities Customerrelated

Customer base Marketing

Costs

Economic

Business development Financial Employees

Economic

Financial Operational

Resources Social

Stakeholders

Labor

Risks

Economic

Financial Business processes Security Communication

Social

Labor Stakeholders

All networks Alternatives

96

4

Outsourcing a Firm’s Application Development Group

How should companies staff their application development functions?

Goal

Control Criteria

Economic

Technological

Fig. 2 Benefits model

Under Economic benefits, there are two clusters: Financial and Operational (See Fig. 3). These clusters include the following nodes. • Financial nodes: IT assets, Personnel, and Legal. IT Assets refers to the reduction of IT infrastructure costs such as workstations, servers, and licensing; Personnel refers to the reduction of costs for activities such as salaries, health insurance, pension benefits; Legal refers to the avoidance of costs associated with contract negotiations. • Operational nodes: Time to finish project/job, Use of project management, Knowledge transfer during requirements definition, Control/influence over human resources, and Fast time-to-market. The concepts behind these items are

1 Alternatives 1 Outsource all application development work 2 Outsource the design and programming phases 3 Do not outsource any application development work

2 Financial

3 Operational

1 IT assets

1 Time to finish project / job

2 Personnel

2 Use of project management

3 Legal

3 Knowledge transfer during requirements def 4 Control / influence over human resources 5 Fast time-to-market

Fig. 3 Clusters with elements under economic benefits

2 The Model

97

Fig. 4 Clusters with elements under technological benefits

rather self-explanatory; however to expand upon a couple may be necessary. Knowledge transfer during requirements definition is a key item when it comes to documenting system and application requirements and communicating those effectively to the persons programming and testing the application. Fast timeto-market relates to an enterprise’s ability to quickly and with agility, meet its customer needs and wants through use of IT solutions. Under Technological benefits, there are also two clusters: Technology and Resources (see Fig. 4). These clusters include the following nodes. • Technology nodes: Leverage solutions from previous business problems and newest technologies available. The first item relates to an application development group’s ability to take what it has learned from solving similar or other business problems in the past, and leveraging or applying that experience to a current or new problem. The second item relates to an enterprise being able to take advantage of newer technologies without a lot of cost to the firm in terms of ramping up its IT infrastructure. • Resources nodes: Knowledge of latest technologies and immediately available. These speak to the human resource aspect of technology benefits in that people are knowledgeable in the newest ways to use technology and these people are readily available to work on a new high priority project. Opportunities Economic and Customer-related opportunities were identified for this portion of the model (see Fig. 5). Under Economic opportunities, there are three clusters: Business development, Financial, and Employees (see Fig. 6). These clusters include the following nodes.

98

4

Outsourcing a Firm’s Application Development Group

How should companies staff their application development functions?

Goal

Control Criteria

Customer - related

Economic

Fig. 5 Opportunities model

• Business development nodes: Expansion into foreign countries and Expand product line. Expanding into foreign countries is an opportunity when outsourcing with non-U.S. vendors. Expanding product line may be a stretch, but it is identified as an opportunity because the cost reduction provided by outsourcing may enable expansion of a firm’s offering. • Financial nodes: Make investments and Reduce debt. Opportunities to engage in these financial activities may be present more readily when outsourcing as opposed to not outsourcing (i.e., rather than investing in a firm’s own IT assets 1 Alternatives 1 Outsource all application development work 2 Outsource the design and programming phases 3 Do not outsource any application development work

2 Business Development

3 Financial

1 Expansion into foreign countries

1 Make investments

2 Expand product line

2 Reduce debt

4 Employees 1 Focus - quality assurance of software 2 Focus - firm's core capabilities 3 Focus - software alignment with business 4 Productivity

Fig. 6 Clusters with elements under economic opportunities

2 The Model

99 1 Alternatives 1 Outsource all application development work 2 Outsource the design and programming phases 3 Do not outsource any application development work

2 Customer Base 1 Grow into other countries 2 Customer retention

3 Marketing 1 Agile, quick response to customer requests 2 New features / functionality

Fig. 7 Clusters with elements under customer-related opportunities

and personnel, the firm may identify an opportunity to invest money saved through outsourcing.) • Employees nodes: Focus-quality assurance of software, Focus-firm’s core capabilities, Focus-software alignment with business, and Productivity. The three ‘‘focus’’ opportunities identified relate to having IT employees concentrate on these value-added competencies rather than focusing on the tasks of programming or coding. An opportunity to increase productivity among employees may also be present when outsourcing. Under Customer-related opportunities, there are two clusters: Customer base and Marketing (see Fig. 7). These clusters include the following nodes. • Customer base nodes: Grow into other countries and Customer retention. Expansion of customer base by growing into other countries may be an opportunity with respect to the outsourcing alternatives. By meeting (exceeding) customer business needs and requirements through technology, a firm has an opportunity to better retain its existing customers. • Marketing nodes: Agile, quick response to customer requirements and New features/functionality. By having an applications development process that is able to quickly address customer requirements, a firm has an opportunity to improve its marketing to new and existing customers. New features/functionality in an application can be marketed and present another customer-based opportunity for the firm. Costs Economic and Social costs were identified for this portion of the model (see Fig. 8). Under Economic costs, there are three clusters: Financial, Operational, and Resources (see Fig. 9). These clusters include the following nodes.

100

4

Outsourcing a Firm’s Application Development Group

How should companies staff their application development functions?

Goal

Control Criteria

Economic

Social

Fig. 8 Costs model

• Financial nodes: IT Assets, Personnel, and Legal. IT Assets refers to the cost of retaining IT infrastructure for things such as workstations, servers, and licensing. Personnel refers to the retention of costs for things such as salaries, health insurance, pension benefits; Legal refers to the accumulation of costs associated with contract negotiations. • Operational nodes: Time to finish project/job, Use of project management, Knowledge transfer during requirements definition, Control/influence over human resources, and Fast time-to-market. In terms of cost, the first four items’ cost increases with outsourcing. They are interrelated with or without

1 Alternatives 1 Outsource all application development work 2 Outsource the design and programming phases 3 Do not outsource any application development work

2 Financial

4 Resources

1 1 IT ITassets assets of of latest technologies 11 Knowledge Knowledge latest technologies

2 Personnel Personnel 22Immediately available Immediately available 33 Legal Legal

3 Operational Time to project / job/ job 11 Time tofinish finish project Use of management 22 Use ofproject project management Knowledge transfer during requirements def 33 Knowledge transfer during requirements def Control / /influence over human resources 44 Control influence over human resources Time-to-market 55 Time-to-market

Fig. 9 Clusters with elements under economic costs

2 The Model

101 1 Alternatives 1 Outsource all application development work

2 Outsource the design and programming phases

3 Do not outsource any application development work

3 Stakeholders 1 Company shareholders perception 2 Media criticism 3 Company executives / managers perception 4 Company employees perception

2 Labor 1 US unemployment 2 Employee morale 3 Control / influence over human resources 4 Productivity

Fig. 10 Clusters with elements under social costs

outsourcing. Fast time-to-market relates to an enterprise’s ability to quickly and with agility, meet its customer needs and wants through use of IT solutions. Without outsourcing, this becomes a cost. • Resources nodes: Knowledge of latest technologies and availability. Without outsourcing, these two items become costs; resources with knowledge of the latest technologies may not be available quickly. Under Social costs, there are two clusters: Stakeholders and Labor (see Fig. 10). These clusters include the following nodes. • Stakeholders nodes: Company shareholders’ perception, Media criticism, Company executives/managers’ perception and Company employees’ perception. These four nodes are rather self-explanatory and represent the various stakeholders’ perceptions’ influence on this decision. • Labor nodes: U.S. unemployment, Employee morale, Control/influence over human resources and Productivity. Again, these nodes are rather self-explanatory in terms of costs for the alternatives. Risks Economic and Social risks were identified for this portion of the model (see Fig. 11). Under Economic risks, there are four clusters: Financial, Security, Communication and Business processes (see Fig. 12). These clusters include the following nodes. • Financial node: Legal costs. The risk of incurring legal costs is represented here.

102

4

Outsourcing a Firm’s Application Development Group

How should companies staff their application development functions?

Goal

Control Criteria

Economic

Social

Fig. 11 Risks model

• Security nodes: Physical, Intellectual property, and Geopolitical environment— stability. The risk to the physical security of servers and other IT equipment is represented through the Physical node. The Intellectual property node represents the risk of losing control or ownership of programs and software written for an enterprise. The Geopolitical environment risk pertains to the increased risk of outsourcing a firm’s programming function to an area of the world that is or soon may be at war. • Communication nodes: Geographic distance, Communication tool availability— email/voice mail, H-1B and L-1 visa availability and Language differences. Distance, communication tool availability, and language differences represent the risks of poor communication as a result of outsourcing. With the risk that H-1B and L-1 visas will be limited, a firm may have a much more difficult time 1 Alternatives 1 Outsource all application development work 2 Outsource the design and programming phases 3 Do not outsource any application development work

2 Business Process

5 Financial 1 Legal costs

1 Business process knowledge 2 Business continuity 3 Quality assurance

4 Security 1 Physical

3 Communication 1 Geographic distance

2 Intellectual property

2 Communication tool availability - email voice mail

3 Geopolitical environment - stability

3 H-1B and L-1 visa availability 4 Language differences

Fig. 12 Clusters with elements under economic risks

2 The Model

103 1 Alternatives 1 Outsource all application development work 2 Outsource the design and programming phases 3 Do not outsource any application development work

2 Financial 1 Employee morale 2 Productivity 3 US unemployment

2 Stakeholders 1 Company shareholders perception 2 Media criticism 3 Company executives / managers perception 4 Company employees perception

Fig. 13 Clusters with elements under social risks

bringing in foreign outsourcers to work closely and communication with its U.S.-based personnel. • Business processes nodes: Business process knowledge, Business continuity, and Quality assurance. By outsourcing the areas represented by these nodes reflects the risk that any of these could suffer. Under Social risks, there are two clusters: Labor and Stakeholders (see Fig. 13). These clusters include the following nodes. • Labor nodes: Employee morale, Productivity and U.S. unemployment. These nodes are rather self-explanatory in terms of risks and influence on the alternatives. • Stakeholders nodes: Company shareholders’ perception, Media criticism, Company executives/managers’ perception, and Company employees’ perception. These four nodes are rather self-explanatory and represent the various stakeholders’ perceptions’ influence on this decision in terms of risk.

3 BOCR Priorities The elements under each of the BOCR merits received priorities through pairwise comparisons as shown in Table 2. Table 3 represents priorities for the ideal alternatives under each BOCR control criterion. To obtain the priorities of Table 2, we fist prioritize the clusters constituting the subnets under the control criteria corresponding to each of the merits. For example, consider Fig. 3. Under the control criterion Economic benefits there are three

Economic 0.75

Customer related 0.25

Clusters

Financial

Business development

Alternatives

Marketing

Customer base

Alternatives

Technology

Resources

Alternatives

Operational

Financial

Alternatives

Outsource all application dev. func. Outsource the design… Do not outsource IT assets Personnel Legal Time to finish project/job Use of project management Knowledge transfer during requirements def Control/influence over human resources Fast time-to-market Outsource all application dev. func. Outsource the design… Do not outsource Knowledge of latest technologies Immediately available Leverage solutions from prev. business Newest technology available Outsource all application dev. func. Outsource the design… Do not outsource Grow into other countries Customer retention Agile, quick response to customer requests New features/functionality Outsource all application dev. func. Outsource the design… Do not outsource Expansion into foreign countries Expand product line Make investments Reduce debt

1. 2. 3. 1. 2. 3. 1. 2. 3. 4. 5. 1. 2. 3. 1. 2. 1. 2. 1. 2. 3. 1. 2. 1. 2. 1. 2. 3. 1. 2. 1. 2.

Elements

0.3748 0.1678 0.2848 0.7152 0.8333 0.1667 0.4362 0.3381 0.2257 0.5 0.5 0.6667 0.3333

0.5824 0.2166 0.211 0.4505 0.1758 0.3737 0.1745 0.2296 0.2274 0.1208 0.2475 0.4437 0.4437 0.1126 0.1852 0.8148 0.8 0.2 0.4573

Local priorities

(continued)

0.1666 0.0746 0.0949 0.2384 0.1852 0.037 0.2053 0.1582 0.1062 0.0828 0.0828 0.1104 0.0552

0.2821 0.1048 0.0874 0.1081 0.0426 0.0805 0.0477 0.0628 0.0626 0.0331 0.0677 0.2168 0.0168 0.055 0.0453 0.1881 0.2136 0.0534 0.2033

Global priorities

4

Opportunities

Benefits

Technological 0.1667

Criteria

Economic 0.8333

BOCR

Table 2 Criteria and elements with their priorities

104 Outsourcing a Firm’s Application Development Group

Economic 0.8333

Costs

Social 0.1667

Criteria

BOCR

Table 2 (continued)

Labor

Stakeholders

Alternatives

Resources

Operational

Financial

Alternatives

Focus—quality assurance of software Focus—firm’s core capabilities Focus—software alignment with business Productivity Outsource all application dev. func. Outsource the design… Do not outsource IT assets Personnel Legal Time to finish project/job Use of project management Knowledge transfer during requirements def Control/influence over human resources Time-to-market Knowledge of latest technologies Immediately available Outsource all application dev. func. Outsource the desiqn… Do not outsource Company shareholders perception Media criticism Company executives/managers perception Company employees perception US unemployment Employee morale Control/influence over human resources Productivity

Elements 1. 2. 3. 4. 1. 2. 3. 1. 2. 3. 1. 2. 3. 4. 5. 1. 2. 1. 2. 3. 1. 2. 3. 4. 1. 2. 3. 4.

Clusters

Employees

0.3121 0.2281 0.2639 0.1948 0.2882 0.2797 0.432 0.2631 0.5472 0.1897 0.2458 0.1457 0.2168 0.0832 0.3084 0.2589 0.7411 0.3682 0.3416 0.2902 0.1486 0.2695 0.2261 0.3558 0.0621 0.2995 0.1204 0.518

Local priorities

Global priorities

(continued)

0.0618 0.0454 0.0523 0.0386 0.1307 0.1268 0.1958 0.0338 0.0827 0.0287 0.0601 0.0356 0.053 0.0203 0.0754 0.0391 0.112 0.1003 0.0931 0.0791 0.0379 0.0687 0.0577 0.0307 0.0294 0.1415 0.0569 0.2448

3 BOCR Priorities 105

Risks

Stakeholders

Labor

Alternatives

Communication

Security

Financial Business process

Alternatives

Clusters

Elements 1. Outsource all application dev. func. 2. Outsource the design… 3. Do not outsource 1. Legal costs 1. Business process knowledge 2. Business continuity 3. Quality assurance 1. Physical 2. Intellectual property 3 Geopolitical environment—stability 1. Geographic distance 2. Communication tool availability - email voice mail 3. H-1B and L-1 visa availability 4. Language differences 1. 0utsource all application dev. func. 2. Outsource the design… 3. Do not outsource 1. Employee morale 2. Productivity 3. US unemployment 1. Company shareholders perception 2. Media criticism 3. Company enecutives/managers perception 4. Company employees perception

0.4332 0.4332 0.1336 1 0.2744 0.4423 0.2833 0.2741 0.4452 0.2807 0.0823 0.3638 0.2163 0.3376 0.3779 0.3779 0.2442 0.4854 0.3874 0.1472 0.1486 0.2298 0.3939 0.2276

Local priorities 0.1979 0.1979 0.061 0.1142 0.0475 0.0765 0.049 0.0345 0.0561 0.0354 0.0107 0.0473 0.0281 0.0439 0.1591 0.1591 0.1028 0.154 0.1282 0.0487 0.0369 0.057 0.0977 0.0564

Global priorities

4

Social 0.25

Criteria

Economic 0.75

BOCR

Table 2 (continued)

106 Outsourcing a Firm’s Application Development Group

3 BOCR Priorities

107

Table 3 Clusters Influences Economic Alternatives

Financial

Operational

Alternatives Financial Operational

X 0 0

X 0 X

0 X X

clusters, Alternatives, Financial and Operational. The influence of a cluster on the other clusters is represented in matrix form in Table 3. Thus, the Alternatives cluster is influenced by Financial and Operational clusters (column 1 in Table 3), Financial is influenced by the Alternatives (column 2) and Operational is influenced by the Alternatives and itself (column 3). These influences are prioritized by asking the question: For the control criterion in question, in this case Economic benefits, given a cluster, for example, the Alternatives, which cluster influences it more, Financial or Operational, and how much more? The result is the following matrix of paired comparisons: Alternatives

Financial

Operational

Priorities

Financial Operational

1 1/5

5 1

0.8333 0.1667

Comparing all the clusters yields the matrix of priorities given in Table 4. Next, the elements in a cluster are prioritized with respect to the elements of the other clusters that have an influence on it. For example, for the economic control criterion, given Alternative 1, Outsource all application development work, and two elements in the Financial cluster, for example, IT Assets and Personnel, which element influences Alternative 1 more and how much more? The answer to this question is given in the (1, 2) position in Table 5. The result is the matrix of paired comparisons given in Table 5. The priorities from Table 5 are inserted in the matrix given in Table 6 in the highlighted block (F, A1). Next these priorities are multiplied by the weight of the cluster in the cell (Financial, Alternatives) from Table 4. The result is the highlighted block (F, A1) in Table 7. This table is now used to obtain the limiting priorities of the elements in the clusters under the control criterion Economic benefits (Table 8). The priorities of the alternatives are then idealized by dividing by the largest priority (Table 9). Doing this for all the control criteria yields Table 10. The synthesized priorities for the merits are given in Table 11. Table 4 Clusters Priorities

Alternatives Financial Operational

Alternatives 0 0.8333 0.1667

Financial 1 0 0

Operational 0.3333 0 0.6667

108

4

Outsourcing a Firm’s Application Development Group

Table 5 Relative Influence of Financial Elements on Alternative 1 Outsource all application development work,

IT Assets 1 1/4 1

IT Assets Personnel Legal

Personnel 4 1 3

Legal 1 1/3 1

Priorities 0.4579 0.1260 0.4161

Table 6 Unweighted Supermatrix

A

F

O

A1

A A2

A3

F1

F F2

F3

O1

O2

O O3

O4

O5

A1

Outsource all application development work,

0

0

0

0.7536

0.7536

0.7536

0.6267

0.5584

0.0881

0.0914

0.6442

A2

Outsource the design and programming phases,

0

0

0

0.1811

0.1811

0.1811

0.2797

0.3196

0.1947

0.2176

0.2706

0 0.4579 0.1260 0.4161 0.1853 0.3455 0.1132 0.0602 0.2958

0 0.5396 0.1634 0.2970 0.2232 0.1159 0.2605 0.0995 0.3009

0 0.3333 0.3333 0.3333 0.0773 0.1643 0.3512 0.1973 0.2098

0.0653 0 0 0 0 0 0 0 0

0.0653 0 0 0 0 0 0 0 0

0.0653 0 0 0 0 0 0 0 0

0.0936 0 0 0 0 0 0 0 0

0.1220 0 0 0 0.1958 0 0.4934 0.3108 0

0.7172 0 0 0 0 0 0 0 0

0.6910 0 0 0 0 0 0 0 0

0.0852 0 0 0 0 0 0 0 0

A3 F1 F2 F3 O1 O2 O3 O4 O5

Do not outsource any application development work

IT Assets Personnel Legal Time to Finish Use of Project Mgmt. Knowledge Transfer Control Fast Time-to-market

Table 7 Weighted Supermatrix A1 A

F

O

A2 A3 F1 F2 F3 O1 O2 O3 O4 O5

Outsource all application development work, Outsource the design and programming phases, Do not outsource any application development work

IT Assets Personnel Legal Time to Finish Use of Project Mgmt. Knowledge Transfer Control Fast Time-to-market

A1

A A2

A3

F1

F F2

F3

O1

O2

O O3

O4

O5

0

0

0

0.7536

0.7536

0.7536

0.6267

0.1861

0.0881

0.0914

0.6442

0

0

0

0.1811

0.1811

0.1811

0.2797

0.1065

0.1947

0.2176

0.2706

0 0.3815 0.1050 0.3468 0.0309 0.0576 0.0189 0.0100 0.0493

0 0.4497 0.1362 0.2475 0.0372 0.0193 0.0434 0.0166 0.0502

0 0.2778 0.2778 0.2778 0.0129 0.0274 0.0586 0.0329 0.0350

0.0653 0 0 0 0 0 0 0 0

0.0653 0 0 0 0 0 0 0 0

0.0653 0 0 0 0 0 0 0 0

0.0936 0 0 0 0 0 0 0 0

0.0407 0 0 0 0.1305 0 0.3289 0.2072 0

0.7172 0 0 0 0 0 0 0 0

0.6910 0 0 0 0 0 0 0 0

0.0852 0 0 0 0 0 0 0 0

Table 8 Limiting supermatrix A1 A

F

O

A2 A3 F1 F2 F3 O1 O2 O3 O4 O5

Outsource all application development work, Outsource the design and programming phases, Do not outsource any application development work

IT Assets Personnel Legal Time to Finish Use of Project Mgmt. Knowledge Transfer Control Fast Time-to-market

A1

A A2

A3

F1

F F2

F3

O1

O2

O O3

O4

O5

0.34274

0.34274

0.34274

0.3427

0.3427

0.3427

0.3427

0.3427

0.3427

0.3427

0.3427

0.09482

0.09482

0.09482

0.0948

0.0948

0.0948

0.0948

0.0948

0.0948

0.0948

0.0948

0.05475 0.1886 0.0641 0.1575 0.0178 0.0231 0.0214 0.0116 0.0236

0.05475 0.1886 0.0641 0.1575 0.0178 0.0231 0.0214 0.0116 0.0236

0.05475 0.1886 0.0641 0.1575 0.0178 0.0231 0.0214 0.0116 0.0236

0.0548 0.18862 0.06411 0.15752 0.01783 0.02307 0.02138 0.01159 0.02357

0.0548 0.18862 0.06411 0.15752 0.01783 0.02307 0.02138 0.01159 0.02357

0.0548 0.18862 0.06411 0.15752 0.01783 0.02307 0.02138 0.01159 0.02357

0.0548 0.18862 0.06411 0.15752 0.01783 0.02307 0.02138 0.01159 0.02357

0.0548 0.18862 0.06411 0.15752 0.0178 0.02307 0.0214 0.0116 0.02357

0.0548 0.18862 0.06411 0.15752 0.01783 0.02307 0.02138 0.01159 0.02357

0.0548 0.18862 0.06411 0.15752 0.01783 0.02307 0.02138 0.01159 0.02357

0.0548 0.18862 0.06411 0.15752 0.01783 0.02307 0.02138 0.01159 0.02357

Table 9 Priorities of the alternatives for economic benefits in ideal form Alternatives Priorities (ideal form) Outsource all application development work Outsource the design and programming phases Do not outsource any application development work

1 0.2767 0.1597

1 Outsource all application development work 2 Outsource the design and programming phases 3 Do not outsource any application development work

1.0000 0.2766 0.1597

Econ. (0.8333)

Table 10 Priorities for alternatives under BOCR control criteria Alternatives Benefits

1.0000 1.0000 0.2669

Techn. (0.1667) 1.0000 0.8655 0.3477

Cust–rel (0.2500) 1.0000 0.8151 0.5385

Econ. (0.7500)

Opportunities

0.7975 0.7122 1.0000

Econ. (0.8333)

Costs

1.0000 0.9195 0.8552

Soc. (0.1667)

1.0000 1.0000 0.2944

Econ. (0.7500)

Risks

1.0000 1.0000 0.5446

Soc. (0.2500)

3 BOCR Priorities 109

110

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Outsourcing a Firm’s Application Development Group

Table 11 Priorities for Alternatives under BOCR Alternatives

Benefits Opportunities Costs

1 Outsource all application development work 1 2 Outsource the design and programming phases 0.3972 3 Do not outsource any application development work 0.1776

1 0.8277 0.4908

Risks

0.8313 1 0.7468 1 0.9759 0.3570

STRATEGIC CRITERIA

FINANCIAL 0.4476

TECHNOLOGY 0.1605 SOCIAL 0.1357 Availability of experts 0.6667 TIME-TO-MARKET 0.2562 Media perception 0.2500 Flexibility 0.3333 Shareholder & employee perception 0.7500

Fig. 14 Strategic criteria

The next step is to identify the Strategic criteria (shown in Fig. 14): 1. Financial 2. Technology: (a) Availability of experts (b) Flexibility Table 12 Strategic criteria scale for ratings—priorities (ideals) Financial Availability Flexibility Time–toMedia market perception of experts 0.0535 0.2562 0.0339 0.1070 High possibility to reduce costs 0.5909 (1.0000) Moderate possibility to reduce costs 0.2754 (0.4660) Somewhat unlikely to reduce costs 0.0905 (0.1531) Unlikely to reduce costs 0.0432 (0.0731)

Immediately Hi 0.6267 0.6267 (1.0000) (1.0000)

Shareholder and employee perception 0.1018

Fast 0.4626 (1.0000)

Very supportive Very supportive 0.4626 0.4626 (1.0000) (1.0000)

Moderately 0.2797 (0.4463)

Medium 0.2797 (0.4463)

Moderately fast 0.3073 (0.6643)

Moderately supportive 0.3073 (0.6643)

Moderately supportive 0.3073 (0.6643)

Delayed 0.0936 (1494)

Low 0.0936 (0.1494)

Average 0.1416 (0.3061)

Neutral 0.1416 (0.3061)

Neutral 0.1416 (0.3061)

Moderately slow 0.0584 (0.1263) Slow

Moderately unsupportive 0.0584 (0.1263) Very unsupportive 0.0299 (0.0647)

Moderately unsupportive 0.0584 (0.1263) Very unsupportive 0.0299 (0.0647)

0.0299 (0.0647)

Risks

Costs

Opportunities

Immediately

Moderately

Immediately

Hi

Med

Hi

Hi

Fast

Average

Fast

Fast

Immediately

Benefits

High possibility to reduce costs High possibility to reduce costs Somewhat unlikely to reduce High possibility to reduce costs

Time-tomarket

Table 13 Rating Importance of Benefits, Opportunities, Costs and Risks Financial Availability Flexibility of experts Moderately unsupportive Moderately unsupportive Moderately supportive Moderately unsupportive

Media perception

Moderately unsupportive

Moderately supportive

Moderately unsupportive

Moderately unsupportive

Shareholder and employee perception

0.2985

0.1045

0.2985

0.2985

Priorities

3 BOCR Priorities 111

112

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Outsourcing a Firm’s Application Development Group

Table 14 Overall outcome Alternatives Benefits Opportunities 0.2983 0.2983

Costs 0.1051

Risks 0.2983

Outcome BO/CR

Outcome bB ? oO -cC-rR

1a 2b 3c

0.8313 0.7468 0.9759

1 1 0.3570

1.2029 0.4402 0.2502

0.2109 -0.0114 -0.0097

1 0.3972 0.1776

1 0.8277 0.4908

a —Outsource all application development work, b —Outsource the design and programming phases, c —Do not outsource any application development work

3. Time-to-market 4. Social: (a) Media perception (b) Shareholder & employee perception • The ratings scale shown in Table 12 was used to rate BOCR with respect to the strategic criteria using the top ranked alternative for each merit. • The merits’ ratings using the top ranked alternative for each merit are given in Table 13.

4 Results After pairwise comparisons of the alternatives and ratings comparisons of the merits, our model shows that Alternative #1: ‘‘Outsource all application development work’’, is the best choice (see Table 14). The main driver for this result is the financial benefits. Using background research and personal interviews to describe this model and compare and rate its nodes, the authors of this chapter are not surprised by this outcome.

5 Sensitivity Analysis Figures 15, 16, 17, 18.

6 Where to Outsource A separate study was made by Ozlem Arisoy and Shengnan Wu in the Fall of 2005 to determine the best country where to outsource, for a company in Pennsylvania. The results of that study are given in Tables 15, 16, and 17 below. It suggests that Taiwan should be the outsourcing location.

6 Where to Outsource

113

Fig. 15 Sensitivity analysis for benefits 1

2

3

1 – Outsource all application development work 2 – Outsource the design and programming phases 3 – Do not outsource any application development work

Fig. 16 Sensitivity analysis for opportunities

1 2 3

1 – Outsource all application development work 2 – Outsource the design and programming phases 3 – Do not outsource any application development work

By way of validation, it was announced in December 2005 that Taiwan’s Quanta, the world’s largest maker of notebook computers, was selected to manufacture an ultra-low-cost laptop developed by Nicholas Negroponte, the chairman of the Massachusetts Institute of Technology’s Media Laboratory.

114

4

Outsourcing a Firm’s Application Development Group

Fig. 17 Sensitivity analysis for costs

1

3 2

1 – Outsource all application development work 2 – Outsource the design and programming phases 3 – Do not outsource any application development work

Fig. 18 Sensitivity analysis for risks

1

2

3

1 – Outsource all application development work 2 – Outsource the design and programming phases 3 – Do not outsource any application development work

6 Where to Outsource

115

Table 15 Benefits and opportunities priorities Benefits Economic Organization Control criterion (CC) Normalized Alternatives Mainland China Taiwan Hong Kong Japan India Opportunities Control Criterion (CC) Normalized Alternatives Mainland China Taiwan Hong Kong Japan India

Production

Limiting CC

Limiting CC

Limiting CC

0.6483 Ideal

0.1220 Ideal

0.2297 Ideal

Synthesis

0.9538 1.0000 0.7424 0.5319 0.4166 Global long term Limiting CC

0.3526 1.0000 0.9005 0.3509 0.2754 Global short term Limiting CC

0.3310 0.5798 0.7665 1.0000 0.1915 Local long term Limiting CC

0.7374 0.9035 0.7672 0.6173 0.3477 Local short term Limiting CC

0.3216 Ideal

0.3341 Ideal

0.2232 Ideal

0.1211 Ideal

Synthesis

1.0000 0.5606 0.5537 0.5201 0.5066

1.0000 0.5940 0.3098 0.4075 0.2370

1.0000 0.6119 0.4628 0.8361 0.3748

1.0000 0.3616 0.2882 0.2891 0.4545

1.0000 0.5591 0.4198 0.5250 0.3808

Table 16 Costs and risks Priorities Costs Manufacturing Control Criterion (CC) Normalized Alternatives Mainland China T aiwan Hong Kong Japan India Risks Control Criterion (CC) Normalized Alternatives Mainland China Taiwan Hong Kong Japan India

Marketing

Implementation

Limiting CC 0.2790 Ideal

Limiting CC 0.6491 Ideal

Limiting CC 0.0719 Ideal

0.1527 0.3835 0.6172 1.0000 0.1409 Operations Limiting CC 0.1365 Ideal

0.2647 0.4165 0.7043 1.0000 0.2422 Implementation Limiting CC 0.6250 Ideal

0.3931 0.4926 0.7169 1.0000 0.3138 Performance Limiting CC 0.2385 Ideal

0.2427 0.4128 0.6809 1.0000 0.2191

1.0000 0.3634 0.2052 0.1168 0.6376

1.0000 0.5353 0.4604 0.4559 0.9480

1.0000 0.3966 0.5609 0.1596 0.9403

1.0000 0.4788 0.4495 0.3389 0.9038

Synthesis

Synthesis

116

4

Outsourcing a Firm’s Application Development Group

Table 17 Priorities of the Alternatives from BOCR Models and synthesis Benefits

O pportunities

Costs

Risks

Synthesis

Alternatives

0.2050

0.2046

0.2046

0.3858

bB+oO -cC-rR

Mainland China

0.7374

1.0000

0.2427

1.0000

-0.0797

T aiwan

0.9035

0.5591

0.4128

0.4788

0.0305

Hong Kong

0.7672

0.4198

0.6809

0.4495

-0.0696

Japan

0.6173

0.5250

1.0000

0.3389

-0.1014

India

0.3477

0.3808

0.2191

0.9038

-0.2443

Bibliography Annett, Creighton, and Wong. ‘‘Understanding Outsourcing: An Online Journal Roundtable.’’ Wall Street Journal. March 1, 2004. Aron, Ravi. ‘‘Sourcing in the Right Light.’’ Optimize. June 1, 2003. CMP Media. LexisNexis. Sept. 15, 2003. Beck, Jennifer. ‘‘IT Services Outsourcing Goes Strategic.’’ CIO Magazine. July 19, 2002. Oct. 20, 2003. http://www.cio.com/analyst/report372.html. Carr, Jim. ‘‘Contract Manufacturer Leverages Outsourcing….’’ Network Magazine. Sept. 1, 2003. CMP Media. Sept. 15, 2003. Champy, James. ‘‘Re-examining the Infrastructure $.’’ Optimize. Sept. 1, 2003. CMP Media. LexisNexis. Sept. 15, 2003. Chandras, Rajan. ‘‘Going Offshore Without Going Off the Deep End.’’ Intelligent Enterprise. Aug. 10, 2003. CMP Media. LexisNexis. Sept. 15, 2003. ‘‘Changing Strategies.’’ Computer Business Review Online. Jan. 8, 2003. Sept. 9, 2003. http:// www.cbronline.com/print_friendly/de9664c065b4ed56c2256d7800329e23. Davis and Harwood. ‘‘Kerry Targets Job Outsourcing with Corporate-Tax Overhaul.’’ Wall Street Journal. March 26, 2004. Depner, Jason. Personal interviews. Dec. 1, 2003 and March 29, 2004. Dikerson, Schwartz, Udell, and Yager. ‘‘To Offshore… or Not.’’ InfoWorld. March 8, 2004. Issue 10. Dubie, Denise. ‘‘Net Execs are Bullish on Outsourcing.’’ NetworkWorldFusion. Oct. 27, 2003. Nov. 13, 2003. http://www.nwfusion.com/news/2003/1027vanguard.html. Elk, Arlene. Personal interview. Dec. 3, 2003. Frankhouser, Tami. Personal interview. Dec. 3, 2003. Fitzgerald, Michael. ‘‘At Risk Offshore.’’ CIO Magazine. Nov. 15, 2003. Nov. 25, 2003. http:// www.cio.com/archive/111503/offshore.html?printversion=yes. Gross, Grant. ‘‘CEOs Defend Moving Jobs Offshore at Tech Summit.’’ NeworkWorldFusion. Oct. 9, 2003. Oct. 20, 2003. http://www.nwfusion.com/news/2003/1009ceosdefend.html. Hall, Mark. ‘‘Outsourcing Deals Fail Half the Time….’’ ComputerWorld. Nov. 3, 2003. Nov. 13, 2003. http://www.computerworld.com/printthis/2003/9,4814,86748,00.html. Haniffa, Aziz. ‘‘US May Eliminate H1-B Visas.’’ Nov. 29, 2003. http://www.rediff.com/money/ 2003/jul/16bpo.htm. Hayes, Frank. ‘‘Businessy IT.’’ ComputerWorld. Nov. 3, 2003. Nov. 3, 2003. http:// www.computerworld.com/printthis/2003/0,4814,86783,00.html. Hayes, Mary. ‘‘Precious Connections.’’ InformationWeek Oct. 20, 2003. Pg. 35-50. Hayes and McDougall. ‘‘Gaining Ground.’’ InformationWeek March 31, 2003. CMP Media LexisNexis. Sept. 15, 2003. ‘‘IT Majors Need to Work on Brand Equity.’’ Financial Times Information. Aug. 16, 2003. Global News Wire. LexisNexis. Sept. 15, 2003.

Bibliography

117

‘‘JD Edwards to Farm Out Development to Covansys.’’ Financial Times Information. March 26, 2003. Global News Wire. LexisNexis. Sept. 15, 2003. Kalakota and Robinson. ‘‘Offshore Outsourcing: Will Your Job Disappear in 2004?’’ InformIT. February 27, 2004. King, Julia. ‘‘ITs Global Itinerary.’’ ComputerWorld. Sept. 15, 2003. LexisNexis. Sept. 15, 2003. Kleinhammer, Nelsen, and Warner. ‘‘Balancing the Risks.’’ Darwin Magazine. June, 2003. Oct. 20, 2003. http://www.darwinmag.com/read/060103/risk.html?action=print. Law, Gillian. ‘‘Outsourcing to Transform IT, Gartner Says.’’ NetworkWorldFusion. Oct. 3, 2003. Oct. 20, 2003. http://www.nwfusion.com/news/2003/1003outsototr.html. Maher, Kris. ‘‘Next on the Outsourcing List.’’ Wall Street Journal. March 23, 2004. Margulius, David L. ‘‘Staying Stateside.’’ InfoWorld. March 8, 2004. Issue 10. Mariani, Bill. Personal interview. Dec. 2, 2003. McDougall, Paul. ‘‘Opportunity on the Line.’’ InformationWeek. Oct. 20, 2003. Pg. 53-56. Messmer, Ellen. ‘‘Overseas Outsourcing Gains Momentum.’’ NetworkWorldFusion. June 30, 2003. Oct. 20, 2003. http://www.nwfusion.com/news/2003/0630outsourcing.html. Mitchell, Robert L. ‘‘Opinion: How IT has Outsourced Itself.’’ ComputerWorld. March 15, 2004. Musthaler, Linda. ‘‘Managing Outsourcing.’’ NetworkWorldFusion. Nov. 3, 2003. Nov. 13, 2003. http://www.nwfusion.com/newsletters/techexec/2003/1103techexec1.html. Overby, Stephanie. ‘‘The Hottest Trend in Outsourcing Management.’’ CIO Magazine. June 1, 2003. Oct. 20, 2003. http://www.cio.com/archive/060103/outsourcing_sidebar_3.html. Overby, Stephanie. ‘‘Inside Outsourcing in India.’’ CIO Magazine. June 1, 2003. Oct. 20, 2003. http://www.cio.com/archive/060103/outsourcing.html. Overby, Stephanie. ‘‘Your Monthly Metrics Checklist.’’ CIO Magazine. June 1, 2003. Oct. 20, 2003. http://www.cio.com/archive/060103/outsourcing_sidebar_2.html. Perkins, Bart. ‘‘A Reality Check on Going Offshore.’’ ComputerWorld. June 16, 2003. LexisNexis. Sept. 15, 2003. Perkins, Bart. ‘‘Offshore: The Third Time’s the Charm.’’ ComputerWorld. Oct. 13, 2003. Oct. 20, 2003. http://www.computerworld.com/printthis/2003/0,4814,85899,00.html. Perkins, Bart. ‘‘Outsourcing’s Dirty Little Secret.’’ ComputerWorld. Nov. 10, 2003. Nov. 11, 2003. http://www.computerworld.com/printthis/2003/0,4814,86959,00.html. www.pmi.org. Read, Brendan B. ‘‘Out of Center Call Centers.’’ Call Center May 1, 2003. Gale Group, Inc. LexisNexis. Sept. 15, 2003. ‘‘Taking the Lead in Responding to IT Industry Needs’’ PMI Today. November 2003. Tamanini, Kristin. Personal interview. Dec. 4, 2003. Thibodeau, Patrick. ‘‘Anti-offshore-outsourcing Groups Banding Together.’’ ComputerWorld. February 24, 2004. Tripathi, Ravi. ‘‘Outsourcing – the Myths and the Facts.’’ Wall Street Journal. March 1, 2004. Weiss, Todd R. ‘‘Proposed Bill Would Ban Some Forms of Government Outsourcing.’’ ComputerWorld. February 24, 2004. Wriston, Walter B. ‘‘Ever Heard of Insourcing?’’ Wall Street Journal. March 24, 2004.

Chapter 5

ANWR: Artic National Wildlife Refuge an ANP Validation Example

1 Introduction ANWR-Arctic National Wildlife Refuge covers 19 million acres on the Northern coast of Alaska. The entire refuge lies north of the Arctic Circle and 1,300 miles south of the North Pole. The Coastal Plain area comprising 1.5 million acres on the northern edge of ANWR, is bordered on the north by the Beaufort Sea, on the east by the U.S. Canadian border and on the west by the Canning River. The consensus of the geologic community is that the Coastal Plain of ANWR represents the highest petroleum potential onshore area yet to be explored in North America. If explored, it is estimated that it will take 15 years or more before oil and gas will reach the market. President Eisenhower originally protected this coastal plain area, also known as area 1002, in 1960. Twenty years later President Carter signed the Alaska National Interest Conservation Act. This legislation was important as it created a majority of the National Parks in Alaska and expanded ANWR to its current size. A compromise was reached to pass the legislation, in return for designating a majority of the areaprotected land. Area 1002 was left unprotected and thus open for exploration. Each administration since has had its own opinion regarding the land and what should be done with it. The Reagan Administration was ready to drill but was derailed by the Exxon Valdez catastrophe. The first Bush Administration likewise was unsuccessful. The Clinton Administration designated the area for protection and it has been since. The second Bush Administration, in response to ongoing Middle East violence and recent terrorist attacks, namely 9/11, sees drilling in ANWR as vital not only for economic but national security reasons. Several environmental groups consider ANWR a great American natural treasure and one of the last places on the earth where an intact expanse of arctic and sub-arctic lands remain protected. They feel the habitat, the wildlife, and the culture need to be protected from the exploration of gas and oil. An ANP model (Fig. 1) was developed as a way of coming to a decision regarding the use of this land. This model incorporates pairwise comparisons of T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_5,  Springer Science+Business Media New York 2013

119

120

5 ANWR: Artic National Wildlife Refuge

Fig. 1 BOCR model

benefits, opportunities, costs, and risks associated with drilling or not drilling. By making these comparisons and choosing the answers that best represent the use of this land we were able to come to a plausible conclusion on whether or not the land should be further explored.

2 BOCR Model for ANWR The ANWR Model depicted in Fig. 1 considers strategic criteria used to evaluate the benefits, opportunities, costs and risks of the alternatives Drill/Do Not Drill for Oil. These criteria are: • General public opinion: Local, national and international public opinion. • International Politics: The implications of the Drill/Do Not Drill decision on the relations with OPEC nations.

2 BOCR Model for ANWR

121

• Amount of oil: The quantity of oil that is available in the ANWR area. For example, if the amount of oil in ANWR is very low, one would expect that the outcome of this criterion would lean towards the Do Not Drill for oil decision. The structure of the benefits, opportunities, costs and risks subnets are given in Figs. 2, 3, 4, and 5. The meaning of the control criteria, in each of the subnets, is given below. The benefits, opportunities, costs and risks are divided into economic, political and social. (1) Benefits Network Benefits/Economic criteria • Local Labor: Local work force and Local Jobs • Local resources: Use of local raw materials that would boost other local industries in Alaska • Property values: The effects of ANWR on the nearby property values • Reliance on Foreign Oil: Whether or not the US would be able to use its own oil instead of relying on the Middle East and other nations • Taxes: What effect would this have on taxes. Benefits/Political criteria • Clout: Political Power resulting from drilling or not drilling for oil • Elections: The effect drilling or not drilling would have on democratic and republican elections • Reliance on foreign oil: How drilling or not drilling would affect the US and the use of foreign oil. • Taxes: What would the effect be on taxes? Benefits/Social criteria • • • • •

Development: Development of socialization locally Oil Companies contributions: Effect of oil companies contributing funds Public Program Funding: Public funding provided to help residents succeed Revitalization: re-stimulate the local social atmosphere Taxes: Effect on taxes.

(2) Opportunities network Opportunities/Economic criteria • • • •

Exports: Value of exports Local Business: Use of local businesses ROI: Return on investment Tax: New tax rate.

5 ANWR: Artic National Wildlife Refuge

Fig. 2 Benefits subnet

122

Fig. 3 Opportunities subnet

2 BOCR Model for ANWR 123

5 ANWR: Artic National Wildlife Refuge

Fig. 4 Costs subnet

124

125

Fig. 5 Risks subnet

2 BOCR Model for ANWR

126

5 ANWR: Artic National Wildlife Refuge

Opportunities/Political criteria • • • •

Clout: Political power Community Support: Support received locally Lobbying: Lobbying for votes National support: Support received nationally. Opportunities/Social criteria

• Development: Development of surrounding areas • Jobs: Jobs created locally (3) Costs network Costs/Economic criteria • Infrastructure: Cost of roads and railways to access the area • Labor: Cost of labor needed to build and run new facility • Property Value: What will happen to property value of nearby residents and businesses • Raw Materials: Cost of raw materials needed. Costs/Political criteria • • • •

Assessment Time: The time it takes to access the situation Political Fallout: What will cause political fallout Taxes: What is the cost of new taxes World Wide Instability: cost of causing world wide stability. Costs/Social criteria

• • • • •

Crime: Crime rate Cultural: Historical cultural issues Environmental: effects on the environment Inconvenience: Inconvenience to inhabitants Noise: Noise pollution.

(4) Risks network Risks/Economic criteria • Bad Luck Events: – Pollution: Pollution created – Spills: Oil Spills • Reasons: Description – – – –

Investments: Investing in US companies Jobs: Jobs created Other Energy Sources: Wind, solar, gas, etc. Reliance on Foreign Oil: US oil Versus Foreign oil.

2 BOCR Model for ANWR

127

Table 1 Priorities from benefits, opportunities, costs and risks subnets and from BOCR ratings Criteria Priorities Benefits 1.0000 (0.4252)

Economic 0.6910

Political 0.2176

Social 0.0914

Opportunities 0.8940 (0.3801)

Economic 0.2790

Political 0.0719

Costs 0.1102 (0.0469)

Social 0.6491 Economic 0.6491

Political 0.0719

Social 0.2790

Risks 0.3478 (0.1479)

Economic 0.1939

Local Labor Local resources Property values Reliance on foreing Oil Taxes Clout Elections Reliance on Foreign oil Taxes Development Oil companies contributions Public program funding Revitalization Taxes Exports Local business ROI Tax Clout Community support Lobbying National support Development Jobs Infrastructure Labor Property value Raw materials Taxes Assessment time Political fallout Taxes World wide instability Crime Cultural Environmental Inconvenience Noise Pollution Spills Investments Jobs Other energy sources

0.2248 0.0984 0.1784 0.4353 0.0630 0.1051 0.3255 0.4530 0.1164 0.3010 0.0649 0.1057 0.3403 0.1881 0.1375 0.6124 0.1490 0.1011 0.2619 0.4315 0.1804 0.1263 0.4165 0.5835 0.1519 0.4853 0.1271 0.1655 0.0702 0.2123 0.6127 0.0929 0.0822 0.3096 0.1982 0.1795 0.1107 0.2020 0.3948 0.6052 0.1126 0.2151 0.5587 (continued)

128

5 ANWR: Artic National Wildlife Refuge

Table 1 (continued)

Political 0.0633 Social 0.7429

Criteria

Priorities

Reliance on foreign oil Elections Local image National image Cultural Environmental Health Jobs

0.1136 0.3875 0.4253 0.1872 0.1171 0.3706 0.2232 0.2891

Risks/Political criteria • Elections: Election outcomes • Local Image: Local image created • National Image: Portrayed national image. Risks/Social criteria • • • •

Cultural: Cultural effects Environmental: Effects on environment Health: Effects on health Jobs: Jobs created.

Table 2 Priorities of alternatives from BOCR models Economic Political Benefits Drill Do Not Drill Opportunities Drill Do not drill Costs Drill Do not drill Risks Drill Do not drill

0.6910 1.0000 0.3073 0.2790 1.0000 0.1647 0.6491 1.0000 0.1721 0.1939 0.4978 1.0000

0.2176 1.0000 0.4537 0.0719 1.0000 0.3557 0.0719 1.0000 0.1656 0.0633 0.7941 1.0000

Social 0.0914 1.0000 0.2900 0.6491 1.0000 0.1940 0.2790 1.0000 0.6760 0.7429 0.5461 1.0000

Synthesis 1.0000 0.3376 Synthesis 1.0000 0.1975 Synthesis 1.0000 0.3122 Synthesis 0.5524 1.0000

2 BOCR Model for ANWR Table 3 BOCR Ratings General public opinion 0.1007 Benefits Opportunities Costs Risks Intensities

High (1.0000) Low (0.0947) Low (0.0947) Low (0.0947) High 1.0000

129

International politics 0.2255

Amount of oil 0.6738

Medium (0.3770) Medium (0.3770) Low (0.0947) High (1.0000) Medium 0.3770

High (1.0000) High (1.0000) Low (0.0947) Low (0.0947) Low 0.0947

Table 4 BOCR Synthesis Benefits Opportunities Drill Do Not Drill

Total

Priorities

0.8595

0.4252

0.7684

0.3801

0.0947

0.0469

0.2989

0.1479

Costs

Risks

bB ? oO ? c(1-C) ? r(1-R)

0.4252

0.3801

0.0469

0.1479

Total

Normalized

1.0000 0.3376

1.0000 0.1975

1.0000 0.3122

0.5524 1.0000

0.8715 0.2508

0.7765 0.2235

Fig. 6 Poll’s results

Fig. 7 Poll’s Results for Geographical Subgroups. Gray = support for opening ANWR Black = Does not support opening ANWR

130

5 ANWR: Artic National Wildlife Refuge

Do Not Drill

Drill

Fig. 8 Sensitivity analysis of the alternatives under costs

Drill

Do Not Drill

Fig. 9 Sensitivity analysis of the alternatives under all BOCR models

3 Results

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3 Results Table 1 shows the priorities of the criteria for the economic, political and social benefits, opportunities, costs and risks networks. Table 2 gives the priorities of the alternatives Drill/Do Not Drill for the benefits, opportunities, costs and risks. Benefits, opportunities, costs and risks are now rated using the three strategic criteria depicted in Fig. 1, according to the best alternative under each of the BOCR models. The results are given in Table 3. Finally, the priorities of the BOCR models are used to synthesize the individual priorities of the alternatives under each model. Table 4 gives the results from the additive probabilistic (predictive) synthesis.

4 Conclusion and Sensitivity Analyses In sum, exploring for oil and gas seems to be a better alternative for ANWR. The model indicates that ANWR should be opened to oil and gas exploration by 77.65 %. This result appears to be in agreement with a recent poll of native Alaskans in which they show support for opening ANWR to oil and gas exploration. The question asked was ‘‘Do you believe oil and gas exploration should or should not be allowed within the ANWR Coastal Plain?’’ The poll results are show in Fig. 6. The Unsure 6 %, divided equally between Should and Should not makes their values 78 and 22 % respectively, resulting in nearly identical values to those obtained from the model. This outcome is consistent with our findings and it also appears to be with all geographic subgroups in Alaska (See Fig. 7). The decision to Drill is dominant and stable under benefits, opportunities and risks. Only under costs Drill and Do Not Drill change rankings. If the priority of costs is below 40 percent, the decision to Drill dominates. When the priority of costs is above 40 %, the Do Not Drill decision is preferred (see Fig. 8). Combining benefits, opportunities, costs and risks, the Drill decision dominates in almost the entire spectrum with very few exceptions characterized by high priorities in costs and risks combined. Fig. 9 shows the fluctuations in the priorities of the alternatives as the weights of the BOCR models change.

Chapter 6

The Ford Explorer Case

1 Introduction In August 9, 2000 the companies Firestone and Ford announced a recall1 of 6.5 million tires that contained a safety-related defect. The recall was the result of an abnormal high rate of treads separations that caused catastrophic rollover crashes2 which maimed and killed drivers and passengers. At that time, the companies’ had jointly decides that Decatur was the appropriate focus for a recall of Wilderness AT tires, thus excluding millions of identical tires made in Firestone’s Wilson, North Carolina and Joilette, Quebec, Canada plants. The tires had been sold as original equipment on Ford’s Explorer SUV, and manufactured according to specifications from Ford. Ford announced in March 2001 that the company would redesign the Explorer model (creating the new Explorer) adding a wider body and incorporating some ‘‘rollover’’ features. In May 2001, the Ford Motor Company also announced a new recall of 13 million tires from the Ford Explorer models and termination of the business relationship with Firestone. There are several key players in the tire separation tread case. The first is the company that designed and manufactured the tires: Firestone. The second is the company that designed and manufactured the vehicles: Ford Motor Company. The third is the governmental regulation agency: the National Highway Safety Administration (NHTSA).

1

The recall included all 15-inch ATX II tires and those 15-inch Wilderness AT tires manufactured by Firestone plant in Decatur, Illinois. 2 148 deaths and 525 injuries by the end of year 2000. T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_6,  Springer Science+Business Media New York 2013

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2 Creating the Model The model for finding the optimal decision for Ford regarding the Explorer/ Firestone conflict was designed using a benefits, costs, and risks model. The benefits model would indicate the decision that gives the most benefits, whereas the costs and risks models indicate the decisions that are most costly and risky. Using the ANP program Super Decisions, the calculation of the formula is done automatically.

2.1 Alternatives Discontinue Explorer production: Ford would stop the Explorer model production. Redesign the Explorer model: Ford would continue producing the Explorer model but the company would redesign some parts of the Sport Utility Vehicles (SUV) in order to increase the safety level of the vehicle. Maintain the production of Explorer Model: Ford would keep on producing the Explorer model without any modifications. Maintain the production of Explorer Model, but change the tire supplier: Ford would keep on producing and commercializing the current Explorer model equipped with tires from a different supplier.

2.2 Cluster Definitions Under the benefits, costs, and risks models, there are different clusters defined that interact with respect to the control hierarchy established. For benefits and risks, the control hierarchy consists of social and economic factors; while the costs control hierarchy includes social, economic, and political factors. Although the clusters and the specific elements assigned to each network vary due to their interactions, the following general definitions apply to all. a. Alternative Decisions The alternative decisions cluster includes the potential decisions for the Ford Motor Company regarding the Ford/Firestone conflict. The potential decisions included are: • • • •

Discontinue Explorer production. Redesign the Explorer model. Maintain the production of Explorer Model. Maintain the production of Explorer Model, but change the tire supplier.

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b. Stakeholders The stakeholders include people or groups that would be impacted by the alternative decisions made by Ford. The elements in this cluster are the following: • Customers: current and potential buyers • Community: people who may not be a customer but could be affected by the alternative decisions • Employees: Ford Motor Company employees, including labor and management • Nation’s Highway Safety Agency: government agency. c. Tire Suppliers This cluster considers current and potential tire suppliers for Ford. The elements in this cluster are the following: Firestone, Goodyear, Michelin, and Other Tire Suppliers. d. Competition The competition cluster includes other SUV brands and models owned by Ford and other companies. The elements in this cluster are the following: • Ford’s other SUV brands (e.g. Escape) • Ford affiliates’ SUV brands (e.g. Land Rover) • Other companies’ SUV brands (e.g. GM, Honda, Lexus, Dodge, etc.). e. Public Relation This cluster considers elements that would impact the company’s relationships with the stakeholders. The elements in this cluster are the following: • Image: the company’s image in public • Trust: reliability in the company’s name • Accountability: how the company react to community threats caused by Ford Motor Company’s products • Legal Matters: current and potential lawsuits filed against the company. f. Brand Image The Brand Image cluster describes major aspects of the products that would impact the company’s image. The elements in this cluster are the following: Quality, Safety, Prestige, and Service. g. Cost of Resources The cost of resources refers to those costs that Ford may incur when choosing the alternative decisions. The elements in this cluster are the following: • Layoff costs: the cost that the company would incur in case it decides to reduce the number of employees.

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• Launching costs: the cost that the company would incur in case they decide to launch a new product. • Write-off costs: the cost that the company would incur in case they decide to reduce the inventory of discontinued products. • Production costs: the cost that the company incurs during the production stage h. Resources The Resources cluster includes: Revenues, Production Capacity, and Market Share.

2.3 Procedure The benefits, costs and risks in the decision that Ford would have to make regarding the Ford Explorer Model, were rated on three criteria: Domestic Issues, International Relations and Human Well-Being. In Domestic Issues, the sub criteria were: (a) Ford’s reputation, (b) Car Industry’s reputation and (c) US Government’s reputation. In the case of International Relations, the sub criteria were: (a) Relationship with customers in other countries, (b) Relationship with suppliers in other countries and (c) Relationship with other countries’ governments. Finally, in the case of Human Well-Being, the sub criteria were: (a) Future Safety Factors, (b) Confidence in government agencies and (c) Confidence in the Justice system.

3 Benefits Model Frequently, the alternatives from which a choice must be made in a decisionmaking situation have both benefits and costs associated with them. This is the case for the Ford Motor Company decision. Generally, benefits, costs and risks cannot be combined; they are opposing forces. Thus, in our model, it is useful to construct separate benefits, costs and risks networks, with the same decision alternatives located on each. Benefits in our model are gains and advantages from making a given decision, partitioned into two categories: economic and social. Economic benefits refer to a decision’s positive effect on stakeholders, tire suppliers, competition and resources. Last, social benefits describe a decision’s positive effect on stakeholders, tire suppliers, competition and resources.

3.1 Economic Benefits Clusters, Links and Judgments Table 1 illustrates the clusters in this network and their respective elements. The inner and outer dependencies of clusters are shown in Figs. 1 and 2.

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Table 1 Economic benefits cluster and elements Clusters Elements Alternative sites

Stakeholders Tires suppliers Competition

Public image Resources

• Discontinue explorer production • Redesign the explorer model • Maintain the production of explorer model • Maintain the production of explorer model, but change the tire supplier Customers, Community, Employees and NHSA Firestone, Goodyear, Michelin and other tire suppliers • Ford’s other SUV brands • Ford affiliates’ SUV brands • Other companies’ SUV brands Image, Trust, Accountability and Legal matters Revenue, Production capacity and Market share

Fig. 1 Macro view of economic benefits networks

The ‘stakeholders’ cluster, obviously, refers to the people or group of people who could potentially benefit economically, based on different decision alternatives taken by Ford. This cluster also affects the ‘competition’ cluster, because the decisions made may drive the stakeholder to provide economic benefits to either one of the competitors. The ‘stakeholders’ cluster also affects the ‘resources’ cluster. The ‘resources’ cluster refers to the internal resources that the company has. For example, the company’s revenue would be impacted by some of the actions taken by the stakeholders. The ‘tire suppliers’ cluster refers to tire companies that may gain economic benefits based on the decision alternatives taken by Ford. This cluster would also affect the ‘public image’ cluster; more specifically, legal matters. The ‘stakeholders’ and ‘tire suppliers’ clusters have more inter-links than the other clusters. This is due to the nature of the network, economic benefits, which usually has more impact on a person or a group of persons. In this network, there is no inter-dependence in any of the clusters.

6 The Ford Explorer Case

Fig. 2 Micro view of economic benefits network

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3.2 Social Benefits Clusters, Links and Judgments Table 2 illustrates the clusters in this network and their respective elements: The inner and outer dependencies of clusters in the Social Benefits model are shown in Figs. 3 and 4.

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Table 2 Social benefits clusters and elements Clusters Elements Alternative sites

Stakeholders Tires suppliers Competition

Public image Brand image

• Discontinue explorer production • Redesign explorer model • Maintain the production of explorer model • Maintain the production of explorer model, but change the tire supplier Customers, Community, Employees and NHSA Firestone, Goodyear, Michelin and other tire suppliers • Ford’s other SUV brands • Ford affiliates’ SUV brands • Other companies’ SUV brands Image, Trust, Accountability and Legal matters Quality, Safety, Prestige, and Service

Fig. 3 Macro View of Social Benefits Networks

The ‘stakeholders’ cluster, refers to the people or group of people who could potentially benefit socially, based on different decision alternatives taken by Ford. There is a link between this cluster and the ‘tire suppliers’ cluster. However, this link only reflects an equal importance to the nodes in the ‘tire suppliers’ cluster. From the stakeholders’ point of view, there are no social benefits in choosing one tire supplier over the other. The ‘stakeholders’ cluster also affects the ‘competition’ cluster, because the decisions made may drive the stakeholder to provide social benefits to either one of the competitors. The next cluster that is affected is the ‘public image’ cluster. The stakeholders can provide social benefits based on the alternative decisions taken by Ford, and that would impact how they see the company’s public image in terms of trust, image, accountability, and legal matters. The last cluster that is impacted is the ‘brand image’ itself. This requires no further explanation, as the alternative decisions taken would clearly have the power to change how stakeholders perceive the brand’s image. Different stakeholder may value different brand images, but overall, this cluster would be very much influenced by the stakeholders.

6 The Ford Explorer Case

Fig. 4 Micro View of Social Benefits Network

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The ‘stakeholders’ cluster plays an important role in this network, and as in the Economic Benefits network, there is no inter-dependence in any of the clusters in the Social Benefits network.

3.3 Synthesis of Judgments in the Benefits Model Both networks in the benefits have independent results that would then feed into the higher-level network (the overall benefits network). The combined results from the Economic and Social Benefits networks are shown in Table 3.

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Table 3 Synthesized Judgments in the Benefits Model Alternatives Benefits

Discontinue explorer Redesign model Maintain current model Maintain model, change tire supplier

Synthesis

Economic 0.8

Social 0.2

1.0000 0.3699 0.1241 0.5869

1.0000 0.5929 0.0194 0.2145

1.0000 0.4145 0.1031 0.5124

This result indicates that from the Benefits point of view, the alternative decision of discontinuing Explorer gives the highest benefit, both from the economic and social standpoints. Another observation is that the overall priority for the first ranked alternative, i.e. to discontinue Explorer, has a significantly larger value than the next alternative. As seen from the table, the alternative ‘Discontinue Explorer’ is the best under both Economic and Social benefits, while the second best alternative, i.e. ‘maintain model, change tire supplier’, only has 0.5124 priority. The ratio is almost twice as much, which shows how important the first ranked alternative is compared to the other alternatives.

4 Costs Model The costs to Ford for choosing one alternative over the others can be divided into economic, social and political costs, which comprise the control hierarchy for this model. Economic costs are costs to which a monetary value can be assigned such as production and advertising costs involved in the redesign of the Ford Explorer. Social costs are defined as the expense to society in terms of stakeholder exposure to decisions made regarding the Ford Explorer. Finally, political costs can be defined as the intangible costs due to the decision taken, such as breaking the relationship between Ford and its tire supplier.

4.1 Economic Costs Clusters, Links and Judgments Table 4 illustrates the clusters in this network and their respective elements. The inner and outer dependencies of clusters in the economic costs model are shown in Figs. 5 and 6. The ‘stakeholders’ cluster refers to the people or group of people who could potentially be affected economically, based on different decision alternatives taken by Ford. This cluster also affects the ‘public image’ cluster, more specifically, ‘legal matters’. The decision made by the company may

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Table 4 Economic costs clusters and elements Clusters Elements Alternative sites

Stakeholders Tires suppliers Competition

Public image Cost of resources Resources

• Discontinue explorer production • Redesign the explorer model • Maintain the production of explorer model • Maintain the production of explorer model, but change the tire supplier Customers, Community, Employees and NHSA Firestone, Goodyear, Michelin and other tire suppliers • Ford’s other SUV brands • Ford affiliates’ SUV brands • Other companies’ SUV brands Image, Trust, Accountability and Legal matters Layoff Costs, Launching Costs, Writeoff Costs and Production Costs Revenue, Production Capacity and Market Share

encourage customers to influence the economic costs by increasing the number of lawsuits filed against the company. The ‘tire suppliers’ cluster refers to tire companies that may suffer economic costs based on the decision alternatives taken by Ford. This cluster would also affect the ‘public image’ cluster; more specifically, ‘legal matters.’ Again, the decision taken by the Ford Company could affect the relationship between Firestone and Ford, increasing the economic costs caused by potential lawsuits filed by Firestone against the company. The cluster ‘cost of resources’ refers to the economic costs involved in any potential decision. The rationale used in this cluster is that the decision of layingoff would have a negative economic impact for the company. The cluster ‘resources’ refers to the economic cost of making a decision, and basically its impact on the cluster’s components such as Revenues, Market Share and Production Capacity. For example, if the company decides to discontinue the Ford Explorer production there would be economic costs such as a decrease in Market Share and in Revenues to the company.

Fig. 5 Macro View of Economic Costs Network

Fig. 6 Micro View of Economic Costs Network

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The cluster ‘public image’ is also affected by the alternatives. This cluster refers to the economic costs that could impact the company such as higher legal costs caused, for example, by the decision of maintaining production of the Explorer Model without any change of tire suppliers. The cluster ‘competition’ refers to the economic costs of making a decision related to the competition. For example, if the company decides to discontinue production of the Ford Explorer model, other brands of the Ford Company would also be affected by the decision since customers would perceive the Ford SUV’s not as safe as they expected and this could cause additional economic costs.

4.2 Political Costs Clusters, Links and Judgments Table 5 illustrates the clusters in this network and their respective elements. The inner and outer dependencies of clusters in this model are shown in Figs. 7 and 8. The ‘stakeholders’ cluster, refers to the people or group of people who would be negatively affected by decisions made by Ford and that would be defined as

Table 5 Political costs clusters and elements Clusters Elements Alternative sites

Stakeholders Tires suppliers Public image Cost of resources

• Discontinue Explorer production • Redesign the Explorer model • Maintain the production of Explorer Model • Maintain the production of Explorer Model, but change the tire supplier Customers, Community, Employees and NHSA Firestone, Goodyear, Michelin and Other tire suppliers Image, Trust, Accountability and Legal matters Layoff Costs, Launching Costs, Writeoff Costs and Production Costs

Fig. 7 Macro View of Political Costs Network

Fig. 8 Micro View of Political Costs Network

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political costs. For example, if the company decides to discontinue the model, then there would be additional political costs due to layoffs. The ‘public image’ cluster would also be affected by the decision made by Ford. The legal matters would be the most important political costs incurred by the company. The ‘tire suppliers’ cluster refers to the suppliers that could increase the political costs of the company by some of the decisions the company could take. For example, if the company decides to change the tire suppliers, they may incur new political costs with Firestone. Finally, the cluster ‘Cost of resources’ refers to the political costs that the company would incur by taking any of the decisions. For example, if the company decides to discontinue the model, then they would probably incur political costs based on the decision of laying-off some of the employees from the Ford Explorer production line.

4.3 Social Costs Clusters, Links and Judgments Table 6 illustrates the clusters in this network and their respective elements. The inner and outer dependencies of clusters in the social costs model are shown in Figs. 9 and 10.

Table 6 Social costs clusters and elements Clusters Elements Alternative sites

Stakeholders Public image Brand image

• Discontinue explorer production • Redesign the explorer model • Maintain the production of explorer model • Maintain the production of explorer model, but change the tire supplier Customers, Community, Employees and NHSA Image, Trust, Accountability and Legal matters Quality, Safety, Prestige, Service

Fig. 9 Macro View of Social Costs Network

Fig. 10 Micro View of Social Costs Network

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The ‘stakeholders’ cluster, refers to the people or group of people who would incur social costs, based on different decision alternatives taken by Ford. There is a link between this cluster and the ‘public image’ cluster. This means that, for example, if Ford maintains the Explorer model, then the customers would probably have a social cost, that would affect the Image and Trust in the vehicles from Ford. The same thing would happen between Stakeholders and some components of the ‘brand image’ cluster. The next cluster that is affected is the ‘public image’ cluster. A bad image of the company as a consequence of a decision could cause social costs for the company in terms of Image and Trust. Again, as previously explained for the case of stakeholders, this cluster is also linked to (and it would affect) brand image and stakeholders. The last cluster that is impacted is the ‘brand image’ itself. This requires no further explanation, as the alternative decisions taken would clearly have the power to change how stakeholders perceive the brand’s image, with a probable negative impact that we refer to as a social cost for the company.

4.4 Synthesis of Judgments in the Costs Model The combined results from Economic Costs, Political Costs and Social Costs networks can be seen in Table 7. This result indicates that from the Costs Model point of view, the alternative decision of discontinuing Explorer gives the highest cost to Ford, and the Redesign alternative would have the smallest impact on the company’s costs.

5 Risks Model Unlike the Benefits and Costs models, the Risks model is slightly different. The Risks model contains indefinite interactions and results. In the case of FordFirestone risks are defined as the negative uncertainties in the decisions taken by

Table 7 Synthesis of Costs priorities Alternatives

Discontinue explorer Redesign model Maintain current model Maintain model, change tire supplier

Costs

Synthesis

Economic 0.6567

Political 0.0827

Social 0.2606

0.3825 1.0000 0.8849 0.4701

0.0966 1.0000 0.3258 0.4300

0.0989 0.0000 0.1264 1.0000

0.2592 0.7394 0.6081 0.3443

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Ford regarding the Ford Explorer/Firestone matters. We can classify risks into two categories, economic and social. Economic risks refer to financial risks that may occur as a result of the decisions taken by Ford. For example, if the decision is to discontinue Explorer, there is a risk that Ford would jeopardize its relationship with Firestone which may impact its relationship with other Ford brands. Social risks describe other than financial risks that may occur as a result of the decision taken by Ford. For example, if the decision is to maintain the current Explorer model, there is a risk that the number of accidents to customers who drive this car would increase.

5.1 Economic Risks Clusters, Links and Judgments Table 8 illustrates the clusters in this network and their respective elements. The inner and outer dependencies of clusters in the economic risks model are shown in Figs. 11 and 12. The ‘tire suppliers’ cluster refers to tire companies that may encounter economic risks based on the decision alternatives taken by Ford. This cluster would also affect the ‘public image’ cluster; more specifically, ‘legal matters.’ There is

Table 8 Economic risks clusters and elements Clusters Elements Alternative sites

Tires suppliers Competition

Public image Cost of resources Resources

• Discontinue explorer production • Redesign the explorer model • Maintain the production of explorer model • Maintain the production of explorer model, but change the tire supplier Firestone, Goodyear, Michelin and other tire suppliers • Ford’s other SUV brands • Ford affiliates’ SUV brands • Other companies’ SUV brands Image, Trust, Accountability and Legal matters Lay off costs, Launching costs, Write off costs, and Production costs Revenue, Production Capacity and Market Share

Fig. 11 Macro View of Economic Risks Network

Fig. 12 Micro View of Economic Risks Network

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also an inter-dependence among the nodes in the ‘tire suppliers’ cluster. This is because what one tire supplier does may impact how the other tire suppliers react. The ‘competition’ cluster has no link with any other clusters except the ‘alternatives’ cluster. It is clear that the decision taken by Ford regarding the Explorer would impact how the competition would behave. However, there is inter-dependence among the nodes in the ‘competition’ clusters. Similar to tire suppliers, what one competitor does may impact how the other competitors react. The last two clusters that are impacted are the ‘resources’ and the ‘cost of resources’. These two clusters refer to internal resources, both financial and nonfinancial resources. It is typical that the internal resources of a company would have economic risks due to a decision taken by the top management of the company. For example, there would be an economic risk for the revenue and lay off costs due to the decision taken.

5.2 Social Risks Clusters, Links and Judgments Table 9 illustrates the clusters in this network and their respective elements. The inner and outer dependencies of clusters in the Social Benefits model are shown in Figs. 13 and 14. The ‘stakeholders’ cluster refers to the people or group of people, who could have social risks, based on the different decision alternatives taken by Ford. This cluster practically affects all other clusters in this network, including the ‘public Table 9 Social risks clusters and elements Clusters Elements Alternative sites

Stakeholders Public image Brand image

• Discontinue Explorer production • Redesign the Explorer model • Maintain the production of Explorer Model • Maintain the production of Explorer Model, but change the tire supplier Customers, Community, Employees and NHSA Image, Trust, Accountability and Legal matters Quality, Safety, Prestige, and Service

Fig. 13 Macro View of Social Risks Network

Fig. 14 Micro View of Social Risks Network

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image’ and ‘brand image’ clusters. In this network, customers and community have higher impact on the network than the other two stakeholders. The stakeholders can imply social risks to ‘public image’ cluster that would affect how they see the company’s public image in terms of trust and image. The stakeholders also affect the ‘brand image’ cluster along line similar to the ‘public image’ cluster. In this network, safety and prestige are considered to be more significant than the two types of image. The ‘stakeholders’ cluster plays an important role in this network because it has the highest social risks related to the decisions taken by Ford.

5.3 Synthesis of Judgments in the Risks Model Both networks in the risks model have independent results that would then feed the higher-level network (the overall risks network). The combined results, from the Economic Risks and Social Risks networks, are shown in Table 10. The result in Table 10 indicates that from the risks point of view, the alternative decision of maintaining the current car model gives the highest risks, both from the economic and the social standpoints. The least risky alternative would be to redesign the model.

6 Ratings and Synthesis The final synthesized priorities of the alternatives for the benefits, costs and risks from Tables 3, 7 and 10, respectively are given in Table 11. Table 10 Synthesized priorities in the Risks Model Alternatives Risks

Discontinue explorer Redesign model Maintain current model Maintain Model, Change tire supplier

Synthesis

Economic 0.25

Social 0.75

0.5591 1.0000 0.5613 0.6982

0.1705 1.0000 0.0884 0.4037

0.2676 1.0000 0.2066 0.4773

Table 11 Synthesized alternatives for B, C and R in ideal form Values of Alternatives for B, C and R Benefits (B)

Costs (C)

Risks (R)

Discontinue explorer Redesign model Maintain current model Maintain Model, Change tire supplier

0.2592 0.7394 0.6081 0.3443

0.2676 1 0.2066 0.4773

1 0.4145 0.1031 0.5124

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Table 12 Intensity values in ideal form for rating B, C and R Very high High Medium

Low

Very low

1.000

0.118

0.063

0.578

0.235

Table 13 Final Ranking of Alternatives in Normalized Form Ratio (B/CR)

Total (bB-cC-rR)

Discontinue explorer Redesign model Maintain current model Maintain MODEL, CHANGE tire supplier

0.017 0.074 -0.274 0.006

1.69 1.55 0.239 3.169

Strategic criteria are now used to rate the merits. Table 12 shows the priorities of the intensities in ideal form, that is, normalized by dividing each by the largest. These priorities were pairwise compared for preference and the same intensities derived by making pairwise comparisons (they are the same for all criteria). Table 14 shows the strategic criteria and their subcriteria with their priorities obtained by using paired comparisons. The BCR merits are then rated, by first taking the ideal alternative for each merit, from Table 11, and then selecting the appropriate intensity, for that ideal alternative, from Table 12, for each strategic subcriterion. The overall weighted outcome unnormalized and normalized is shown on the right in Table 14. Using these three normalized values for B, C, and R, the final ranking of the alternatives is shown in Table 13 computed with two different formulas: the multiplicative (ratio) and the additive (total). The total is what is of interest to us. In this case, the ratio outcome formula that is concerned with marginal returns, without considering the total resources needed to complete the projects, does not give the same ranking as the total outcome. Redesign is the best outcome, which is what Ford did anyway.3 Both this analysis and Ford’s decision where independently done at the same time in 2001.

7 Sensitivity Analysis In order to determine when different alternatives become preferable, sensitivity analysis was performed by varying weights and ratings in the model. The analysis began by increasing (and decreasing) the weight of the Benefits (See Fig. 15). Table 15 interprets the results of Fig. 15.

3

These results are supported by the decision taken by Ford to redesign the Explorer in March 2001.

Risks

Medium (0.235)

Weight (0.731) Global 0.160 weight Benefits Very high (1.000) Costs Very high (1.000)

Low (0.118)

Very low (0.063)

Low Medium (0.118) (0.235)

Medium Medium Low (0.235) (0.235) (0.118) Low (0.118) High Very low (0.578) (0.063)

(0.105) 0.007

High (0.578) Medium (0.235)

(0.637) 0.043

(0.188) 0.041

(0.081) 0.018

(0.731) 0.522

Low (0.118) Medium (0.235)

Medium Very high (0.235) (1.000) Low (0.118) Very high (1.000)

(0.258) 0.017

Very high (1.000) Very low (0.063) Medium (0.235)

(0.188) 0.135

Very low (0.063)

High (0.578) Very low (0.063)

(0.881) 0.058

Table 14 Rating of BCR with respect to strategic sub criteria Domestic issue (0.218) International relations (0.067) Human well being (0.714) Sub criteria Ford Car US Foreign Foreign Foreign Safety Confidence Confidence interests industry government customers suppliers governments factors in in justice interests interests government

0.209 r = 0.115

0.730 c = 0.400

0.885 b = 0.48 5

Total Normalized

7 Sensitivity Analysis 155

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1

2

4

3

Increasing Benefits weights 1 – Discontinue Explorer 2 – Redesign Model 3 – Maintain Current Model 4 – Maintain Model, Change Tire Supplier Fig. 15 Sensitivity analysis of benefits

Next, sensitivity analysis was performed for the Costs variable. The results obtained by increasing the weight of the costs are as follows: redesign model, maintain current model, maintain model and change tire supplier, and discontinue the Explorer model production. This means that if the company perceives the costs as the most important criterion to make the decision, they would decide to redesign the model. From this result, one is led to conclude that this alternative seems to be the best choice from the costs standpoint. On the other hand, if the weight of the Table 15 Ranking of alternatives as benefits increase/decrease Weight of benefits Alternatives

\0.147

[0.147,0.305)

[0.305,0.534)

[0.534,0.765)

[0.765

Discontinue explorer Redesign model Maintain current model Maintain model, change tire supplier

4 1 3 2

3 1 4 2

1 2 4 3

1 2 4 3

1 3 4 2

7 Sensitivity Analysis

157

costs is decreased, the result would be to discontinue, redesign model, maintain model and change tire supplier, maintain current model, in that order. This means that the risks criterion appears to be more important than the benefits, which leads to the decision of discontinuing production of the Ford Explorer model. The last criterion was the risks. When risks are increased the outcome was: redesign model, maintain model and change tire supplier, discontinue, maintain current model. The conclusion supports the initial thought that maintaining the current model (without changing the tire supplier) is the riskiest decision for the company to make. Finally, when the weight of the risks was decreased the results were: discontinue Explorer, redesign model, maintain model and change tire supplier, maintain current model.

Bibliography Bridgestone/Firestone voluntary tire recall. (2000, August 9). Retrieved 6/1/01 from the World Wide Web: http://bridgestone-firestone.com/news/corporate/news/00809b.htm. Firestone recalls (2001, February 6). Retrieved 6/3/01 from the World Wide Web: http:// www.nhtsa.dot.gov/hot/firestone/Update.html. Government investigators seek to wrap up Firestone probe. (2000, Dec. 21). Retrieved 5/30/01 from the World Wide Web: http://www.cnn.com/2000/US/12/21/firestone.nhtsa/index.html. NHTSA investigating failure of Firestone brand tires. (2000, Aug. 3). Retrieved 1/6/01 from the World Wide Web: http://www.cnn.com/. Public Citizen and Safetyforum.com with C.Tab Turner; The Real Root Cause of the Ford/ Firestone Tragedy : Why The Public is Still At Risk (April 2001). Schaefer, G. (2000, December 20). Wheeling and dealing: Bridgestone admits some blame for deadly tire failures. Retrieved 4/21/01 from the World Wide Web: http://more.abcnews. go.com/sections/us/dailynews/tires001220.htm. Valenti, C. (2000, September 5). What cost recalls? Retrieved 4/22/01 from the World Wide Web: http://abcnews.go.com/sections/business/TheStreet/firestonetire_recall000905.htm.

Chapter 7

Synthesis of Complex Criteria Decision Making: A Case Towards a Consensus Agreement for a Middle East Conflict Resolution

1 Introduction The Middle East conflict is not a series of wars tending toward peace, but a state of continued belligerency interrupted by war. It is not a single isolated problem to be solved but a system of people with conflicting aspirations. Physically, the problem is geographic with two parties desiring the same piece of land, but its origins are deeply rooted in people’s beliefs and in their attachments to a land consecrated by their great religions. There are claims made by these people of rights to live in the land and to have a state to maintain an identity. The problem is greatly compounded by widespread activities in the area, to include arms supply, cause support and the development of vested interests, thereby placing the problem in a complex global framework. Although one might expect that the global framework might accelerate a solution, in fact it complicates it due to the diversity of each participant’s interests. Hence, a solution has eluded the global community. The IsraeliPalestinian conflict continues to plague the Middle East and threaten stability, not just regionally, but also globally by inciting some terrorist claims. Despite the best efforts of diplomats and world leaders, a satisfactory resolution has not emerged. Hence, it is with some degree of hubris that we present a solution that we expect will outperform other efforts. What we suggest is a holistic model that explores feedback from various criteria and input from key constituents. The Wall Street Journal of November 1, 2007 reports that Karen Hughes, who led efforts to improve the U.S. image abroad and was one of President Bush’s last remaining advisors from the close circle of Texas aides said the Iraq war was usually the second issue that Muslims and Arabs raised with her, after the longstanding conflict between Israel and the Palestinians. Ms. Hughes said she advised Mr. Bush and Ms. Rice 2 years ago that U.S. help in ending the six-decade-old fight over Israel would probably do more than anything else to improve the U.S. standing world-wide’’. There are two widely known quantitative mathematical ways to deal with conflict resolution is which the use of complex structures to incorporate all the necessary details is largely absent because of limits imposed by the kind of scale T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_7,  Springer Science+Business Media New York 2013

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and hence also the associated mathematics used. One is game theory with its ordinal payoffs on both tangibles and intangibles and the other is utility theory with its interval scale measurements. In both theories there is no agreed upon way to combine individual judgments into a representative group judgments, particularly highlighted by Arrow’s Impossibility Theorem. Professor Michael Maschler, the renowned game theorist and one of the editors of the International Journal of Game Theory recently wrote to the fifth author, Saaty, in a private communication: ‘‘People simply do not possess a utility function, or make mistakes when reporting their priorities. If you ask enough questions they will even state priorities that are not transitive. Thus you cannot even determine a useful ordinal utility function. I do not know how to alleviate this difficulty. Therefore, at present, non-cooperative game theory can at best shed some insight on the real-life situation but usually it is not capable in suggesting definite recommendations (except for simple cases)’’. The bottom line is that there have been no quantitative models which embrace all the necessary tangible and intangible factors that tell us what to do. A major problem in analyzing conflicts in quantitative terms is how to deal with the measurement of intangible factors that arise in order to make tradeoffs with the other tangible factors when both benefits and potential benefits, costs and potential costs are involved. The goal of this chapter is to show how to use the Analytic Network Process (ANP) in a benefits, opportunities, costs and risks (BOCR) framework to develop and project the most likely best solution that takes into consideration the interests and influences of all the parties involved in the ongoing conflict in the Middle East. It is the overall influences that determine what would be best that is not subject to change or caprice. We need a practical quantitative approach that enables one to synthesize payoffs on different criteria. It delves in greater depth into the fine structures of strategies according to their merits and weaknesses when confronted with those of the opponent than does a game theoretic approach. It makes it possible for the parties to recognize and account for the strengths and weaknesses (political, military, social and so on) of their strategies against those of the opposition. The parties can work together through their representatives (perhaps often through the UN and in the presence of other parties to mitigate exaggerations and excessive claims) or do the analysis on their own with their own judgments partly imputed to what they think the opposition desires. In the absence of one party the judgments are surmised by the analyst from publicly declared positions and subjected to sensitivity analysis in case of uncertainties. In this manner one can evaluate the strategies of each party according to its merits against the strategies of the opponent(s) to improve the parties’ understanding of the conflict in which they are involved. This type of analysis involves multi-criteria decisions with intangible payoffs derived from paired comparisons of the relative merits of the strategies against each of the opponent’s strategies and then synthesizing the outcome across all merits and weaknesses, analyzed in short, medium and long range time frames.

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2 Background Peace is almost always secured through accommodation, bargaining, and compromise—even after an overwhelming victory is obtained by one side. Our approach utilizes the Analytic Network Process, because it fits the realism in eliciting and capturing the intensity of judgments regarding the dominance of some factors over other factors, the synthesis of group judgments, and the performance of sensitivity analysis for the stability of the outcome. The study involved a mixed group of Palestinians, knowledgeable pro-Israeli experts, and others from the outside, like China, Saudi Arabia, Turkey, and the US. Over a 3 day period, the panel structured the problem, defined the constituents and developed several potential alternatives. The process was not without conflict and negotiation of its own. At times, the panel differed on various definitions, on the structure of the model, and on the potential solutions. However, there was nearly always unanimous agreement on the nature of the conflict, with little debate within either side about the underlying concerns or where the power and influence belonged that could bring about termination of a 58 year old confrontation. Similarly, there was practically no problem in identifying the key constituents. However, since the beginning of the conflict, leaders and others have proposed many alternatives solutions. These influenced the perception of the participants in regard to potential alternatives. In fact, one person suggested that the participants could have difficulty ‘‘thinking outside the box’’. He thought that the group was so influenced by previous attempts that they experienced difficulty in conceptualizing ‘creative’ alternatives that had not been proposed previously. With the help of intelligent informed people we felt that we could identify the major influences operating in the Middle East Conflict, prioritize them and find the most likely outcome. We had some objectivity because we had participants to represent the viewpoint of the Palestinians, the Israelis and the Americans, the major parties that will have to be involved in any solution. So we had sufficient information to represent the different interests and did not necessarily have to have the actual leaders and politicians. We were fairly aware what the extremist positions are and what they could do and we included that in the model’s structure and the judgments we gave. In the end sensitivity analysis determined the stability of our recommended solution in view of all sorts of variations produced by different interests whether moderate or extremist. Unlike the use of statistics it is not always necessary in the analysis of complex problems to involve a large sample of diverse people who may or may not have the complete understanding needed to resolve a problem. What follows is a brief account of the method employed, the model, the structure of the problem as a decision with benefits, opportunities, costs and risks and how comparisons were made in the analysis of the outcomes, recommendations for implementation, summary, and recommendations for getting others to look at the problem in this integrated and comprehensive framework.

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3 Methodology In making a decision, we need to distinguish between the hierarchic and the network structures that we use to represent that decision. In a hierarchy we have levels arranged in a descending order of importance. The elements in each level are compared according to dominance or influence with respect to the elements in the level immediately above that level. The arrows descend downwards from the goal even if influence, which is a kind of service, is sought for in elements in lower levels that contribute to the well-being and success of elements in higher levels. We can interpret the downward pointing of the arrows as a process of stimulating the influence of the elements in the lower level on those in the level above. In a network, the components (counterparts of levels in a hierarchy) are not arranged in any particular order, but are connected as appropriate in pairs with directed lines. Again an arrow points from one component to another to simulate the influence of the elements of the second component on those in the first. Influence may be evaluated in terms of importance, preference or likelihood. A network is generally made up of clusters whereby each cluster has one or more elements. The pairwise comparisons of elements in a component are made according to the dominance of influence of each member of a pair on an element in the same or in another component with respect to a control criterion. Examples of control criteria are economic influences, political influences, social influences, technological influences and a few other similar criteria that enable us to focus on the kind of influence there is among the elements and clusters. I this manner a network is divided into sub-networks each relating to a different control criterion and all the connections that represent influence with respect to that criterion. In the end the priorities of the alternative outcomes in the different sub-networks are combined by weighting and adding with respect to the priorities of the control criteria. In addition, in a network, the system of components may be regarded as elements that interact and influence each other with respect to a criterion or attribute that is outside the system of influences. That attribute itself must be of a higher order of complexity than the components and thus of higher order than the elements contained in the components. We call such an attribute a control criterion. Thus even in a network, there is a hierarchic structure that lists control criteria above the networks. Also, in any decision one expects to consider favorable and unfavorable concerns. Some are sure things, others are less certain and have a likelihood of materializing. The sure concerns are called Benefits and Costs, while the uncertain concerns are called Opportunities and Risks. We refer to the four concerns collectively as BOCR. For each of the four BOCR merits we have a system of control criteria that we use to assess influence. The result is that such control criteria and/or their sub criteria serve as the basis for all comparisons made under them, both for the components and for the elements in these components. In a hierarchy one does not compare levels according to influence because they are already arranged in a predetermined order of importance from top to bottom. The

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criteria for comparisons are either included in a level, or more often implicitly replaced by using the idea of ‘‘importance, preference or likelihood’’ with respect to the goal, without being more finely detailed about what kind of importance it is. The control criteria for comparisons in a network are intended to be explicit about the importance of the influence that they represent. In a hierarchy, we ask the question for making a comparison, which of two elements is more dominant or has more influence (or in the opposite sense is influenced more) with respect to a certain element in the level above? In a network we ask, which of two elements is more dominant in influencing another element in the same or in another component with respect to a control criterion? In both hierarchies and networks the sense of having influence or being influenced must be maintained in the entire analysis; the two should not be mixed together. The ANP frees us from the burden of ordering the components in the form of a directed chain as in a hierarchy. We can represent any decision as a directed network. While the Analytic Hierarchy Process (AHP) has a visibly better structure that derives from a strict understanding of the flow of influence, the ANP allows the structure to develop more naturally, and therefore is a better way to describe faithfully what can happen in the real world. These observations lead us to conclude that hierarchic decisions, because of imposed structure are likely to be more subjective, dependent on expert knowledge and predetermined. Further, by including dependence and feedback and by cycling their influence with the supermatrix, the ANP is more objective and more likely to capture what happens in the real world. It does things that the mind cannot do in a precise and thorough way. Putting the two observations together, the ANP is likely to be a strongly more effective decision-making tool in practice than the AHP. The ANP has a four phase structure of complex decisions: (1) the hierarchies or networks of influences and ‘‘objective’’ facts that make one alternative of the decision more desirable than another for each of the control criteria under the BOCR merits; (2) pairwise comparisons of the elements in each component according to inner or outer influences and derivation of the priorities of the elements and then also of the component of these elements according to their influence on each components to make the supermatrices of priority vectors stochastic and raise it to limiting powers; (3) a relatively subjective value system for evaluating whether or not to make a decision and if it is made what the different priorities of each of the BOCR merits are used to combine the four outcomes and obtain an overall ranking of the alternatives; and (4) sensitivity analysis to determine the stability of the best outcome subject to perturbations in judgments. In each of these phases there are major concerns that are subdivided into less major ones and these in turn into still smaller ones. Knowledge about the level of subjective values where one must use the absolute mode of measurement of the AHP can be enriched by information from what goes before it, but does not depend on them for its priorities. It provides the intensities on which the BOCR merits are rated one at a time and then normalized. This level cannot be conveniently integrated into a single structure with the other two that precede it, and thus it appears that most decisions, despite their use of network structure due to the subjective

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thinking involved, are embedded in a higher order hierarchic structure. A decision may involve three or four adjacent ranges of homogeneous elements in each to represent personal values (Maslow put them into seven groups). Roughly speaking, we have lumped them in decreasing order of importance: (1) Survival, health, security, family, friends and basic religious beliefs some people were known to die for; (2) Career, education, productivity and lifestyle; (3) Political and social beliefs and activities; (4) Philosophical thoughts and ideas and things that are changeable, and it does not matter exactly how one advocates or uses them. There are similar values for a group, a corporation, a country and for the entire world as represented for example by the United Nations. In sum, the ANP provides: 1. A methodical approach that is useful for making it possible for different individuals and groups to provide and combine their judgments according to their own importance, which is included in the judgments. Although both theory and software can do it, in this exercise consensus was used to record each pairwise comparison judgment; 2. A structure to represent all the elements of the problem proposed by anyone present or known from other sources so that nothing is left out because of complexity. The comprehensive structure puts people at ease that nothing is hidden or left out. It facilitates agreement on the judgments used to derive the best alternative outcome; 3. The stability of the outcome to possible changes or future threats. (For further details on the AHP/ANP methodology readers are referred to: Saaty 1999, 2001, 2005; Saaty and Vargas 2006).

4 Structuring the ANP Model for the Middle East Conflict Resolution We defined the problem as an attempt to understand what forces and influences, because of their relative importance, would implicitly drive the outcome towards a consensus peace accord for the conflict between Israel and the Palestinians. To accomplish this task, a panel of 8 individuals was assembled to represent a cross section of people: international thinking representatives (3), Israeli thinking representatives (2), a Palestinian (1) and Muslim thinking representatives (3). In most cases, the individuals crossed the various categories and interests and did not fall into discrete separate groups. It was recognized that the panel did not represent a valid cross-sample or that the size of the panel was adequate to represent the different population sizes involved. It was agreed that the work is exploratory in nature, intended to demonstrate how the method can be used over a short period of time to arrive at a reasonable solution that is not outlandish to any of the sides.

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It was agreed by all participants that no part of the decision would be done without consensus agreement whether it is what to add or delete from the model or to make or not make comparison judgments on low priority criteria in order to save time to arrive at an answer in 3 days. It was justified to do that because it was clear that such factors and their contributing judgments were not worth the effort. It was the role of the moderator to facilitate the process and ensure that all parties agreed before moving on to the next step in the process. However, the moderator made no contribution to the agreement but facilitated mutual understanding among the participants. Since pairwise comparisons are made in the prioritization stage of the ANP, it is critical that all parties understand the definitions of the terms used. Moreover, as illustrated later in the paper, many questions about what dominated what with respect to a certain factor and how strongly it dominated it was often difficult to understand and even more difficult to conceptualize in practice. Hence, many of the questions were developed at length and repeatedly until they were well understood by all. This underscores the specific nature of the Middle East conflict and the necessity for consensus. Language and understanding matter! To ensure mutual understanding, the moderator needed to track the events on a screen projected for the participants and to use an additional measure to track the questions that were currently under consideration. In addition, the moderator maintained on the first screen the following items: 1. 2. 3. 4.

The software used for the ANP model; Documentation of the definitions, terms and criteria agreed upon; Notes on the ‘process’ and the steps taken to reach consensus; Agenda.

Although the level of detail and effort taken to document the process seemed excessive at first, it was clear from the start that not only were the initial steps taken helpful but they had to be augmented further. The augmentation included the use of other visualization tools in order to gain consensus. Hence, the steps taken to document the panel’s efforts are a nontrivial event. In fact, the use of the various ‘tools’ were necessary on multiple occasions to overcome objections. We believe that without these various tools, the group would have experienced greater hardships in reaching consensus. As mentioned above, at no point in the development and evaluation of the problem was the process easy and we caution against the belief that this was anyone’s intention. In fact, the ‘‘purpose’’ of the exercise was not easily agreed upon and on several occasions in the 3 days over which the panel met, the question about the purpose of the exercise was repeatedly readdressed. The panel agreed that its goal was to move toward a consensus agreement for what outcome is the best resolution of the Middle East Conflict. The group looked at the purpose of the project from various perspectives. First, the panel suggested that potential definitions for the panel’s purpose could include: • Peace in the region; • Impact on global peace;

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• Recognition of defined borders; • Long-term future stability. It was also recognized that there is an equally legitimate claim to view the problem from the vantage point of a more extremist Palestinian whose goals might include: • • • • •

Let them return (the Israelis) to where they came from; Right to return that creates a Palestinian majority; Allocation of natural resources including land; Infiltration of patriots—‘terrorists’; Elimination of Israeli nuclear threat.

Finally, one might take the position of more extremist Israeli views whose goals might include: • Status quo; Palestinians remain squeezed into small territories with restricted movement; • Deport all Palestinians; • Continued control of all resources; • No pro-Palestinian country should be able neutralize Israel’s nuclear power. After considerable discussion and we overly compress the process here, the panel agreed that any resolution is a process that requires consensus and it is consensus ‘‘buy-in’’ that encourages participation of all constituents. Agreement on the ‘purpose’ of the panel was not the only portion of the model that needed some dialogue. In fact, every step along the ‘process’ required negotiation and consensus. Several ways were proposed within the panel about how to construct the model and develop the issues. It was agreed that any solution would have benefits, opportunities, costs and risks (BOCR). However, it was not as easy for the panel to agree on the strategic criteria in terms of which they would evaluate and synthesize. The Strategic Criteria used to evaluate the BOCR are representative of the impact that a selected alternative would have on Global Peace, Long-Term Stability, Peace in the Region, and Recognition of Defined Boundaries. Although the panel selected the four strategic criteria in Fig. 1, they later agreed that Global Peace should be removed from the comparisons since stability and regional peace are believed to be strongly correlated with Global Peace. While the strategic criteria and their meanings were still fresh and prior to moving into the development of the BOCR sub-networks (subnets), the panel evaluated the Strategic Criteria with respect to the purpose of the undertaking. The results of the comparisons are shown in Sect. 5, Prioritization. However, we believe that it is useful to detail the nature of the comparison for the Strategic Criteria at this point in order to mirror the efforts and document the methodology that we used in this case. The panel was presented with the pairwise comparisons of the four Strategic Criteria with the following questions involving pairs of criteria: Which factors contribute more strongly and how much more strongly to

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PURPOSE: Toward a consensus agreement for a Middle East Conflict Resolution

STRATEGIC CRITERIA

GLOBAL PEACE (Omitted from final Model)

LONG-TERM FUTURE STABILITY

PEACE IN REGION

RECOGNITION OF DEFINED BOUNDARIES

BENEFITS

OPPORTUNITIES

COSTS

RISK

SUB-NET

SUB-NET

SUB-NET

SUB-NET

Fig. 1 The ANP main top-level structure for the middle east conflict resolution model

resolving the conflict in the Middle East according to the desire of all the parties for (1) Global Peace or for Long-Term Future Stability in the Region, (2) Global peace or Peace in Region, (3) Global Peace or Recognition of Defined Boundaries, (4) Long-Term Future Stability or Peace in Region, (5) Long-Term Future Stability or Recognition of Defined Boundaries and finally (6) Peace in Region or Recognition of Defined Boundaries? Because Global Peace was eliminated, only the last three comparisons were made. Now we consider what numbers to use to express the judgments about dominance. Physics depends on measurements and on experts to interpret the meanings of those measurements. The ANP depends on individuals in each decision problem to represent what they think the people involved prefer or think is more important in that decision. Table 1 gives the pairwise comparisons of the strategic criteria.

Table 1 Strategic criteria judgments

Long-term future stability Peace in region Recognition of defined borders

Long-term future stability

Peace in region

Recognition of defined borders

1 4 1

1/4 1 1/3

1 3 1

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4.1 Merits Returning to our conflict problem, the top-level structure has the four Benefits/ Opportunities/Costs/Risks (BOCR) merits and their sub criteria shown in Fig. 1 which represents the total initial model. Some of the nodes in both the Strategic Criteria and the subordinate networks of the BOCR were eliminated after the initial ratings due to the level of insignificant contributions that they added to the overall result because of their low priorities as compared with the other factors. The subnets under each of the four BOCR merits were developed independently. The benefits and costs were conceptualized as the short-term or internal aspects of the alternative evaluation while the opportunities and risks were thought of as those elements that have long-term influences.

4.2 The Benefits Subnet The benefits are defined as the short-term gains that any group might experience given the criteria below. • Economic Status in this network is defined as the short-term potential gains that might be realized given the implementation of one of the alternatives. • Human Rights are defined as the short-term improvements in how the United Nations state what constitutes basic human liberties/freedoms. • Safeguard the oil supply is defined as the incremental stability to the consistent delivery of oil; i.e. limited disruption to oil production. • Saves Lives is defined as the reduction in the loss of lives. • Standard of Living is defined as the incremental improvement for overall living conditions. In the initial phases of developing the model, the panel faced the challenge to build a ‘robust’ model that includes all the criteria that they felt were important to accurately reflect those elements that would be important to reach a resolution. With respect to the short-term gains that might be realized by the constituents, the foregoing five criteria are the full set of short-term benefits necessary to realize a full benefits model. As the panel developed the connections among the various nodes in the cluster, they reached a consensus that not all five of the nodes were essential. Economic Status and Human Rights were retained, but it was believed that Saves Lives and Standard of Living were subsumed under them. Safeguarding the oil supply was not a valid criterion for the benefits network. In addition, the model provided legitimacy for what the members of the panel felt intuitively; the two excluded criteria were not significant to the model. In fact at first the two deleted criteria were included and were omitted after their priorities turned out to be very low in relation to the other three criteria.

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The Benefits subnet is shown in Fig. 2 as a sample of what the subnets under the BOCR model look like. The circular arrow shown in Fig. 2 represents the fact that the ‘‘Constituents’’ cluster has feedback within the cluster. The implication of feedback within the alternative cluster is that each of the various constituents within this cluster influences the others within the cluster. For instance, a decision made by one party in the cluster influences the other parties in that cluster so that a movement toward peace by the Israelis and the Palestinians for example would have positive implications for both the United States and ‘Others’. More detail about the implications of feedback and dependency will be discussed in the findings section of the chapter.

4.3 The Costs Subnet The costs represent the short-term expenses and pains incurred by the constituents. • Arms industry includes those costs that would be experienced by the arms industries through either loss of income or additional limitations to trade/sale placed on suppliers. • Internal chaos in Israel is the attempt to capture the ‘price’ paid for disruption to lives that may be realized through the selection of any resolution alternative. • Making sacrifices identifies the real expense incurred through both monetary and non-monetary forfeitures that may be incurred through any one of the various alternatives. • Relocation/dislocation node represents the real expense of dislocation caused by the option of any one of the alternatives. • Reparations are the price that would need to be paid for conciliatory actions.

Constiuents Israelis

Other

Nuclear Use

One-State Solution Alternatives

Fig. 2 Benefits Subnetwork

Palestine

United States

Status Quo

Two State Viable Solution

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The panel used the same process for the Costs subnets that they used for the Benefits subnet. Once the initial comparisons were made, the Arms Industry and Relocation/Dislocation were omitted since these two criteria accounted for insignificant priorities. The two omissions are not surprising since Relocation was captured by the Reparations criteria and the costs to the Arms industry are significantly outweighed by the potential costs of the other criteria.

4.4 The Opportunities Subnet The opportunities are the long-term positive potentials that exist for the constituents. • Global Stability is the opportunity for greater stability throughout the world in order to foster a secure environment. • Regional Stability focuses on the regional stability surrounding the immediate parties to the conflict. • Return ‘home’ represents the right of return for all displaced parties. • Safeguard the oil supply refers to the long-term safety to the global distribution of oil. The panel went through similar efforts in the Opportunities subnet as they did with the Benefits subnet. In the initial development of this subnet, four criteria were included as given above; the final model only contained Regional Stability and Return ‘home’. Once again, Safeguard the oil supply was not deemed appropriate for the final consideration due to its low priority.

4.5 The Risk Subnet • ‘Wrong’ people return is the risk that the people who would return under the right to return option will be subversive types looking to incite further disruption instead of the type who want to foster sensus communities. • Further increase in radicalism is the risk that selection of any one of the alternatives would lead to an increase in radical activities. • Further instability in region is the potential of an alternative to lead to increased instability via continued fighting. • Limited longevity that promotes return to conflict refers to the fact that an alternative, if opted for, may not be viable for long-term. Hence, the probability that it returns to a state of conflict may increase the problem since it may be seen as a continued failures of the leadership to implement a resolution. Under the Risk subnet, only ‘Wrong’ people return had sufficiently low priority to delete it from the model; the remaining criteria were maintained throughout the analysis.

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Figure 3 summarizes the BOCR merits networks. In other words, it highlights both the short-term and long-term aspects of the model as well as the gains and losses that impact the alternatives. Each of the criteria in Fig. 3 under the BOCR merits model was evaluated with respect to the various constituents that influence the outcome of the model. Figure 4 illustrates the network of the various constituents. The constituent network captures the feedback and interdependence among the various parties. Although it may appear intuitive that choices made by Israel impact the Palestinians, the nature of the feedback and dependence involving the other parties (the U.S., Arabs, Muslims and the rest of the world) was not adequately understood until implemented in the model. The outcome of the dynamics between the various constituents is further explored below.

4.6 Alternatives The panel had to consider not only those initiatives that are ‘popular’ but also to develop ‘creative’ alternatives that may not have been explored or even present novel approaches. Furthermore, the group was instructed to think of alternatives as Short-term

Gains

Benefits

Opportunities

Economic Status Human Rights Safeguards the oil supply Saves Lives Standard of living

Global Stability Regional Stability Return ‘home’ Safeguard the oil supply

ALTERNATIVES

ALTERNATIVES

Costs

Loses

Long-term

Arms industry Internal chaos in Israel Making Sacrifices Relocations / Dislocation Reparations ALTERNATIVES

Fig. 3 Summary of the merits networks

Risks

‘Wrong’ people return home Further increases in radicalism Further instability in region Limited longevity with a return to conflict ALTERNATIVES

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Fig. 4 Constituent network Israelis

Palestinians

United States

Others: Arabs, Muslims, Etc.

if there were no limits or boundaries. However, it was not easy to develop novel alternatives because of the enduring nature of the conflict and because of the scope of alternatives that have been developed thus far. The full list of alternatives considered is as follows: • • • • • • • • • •

Status Quo Two-viable-state solution Nuclear use One-state solution Legal solution enforced by the U.N. Two-viable-state solution (Positive initiative by Israel, economic contribution, etc.) Two-viable-state solution (Change in U.S. policy) Two-viable-state solution (Saudi initiative (2002)/Beirut Declaration). United Nations partition (1947) Jewish state.

We consider the four highlighted bullets above as the final alternatives to determine which has the greatest likelihood of long term success according to the projected ability of the parties to exert the influences needed to bring them about. The most significant part of the ‘process’ to note is that reducing the list to a select few options was the result of the group negotiating an agreement. The panel came to a consensus that the various two-viable-state solutions could be captured under one alternative with the understanding that the details of implementation would be worked out as part of the long-term process. The Two-viable-State Solution captures the various forms that include the Bush Model, or the Saudi Initiative. This model recognizes the various independent states as autonomous. The threat of Nuclear Use captures the potential of a party in the conflict using a nuclear device to influence the outcome. The threat of use means Israel’s possession of nuclear weapons as a deterrent for other groups to use but it also captures a potential radical group’s ability to obtain and utilize nuclear weapons. Of all of the alternatives, this was the most difficult one to conceptualize when assessing the priorities in the evaluation process. In general, the group agreed that

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this was the least likely alternative but that it was necessary to include in the model since the threat exists and remains an option. One-state solution combines both the Palestinians and the Israelis into a single unified state that recognizes all individuals as politically and socially equal as in a democracy. Status Quo is a continued condition that has periodic rises in hostility and warfare. To make this alternative sound plausible, one of the Palestinian participants humorously suggested that the most rapid way to resolve the conflict is for all Palestinians to convert to Judaism; he was told by an Israeli friend that many Russians had been brought into Israel and later converted to Judaism.

5 Prioritization 5.1 Strategic Criteria and Their Priorities As explained above, the three strategic criteria were evaluated and their priorities shown below were used as the guiding factors of the BOCR merits. A sample of the questionnaire that uses the fundamental scale of absolute numbers and questions is shown in Table 1. Strategic Criteria Judgments and the results of those comparisons are shown in Fig. 5 and explained below. • Long-Term Future Stability captures the belief of the panel that any alternative that does not address and promote continuous stability in the region may contribute more harm than benefit. Additionally, the panel’s consensus is that economic, political, and social developments in the region are dependent upon the ‘stability’ of the environment. • Peace in Region identifies the panel’s conviction that economic, social, and political growth in the region are dependent upon long-term peace. Hence, any alternative must be evaluated against the potential of the choice to promote regional peace.

PURPOSE: Toward a consensus agreement for a Middle-East Conflict Resolution

STRATEGIC CRITERIA GLOBAL PEACE (omitted from final model)

LONG TERM FUTURE STABILITY 0.174

Fig. 5 Hierarchy for rating the BOCR merits

RECOGNITION PEACE IN REGION OF DEFINED 0.634 BOUNDARIES 0.192

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• Recognition of Defined Boundaries was identified by the panel as a strategic criterion because agreed upon boundaries are a necessary component in selecting a resolution alternative. Among the three strategic criteria to evaluate the BOCR merits, Peace in the Region has the highest priority (0.634) in contrast with Recognition of Defined Borders (0.192) and Long-Term Future Stability of (0.174). Therefore, we can qualify these priorities with the observation that any alternative selected must contribute to the long-term future stability of the region. The significant difference in the priorities underscores the overall importance that the panel placed on longterm stability since economic, social, and political development in the region depend on stability.

5.2 BOCR Merits and Their Priorities The importance of the four BOCR merits with respect to the strategic criteria is determined by prioritizing them according to the following five intensities: Intensities

Very high 0.42

High 0.26

Medium 0.16

Low 0.10

Very low 0.06

and their priorities derived through pairwise comparisons along with their priorities that are obtained at the outset and shown in Fig. 5. The rating outcome and final weights for each of the four merits are summarized in Table 2. These values are used as default values in an additive formula in developing the ANP model later on. For example, we asked the question for each of the merits: ‘‘what is the ‘merit’ of the top alternative under Benefits with respect to each of the Strategic Criteria?’’ This process was carried out in a similar way for Opportunities, Costs, and finally Risks. For instance, it was observed that there is a very high potential Benefits with respect to the first strategic criterion, i.e., LongTerm Future Stability. Once consensus was reached on the ratings for each of the merits, the resultant weights of the merits were derived as given in column 6 of Table 2. Table 2 Ratings for the merits: with respect to the strategic criteria Recognition of defined Sum of Merits Long-term future Peace in weighted region 0.634 boundaries 0.192 stability 0.174 values

Normalized

B O C R

0.2 0.19 0.31 0.31

Very high High Very high Very high

High High Very high Very high

Medium High Very high Very high

0.64 0.61 1 1

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5.3 Decision Networks Considerable time was invested in defining terms, constructing the model, and reaching agreement on various aspects of the pairwise comparisons made in the evaluation of the BOCR merits. Substantial use of the various media was made during this portion of the evaluation in order to reach consensus. Table 3 shows a sample of the ratings that the panel used to reach a consensus. Note that each of the numbers entered into the comparison sheet was agreed on by the group. At times, the discussion that ensued from the nature of the question was lengthy. Conversely, there were some questions on which the group was able to reach immediate agreement. Ten decision networks were created, one for each of the surviving BOCR criteria. As explained earlier each decision network contains the cluster of alternatives in addition to a cluster of the constituents. Table 5 shows each of a total 10 ratings for the BOCR constituents prioritized by pairwise comparisons and its corresponding value in relation to the criteria whose priorities were also obtained through pairwise comparisons. Both the local and global priorities are shown with respect to the various merits in the model. The values of global priorities were obtained as the product of BOCR rating (Table 3) times the corresponding local priority times the priority of its constituent: (a) Benefits Among the two benefits criteria, the human rights criterion has the highest priority of 0.9 as compared with the economic benefits criterion of 0.1. Among the benefits criteria, the highest priority given by those representing the Palestinians with respect to human rights is (0.340). Interpretation of the priorities suggests that with respect to benefits, the Palestinians have the most to gain in the short run due to immediate improvement in human rights. Although the United States has the next highest priority under economic benefits in Table 4, it also had the next highest priority for human rights since under the benefits node, human rights has the highest priority and the global rating for the United States is higher under this cluster. We interpret the United States’ high rating under the benefits cluster to be indicative of public perception and political motivation. The overall results of the Benefits subnets are given in Table 5.

Table 3 Sample Fundamental scale of absolute numbers Questionnaire for BOCR Merit Israelis Palestinians U.S. Other Israelis Palestinians U.S. Other

1 4 3 1/2

1/4 1 1/2 1/6

1/3 2 1 1/3

2 6 3 1

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Table 4 Criteria and their priorities Merits Criteria Benefits

Human rights 0.90

Constituents

Israelis Palestinians United States Others Economic status 0.10 Israelis Palestinians United States Others Opportunities Regional stability 0.50 Israelis Palestinians United States Others Return home 0.50 Israelis Palestinians United States Others Costs Internal chaos in Israel 0.12 Israelis Palestinians United States Others Making sacrifices 0.74 Israelis Palestinians United States Others Reparations / Relocations 0.15 Israelis Palestinians United States Others Risks Further increase in radicalism Israelis 0.46 Palestinians United States Others Further instability in region 0.34 Israelis Palestinians United States Others Limited longevity that promotes Israelis return to conflict 0.21 Palestinians United States Others

Local Global Priorities Priorities 0.141 0.340 0.300 0.218 0.154 0.274 0.310 0.263 0.340 0.232 0.268 0.159 0.141 0.507 0.112 0.240 0.460 0.397 0.058 0.064 0.395 0.392 0.099 0.114 0.253 0.338 0.201 0.210 0.421 0.332 0.125 0.122 0.277 0.330 0.110 0.262 0.493 0.318 0.079 0.111

0.025 0.061 0.054 0.039 0.003 0.005 0.006 0.005 0.032 0.022 0.025 0.015 0.013 0.046 0.011 0.023 0.017 0.015 0.002 0.003 0.091 0.090 0.023 0.026 0.012 0.016 0.009 0.010 0.056 0.046 0.017 0.017 0.028 0.024 0.011 0.029 0.031 0.020 0.005 0.007

(b) Opportunities Within the opportunities cluster, both criteria had the same weighting which demonstrates that both regional stability and the right to return home have equal

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Table 5 Benefits’ overall results Criteria alternatives Economic status 0.10

Human rights 0.90

Final outcome

Nuclear use One-state solution Status quo Two-viable-state solution

0.111 0.960 0.588 1

0.111 0.959 0.592 1

0.113 0.944 0.633 1

Table 6 Opportunities’ Overall Results Criteria alternatives Regional Stability 0.5

Return Home 0.5

Final Outcome

Nuclear use One-state solution Status quo Two-viable-state solution

0.13 0.55 0.16 1

0.23 0.76 0.35 1

0.32 0.86 0.54 1

weights (0.50). However, it is interesting to note that within the regional criterion, the Israelis have the greatest weight (0.340) while in returning home (0.507), the Palestinians have the greatest weight. In the long run, the Israelis perceive the greatest opportunity in the region’s stability whereas the Palestinians believe that they have the greatest opportunity with the right to return home. Further, given that the Palestinians have the greatest global weight (0.048), suggests that overall the Palestinians’ right to return home has the greatest global opportunity within the model. Table 6 presents the overall ranking of the alternatives with respect to opportunities. (c) Costs Among the three costs criteria, the Making Sacrifices costs criterion has the highest priority of 0.74 compared with the Reparations/Relocations costs criterion of 0.15 and the internal chaos costs criterion of 0.12. Among the costs constituents, the highest priority emerged from the rather evident conviction that both the Palestinians (0.392) and the Israelis (0.395) would have to make many sacrifices in the short run. Given that the global ratings of the other constituents on the other cost criteria are relatively low, we believe that implementation of a best alternative to a peace agreement will need to pay attention to the short term sacrifices that

Table 7 Costs’ overall results Internal chaos Criteria Israel 0.12 alternatives Nuclear use One-state solution Status quo Two-viable-state solution

1 0.38 0.56 0.30

Making sacrifices 0.74

Reparations Relocations 0.15

Final outcome

1 0.38 0.71 0.31

1 0.26 0.16 0.44

1 0.36 0.61 0.32

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both groups will have to make. Table 7 shows the overall results of the alternatives with respect to the costs. (d) Risks Among the three risk criteria, the criterion Further Increase in Radicalism has the highest priority of 0.46 compared with Further Instability in the Region (0.34) and with Limited Longevity with a Return to Instability (0.21). Interpretation of the results given in the risks merit is that the greatest long-term risk is that a selected alternative might result in an increase in radicalism that would further promote conflict in the region. This is followed by the risk that there might be an increase in instability due to implementation of one of the alternatives. Among the risks constituents, the highest priority is Israel’s for both Increase in Radicalism (0.421) and for Limited Longevity with a Return to Instability (0.493). The findings presented here suggest that the Israelis are most concerned with the longterm risk of violence in the region (0.058). Similarly, with respect to the global priorities, we see that the Palestinians are also concerned with Long-Term Violence in the region (0.046). The final outcome for risks is given in Table 8. It is worth noting that the local and global priorities are significant from a conflict resolution management perspective. These outcomes provide leaders with information important to overcoming obstacles toward a consensus agreement for a Middle East Conflict Resolution. For instance, the panel’s evaluation under Benefits indicates that Human Rights have the higher of the two priorities. Furthermore, the Local Priorities under Human Rights suggests that both the Palestinians and the United States are fairly equal. Therefore, those leaders managing the process will know that with respect to Benefits (i.e. short-term gains); one ought to focus on the two groups with the highest ratings in order to ensure success. The remaining entries in Table 4 may be used similarly.

6 Synthesis of the BOCR Merits Until about the year 1999, many examples of the ANP used the BO/CR ratio to evaluate the alternatives in the final decision. This ‘‘marginal’’ ratio assumes that all four merits are equally important which of course need not be the case. Even if

Table 8 Risks’ Overall Results Further increase in Criteria radicalism alternatives 0.46 Nuclear use One-state solution Status quo Two-viable-state solution

0.60 0.40 1 0.35

Further instability in region 0.34

Limited longevity with a return to instability 0.21

Final outcome

l 0.24 055 0.17

1 0.43 0.76 0.37

1 0.43 0.96 0.33

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not equally important and therefore weighted by the priorities of the BOCR merits, it would be multiplied by a positive constant that is greater or less than one indicating overall gain or loss over the short term. In 1999, the fifth author developed a way to derive priorities for each of the four merits B, O, C, R, through ratings with respect to strategic criteria and use them to compose the weights of the alternatives by multiplying them by the corresponding priority of their merit adding the results for benefits and opportunities and subtracting from that the results for the costs and risks. This method gives the correct outcome when for example dollars are used. The priorities of the BOCR are rated with respect to strategic criteria that are used when there are many decisions to be taken to decide which one to take first and which second and so on. It is what individuals do in a day or over a period of time to prioritize all the decisions they face, or governments to allocate resources to their many decisions over a period of time. Instead of multicriteria decision making, it is a multi-decisions problem. The results obtained from the rating system (Table 2) and the overall results of the BOCR Merits are normalized and synthesized in order to capture the final outcome of the entire process. For our purpose, we used the multiplicative power weighted formula which is expressed as ((bB)(oO))/((cC)(rR)) and referred to as Multiplicative or Marginal Synthesis. For the Additive or Total Synthesis, we used the negative formulation expressed as ((bB) ? (oO)) - ((cC) - (rR)). Multiplicative Synthesis illustrates which of the alternatives is preferable in the short term given all of the criteria under consideration; Additive Synthesis illustrates the alternative that is preferable in the long term (Saaty 2005). We see that under both short and the long term the Two-State option is the best alternative. After 3 days of discussion, analysis and evaluation, it turned out that the best alternative is a Two-state Solution and this was neither voiced nor explicitly subscribed to in advance. Recall that the group defined the Two-state solution to include the various forms suggested through the years which includes for example the rather well-known Bush Model, or the Saudi Initiative which also recognizes two independent autonomous states. The priorities also highlight points to keep in mind in the process of reaching agreement on a solution to resolve the Middle East Conflict where ‘trouble’ might arise and give leaders prior indication in order to avoid those pitfalls. The results shown in Table 9 suggest also that the One-state Solution may be a viable option but with nearly half the priority of the best alternative. Recall that the One-state Solution was defined by the panel as the commingling of both the Table 9 Synthesis of the alternatives (overall results) Alternatives Benefits Opportunities Costs Risks Multiplicative Additive synthesis 0.307 0.307 synthesis 0.199 0.196 Nuclear use One-state solution Status quo Two-viable-state Solution

0.11 0.96 0.59 1.00

0.23 0.76 0.35 1.00

1.00 0.36 0.61 0.32

0.82 0.35 0.80 0.29

0.00 0.34 0.26 0.62

(0.49) 0.11 (0.25) 0.20

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Palestinians and the Israelis under one unified state structure that recognizes all individuals as politically and socially equal under the generally understood notion of democracy. Given the relative nearness of the outcomes, leaders will need to monitor the process to gain insight into which direction seems more likely to succeed. It is the Two-state-viable solution that comes out as the best alternative under all situations. Table 9 demonstrates that under both the multiplicative and the additive forms of synthesis, the Two-state solution is the best alternative. There are far reaching implications for both the decision and implementation of the alternative derived in the model. Given that the Status Quo and the Nuclear Use options come out as clear negatives in the long run, we conclude that under no circumstance should either option be considered. This seems intuitive for the nuclear use option but may not have appeared so for the status quo. However, it is not difficult to determine that the current situation is not working given the periodic unrest in the Middle East and hence a negative outcome arises in the model that the panel put together. Interpretation of the difference between the one-state solution and the two-state solution needs further elaboration. In Table 9, we see that there is a sizable difference between the one-state and the two-state solutions. One might expect that the one-state solution is a more viable option given the efficiencies that might arise from the two peoples coming together and in the integration of the land. However, given the BOCR results above, we see that there is greater B and O and less C and R in the two-state solution then there is in the one-state solution; this provides some insight into where our investigation into the management of resolving the conflict ought to begin. For instance, Table 4 shows that the Israelis could have the greatest ‘risk’ of increased radicalism and limited longevity whereas for the Palestinians the greatest risk is that there will be greater instability in the region. When we consider it along with the results presented in Table 8. Risks’ Overall Results, we conclude that for the panel the concern was that the One-state solution poses the greatest risk for an increase in radicalism and limited longevity for the Israelis whereas for the Palestinians there is a concern that this solution will promote an increase in regional instability. The major difficulty that we experience when we attempt to reach a conflict resolution roadmap in a conventional way is that it is difficult to keep all of the alternatives in mind at once in order to evaluate them. It is even more difficult to maintain cognitive attention of all of our judgments simultaneously in order to measure the importance of the alternatives with respect to the criteria that one puts forth. The outcome would be a matter of which of the highly respected or dominant participants puts forth the best argument that captures the minds of the others. The result of dominance over rational participation as described in this paper is that one of the parties does not have a buy-into the solution. A program such as the Analytic Network Process facilitates the cognitive mapping, simultaneous prioritization, and participation that make ‘buy-in’ possible. Further, what was once viewed as an esoteric prioritization process of the decision makers is now

6 Synthesis of the BOCR Merits

Benefits

Costs

Fig. 6 Sample sensitivity analysis

181

Opportunities

Risks

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reduced to codified decisions by all the parties. The result of the codification process is joint-agreement and documentation for future review and follow-up. Incidentally, BOCR to an economist is concerned with short and long term influences including all objects and factors in the problem, whereas strengths, weaknesses, opportunities and threats (SWOT) to a planner or manager are concerned with internal and external factors at a single instant but repeat for different periods of time. SWOT assigns ordinal numbers to the factors’ importance without making comparisons and also assign probabilities to their occurrence, multiply the probabilities by the importance and calculate overall strengths, weaknesses etc. and then take the difference S–W and O–T obtaining two numbers as coordinates of a point on two axes, whose positive variable parts are S and O and negative part W and T. Then they develop managerial instructions for what to do if the point lies in the four different quadrants. An expert in strategic planning pointed out to us that most people use SWOT analysis qualitatively, not quantitatively and it always precedes the decision on what actions to take in the process of planning.

7 Sensitivity Analysis An interesting aspect of the model is that no matter how the criteria are adjusted or perturbed, the outcome remains stable. Figure 6 is a sample sensitivity analysis that is indicative of all of those produced in this model. The sensitivity results from this model suggest that the model is extremely insensitive implying that if the decision-makers focus on the simple outcomes suggested in this model a long-term solution may be reached.

8 Conclusions The final outcome suggests that the best policy to resolve the Middle East Conflict is to establish a two state solution. Since there is more than one proposal on the details of such a solution, it is equally important to develop each proposed model in ways that address a given set of criteria that would guarantee the long term stability and peace in the region. Then another ANP model must be developed to evaluate each proposal against its criteria to select the most viable one that will serve the ultimate goal of this project. The authors agree that this work should be expanded to explore the opinions of those who are living in the region, regardless of their ethnic background or religion. An ANP based questionnaire might have an interesting result for academia and politicians as well. Such investigation should cover this phase of the research and the second one regarding the best outcome. The model and the results given in this paper suggest a variety of ways to manage the conflict resolution process and the implementation. The work presented here provides the reader with areas of potential concern for the leaders that

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must address the concerns of the various constituents and the people who must live in the environment. The most significant results of the model do not come from the numbers that are generated from the process, but rather the efforts and road-map that are generated. The results suggest that in order for any solution to work, the Israelis must recognize the Palestinians and their cause as an independent people with certain rights and concerns and the Palestinians will need to recognize Israel as an independent people with certain rights and concerns. The priorities generated reinforce the need for both parties (Israelis and Palestinians) to embrace the Middle East resolution as the leaders of the process in order to facilitate the development of communitas toward the resolution. Finally, the reader might question why one should accept the judgments of the particular set of judges? Would different experts produce a different result? We believe that the structure of the problem is sufficiently general that people are not likely to differ on what factors to include. Let us consider the judgments. Had the audience included radical thinkers such for example as those Palestinians who are very angry and do not wish Israel well, or Israelis who wish the Palestinians would simply go away and disappear, the outcome could have been different. There are people in Israel who look at things in the long term and would like to keep the land a hostage in the hope that time would be on their side, but it is certain that the majority of people in Israel would like to live in peace with the Palestinians but do not know exactly how to bring that about because of a great feeling of insecurity. Reluctantly, we believe that radicals tend to move away from rationality due to their excessive passion. What we have established here is a compelling framework for radicals to consider. To solve a difficult problem such as this, one brings to the table people who are willing to compromise and not extremists. Had a different rational group done the exercise we feel certain that their answer would have been similar. The way to test the stability of this outcome, which we also did, is through sensitivity analysis. Doing that by varying the emphases provides considerable reassurance that the outcome is stable to variations in the judgments when they are not too intractable on important items. Acknowledgments The authors were very fortunate to be part of the panel of experts participating over three days in analyzing the problem debating and providing informed judgments. In addition to the five authors, the panel included : Professor Andrew Blair of University of Pittsburgh, Professor Eugene Fram of the Rochester Institute of Technology, Cengiz Karpak From Bayer, Istanbul and Zhongcheng Lu of the Beijing Institute of Technology Beijing, China. We wish to express our gratitude to Professor Josephine Olson, Director of the International Business Center, University of Pittsburgh, for financial support to bring about the three day meeting.

References Saaty, T.L. and L. Vargas, 2006, ‘‘Decision Making with The Analytic Network Process, Economics, Political, Social and Technological Applications with Benefits, Opportunities, Costs, and Risks’’, Springer.

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Saaty, T.L. 2005, ‘‘Theory and Applications of The Analytic Network Process’’, RWS Publications. Saaty, T.L. 2001, ‘‘The Analytic Network Process’’, 2nd edition, RWS Publications. Saaty, T.L. 1999, ‘‘Decision Making for Leaders’’, 2nd edition, RWS Publications.

Additional Readings Rapoport, A., Fights, games and debates, University of Michigan Press, 1960. Von Neumann, J. and O. Morgenstern, Theory of Games and economic Behavior, Princeton University Press, 1944. Barash, D. P., The Survival Game: How Game Theory Explains the Biology of Cooperation and Competition, Owl Books. Myerson, R. B. Game Theory: Analysis of Conflict, Harvard University Press 1991. Axelrod, R. The evolution of cooperation, Basic Books, 1984. MacKay, A.F., Arrow’s Theorem: The Paradox of Social Choice - A Case Study in the philosophy of Economics, New Haven and London: Yale University Press, (1980). Luce, R. D., and H. Raiffa, Games and Decisions: Introduction and Critical Survey,Wiley, 1957. Isaacs, R., Differential games a mathematical theory with applications to warfare and pursuit, control and optimization, Dover Publications, 1999. Weibull, J. W., Evolutionary Game Theory, MIT Press, 1995. Brams, S. J., Theory of Moves, Cambridge University, 1994. Ritzberger, K., Foundations of Non-Cooperative Game Theory, Oxford University Press, 2002. Fudenberg D., and D. K. Levine, The Theory of learning in Games, The MIT Press, 1998. Elster, J., Solomonic Judgements: Studies in the Limitations of Rationality, Cambridge University, 1990. Kremenyuk V. A. (ed.), International Negotiation, Jossey-Bass, 2001. Moffit Michael L:; Bordone Robert C. (eds.), The Handbook of Dispute Resolution, Jossey-Bass, 2005. Raiffa H., The Art and Science of Negotiation, Harvard University Press, 2000. Susskind L., Dealing With an Angry Public, Free Press, 1996. Ury W., Getting Past No, Bantam Books, 1993.

Chapter 8

U. S. Energy Security

1 Introduction There has been an ongoing debate in the United States ever since the Report of the National Energy Policy Development Group1 was submitted for consideration by Vice President Dick Cheney to President George W. Bush on May 16, 2001. The statements and recommendations of the report have been so controversial since its public release that senate and house committee meetings have been held along with requests that the Vice President come before Congress to explain what was discussed behind closed doors. Energy is a pivotal factor in society and will continue to be in the future so long as humanity is driven to develop technologies to meet its needs that are powered by energy. The U.S. faces a serious energy problem in the near future. How can the U.S. sustain its growth? What fuels will power its vehicles, heat its homes, and generate electricity that comes on with the flip of switch to turn the lights on? An Analytic Network Process model, ‘‘Energy Security of the US’’, was developed to provide statistical support to intuition and judgment based on knowledge and expertise of the subject matter. The model takes into account all the significant factors and forces indicated by intuition to influence the direction of U.S. Energy Policy. This model was not designed to justify National Energy Policy advocated by Vice President Cheney, but to determine which of four alternatives provides the U.S. the best direction to secure its energy future. The alternatives are: 1. 2. 3. 4.

Status Quo Energy Independence Emphasis Complete Energy Independence Comparative Advantage Approach.

The ANP model has four feedback sub-networks of control criteria called benefits, opportunities, costs, and risks (BOCR). All four sub-networks have control criteria clusters that are specific to the BOCR that are used in this report. Each 1

National Energy Policy 2001.

T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_8,  Springer Science+Business Media New York 2013

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control criterion cluster may have one or two level subcriteria clusters that are also specific to the parent node, cluster and sub-network. An alternatives sub-network is located at the top 70 % priority nodes within each BOCR sub-network that is also specific to the issue being addressed at that point in the model. In addition, a strategic rating criteria model is developed to weight the BOCR in terms of Energy Security, International Competitiveness, and Environmental Quality. There are many reports, papers, studies and presentations which say when, not if, the world and the US will be in an energy crisis. This statement in itself should be sufficient to keep one up at night thinking about what will ‘‘our way of life’’ be in ten or 20 years. The National Energy Policy report mentioned above provides a clear picture of what is happening and is forecasted for the U.S. (See Fig. 1). As forecasted for the next 20 years the energy consumption of the United States will outpace domestic energy production significantly. We have already felt this effect at the gasoline pump, home heating monthly winter bills, summer cooling electricity bills, the constant increase of everyday goods, and the jobs lost due to

Fig. 1 Growth in the U.S. energy consumption is outpacing production

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domestic companies outsourcing to foreign manufacturers in many cases due to the increase in domestic fuel costs. Reports from Simmons & Company International indicates the following 2 (Fig. 2):

Fig. 2 Simmons & Company international presentation, February 24, 2004

This one slide is supported by a consistent steady increase in natural gas prices from $2/MMBtu to more than $5/MMBTU for the month of March 2004 and gasoline prices averaging $1.70/gallon for regular grade for example. Some have stated that Liquefied Natural Gas (LNG) imports would provide the energy needed to meet U.S. demands with no cause for alarm since there have been over 33,000 tanker voyages with no major incident over the past 40 years. These statements now fall short since the January 2004 Algerian LNG complex accident that killed 27 people. There are other historical observations to make: 1. Recent OPEC decision to reduce production in order to sustain the $38/barrel price of crude oil. State aid3 and bailouts of foreign companies that have injured U.S. power generation companies,4 such as the French Bailout of Alstom in September 2003. 2

Simmons (2004). According to the definition set out in Article 87(1) of the EC Treaty, State aid is incompatible with the common market if it is granted by a Member State or through State resources, if it distorts or threatens to distort competition by conferring an advantage on certain undertakings or the production of certain goods and if it is liable to affect trade between Member States. The form in which the aid is granted (interest rebates, tax reductions, loan guarantees, supply of goods or services on preferential terms or capital injections on terms not acceptable to a private investor) is irrelevant. 4 Foster Wheeler is a power generation manufacturer and engineering company, which is expected to report a 50 % decrease in its workforce in it 2003 annual report. Babcock and Wilcox 3

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Also with national security always on our minds due to the war on terrorism in Iraq, Afghanistan, Spain, and at home, Picture 3, there is an increasing need to determine what direction the United States should take with regard to its energy policy.

2 ANP Model Description The Analytical Network Process model developed for this project has four feedback sub-networks of control criteria called benefits (Fig. 3), opportunities (Fig. 4), costs (Fig. 5) and risks (Fig. 6) (BOCR). Their sub-network control criteria, sub-criteria, nodes, and alternative sub-networks are identified in the next section.

2.1 BOCR Model The BOCR model is a feedback sub-network that addresses the benefits, opportunities, costs, and risks associated to the energy security of the United States. Descriptions of each cluster and node with the clusters are indicated below. Nodes with an asterisk (*) have a subnetwork under them whose generic structure is given in Fig. 7. This subnetwork may vary from node to node. For the sake of simplicity we will omit the minor differences. An identification system is utilized throughout the model in order to maintain a hierarchal structure and order. For example, the first letter indicates whether it is a Benefit, Opportunities, Costs, or Risks cluster or node. The numbering system is self explanatory for a hierarchal structure. B11 means B ! Benefits; 1 ! Political node; 2nd 1 ! International node (B) BENEFITS CLUSTER/NODE DESCRIPTIONS (Fig. 3) B1 Political Control Subcriteria B11 International B111 Bargaining Power. B112 Energy Policy Leadership B12 Domestic Political Stability

(Footnote 4 continued) is a U.S. boiler and power generation manufacturer which has filed for Chapter 11 protection several years ago.

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Fig. 3 Benefits subnet

2 ANP Model Description

Fig. 4 Opportunities subnet

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Fig. 5 Costs subnet

2 ANP Model Description

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Fig. 6 Risks subnet

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Fig. 7 Alternatives subnet model template

B2 Societal Control Subcriteria B21 Technology Development B22 Sense of Well Being *B221 Job Security B222 National Pride B223 Energy Assurance *B23 Controlling the Consumer Cost of Energy B3 Economic Control Subcriteria *B31 Domestic Energy Cost Control B32 Domestic Economic Security *B321 Domestic Employment Growth B322 Domestic Manufacturing Growth B33 International Growth: The economic benefits associated with international import/export. Import in that the consumer has increased disposable income and export in that we have an abundant source of low cost of energy domestically increasing US exports and positively impacting the trade balance.

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B4 Technological Control Subcriteria B41 Domestic Environmental Quality B42 Domestic Technology Superiority B43 International Trade: The benefit of exporting US technologies. B44 International Technology Leadership: The benefit of being the driving force related to energy policy and technologies. B5 National Security Control Subcriteria B51 Military: Military benefits associated with energy security in the US. Should there be a conflict the military has abundant indigenous resources. *B52 Less Dependence on Foreign Influences B6 Environmental Control Subcriteria *B61 Oil Peaking: The environmental benefits to oil peaking associated to the energy security of the US. i.e. Creates a driver for other fuel sources that are less harmful to the environment. (O) OPPORTUNITIES CLUSTER/NODE DESCRIPTIONS (Fig. 4) O1 Political Control Subcriteria O11 International O111 Bargaining Power O112 Energy Policy Leadership *O12 Domestic Political Stability. O2 Economic Control Subcriteria O21 Domestic Energy Cost Control O22 Domestic Economic Security O221 Domestic Employment Growth *O222 Domestic Manufacturing Growth *O23 International Growth. *O24 Oil Peaking O3 Technological Control Subcriteria O31 O32 O33 O34

Domestic Environmental Quality Domestic Technology Superiority International Trade International Technology Leadership

(C) COSTS CLUSTER/NODE DESCRIPTIONS (Fig. 5) C1 Political Control Subcriteria C11 International

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C111 Bargaining Power: The loss of international political bargaining power. C112 Foreign Political Backlash C12 Domestic - Special Interest Groups: Domestic political costs from special interests groups. C121 Environmental: Political costs by environmental special interest groups. C122 Business: Political costs by business related special interest groups. C2 Societal Control Subcriteria C21 Sense of Well Being C211 Petroleum products: Society’s sense of well being related to the amount of petroleum included in the energy mix. C212 Coal:Society’s well being associated to the percentage of coal utilized in the energy mix. C213 LNG:Society’s sense of well being associated with LNG as part of the energy mix. C214 Natural Gas: The cost associated to society’s sense of well being related to natural gas. C215 Hydrogen Economy: The cost associated to society’s sense of well being related to hydrogen. C216 Nuclear: The cost associated to society’s sense of well being related to nuclear. C217 Renewable: The cost associated to society’s sense of well being related to renewables. C22 Short-term consumer cost increase: The short term energy cost increase associated with the energy security of the US. C3 Economic Control Subcriteria C31 Domestic *C311 Domestic Employment Loss: The domestic economic costs due to employment loss associated to the energy security of the US. *C312 Domestic Grid Instability: The economic costs associated with grid instability based on the energy mix. C32 International C321 International Exports: The costs associated with international exports. Exports may become more expensive since US investments and FDI are greater domestically than previously. C322 International Trade/Tariffs/Sanctions C4 Technological Control Subcriteria C41 Domestic R&D Costs C42 Domestic Deployment Costs C43 Domestic Transition Costs: The costs associated to transitioning from our current energy mix to a moderately to significant energy mix.

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C44 International Trade Costs: The costs associated by foreign concerns to our energy security policy, especially when it may affect their trade balance with the US. C5 National Security Control Subcriteria C51 Increased Terrorism: Costs due to terrorism. Since US is no longer as dependent on foreign sources of fuel, then a cascade effect in all sectors of the economy are expected. Outsourcing may not be required. *C52 Oil Peaking (R) RISKS CLUSTER/NODE DESCRIPTIONS (Fig. 6) R1 Energy Policy Failure Control Subcriteria R11 International Backlash: The political risks from an International backlash. R12 Domestic Instability: The political instability that will be created due to opposing sides of the energy policy issue. Should it not work, the two political parties would blame the other leading to little or no compromising on any political issue. *R13 Economic Calamity: The political risks associated due to an economic calamity because the correct energy security policy was not implemented. R14 Society: The political risks associated to the unrest and discontent with the political leaders, i.e. civil unrest. R15 National Security Compromised: description R2 Technological Control Subcriteria. R21 Fuel Choice: The technological risks associated with the fuel mix selected to ensure the energy security of the US. R121 Environmental: Political costs by environmental special interest groups. C122 Business: Political costs by business related special interest groups associated with the energy security of the US. R22 Research and Development: The technological risks associated with R&D to support the energy security policy of the US. R23 Infrastructure: The technological risks associated to infrastructure impacts that would support the energy security policy of the US. R3 Environmental Control Subcriteria R31 Increased Emissions *R32 Political R33 Health: The health risks due to environmental emissions associated with the energy security policy of the US. R34 Fuel Choice: The environmental risks associated with the fuel mix selected for the energy security of the US.

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*R341 Petroleum Products. R342 Coal R343 LNG R344 Natural Gas R345 Hydrogen Economy *R346 Nuclear R347 Renewables R4 Economic Control Subcriteria *R41 Oil Peaking.

2.2 Strategic Rating Model The strategic rating model was developed separately to obtain the weighting values of the BOCR against three fundamental criteria associated with the energy security of the United States. Those criteria are Energy Security, International Competitiveness, and Environmental Quality.5 A High, Moderate, and Low category scale was used to rate the criteria against the BOCR specific to the highest alternative from the BOCR model. In the case of Benefits and Opportunities it was the Energy Independence Emphasis, and for Costs and Risks it was the Comparative Advantage Approach. a. Criteria Description The three criteria used to answer the strategic rating model goal, ‘‘What direction should the United States energy policy provide?’’ are energy security, international competitiveness, and environmental quality. b. Alternatives Description The role of alternatives for the strategic rating model is played by the benefits, opportunities, costs, and risks. 1. Benefits The alternative considered for Benefits against the three criteria indicated was energy independence emphasis. The rating chosen for the three criteria was high for energy security, high for international competitiveness and low for environmental quality. A low was chosen for environmental quality for two reasons. They were that sufficient environmental technologies existed to maintain a satisfactory level of environmental quality in the US from US produced emissions and that depending on the fuels being used from a particular point source the environmental quality might be better or worse dependent on the regulations at the time. 5

US Department of Energy 2004.

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2. Opportunities The alternative considered for Opportunities against the three criteria was energy independence emphasis. The rating chosen for the three criteria was high for energy security, high for international competitiveness and moderate for environmental quality. A moderate factor was chosen for environmental quality because it was believed that advancements in technology to mitigate emissions from point or distributive sources would be developed. These developments in turn could create economic opportunities domestically and internationally through imports. The technology leadership that the US would have would not only reduce US produced emissions but those generated by foreign countries that pollute the US due to global effects. 3. Costs The alternative considered for Costs against the three criteria was comparative advantage approach. The rating chosen for the three criteria was moderate for energy security, moderate for international competitiveness and low for environmental quality. A moderate factor was chosen for energy security and international competitiveness because many of the technologies needed to generate efficient power cycles have been developed or at applied research stages of development. True that there may be breakthroughs in science that could alter the power generation cycle but that option was not considered in this analysis. In addition, a comparative approach as an energy policy would provide costs associated to the market forces and international influences associated with the energy production countries. One example is OPEC’s decision to decrease production levels in order to maintain high prices. The control that OPEC has and other fuel producing nations which reside in chaotic regions of the world only increases the costs to the US as it relates to politics, economy, society, international competitiveness, and national security. 4. Risks The alternative considered for Risks against the three criteria was comparative advantage approach. The rating chosen for the three criteria was high for energy security, moderate for international competitiveness and low for environmental quality. A high was chosen for energy security because foreign influences would determine the availability of the fuel that drives our economy that in turn determines or standard of living and the potential of the nation. Moderate for International competitiveness for the same reasons as energy security but offset slightly by the fact hat the Unites States produces/invents products that cannot be initially obtained anywhere else in the world. A low rank for environmental quality because the US would most likely become more dependent on natural gas or LNG which is significantly environmentally friendly compared to coal or nuclear (Environmental equipment required for coal and nuclear to match less equipment required natural gas systems).

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2.3 Alternatives Model The alternatives model is shown in Fig. 7. It is a template that was used to indicate all of the influences as they relate to the alternatives and each other. It is a very complex sub-network that was modified according to the high priority node within each BOCR sub-network. Specific information is provided herein to demonstrate that the template was useful in minimizing the model development time. In some cases other clusters and nodes were added because they were relevant to the point in the model being considered. Descriptions of the nodes were not included because they were considered self-explanatory. The four alternatives considered for this model were selected because it provided a range of options that went from a comparative advantage approach to complete energy independence. They ranged from globalization to isolationism, respectively. Status Quo Approach The status quo approach represents current approaches to the energy security of the United States. This takes into consideration that US fossil fuel imports have reached an all time high of 60 % to a domestic fuel source of 40 %. The actual breakdown is not considered at this level instead an indication of the 60/40 split between imports and domestic fuel sources was the point under consideration. Energy Independence Emphasis The energy independence emphasis is the direct reciprocal of the status quo approach that is to have a 40/60 split between imports and domestic fuel sources respectively. This approach would provide energy security with creating a sentiment that the US was moving toward isolationism. Complete Energy Independence The complete energy independence approach relates to 100 % dependence on domestic resources. This was considered as one extreme that would lead to isolationism in the world fuel market and potentially a risky and costly proposition with little benefits and opportunities. Comparative Advantage Approach The comparative advantage approach took the direct opposite approach to complete energy independence. It considered a market driven US energy policy. This approach would only use domestic sources of fossil fuels if it were economical. There are obvious risks and costs associated with this approach but also considered it from a free markets perspective and a potential desire of the US population or political forces to be driven by a particular fuel which the US has limited reserves.

3 Benefits, Opportunities, Costs and Risks Model The BOCR model illustrated in Fig. 8 is the top most part of the model that has its own sub-networks specific to the benefit, opportunities, costs or risks associated to the energy security of the U.S. No two sub-networks are alike.

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This section will elaborate on the different aspects of the model and its results. While the editorial comments may be short it is only because the figures state the results or what is being shown the best. Where further discussion it is given if warranted.

3.1 Benefits Model The Benefits sub-network illustrated in Fig. 2 begins to show the complexity of the model. In this sub-network there are six alternative sub-networks corresponding to the nodes B221, B23, B31, B321, B52 and B61. The matrix illustrated in Table 1 shows the cluster pairwise comparison values for the benefits control criteria. Table 2 gives the synthesized priorities of all the benefits criteria.

3.2 Opportunities Model The Opportunities sub-network illustrated in Fig. 3 shows that there are differences in the BOCR sub-networks due to the question that is being addressed. In this sub-network there are four alternative sub-networks corresponding to the nodes O12, O222, O23 and O24. The matrix illustrated in Table 3 shows the cluster pairwise comparison values for the opportunities control criteria. Table 4 shows the synthesized priorities of the opportunities criteria.

Fig. 8 BOCR model

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Table 1 Pairwise comparisons and priorities of benefits control criteria Political Societal Economic Technological National Environmental

Political 1 5 6 3 7 3

Societal 1/5 1 2 1/3 1 1

Economic 1/6 1/2 1 1/3 1/4 1/2

Technological 1/3 3 3 1 3 4

National 1/7 1 4 1/3 1 2

Environmental 1/3 1 2 1/4 1/2 1

Priorities 0.0520 0.2977 0.2588 0.0739 0.0689 0.2487

Table 2 Benefits priorities Goal - Benefits Control Criteria Hierarchy B1 Political B11 International B111 Bargaining Power B112 Energy Policy Leadership B12 Domestic Political Stability B2 Societal B21 Technology Development B22 Sense of Well Being B221 Job Security B222 National Pride B223 Energy Assurance B23 Controlling the Consumer Cost of Energy

Normalized By Cluster 0.0520 0.2500 0.8572 0.1428 0.7500 0.2977 0.1005 0.4664 0.6483 0.1220 0.2297 0.4331

Limiting Priorities 0.0227 0.0057 0.0049 0.0008 0.0170 0.1301 0.0131 0.0607 0.0393 0.0074 0.0139 0.0563

B3 Economic

0.2588

0.1131

B31 Domestic Energy Cost Control B32 Domestic Economic Security B321 Domestic Employment Growth B322 Domestic Manufacturing Growth B33 International Growth B4 Technological B41 Domestic Environmental Quality B42 Domestic Technology Superiority B43 International Trade B44 International Technology Leadership B5 National Security B51 Military B52 Less Dependence on Foriegn Influences B6 Environmental B61 Oil Peaking

0.3325 0.5278

0.0376 0.0597 0.6667 0.3333

0.0398 0.0199

0.1397

0.0158 0.0323 0.3042 0.0098 0.1205 0.0039 0.4643 0.0150 0.1110 0.0036 0.0689 0.0301 0.2500 0.0075 0.7500 0.0226 0.2487 0.1087 1.0000 0.1087 0.0739

Table 3 Pairwise comparisons and priorities of opportunities control criteria Political Economic Technological

Priorities

Political Economic Technological

0.2628 0.6586 0.0786

1 3 4

1/3 1 1/7

4 7 1

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Table 4 Opportunities Priorities Goal - Opportunities Control Criteria Hierarchy O1 Political O11 International O111 Bargaining Power O112 Energy Policy Leadership O12 Domestic Political Stability O2 Economic O21 Domestic Energy Cost Control O22 Domestic Economic Security O221 Domestic Employment Growth O222 Domestic Manufacturing Growth O23 International Growth O24 Oil Peaking O3 Technological O31 Domestic Environmental Quality O32 Domestic Technology Superiority O33 International Trade O34 International Technology Leadership

Normalized By Cluster 0.2628 0.1667 0.7500 0.2500 0.8333 0.6586 0.0877 0.3533 0.3333 0.6667 0.1305 0.4285 0.0786 0.1702 0.2904 0.4215 0.1180

Limiting Priorities 0.1154 0.0192 0.0144 0.0048 0.0962 0.2893 0.0254 0.1022 0.0341 0.0681 0.0378 0.1240 0.0345 0.0059 0.0100 0.0146 0.0041

3.3 Costs Model The costs sub-network illustrated in Fig. 4 shows the differences compared to the benefits and opportunities sub-networks. Cluster C5 National Security is new and introduces the costs associated to Increased Terrorism and Oil Peaking. In this subnetwork there are only three alternative sub-networks (C311, C312 and C52) because of their impact on costs. What is interesting is that the numerous other nodes are not even close to being significant but do play a role in elevating the Alternative sub-network nodes. The matrix illustrated in Table 5 shows the cluster pairwise comparison values for the costs control criteria. Table 6 gives the synthesized priorities of costs criteria.

3.4 Risks Model The risks sub-network illustrated in Fig. 5 has five alternative sub-networks in its nodes (R13, R32, R341, R346 and R41). It is interesting is that in every instance Oil Peaking has a high priority, both in the costs and risks sub-networks. Table 5 Pairwise comparisons and priorities of costs control criteria Political Societal Economic Technological

National

Priorities

Political Societal Economic Technological National

1/9 1/4 1/3 1/4 1

0.0724 0.1529 0.4247 0.0369 0.3132

1 4 5 7 9

1/4 1 3 2 4

1/5 1/3 1 2 3

1/7 1/2 2 1 4

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Table 6 Costs priorities Goal - Costs Control Criteria Hierarchy C1 Political C11 International C111 Bargaining Power C112 Foriegn Political Backlash C12 Domestic - Special Interest Groups C121 Environmental C122 Business C2 Societal C21 Sense of Well Being C211 Petroleum products C212 Coal C213 LNG C214 Natural Gas C215 Hydrogen Economy C216 Nuclear C217 Renewables C22 Short term consumer cost increase C3 Economic C31 Domestic C311 Domestic Employment Loss C312 Domestic Grid Instability C32 International C321 International Exports C322 International Trade/Tariffs/Sanctions C4 Technological C41 Domestic R&D Costs C42 Domestic Deployment Costs C43 Domestic Transition Costs C44 International Trade Costs C5 National Security C51 Increased Terrorism C52 Oil Peaking

Normalized By Cluster 0.0724 0.7500 0.2000 0.8000 0.2500 0.8334 0.1666 0.1529 0.8750 0.0607 0.0312 0.0646 0.0208 0.4926 0.1870 0.1431 0.1250 0.4247 0.8333 0.8000 0.2000 0.1667 0.6667 0.3333 0.0369 0.0433 0.3055 0.5273 0.1239 0.3132 0.1111 0.8889

Limiting Priorities 0.0275 0.0206 0.0041 0.0165 0.0069 0.0057 0.0011 0.0581 0.0508 0.0031 0.0016 0.0033 0.0011 0.0250 0.0095 0.0073 0.0073 0.1614 0.1345 0.1264 0.0316 0.0269 0.0022 0.0011 0.0140 0.0006 0.0043 0.0074 0.0017 0.1190 0.0132 0.1058

The matrix illustrated in Table 7 shows the cluster pairwise comparison values for the risks control criteria. Table 8 gives the synthesized priorities of the risks criteria.

4 BOCR/Alternative Analysis Table 9 shows how the alternatives were ranked for benefits, opportunities, costs and risks. The benefits and opportunities models rank the Energy Independence Emphasis the highest followed by Complete Energy Independence. For the costs model, the Comparative Advantage Approach was the most costly. Interestingly, the other three alternatives were very close in rating. This suggests that all three

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Table 7 Pairwise comparisons and priorities of risks control criteria Energy policy Technological Environmental

Economic

Priorities

Energy Policy Technological Environmental Economic

1 1/5 1 1

0.3620 0.0767 0.2385 0.3219

1 1/4 1/2 1

4 1 3 5

2 1/3 1 1

Table 8 Risks priorities

Goal - Risks Control Criteria Hierarchy R1 Energy Policy Failure R11 International Backlash R12 Domestic Instability R13 Economic Calamity R14 Society R15 National Security Compromised R2 Technological R21 Fuel Choice R211 Petroleum products R212 Coal R213 LNG R214 Natural Gas R215 Hydrogen Economy R216 Nuclear R217 Renewables R22 Research and Development R23 Infrastructure R3 Environmental R31 Increased Emissions R32 Political R33 Health R34 Fuel Choice R341 Petroleum Products R342 Coal R343 LNG R344 Natural Gas R345 Hydrogen Economy R346 Nuclear R347 Renewables R4 Economic R41 Oil Peaking

Normalized By Cluster 0.1244 0.0598 0.1606 0.4723 0.2275 0.0799 0.0606 0.7306 0.0444 0.0286 0.1679 0.0432 0.4307 0.2585 0.0268 0.0810 0.1884 0.3015 0.0926 0.1889 0.1188 0.5996 0.2871 0.2499 0.0707 0.0497 0.0473 0.2686 0.0269 0.5135 1.0000

Limiting Priorities 0.0559 0.0033 0.0090 0.0264 0.0127 0.0045 0.0272 0.0199 0.0009 0.0006 0.0033 0.0009 0.0086 0.0051 0.0005 0.0022 0.0051 0.1355 0.0126 0.0256 0.0161 0.0813 0.0233 0.0203 0.0057 0.0040 0.0038 0.0218 0.0022 0.2308 0.2308

have about the same level of costs and are interchangeable in a decision as far as costs are concerned. The results of the risks model show the Comparative Advantage Approach to be the most risky followed by Complete Energy Independence.

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To synthesize the benefits, opportunities, costs and risks, they are rated as clusters with respect to three strategic control criteria: Energy Security, International Competitiveness and Environmental Quality. Their priorities of the strategic criteria are given in Table 10. Table 10 also shows the final priorities of benefits, opportunities, costs and risks after the ratings are translated into a numerical scale. Benefits and opportunities are rated as the most significant of the merits.

5 Model Results The synthesized results of the entire model, taking into account the weighting factors of the strategic rating model discussed in Sect. 2, are given in Table 11. The results indicate that the U.S. energy policy should be strongly driven toward an Energy Independence Emphasis. This alternative was perceived to be twice more effective than the alternative Complete Energy Independence and almost three times more than the Status Quo. The Comparative Advantage Approach lagged the other three alternatives and should never be considered as an energy policy option.

6 Sensitivity Analysis A sensitivity analysis was performed to determine if the overall results illustrated in Table 11 would vary due to the judgments made in the model. This section will look at each of the main control criteria identified as the benefits, opportunities, costs, and risks associated with the goal of the energy security of the U.S.

6.1 Benefits The benefits sensitivity analysis illustrated in Fig. 9 indicates that the greatest benefits will always be achieved through Alternative # 2, Energy Independence Table 9 Ranking of alternatives for BOCR Alternatives Benefits (0.3260) 1 Status quo energy policy 2 Energy independence emphasis 3 Complete energy independence 4 Comparative advantage approach

Opportunities (0.3323)

Costs (0.0828)

Risks (0.2588)

0.5228 0.7989

0.2733 0.9541

0.3569 0.3503

0.4448 0.4663

0.5815

0.6725

0.3649

0.6430

0.3841

0.2985

0.9040

0.8204

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Table 10 Ratings and priorities for BOCR with respect to strategic criteria Energy security International competitiveness Environmental quality Priorities 0.137 0.238 0.625 Benefits Opportunities Costs Risks

High High Moderate High

High High Moderate Moderate

Low Low Low Low

Intensities:

High 1.0000

Moderate 0.2404

Low 0.1154

0.3260 0.3323 0.0828 0.2588

Table 11 Synthesized priorities

Alternatives 1 Status Quo Energy Policy 2 Energy Independence Emphasis 3 Complete Energy Independence 4 Comparative Advantage Approach

Synthesis BO/CR bB+oO-cC-rR 0.9000 0.1166 4.6663 0.4278 1.6666 0.2164 0.1546 -0.0628

Emphasis. Alternative # 2 is followed by Alternative # 3, Complete Energy Independence, which is two orders of magnitude and at times three orders of magnitude less significant than Alternative # 2. Alternative # 1, Status Quo Approach, does not present itself as providing any benefit until after a 15 % emphasis on the benefits related to the energy security of the U.S. is considered. The comparative advantage approach, Alternative # 4, begins to provide positive benefits after 40 % emphasis on the benefits related to the energy security issue is considered but at this point Alternative # 2 is at its highest benefit potential of 60 %. This point is captured in the following figure by the dashed vertical line.

6.2 Opportunities The Opportunities sensitivity analysis illustrated in Fig. 10 indicates that the greatest opportunities will be present through Alternative # 2, Energy Independence Emphasis. This alternative with a priority value of 0.562 is followed by Alternative # 3, Complete Energy Independence, with priority equal to 0.284 when there is a 40 % emphasis associated to the opportunities with respect to the energy security of the U.S.. The Status Quo Approach, Alternative # 1, does present higher opportunity potential compared to Alternative 3 below a 10 % emphasis. Above a 10 % emphasis it levels out from a 5 to 10 % opportunity potential.

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Fig. 9 Benefits sensitivity analysis 2

3

1 1 – Status Quo Energy Policy 2 – Energy Independence Emphasis 3 – Complete Energy Independence 4 – Comparative Advantage Approach

4

Fig. 10 Opportunities sensitivity analysis 2

3 1

4 1 – Status Quo Energy Policy 2 – Energy Independence Emphasis 3 – Complete Energy Independence 4 – Comparative Advantage Approach

Likewise, Alternative # 3 increases from a 5 to a 30 % opportunity potential at the extreme emphasis scenario. The Comparative Advantage Approach, Alternative # 4, begins to provide positive opportunities after a 40 % emphasis on the energy security issue is considered but at this point Alternative # 1 is at it highest opportunity potential of 60 %. This point is similar to the benefits sensitivity analysis and is captured in the following figure by the dashed vertical line.

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Fig. 11 Costs sensitivity analysis

1 – Status Quo Energy Policy 2 – Energy Independence Emphasis 3 – Complete Energy Independence 4 – Comparative Advantage Approach

2

3

1 4

Fig. 12 Risks sensitivity analysis

1 – Status Quo Energy Policy 2 – Energy Independence Emphasis 3 – Complete Energy Independence 4 – Comparative Advantage Approach

2

1

3

4

6.3 Costs The Costs sensitivity analysis illustrated in Fig. 11 indicates that the greatest costs will be present through Alternative # 4, Comparative Advantage Approach, at any given emphasis or judgment. The next costly alternative is, Status Quo Approach which is followed by Complete Energy Independence. This leaves the least costly alternative as the Energy Independence Emphasis. As Fig. 11 indicates that not until an emphasis greater than 60 % is considered will Alternative # 2’s cost enter a negative range, but still the least cost when compared to the other three alternatives. What is also interesting in the figure below is that when a cost is the primary emphasis when considering the direction for the energy security of the United States, Alternatives 1–3 converge but are still significantly less costly than Alternative # 4, Comparative Advantage Approach.

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209

Fig. 13 BOCR sensitivity analysis

2 3 1 4

1 – Status Quo Energy Policy 2 – Energy Independence Emphasis 3 – Complete Energy Independence 4 – Comparative Advantage Approach

6.4 Risks The Risks sensitivity analysis illustrated in Fig. 12 indicates that the greatest risks will be present through Alternative # 4, Comparative Advantage Approach, at any given emphasis or judgment. The Status Quo Approach follows as the next riskier alternative until a 53 % emphasis is considered where it changes ranking with the Complete Independence Alternative. Alternative # 2 once again shows to be the best option or creating the least risk. Another convergence point is illustrated when risk concerns are paramount to benefits, opportunities, and cost. That convergence is between Alternative # 1, Status Quo Approach, and Alternative # 2, Energy Independence Emphasis. Considering the benefits, opportunities, costs and risks all at once, the graph of the sensitivity analysis (Fig. 13) shows that Alternative # 2 consistently dominates all others under all possible combinations of changes in the priorities.

7 Conclusion Deciding the direction of the U.S. energy policy to ensure its energy security is a very complex issue with many influences on how that decision will turn out. As the model demonstrated that many of the forces that we would consider as important are not that significant in the grand scheme. They do play a part on how the true drivers or motivators for one alternative versus another is decided so they should not be rapidly dismissed. Table 11 shows that an Energy Independence Emphasis should drive the energy policy of the U.S. and intuitively that is the answer that we would have chosen. It

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created the greatest benefits and opportunities while generating the least costs and risks when considered against the multitude of criteria we modeled. The Status Quo Approach was ranked 3rd and 4th for benefits and opportunities, respectively, and it was also ranked 3rd and 4th least for costs and risks, respectively. This makes sense since this alternative has an order of flexibility but in the long run it is not the best alternative with regard to an energy policy direction. The alternative Complete Energy Independence is twice as significant as the Status Quo Approach with respect to benefits and opportunities and ranked the 2nd highest in cost and risk. The costs associated with converting the entire energy infrastructure to be run from domestic resources would and most likely bankrupt the country. In addition, the isolationism that would be perceived by the global community could increase the risk of terrorism and trade sanctions and tariffs against the U.S. In every instance the Comparative Advantage Approach is the worst alternative for the U.S. It has the highest costs and risks while providing the least benefits and opportunities.

References Alstom Portal – Key Figures. http://www.alstom.com/static/html/acom-AGF_NavPageNavPage_StandardLeft_1039593796107.html (27 September 2003). Alstom SA Press Release. September 22, 2003. Agreement on Revised 3.2 Billion Euro Refinancing Package. http://www.alstom.com/servlet/ContentServer?pagename=acom/AGF_ PressRelease/PressRelease_Detail&c=AGF_PressRelease&cid=1062155999843&rid=103518 8964606&lid=en&pid=1035291507247&static=true. (22 September 2003). Alstom SA: SEC Launches Formal Inquiry Into Accounting at U.S. Unit. The Wall Street Journal. August 12, 2003. Print Media eastern Edition. ProQuest. ProQuest Company (20 September 2003). Associate Press. W Va Invest Mgmt Bd to Pursue Suit Against Alstom. The Wall Street Journal Online. September 26, 2003 (26 September 27 2003). Biswas, Soma. ABB settlement on Hold. The Daily Deal, Business and Company Resource Center. August 22, 2003 (27 September 2003). Brown, Patterson. telephone interview by Jose’ D. Figueroa. Pittsburgh, Pennsylvania. 24 September 2003. Dacher, Paul. telephone interview by Jose’ D. Figueroa. Pittsburgh, Pennsylvania. 23 September 2003. Energy Information Administration. Annual Energy Outlook 2003 online (22 September 2003). Energy Information Administration. International Energy Outlook 2003. p. 135, DOE/EIA0484(2003). May 2003. Kanter, James, EU Monti Says Will Probe France Revision of Alstom Aid, Dow Jones Newswires, October 1, 2003 (1 October 2003). Keller, Greg. Alstom Rescue Stymied by lack of Core Stakeholding. Dow Jones Newswires column. September 19, 2003 (19 September 2003). Keller, Greg. FOCUS: France Quadruples Alstom Aid to Win Plan Approval. Dow Jones Newswires column. September 23, 2003 (23 September 2003).

References

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Kern, Kenneth, interviewed by Jose’ D. Figueroa, Pittsburgh, Pennsylvania, 17 & 29 September 2003. Mathew R. Simmons, February 24, 2004, ‘‘The Saudi Arabian Oil Miracle’’, Presented at the Center for Strategic and International Studies, Washington, D.C. National Energy Policy, May 16, 2001, ‘‘Report of the National Energy Policy Development Group, National Energy Policy’’, http://www.energy.gov/engine/doe/files/dynamic/1952003121758_ national_energy_policy.pdf (16 May 2001). Saaty, T.L., 2001, The Analytic Network Process Decision Making With Dependence and Feedback’’, 2nd Edition, RWS Publications, Pittsburgh, PA. US Department of Energy, February 2004,‘‘Hydrogen Posture Plan – An Integrated Research, Development, and Demonstration Plan’’.

Chapter 9

Stabilizing Social Security for the Long-Term

1 Introduction President Roosevelt founded Social Security in 1935. In 1937, the Federal Insurance Contribution Act (FICA) was signed and mandated that workers contribute 2 % of wages. Over the next sixty-eight years, FICA has been amended numerous times including eight increases to the withholding percentage, which currently stands at 12.4 %. Cost of Living Adjustments (COLA) were added first in 1972 and revised in 1977. In the early 80s, the system was declared actuarially unsound. The National Commission on Social Security Reform was founded and in 1983 called for: 1. An increase in the self-employment tax partial taxation of benefits to upper income retirees. 2. Expansion of coverage to include federal civilian and nonprofit organization employees. 3. An increase in the retirement age from 65 to 67, to be enacted gradually starting in 2000. Again, Social Security was declared actuarially unsound. Of course, this declaration was premature as the Social Security Trustees’ Report of 1996 stated that the Social Security system would start to run deficits in 2012, and the trust funds would be exhausted by 2029. All members of the Advisory Panel agreed that some or all of Social Security’s funds should be invested in the private sector. To keep the unchanged system actuarially sound, payroll taxes would have to be increased 50–18 % of payroll, or benefits would have to be slashed by 30 %. In 1997, all members of the presidential-appointed Social Security Advisory Panel agreed that some or all of Social Security’s funds should be invested in the private sector. They also concurred with the Social Security Trustee’s Report that in order to keep the unchanged system actuarially sound, payroll taxes would have to be increased 50–18 % of payroll, or benefits would have to be slashed by 30 %.’’

T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_9,  Springer Science+Business Media New York 2013

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9 Stabilizing Social Security for the Long-Term

In the eight years since the advisory panel’s recommendation, little has been done to correct the issue only exacerbating the size and scope of the problem. President George W. Bush has put the issue at the forefront of his agenda for the second term with his proposal to privatize a portion of the program. Responses to the President’s proposal range from acceptance, to labeling it as a retrenchment back to the days before Social Security. Moreover, some groups say the problem is overstated, that Social Security only requires minor modifications. The goal is to use ANP (Fig. 1) to determine the best available option for stabilizing Social Security over the long-term.

2 Strategic Criteria Tree strategic criteria were identified to be used when assessing any proposed alternative; they are Program Stability, Adequate Means for Participants, and Perception of Fairness. Program Stability—Program stability suggests that there is a program in place, long-term for all participants. The optimal solution should ensure that the program survives and does not need further significant modifications. Participants should

Fig. 1 Strategic criteria and BOCR model

2 Strategic Criteria

215

have peace of mind that when they retire, the program will be there throughout their lifetime. Adequate Means for Participants—Participants should be able to rely on prescribed level of benefits that are adequate to support participants in their retirement. A stable program that pays some insignificant level of benefits is not considered optimal. No attempt was made to define what that prescribed level of benefits is. Social Security was originally intended to be a supplement to a retiree’s other income. The retiree was also to have a company pension as well as personal savings to rely upon. Over time, there has been an increase in retirees’ reliance on Social Security. At the program’s inception through the forties Social Security only comprised approximately 20–25 % of a retiree’s income. Today, retirees rely on Social Security for 67 % of their income on average. Years of low personal savings levels and pension failures have increased the strain on the Social Security system. Perception of Fairness—Whatever the solution, the program needs to be perceived as a fair system. One segment of the population should not be seen as benefiting unfairly from any proposed changes.

3 Alternatives Fourteen alternatives were considered initially. However, there are overlaps in some, while others were considered not viable. This list of fourteen was then narrowed to five alternatives. They are: Raise Ceiling—This alternative proposes raising the level of income subject to the 12.4 % Social Security withholding. Currently, any income above $90,000 is not subject to Social Security withholding. The cap on the withholding level can be increased as a one-time adjustment, or over a series of years. A more draconian approach would be to remove the cap completely. An increase in the withholding percentage for all participants was also examined. In the current environment, this revenue-enhancing alternative appears to be much more likely. Raise Retirement Age—The normal retirement age has been raised in the past and this option is considered viable in the current situation. Life expectancy of Americans continues to increase. The tendency causes the ratio of years as a payer to years as a payee to change. As the ratio increases, it places increasing strain on the financial resources of the system. All other factors held constant, the system will either need to find another mechanism to increase revenue or to decrease expenditures. Privatize—While there are numerous possible scenarios, the proposal by President Bush where certain participants can elect to have 4 % of their wages diverted to a private investment account is used. Lower and higher percentages have been proposed, but it is believed that this proposal has received adequate scrutiny and analysis to enable one to make an informed opinion as to its benefits, opportunities, costs, and risks.

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Reduce Benefits—This alternative can encompass a broad array of tactics. The mechanics used to reduce benefits could be the subject of another model if this alternative is deemed optimal. Among the choices are a simple one-time cut in benefit, a temporary freeze in benefit levels, or a reduction in future COLA adjustments. The main theme is a method of expenditure control versus revenue enhancing ideas such as ‘‘Raising the Withholding Ceiling’’. Status Quo—This alternative says to leave the Social Security program as it is. There should be no modifications to the system. Proponents of this alternative believe that the current system does not require fixing, and that some external influences will arise to correct the current deficit. While the vast majority of people would agree that some level of correction is required, this alternative was also included because of the tendency to neglect or delay dealing with the problem. The current issues were first identified back in 1996 and have yet to be addressed in any form. History might suggest this as an alternative, no matter how ill-advised.

4 Benefits/Opportunities/Costs/Risk Overview The benefits, opportunities, costs and risks models share the same control criteria. They are: Social, Political, and Economic. The subnets within each, however, may differ depending on the control criterion. Figure 2 shows a sample Control Criteria Hierarchy.

Fig. 2 Hierarchy of benefits control criteria

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Fig. 3 Social subnet

Benefits The Social Subnet (Fig. 3) has two elements within the Stakeholders’ Cluster: • Payee Confidence—confidence of those receiving benefits that their benefits will continue at an acceptable rate • Payer Confidence—confidence of those paying into the program that it is worthwhile and they would see a return on the money they are investing.

Fig. 4 Political subnet

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The Political subnet (Fig. 4) contains two clusters, President and Legislative:

President • Media Coverage—the benefit that comes from positive coverage in media outlets. • Voter Perception—the benefit that comes from a favorable impression in the mind of likely voters. • Legacy Place in History—the benefit that comes from being identified with significant historical achievements.

Legislative • Media Coverage—the benefit that comes from positive coverage in media outlets. • Party Recognition—supporting the alternative results in support or lack of support from the legislator’s political party. • Voter Perception—the benefit that comes from a favorable impression in the mind of likely voters. The Economic subnet (Fig. 5) contains only one cluster, the Financial cluster. This cluster contains two nodes

Fig. 5 Economic subnet

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• Program Stability—Program that is not overly susceptible to normal political or economic fluctuations. • US Economic Stability—Program that does not subject the economy to fluctuations or inhibit growth.

Opportunities The Social Subnet (Fig. 6) has three elements within the Stakeholders Cluster: • Participant Peace of Mind—comfort that comes from the assurance that the program will last throughout the participant’s lifetime. • Encourage Financial Responsibility—encourages participants to educate themselves on financial matters. • Decreased Dependence on Government Programs—potential benefit that comes from a more secure financial future where participants increase personal savings rates.

Fig. 6 Social subnet

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Fig. 7 Political subnet

The Political subnet (Fig. 7) contains two clusters, President and Legislative:

President • Media Coverage—the benefit that comes from positive coverage in media outlets. • Attract New Supporters—the potential benefit from taking a position that brings in likely voters outside the normal base. • Increased Political Capital—the potential benefit that comes from securing a major political victory that translates into more political power on upcoming issues. • Legacy Place in History—the benefit that comes from being identified with significant historical achievements.

Legislative • Media Coverage—the benefit that comes from positive coverage in media outlets. • Party Recognition—supporting the alternative results in support or lack of support from the legislator’s political party. • Attract new supporters—the potential benefit from taking a position that brings in likely voters outside the normal base. • Likelihood of re-election—increase in the likelihood of re-election from association with a significant political issue.

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Fig. 8 Economic subnet

The Economic subnet (Fig. 8) contains two clusters, Financial and Operational:

Financial • Effect on Capital Markets—the potential benefit on interest rates or investment rates from the alternative. • Effect on US Budget—the potential positive impact on the US budget deficit. • Effect on US Economy—the potential opportunity from for positive impact to the US Economy.

Operational • Reduction of Bureaucracy—the potential impact of a reduction in US government bureaucracy and/or a reduction of bureaucracy at employers to comply with the program.

Costs The Social subnet (Fig. 9) has three elements within the Stakeholders Cluster: • Fees—the amounts paid by participants to third parties to have individual accounts managed.

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Fig. 9 Social subnet

• Increased withholding—the cost to participants through increased withholding in a given year. The Political subnet (Fig. 10) contains only the Legislative cluster with one node: • Constituent Alienation—the likelihood that efforts on an alternative would anger or disenfranchise constituents.

Fig. 10 Political subnet

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Fig. 11 Economic subnet

The Economic subnet (Fig. 11) contains one cluster, the Operational cluster:

Operational • Conversion Costs—one-time costs to implement the alternative. • Agency Costs—ongoing costs necessary to implement the alternative. • Marketing/Communication to Public—costs to ensure that the general public understands the alternative sufficient to plan appropriately.

Risks The Social subnet (Fig. 12) has three elements within the Stakeholders‘Cluster: • Payee Confidence—confidence of those receiving benefits that their benefits will continue at an acceptable rate. • Payer Confidence—confidence of those paying into the program that it is worthwhile and they will see a return on the money they are investing. • Increased Potential for Profit—potential that an alternative will lead to higher rate of return on investment.

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Fig. 12 Social subnet

Fig. 13 Political subnet

• Loss of Potential Profit—opportunity cost of not pursuing a different alternative. • Reduced Benefits—risk that an alternative will lead to a reduction in benefits. The Political subnet (Fig. 13) contains two clusters, President and Legislative:

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President • Constituent Alienation—the likelihood that efforts on an alternative would anger or disenfranchise constituents. • Legacy Place in History—benefit that comes from being identified with significant historical achievements. • Media Coverage—benefit that comes from positive coverage in media outlets.

Legislative • Constituent Alienation—the likelihood that efforts on an alternative will anger or disenfranchise constituents. • Likelihood of re-election—increase in the likelihood of re-election from association with a significant political issue. • Media Coverage—benefit that comes from positive coverage in media outlets. • Party Recognition—supporting the alternative results in support or lack of support from the legislator’s political party. The Economic subnet (Fig. 14) contains two clusters, Financial and Operational:

Financial • Long-term Insolvency—risk that an alternative would lead to or contribute to the insolvency of the program.

Fig. 14 Economic subnet

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Operational • 3rd Party Failure—risk that a non-government agency associated with the program would experience bankruptcy. • Increased Corruption—risk that the alternative would lead to increased abuse or corruption.

5 Results To synthesize the priorities of the alternatives from the benefits, opportunities, costs and risks, we first need to rate the BOCR subnets according to the strategic criteria. Using the scale of intensities given in the last row of Table 1, we rate the benefits, opportunities, costs and risks by first selecting the best alternative under each subnet and score it for each strategic criterion. The results are then weighted by the priorities of the strategic criteria. The priorities of the alternatives from each subnet (Figs. 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14) are given in Table 2. The synthesized priorities of the alternatives for benefits, opportunities, costs and risks in ideal form are given in Table 3. The normalized results (column 3 of Table 1) are the priorities used to synthesize the priorities of the alternatives (Table 3). The synthesis of the individual subnets (Table 3) indicates that Raising the Retirement age provides the highest benefits. This is likely due to the fact that it both reduces expenditures as well as raises revenue. Privatization provides the most upside opportunity related to the potential for increased returns from investing in the capital markets. Turning to costs, Privatization also brings with it the highest costs (Table 3). Privatization would have the highest conversion and agency costs as well as any fees associated with maintaining individual personal accounts. Reducing Benefits yields the highest risks (Table 3). The political backlash associated with such a widely unpopular alternative is significant. Table 1 BOCR ratings Normalized priorities

Adequate means for participants 0.2684

Perception of fairness

Program stability

0.1172

0.6144

Benefits Opportunities Costs Risks

High Low High Medium

Low Low Medium Low

High Medium Medium Low

0.3885 0.1847 0.2791 0.1477

Intensities: Very high 1.0000

High 0.5684

Medium 0.3026

Low 0.1595

Very low 0.0927

Privatize Raise ceiling Raise retirement age Reduce benefits Status quo

Control criteria ? Alternatives

Political

0.1429 0.4268 1.0000 0.6289 0.1956 0.3640

Social

0.2857 0.7851 1.0000 0.9742 0.5484 0.5830

0.5714 0.4552 0.4377 0.9127 1.0000 0.2474

Economic 0.4000 1.0000 0.5143 0.5329 0.4223 0.2607

Social 0.2000 1.0000 0.8814 0.5296 0.1724 0.3499

Political

Table 2 Priorities of the alternatives from each subnet in the BOCR model Benefits Opportunities Economic 0.4000 0.8541 0.4131 0.5642 1.0000 0.3039

0.5278 0.8856 0.6019 1.0000 0.3186 0.3186

Social

Costs Political 0.1396 0.2852 0.1230 0.3009 1.0000 0.1759

Economic 0.3325 1.0000 0.0929 0.0929 0.2620 0.0929

0.6250 0.4621 0.2374 0.3730 1.0000 0.4125

Social

Risks Political 0.1365 0.3214 0.1362 0.2283 1.0000 0.3674

Economic 0.2385 0.4820 0.7574 0.5331 0.2647 1.0000

5 Results 227

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Table 3 Synthesized priorities of alternatives in ideal form under BOCR Alternatives Benefits Opportunities Costs Risks BO/CR Privatize Raise ceiling Raise retirement age Reduce benefits Status quo

0.3885

0.1847

0.2791

0.1477

0.5454 0.6787 0.8898 0.7561 0.3599

0.9417 0.5473 0.5448 0.6034 0.2958

0.8398 0.3657 0.6007 0.3949 0.2236

0.4477 0.3476 0.3914 0.8246 0.5464

1.3661 2.9213 2.0613 1.4008 0.8715

bB ? oO-cC-rR 0.0853 0.2113 0.2208 0.1731 0.0513

6 Sensitivity Analysis Except at low levels (below 0.20), the model is relatively insensitive to changes in the priority of Benefits. Raising the Retirement Age consistently delivers more benefits. Below approximately 0.28, Raising the Retirement Age has the highest Opportunity. Above a priority of 0.28, Privatization yields the highest opportunity (Fig. 15). When examining the sensitivity to Costs, Privatization consistently yields the highest costs. Raising the Ceiling and Maintaining the Status Quo share the lowest cost at various degrees of priority (Fig. 16).

1

3 2 4

5

1 – Privatize 2 – Raising Ceiling 3 – Raise Retirement Age 4 – Reduce Benefits 5 – Status Quo

Fig. 15 Sensitivity analysis of opportunities

6 Sensitivity Analysis

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1 – Privatize 2 – Raising Ceiling 3 – Raise Retirement Age 4 – Reduce Benefits 5 – Status Quo

2 5 4 3 1

Fig. 16 Sensitivity analysis of costs

1 – Privatize 2 – Raising Ceiling 3 – Raise Retirement Age 4 – Reduce Benefits 5 – Status Quo

1

3

2

5 4

Fig. 17 Sensitivity analysis of risks

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Raising the Ceiling and Raising the Retirement Age nearly share the lowest risk. Reducing Benefits and Maintaining the Status Quo share the highest risks at differing levels of priorities (Fig. 17).

7 Conclusion Among the major factors influencing the results are: • Approximately 90 % of all wages were subject to Social Security withholding in 1980; by 2004, that percentage had slipped to 85 %. • In 1935, Social Security was designed to support older Americans who were dependent and beyond their productive period, originally calculated to begin at age 65, when men had an average of 12 years ahead of them. • Today, a 65-year-old man can expect to live for 17 more years (women, 20)— 5 years longer than original budget estimates. A system designed for men with 12 years ahead of them today would set the retirement age between 70 and 75 Given the relative scores under the additive model and the sensitivity analysis, the Raise the Ceiling and Raise the Retirement Age alternatives are almost identical in every respect, leaving each or a combination of the two as the optimal alternatives.

Appendix Schedules Alternative Detail Below is the detail of the original fourteen alternatives that were identified and the rationale for either including or excluding the alternative in the final ANP model. Raise Tax Rate—While not specifying a specific amount, this alternative proposes increasing the withholding percentage for all participants from the current level of 12.4 %. This alternative was not included in the final model do to nearly non-existent support to the idea. Raise Retirement age—The normal retirement age has been raised in the past and this option is considered viable in the current situation. The life expectancy of Americans continues to increase. The current normal retirement age ranges from 65 to 67 years of age. This alternative is included in the final model. Eliminate Maximum WH income—This would eliminate the current ceiling on wages that are subject to Social Security withholding. This alternative was included in the final model but was modified to say increase the ceiling. Reduce Benefits—This is a one time global reduction in benefits. The formula for calculating benefit levels would be reduced. This alternative is in the final

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model, but is revised to more-broadly incorporate any mechanism that reduces benefits such as temporary freezes on increases, broad benefit level cuts, or a reduction in COLA levels. Freeze Benefits—This alternative suggests freezing the level of benefits for some period of time, rather than forcing people to deal with a benefit cut. It was deemed more practical than an outright reduction in benefits. This alternative was combined into a broader reduce benefits alternative in the final model. Cut COLA formula—Rather than reduce current benefits or freeze them for a period of time, this alternative seeks to limit the growth in benefit levels and would at first glance be to most practical of the expenditure containing alternatives. This alternative also was combined into a broader reduce benefits alternative in the final model. Overhaul/scale back SSI disability—Support for those unable to care for themselves through disability needs to occur regardless. Elimination or reduction of these benefits would just shift to other federal/state programs such as Medicaid or Medicare. This alternative was rejected because while fixing Social Security it would exacerbate issues in other programs. Divert 4 % to Private accounts—We are using the current proposal by President Bush where certain participants can elect to have 4 % of their wages diverted to a private investment account. This alternative is included in the final model. Increase immigration—This alternative proposes an increase immigration as baby boomers retire to reduce the level of payees-to-payor ratio. This alternative was not deemed viable due the level of immigration that would be required to influence this ratio in any appreciable manner. It could be a viable part of a plan that incorporated numerous alternatives as a solution. Subsidize SS fund by cutting spending in other programs—Given current levels of deficits and that Social Security already comprises a large portion of federal budget expenditures, this alternative in itself is not deemed to be feasible. Social Security is already by far the single large expenditure. The cuts in other programs, including Defense and Education would be too severe to make this an economically viable alternative. Recreate ‘‘lock box’’ (specific SS fund unavailable to the general fund) and invest for higher returns—This alternative is essentially the same as the Divert 4 % to private accounts except for who would bear the risk of loss. There is a great deal of skepticism in making the federal government such a significant force in the capital markets. The federal government in many instances would be both the regulatory body as well as the owner; such conflicts of interest have yet to be overcome. Due to its similarity to another alternative and significant issues yet to be resolved, this alternative was not included in the final model. Base lifetime payments on lifetime contributions—This alternative suggests a link should be established between contributions and payments, moving social security closer to a 401(k) type program. This alternative was rejected because of its potential conflict with the strategic criteria of adequate means for participants. Additionally, justification for rejection of the alternative rests in the fact that for most people age 45 and younger will not recover 100 % of their contributions

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during their retirement. In order to achieve this alternative the benefits of retirees and soon-to-be retirees would need to be cut effective immediately and this alternative has been covered in the Reduce Benefits alternative. Do nothing—This alternative relies on a future positive externality to resolve the current issue. It would also encompass those who believe the current problem is an overstatement or fabrication. These individuals, however minor, do exist. For periods of time, issues with Social Security have been ignored, this too makes this alternative relevant. Phase program out—This alternative suggests that over time, the US should eliminate the Social Security program in its entirety. This alternative was not included in the final model because there is clearly no significant support for the idea. Americans do not want to potentially see a significant number of senior citizens living on below subsistence levels of income.

Bibliography Attitudes of Individuals 50 and Older Toward Phased Retirement, AARP Research Brief, March 2005. CBO Testimony by Douglas Holtz-Eakin before the Senate Finance Committee, February 2-3, 2005. GOP exaggerates shortfall www.factcheck.org/article313.html. Heritage Foundation Social Security Research, www.heritage.org/Research/SocialSecurity/index. cfm. Index the retirement age or else www.hillnews.com/thehill/export/TheHill/Comment/DickMorris/ 011205.html. Long-term Analysis of Plan 2 of the President’s Commission to Strengthen Social Security, Douglas Holtz-Eakin – Director CBO, July 21, 2004. No windfalls for Wall Street www.factcheck.org/article310.html. Our Fight: Keeping Social Security Strong www.aarp.org/money/social_security/Articles/a200410-22-ss_strong.html. Old Age and Survivors Trust Funds, AARP Brief, March 2005. Retirement Age and the Need for Saving, CBO Economic and Budget Issue Brief, May 12, 2004. Read My Lips: The Sequel, The Weekly Standard, March 7, 2005. Social Security Reform Lite?, Business Week, March 3, 2005. Social Security vs Common Sense, Michael Boskin, Wall Street Journal, March 30, 2005. Social Security Debate Continues to Draw Mail, David Wessel, Wall Street Journal, March 22, 2005. Social Security Change Faces Labor Muscle, Jeanne Cummings, Wall Street Journal, March 22, 2005. Social security polls www.pollingreport.com/social.htm. Social security calculator www.heritage.org/research/features/socialsecurity/welcome.asp. Social security numbers game www.hillnews.com/thehill/export/TheHill/News/Frontpage/120804/ socialsecurity.html. Strengthening Social Security and Creating Personal Wealth for All Americans, President’s Commission to Strengthen Social Security, December 21, 2001. System can still pay out but needs reform www.hillnews.com/thehill/export/TheHill/News/ Frontpage/030105/ss_santorum.html.

Bibliography

233

The Future Growth of Social Security: It’s not just Society’s Aging, CBO Economic and Budget Issue Brief, July 1, 2003. The Problems Facing Social Security And The Plan To Preserve Social Security For Future Generations www.gop.com/News/Read.aspx?ID=5129. The Retirement Prospects of Baby Boomers, CBO Economic and Budget Issue Brief, March 18, 2004. The Whitehouse Website, www.whitehouse.gov. Treasury experts split on social security plan www.hillnews.com/thehill/export/TheHill/News/ Frontpage/021505/treasury.html. U.S. Rep. Phil English on the Issues - Retirement Security www.house.gov/english/philissues_ retirement.shtml. US Senator Grassley Surprised By Social Security Opposition, Rob Wells and John Godfrey, Wall Street Journal, April 5, 2005. US Snow: Bush Unlikely To Back Raising Soc Sec Wage Cap, Deborah Lagomarsino, Wall Street Journal, March 28, 2005. Voting and Registration in the Election of November 2002, US Census Bureau, July 2004. The Financing of Social Security http://www.aarp.org/money/social_security/Articles/a2003-0402-ssfinancing.html.

Chapter 10

When Shall Poland Enter the Euro Zone?

1 Introduction January 1, 2002 brought the European Union into life when 300 million EU inhabitants in Austria, Belgium, Finland, France, Greece, Spain, Holland, Ireland, Luxembourg, Germany, Portugal and Italy received a new currency—the Euro. On May 1st 2004, Cyprus, the Czech Republic, Estonia, Lithuania, Latvia, Malta, Poland, the Slovak Republic, Slovenia and Hungary joined the European Union, and on January 1, 2007 Bulgaria and Romania committed themselves to enter the monetary union as soon as possible, after they fulfill convergence criteria established by the Maastricht Treaty of February 7, 1992 by which all EU member countries shall, as the end result, enter the economic and currency union. Entering countries had or have to accept the Treaty without any conditions. Only Great Britain and Denmark had not entered the euro zone, but they have an ‘‘opt-out’’ clause by which they can, but do not have to, enter, whereas Sweden did not manage to get social acceptance on giving up their ‘‘crown’’ and accepting the euro in the 2003 referendum, without defining the date of its entry into the currency union. Bulgaria and Romania have still to convert to the euro currency despite entering the European Union January 1, 2007. Poland’s entering the euro zone is a subject of many academic conferences (Nowak and Ste˛pniak 2003; Strategies 2002, Positive and negative sides 2006), and analyses taking form of articles and books, newspapers’ articles in journals, especially Rzeczpospolita, Gazeta Wyborcza and Wprost. In one of the Internet browsers there are 16.600 items using the search term ‘‘Poland’s entry into the euro zone’’. Poland is divided as far as that issue is concerned. For example, Monetary Policy Council, with its President Prof. Leszek Balcerowicz favours a quick entry, claiming that it shall accelerate its economy (Positive sides 2006). According to him, Poland’s entry into the monetary union shall have a positive impact on: • inflation control, • low, long term interest rates,

T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_10,  Springer Science+Business Media New York 2013

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• better price comparability in euro, • transaction prices costs reduction in the foreign exchange transactions, • lower margins on the money borrowed on international market. L. Balcerowicz claims that Poland loses 0.2 % of its economic growth due to postponing its entry into the euro zone. Similar opinion is shared by A.S. Bratkowski, Pekao bank Main Economist (Poland in the euro zone 2006). However, he does not mention costs and risks related to this entry. Also, there are no detailed calculations related to the loss. On the other hand, Bratkowski’s opinion is not shared by Prof. Jakub Mazur, who identifies Poland’s entry into the euro zone with the loss of national identity (Mazur 2006). In his article ‘‘Arguments for and against the Economic and Monetary Union’’, Mazur (2002) comments on fourteen points presented by the supporters of Poland’s entry into the Economic and Currency Union and fourteen points given by the opponents of the euro zone entry. In conclusion, he divides Polish economists into groups of supporters—those who are for the very fast membership in the euro zone (for example A. Bratkowski, K. Jakubiszyn) and those who suggest a slow or medium-term entering process (e.g. E. Pietrzak, D. Rosati). J. Mazur supports the idea to keeping the Polish currency, the zloty, without entering the euro zone. Similarly, Gary S. Becker, the Noble Prize for Economic Sciences in 1992, discourages Poland from entering the euro zone (Bureaucrats’ currency 2006). Also sceptical towards euro currency were Paul De Grauwe—one of the euro fathers and the late Milton Friedman—the 1976 Nobel Prize for Economic Sciences, and probably the most widely known 20th century economist (Pin´ski and Pin´ski 2012). It is Bogdan Borusewicz, Poland’s Senate President (Positive sides ….2006) who seems to hold the most balanced opinion on that issue, claiming that it would be politically irresponsible on the part of the government if the planned accession were to take place even before Poland reaches a direct level of economic convergence. This decision could result in enormous social costs and the threat of our fast exclusion from the euro zone. He gives as an example Italy where the costs of remaining in the euro zone are higher than the exit costs. Fast entry into the euro zone is supported by the Business Centre Club, motivating their opinion by the foreign investments growth and accelerating the economic growth ratio. Lech Kaczyn´ski, Poland’s President together with the Minister of Finance Zyta Gilowska support the referendum on the date (undetermined) of Poland’s entry into the euro zone. Because of a significant economic distance between Poland and the former 15 ‘‘old’’ EU members (amounting to 20–30 years in relation to the most developed countries), a decision on entering the euro zone shall take into account the following four values: • the benefits that Poland shall obtain after entering the monetary union, • the costs we shall bear in relation to preparation for and presence In the euro zone,

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• the extra benefits, that is opportunities, to be drawn from our presence in the monetary union, and • the extra costs, that is threats, related to our entry into the euro zone. This work aims to estimate those parameters. Sooner or later, Poland has to enter the euro zone. The open question is the timing. Therefore a decision on certain alternatives shall be made. However, each decision on the issue has elements of discovery, irrational incidentally, economic, social, political, organizational, and managerial and other results. The practice decision making concentrates on weighting alternatives that fulfill a set of desired objectives. A decision means a choice of one of them. In each decisional problem there is at least one best decision where it can be objectively stated that there is no other that is a better decision that keeps the decision process neutral, i.e. unbiased. The problem is to choose that alternative that fulfills a set of comprehensive objectives. Poland’s entry into the euro zone is a multicriteria problem that requires the participation of many players whose behavior and opinions differ because of how they perceive reality and the processes involved in this reality. There is also the fact that each person represents a separate world of values, and the participants viewpoints are based on various, often conflicting value systems. This leads to making multicriteria decisions on Poland’s entry into the euro zone. As far as solving multicriteria decisions are concerned, the literature points to various methods (Figueria et al. 2005), but the best ones are AHP, ANP (Adamus and Gre˛da 2005) and they were used here to make a decision on the best timing of Poland’s entry into the economic and monetary union. Following Prof. A. Ste˛pniak (Zone 2003) this work presents three different variants of Poland’s entry into the euro zone, providing other entry dates and countries that can enter the monetary union together with Poland: 1. Early entry into the euro zone (in 2008/2009), together with the following countries: Cyprus, Malta, the Slovak Republic; 2. Medium-term entry into the euro zone (in 2010/2011), with the following countries: Lithuania, Latvia and Estonia; 3. Late entry into the euro zone (after 2011), with the following countries: Czech Republic, Hungary and perhaps Bulgaria and Romania. Those alternatives shall be analyzed in the context of benefits, costs, opportunities and risks. Poland’s entry into the euro zone shall be given a holistic approach that accounts for all the parameters. Poland shall enter the euro zone when the relation between benefits and opportunities exceed costs and risks. The problem thus defined shall be solved with the use of the multicriteria decision support method ANP—Analytic Network Process (Saaty 2001; Figueria et al. 2005). Poland with other EU members (with exception of Great Britain and Denmark) must be ready to enter the monetary union after fulfilling the following conditions: • Conditions for economy stabilization convergence • Institutional adjustments, • European Union acceptance.

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2 Conditions for Euro Zone Membership: Convergence Criteria Defined by the Maastricht Treaty The European Union Treaty, signed on February 7, 1992 in Maastricht, Netherlands, set out to determine macroeconomic criteria provided below, which shall be used to evaluate EU member states aspiring to the monetary union. The Convergence (approximation) criteria hale to be fulfilled by all states in the euro zone not only nominally but also in real sense, that is to say they must hale effective economy in a relatively long period of time: 1. Annual budget deficit (of public finance)—percentage of planned or real GNP deficit measured in market prices shall not exceed 3 % annually. 2. Public debt—the share of debt in GDP in the year preceding the analysis, measured in market prices shall not exceed 60 % of GDP. Exceeding those two most important criteria in 2006 by Hungary (budget deficit amounted to 4 % of GDP, and the economic growth has not exceeded 4 % of GDP) moved the country’s entry into the euro zone to the years 2010–2014. 3. Inflation rate—should be lower than 1.5 % over the average rate in the three EU countries with lowest inflation rate (2.8 % in 2006). 4. Long term interest rate—it should not be higher than the average in the three countries with the lowest inflation level increased by 2 % (approximately 6 % in 2006). Interest rates shall be measured based on the long term state T-bonds or other comparable instruments, taking into account differences in national deficits. 5. Stable currency exchange rates—for 2 years before the euro zone entry the national currency must remain in European Currency Exchange Rates (ERM II) where differences cannot be larger than ±15 % from the central parity. Poland, just like other countries candidates to the euro zone, cannot explain away any preferences in this respect. The interpretation of the convergence criteria for candidate countries is stricter than the one used for the current euro zone members. The example is Lithuania. The EU Committee for Economic and Monetary Affairs rejected Lithuania’s attempts to join the euro zone because its inflation rate exceeded the allowable rate by only 0.03 %. Institutional adjustments The moment it joins the euro zone, Poland as well as other countries shall be forced to adapt its monetary policy instruments to the requirements of the European Central Bank. The most important problem is the overflow of the Polish banking sector that forced the Polish National Bank to take steps contrary to those of the European Central Bank (ECB), which puts the money into the banks instead of taking the overflow from them. Also, the open market operations must be adapted to the system obligatory within the ECB.

2 Conditions for Euro Zone Membership

239

3 Poland’s Economic Position Relative to Other Euro Zone Countries and Those Aspiring to Join the European Union. At the moment, the euro zone includes 13 states: Germany, France, Italy, Holland, Belgium, Luxembourg, Spain, Portugal, Ireland, Austria, Finland, and Greece and since January 1, 2007, Slovenia. New EU members and Sweden, which has not determined in the referendum the date of its entry into the monetary union, are in line to join the union. Table 1 presents selected macroeconomic indicators for the years 1995–2006 of countries already present in the euro zone and of those attempting to join. Indicators can be divided into three groups: • GDP dynamics, • Fiscal criteria (public finance deficit and public debt), and • Inflation. Analyzing GDP dynamics in the years 1995–2006 in relation to countries in the euro zone we may say that GDP tendency in Poland is similar to countries such as Finland or Sweden. Most probably, had it not been for the cooling of the economy in 1995 (Balcerowicz), the GDP dynamics would be one of the highest in Europe. In 2006 GDP in Poland increased by 6 % in comparison to the year 2005, and the analysts predict its growth in 2007 up to 7 %. Unfortunately, this indicator does not take into account many features, such as knowledge, education, health, beauty, cultural and natural resources, sensitivity, courage, in other words, all that makes life sensible. Fiscal criteria are not favorable for Poland. Although the relation of public debt to GDP does not exceed the 60 % limit set by the EU (49.8 % in 2006), yet the budget deficit in 2006 exceeded the admissible limit of 3 %. It should be underlined that Poland uses the right to include resources gathered in pension funds in the public finance sector (up to the year 2008). If part of the pension system reform costs were included in the budget deficit, then one would expect the budget to exceed the allowable limit by an even higher value. Therefore, public finance regulation will, in the future, be the largest challenge before Poland’s entering the euro zone. Amongst the countries attempting to join the euro-zone, it was only Slovenia, the Slovak Republic and the Czech Republic that fulfilled the budget deficit criterion in 2005. From among all EU countries, in 2005 there was a budgetary surplus in Denmark (4.9 %), Sweden (2.9 %), Finland (2.6 %), Spain (1.1 %), Ireland (1.0 %) and Belgium (0.1 %). The largest deficit was experienced by the countries aspiring to the euro zone: Latvia (-12.7 %), Bulgaria (-11.3 %) and Estonia (-10.5 %). From among candidate countries to the monetary union in 2005 the lowest deficit was present in Slovenia (-1.7 %).

4.0

7.0

2000

2.9 3.8 3.1 3.5 3.6 9.1 4.2 3.7 10.1 3.5 5.1 4.4 3.8 4.4 2.6 –

1995

1.0 2.0 3.0 2.2 2.0 3.8 3.0 3.0 12.0 2.0 5.0 2.0 3.0 4.0 3.0 –

2005

0.9 1.8 4.0 0.7 1.5 3.5 3.4 0.8 4.7 1.8 2.2 3.7 1.7 2.6 2.8 4.7 5.5 4.8 9.8 7.6 10.2 3.5 4.1 4.0 5.5 3.9

2006

8.3 3.9

5.8

6.4

2.8 2.0 1.9 2.9 3.2 6.2 3.9 1.3 6.0 3.1 5.5 4.3 2.8 4.2 3.2 2.7

1995

2.9

-3.3 -5.5 -7.6 -4.2 -4.3 2.7 -7.0 -4.6 -2.2 -5.2 -3.7 -0.2 -5.4 -7.9 -2.3 -5.0

2000

3.0

-1.2 -1.4 -0.5 2.2 0.1 5.8 -0.3 -1.5 4.5 -1.6 6.9 -0.8 4.4 4.0 2.5 0.2

2005 -3.3 -1.5 -1.8 -0.3 0.1 -1.9 1.1 -6.0 1.0 -1.5 2.6 -2.4 -3.6 2.9 4.0 1.0 -11.3 -2.6 -10.5 -7.2 12.7 -2.5 -8.6 -1.4 -2.9 -6.1 0–3.0 %

2006

-3.4 -9.2

-3.9

-2.9

-1.7 -2.6 -4.5 0.5 0.1 0.1 1.8 -3.9 2.9 -1.2 3.8 -2.3 -2.9 2.1 4.2 -1.6

1995

51.6

58.3 52.8 125.3 79.0 132.2 5.8 67.2 65.9 78.9 69.4 58.1 110.1 53.9 77.6 73.3 73.4

2000

42.4

60.3 57.4 110.6 56.0 109.3 5.6 60.4 53.4 39.0 63.6 44.0 102.8 45.7 65.7 57.1 70.1

2005 67.7 66.8 106.4 52.9 93.3 6.2 43.2 63.9 27.6 62.9 41.1 107.5 42.8 50.3 35.8 70.8 29.9 30.5 4.5 18.7 12.1 50.2 15.2 29.1 34.5 61.5 =\60.0

2006

37.0 73.2

49.8

35.6

71.4 75.0 119.9 59.7 90.7 9.8 47.1 73.2 30.4 68.9 46.2 92.5 46.6 53.9 34.7 76.1

1995

27.9

1.7 1.8 5.2 1.5 1.1 1.0 2.2 2.2 2.5 1.5 0.3 2.2 2.3 2.7 2.5 2.7

2000

10.8

2.1 1.8 2.6 2.3 2.7 3.2 3.4 2.8 5.3 2.0 3.0 2.9 2.1 1.0 0.3 2.4

2005 2.1 2.0 2.3 1.6 2.6 3.9 3.7 – 2.5 1.9 1.1 3.4 2.1 1.3 2.0 2.3 5.0 1.6 4.1 2.7 6.7 1.3 9.0 2.5 2.8 3.5 =\2.8

2006

4.5 3.9

1.3

2.6

1.7 1.7 2.1 1.2 1.8 2.7 3.5 3.1 3.9 1.4 1.6 3.2 2.3 1.4 1.9 2.2

10

Source Calculations based on: Eurostat CIA FACTBOOK.2006, UniCredit New Europe Research Network

Germany France Italy Holland Belgium Luxembourg Spain Portugal Ireland Austria Finland Greece Great Britain Sweden Denmark Euro Zone Bulgaria The Czech Republic Estonia Lithuenia Latvia Poland Romania Slovenia The Slovak Republic Hungary Maasstricht criterion

Table 1 Selected macroeconomic indicators for the years 1995–2000–2005–2006 of states in the euro zone and attempting to join Country GDP dynamics (%) Budgetary balance (%) Public debt (% PKB) Inflation (%)

240 When Shall Poland Enter the Euro Zone?

3 Poland’s Economic Position Relative

241

The debt of euro zone countries still exceeds the agreed limit of 60 % set by the EU (70.8 average percentage in 2005, 76.1 % in 2006); including the largest countries: Germany, France and Italy. In the Maastricht Treaty, high penalties were levied on the countries not following convergence criteria. Unfortunately, it is impossible to actually implement them. The reference value for inflation in 2005 was 2.8 %. Poland has fulfilled this criterion since 2003 that is since a year before it entered the European Union until May of 2007 when this work was written. From among the countries aspiring to enter the euro zone, in 2005 the criterion was fulfilled only by Poland, the Czech Republic, Lithuania and the Slovak Republic, as well as countries outside the euro zone: Sweden, Denmark and Great Britain. Poland also fulfills the long term interest rate criterion. In this work we do not analyze results for Cyprus and Malta because of the lack of data about all the macroeconomic criteria listed in Table 1. Cyprus and Malta already participate in ERM II and plan to have a common euro currency already in 2008. Also Lithuania, Latvia, Estonia and Denmark have introduced their currencies to the European Rate Mechanism II (2006). Other countries do not hurry to change their domestic currency into euro. Prof. Jan Winiecki of the Polish Economists Society observed that (Glapik 2007), while some countries cannot fulfill or do not agree with the conditions defined in the Maastricht Treaty, others move the entry date to the euro zone for political reasons. The date Poland will enter the euro zone depends on the date all Maastricht Treaty convergence criteria are fulfilled, including the most important one, public finance regulation. Poland’s entry into the euro zone means not only enormous benefits, as some think, but it is also a great responsibility for euro currency stability and the EU economy. The key important element for Poland as part of the European Union is the reasonable and responsible use of synergistic effects, through integration with other EU countries, and the further improvement of its infrastructure. Poland’s entering the monetary union is connected to multiple benefits but also costs, as well as opportunities and risks for the society and the Polish economy. Those values were verbally defined in hundreds of articles and discussions. However, none of those discussions and publications estimated the values for benefits, costs, opportunities and risks. This work attempts to estimate their levels in relative terms.

4 Prioritization of ANP Model Control Criteria for Poland’s Entry into the Euro Zone Table 2 gives the prioritization of the control criteria for the merits: benefits, costs, opportunities and risks. Criteria were divided into economic and social, and compared among each other with respect to benefits, costs, opportunities and risks. With respect to all merits, economic criteria outweighed the social ones.

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Next, local priorities were calculated for 27 subcriteria for all merits. Among benefits it was the economic criterion that achieved the highest priority—Stable economic growth (0.4340), in the category of opportunities the most important economic subcriterion is the growth of export (0.4990) and social—tax lowering (0.7500). Among costs the most important subcriteria proved the following: dependence upon the EU economic trends (0.4030) and the adjustment of monetary policy instruments to the requirements of the European Central Bank (0.3680). A relatively high priority was assigned to social costs—giving up own monetary policy (0.4070). The highest risk was assigned to the lack of competitiveness of products (0.5140) and the increase in energy prices (0.2330). Global priorities vector was normalized to the value of 1. Subcriteria, for which the priorities are equal or exceed 3 % were included in the analysis (marked bald in the table).

5 Decision Subnet Analysis for Each Selected Control Criterion BOCR At this stage, a cluster of three alternatives was introduced into the model. These alternatives had been defined earlier as the following scenarios: (a) early entrance of Poland into the euro-zone, (b) medium-term entrance of Poland into the eurozone, (c) late entrance of Poland into the euro-zone. Figure 1 presents the 13 subcriteria, selected earlier from amongst 27 sub-criteria analyzed using the Super Decisions software. Figure 2 illustrates the ANP model of ‘‘benefits’’ of Poland’s entry into the euro-zone. The sub-criteria with global greater than or equal to 0.03 were analyzed under the subset of ‘‘benefits’’. Figure 3 demonstrates a network of connections and mutual influences between particular elements for the permanent economic growth sub-criterion. It has been assumed that its indicator (Gross Domestic Product—GDP) is dependent on decisions of the following institutions: Government, Parliament, Monetary Policy Council, Ministry of Finance, European Parliament, National Bank of Poland, and on individual decisions of consumers and producers (enterprises). By comparing these elements pairwise, their priorities were estimated, which illustrate their relations in the context of the permanent economic growth. Besides, the three alternatives were compared with each other within a net of their influences and feedbacks with the 3 elements presented by Fig. 3, and their priorities were calculated in the context of the permanent economic growth. Similar procedures were performed for the remaining 12 sub-criteria in relation to all merits, namely: benefits, costs, opportunities and risks. The overall results for all comparisons are shown in Table 3. According to the outcomes presented in Table 3, the optimal date of joining Poland to the euro-zone is the latest possible date, after 2011 to be more specific,

Costs

Opportunities

Benefits

Adaptation of monetary policy instruments to ECB requirements Adaptation of open market operations to ECB requirements Dependence on EU economic trends

Increase of bankrupt companies Flexibility decrease in economic growth Giving up own monetary policy

Social (0.33)

Tax lowering Free market strengthening

Social (0.20)

Economic (0.67)

Export increase Investment capital inflow Manufacturing unit costs decrease Financial system stability

People trust to money Closer tights with EU Unprofitable companies restructuring

Social (0.25)

Economic (0.80)

Eliminating exchange risks Lowering costs of obtaining capital Stable economic growth Public finance improvement Increase in debt support for the economy

Economic (0.75)

0.254 0.339 0.407

0.368 0.229 0.403

0.75 0.25

0.499 0.134 0.083 0.284

0.479 0.281 0.24

0.108 0.051 0.434 0.307 0.1

(continued)

0.023 0.03 0.037

0.067 0.042 0.073

0.028 0.09

0.073 0.02 0.012 0.042

0.039 0.023 0.02

0.027 0.012 0.107 0.075 0.025

Table 2 Prioritization of control criteria and elements of ANP model for benefits, costs, opportunities ands risks of Poland’s entry into the euro zone Merits Criteria Subcriteria Local priorities Global priorities

5 Decision Subnet Analysis for Each Selected Control Criterion BOCR 243

Risks

Social (0.20)

Economic (0.80)

Table 2 (continued) Merits Criteria

Unemployment increase Weakening of national identity Social unrest

Euro rate fall ? strengthening of currencies outside EEA Lack of competitiveness outside new products and quality increase Energy prices increase outside EU Speculating capital inflow

Subcriteria

0.359 0.423 0.218

0.177 0.514 0.233 0.076

Local priorities

0.016 0.018 0.009

0.031 0.089 0.04 0.013

Global priorities

244 10 When Shall Poland Enter the Euro Zone?

5 Decision Subnet Analysis for Each Selected Control Criterion BOCR

Fig. 1 Control hierarchy of dependencies and feedbacks

Fig. 2 ANP subnet model—benefits of ‘‘Poland’s entry into euro zone’’

245

246

10

When Shall Poland Enter the Euro Zone?

together with the countries such as Czech Republic, Hungary and perhaps Bulgaria and Romania. For the 3 sub-criteria analyzed as benefits, only one of them (improved condition of public finances) indicates late entrance to the euro-zone as optimal, while the two remaining (permanent economic growth and people’s trust in money) indicate medium-term period of the entrance. Considering opportunities of Poland’s entrance into the euro-zone, it can be observed that from amongst three components analyzed, only one (increased export) points to the medium-term scenario, while the remaining two components (financial system stability and tax rate decrease) suggest the latest possible entry. Table 3 shows the analysis of the four components related to costs and three components related to risks. Their priorities decisively point to Poland’s late entry to the euro zone. The overall results are shown in Table 4. To select the optimal alternative date of Poland’s entry into the euro-zone, it is essential to link values of the priorities’ alternatives with the control hierarchy of benefits (B), costs (C), opportunities (O) and risks (R). It can be performed in two ways: (1) using the mathematical formula (BO/CR), in which the values of variants’ priorities for benefits multiplied by opportunities (B*O) are divided by the values for costs multiplied by risks (C*R); (2) using the mathematical formula (bB ? oO – cC - rR), which requires defining levels of importance for subsystems of benefits (b), costs (c), opportunities (o) and risks (r). In the latter case, so called strategic criteria are defined, for which their importance is estimated. This stage allows us to look at the problem from more general perspective, that is,

Fig. 3 ANP subnet for economic benefits for ‘‘stable economic growth’’

5 Decision Subnet Analysis for Each Selected Control Criterion BOCR

247

Table 3 Prioritization of decision alternatives for control criteria and subcriteria in the models: benefits, costs, opportunities and risks

from the viewpoint of the criteria such as: increased welfare of Polish society, financial integration of the national banking system with the European Central Bank, social and political integration with the EU countries. Each of the main listed criteria has subcriteria. The model of strategic criteria is illustrated in Fig. 4. The strategic criteria are used to estimate the influence of benefits, opportunities, costs and risks in the final result. The scale (personal criteria) on which the importance of benefits, costs, opportunities and risks have been estimated is presented in Table 5. Table 6 clearly demonstrates that the most important criterion to be considered in analyzing the country’s entrance to the euro-zone is increased welfare of Polish citizens (0.43), followed by financial integration (0.28). The values derived from prioritization of the strategic criteria for benefits (0.3280) and opportunities

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When Shall Poland Enter the Euro Zone?

Table 4 Decision alternatives prioritization for benefits, opportunities, costs and risks Alternatives Benefits Opportunities Costs Risks Late entry into euro zone Medium time frame entry into euro zone Early entry into euro zone

0.8714 0.7237 0.2600

0.6795 0.7629 0.3695

0.0991 0.3414 1.0000

0.1070 0.3819 0.7478

(0.1840) are higher than the respective values derived for costs (0.2720) and risks (0.2160). At this stage, it can be asserted that benefits and opportunities from Poland’s entry to the euro-zone will outweigh the potential costs and risks. Yet, the main research objective of this study is to recommend when Poland should join the euro-zone. As explained in the previous sections, this is the only decision-making option we can consider. In order to provide an explicit answer, third step of analysis was performed, which included the above estimated priorities for benefits, costs, opportunities and risks. Pair-comparisons of three decision-making variants based on importance of the BOCR values allowed selection of the best possible alternative (Table 7).

Fig. 4 Hierarchy of strategic criteria

Table 10.5 Personal criteria estimation Personal criteria Very high High Very high High Medium Low Very low Total

1 1/2 1/3 1/4 1/5 1.00

2 1 1/2 1/3 1/4

Medium

Low

Very low

Pi

3 2 1 1/2 1/3

4 3 2 1 1/2

5 4 3 2 1

0.42 0.26 0.16 0.10 0.06

Social integration (0.18)

Financial integration (0.28)

Improvement of Poles’ living standards (0.43)

Per capita GNP level reaching He EU level (0.14) Economic growth stabilization (0.15) Export dynamic growth (0.14) Direct investment capital (0.14) Private spending increase (0.14) Unemployment rate fall (0.14) Economic development flexibility (0.15) Monetary policy transferred to ECB (0.16) Exchange risk elimination (0.48) Foreign EU currency reserves elimination (0.29) Speculation capital intensive inflow (0.07) Labour mobility increase (0.37) Easier trading exchange between Poland and EU countries UE (0.38) Limits on national sovereignty with respect to own monetary policy (0.25) Average (0.16)

Very low (0.06)

Very high (0.42)

Very low (0.06)

High (0.26) Low (0.10)

Very low (0.06) Low (0.10)

High (0.26) Average (0.16)

High (0.26) High (0.26)

Average (0.16)

Low (0.10)

High (0.26) Average (0.16) High (0.26) Low (0.10) High (0.26) High (0.26)

Very high (0.42) High (0.26) High (0.26) High (0.26) Very high (0.42) Low (0.10)

Costs C Very high (0.42)

High (0.26)

Benefit B

Very low (0.06)

Average (0.16) Average (0.16)

Very low (0.06)

Average (0.16) Average (0.16)

Lowe (0.10)

Average (0.16) Low (0.10) Low (0.10) Average (0.16) Average (0.16) Low (0.10)

Low (0.10)

Opportunities O

(continued)

Average (0.16)

Low (0.10) Low (0.10)

Very high (0.42)

Low (0.10) Low (0.10)

Average (0.16)

Average (0.16) Average (0.16) Average (0.16) Low (0.10) Average (0.16) Average (0.16)

High (0.26)

Risks K

Table 6 Priorities estimation for merits: benefits, costs, opportunities and risks personal criteria: very high (0.42), high (0.26), average (0.16), low (0.10), very low (0.06) Criteria Subcriteria Merits

5 Decision Subnet Analysis for Each Selected Control Criterion BOCR 249

Priorities

Political integration (0.11)

Table 6 (continued) Criteria

European identity acquiring (0.151) Closer ties with EU (0.24) Foregoing national identity (0.15) Decreasing possibility of Competition between governments in fields of investment and manufacturing (0.46)

Subcriteria

(0.26) (0.26) low (0.06) low (0.06)

0.3180

High High Very Very

Benefit B

Merits

0.2720

Average (0.16) High (0.26) Average (0.16) High (0.26)

Costs C

0.1840

Average (0.16) Average (0.16) Low (0.10) Low (0.10)

Opportunities O

0.2160

Low (0.10) Average (0.16) Average (0.16) High (0.26)

Risks K

250 10 When Shall Poland Enter the Euro Zone?

5 Decision Subnet Analysis for Each Selected Control Criterion BOCR

251

Table 7 Final results Multiplicative Additive— Risk Alternatives Benefits Opportunities Costs Subtracting (0.2720) (0.2160) formula (0.3280) (0.1840) BO/CR formula bB ? oO cC - rR Late entry into 0.8714 euro zone Medium time 0.7237 frame entry into euro zone Early entry into 0.2600 euro zone

0.6795

0.0991

0.1070

40.4241

0.3520

0.7629

0.3414

0.3819

3.3219

0.1797

0.3695

1.0000

0.7478

0.0961

-0.3347

The optimal alternative for Poland is late entrance into the euro-zone. Such outcome has been achieved by both formulas: multiplicative and additivenegative. The problem discussed in this work represents a ‘‘hot topic’’ in Poland and was analyzed based on the ANP method. This method allows solving multi-criteria problems in reality. Yet, it requires the advanced knowledge and experience of decision makers, as well as a great amount of work to grasp all significant factors and their mutual interactions. It has been suggested that nearly all complex problems can be solved using this method.

6 Final Conclusions The issue of Poland’s entry into the euro zone is not only very important for Poland but also very complex, strongly related to the main decision makers in Poland—the government, Ministry of Finance, Poland’s economy, European Central Bank, other banks in Poland and so on. Those relations are internally and externally connected with feedbacks and loops. Poland, preparing to enter the euro zone, should first of all strengthen its economic growth, and then during a longer period of time fulfill all the criteria of the Maastricht Treaty. Only such sequence can improve the welfare of the Poland’s citizens, which will be beneficial not only for Poland but also the European Union. Poland’s entry into the euro zone shall take place as soon as possible, but only after the benefits and opportunities will overweigh costs and risks. The date of the entry into the euro zone shall be determined in the group of experts (academics, politicians, practitioners) with the use of ANP method. The problem of entry date shall not be solved by means of a referendum. Finding appropriate solution requires significant knowledge and experience, accounting for all possible criteria and their mutual dependence both within and

252

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outside the system. As a result of a detailed network analysis of the problem with use of Analytic Network Process and the solution achieved with Super Decisions the following conclusions can be drawn: 1. The ANP model accounts for 27 BOCR criteria, they include economic and social factors determining Poland’s entry into the euro zone 2. As a result of prioritization, both mathematical formulae give the same results for Poland’s late entry in the euro zone as the best alternative 3. Poland’s entry into the euro zone stall only take place when joint benefits and opportunities exceed costs and risks 4. Sensitivity analysis may slightly change the priorities of discussed analyses but that would require extreme conditions for BOCR prioritization and their control criteria. 5. From the Analytic Network Process perspective, the problem to be solved reveals its significant complexity, various dependencies with main decision makers in Poland and the economy and culture of Poland, European Union and the rest of the World.

References Adamus W., Gre˛da A., (2005). Wspomaganie decyzji wielokryterialnych w rozwia˛zywaniu wybranych problemów organizacyjnego i mened_zerskich (in Polish), Multiple Criteria Decision Suport in Organizational and Management Chosen Problems Solving, Badania Operacyjne i Decyzje, Nr 2. Blaski i cienie wejs´cia Polski do strefy euro (Light and Shade of Poland’s entrance into the eurozone). Conference organized by the Senate Committee for the European Union, 15.11.2006, www.senat.gov.pl.k6/agendaseminar/blaski/061115.htm. Figueria J., Greco S., Ehrgott M. (edit.) (2005). Multiple Criteria Decision Analysis: State of the Art Surveys, Springer Science ? Business Media, Inc. Glapik E. (2007). Blakna˛cy czar wspólnej waluty (Fading light of common currency). Rzeczpospolita 12.03.2007. Mazur J. (2002). Argumenty za i przeciw Unii Gospodarczej i Walutowej (Arguments for and against the European Economic and Monetary Union). Głos 31.08.2002. Mazur J. (2006). Likwidacja polskiego złotego, likwidacja pan´stwa (Elimination of the Polish zloty, elimination of the state), http://web.1asphost.com (Tera 2) likwidacja pan´stwa polskiego.htm. Pin´ski A., Pin´ski J., Euro 2012. Wprost, 19 (14 May 2006 r), s. 44 – 48. Polska w strefie euro: szanse i wyzwania (Poland in the euro zone: opportunities and challenges). Conference organized by the Institute for International Affairs and the Polish Sejm 13.10.2006, Rzeczpospolita: head-arok 22.gif. Saaty R.W., (2002). Decision Making. The Analytic Network Process (ANP) for Dependence and Feedback, a manual for the ANP Software Super Decisions, Creative Decisions Foundation, Pittsburgh, PA. Saaty T.L., (1980). The Analytic Hierarchy Process, McGraw-Hill, New York Saaty T.L. (2001). The Analytic Network Process. RWS. Publications 4922 Elsworth Avenue Pittsburgh, PA, 15213 USA.

References

253

Saaty T.L. (2005). Theory and Applications of the Analytic Network Process, RWS Publications, 4922 Ellsworth Avenue. Pittsburgh, PA. 19213. Schael T., (1997). Theorie et Practique du Workflow, Springer, Paris. Strategia integracyjna z Unia˛ Europejska˛ na okres poakcesyjny 2004 – 2015 (European Integration strategy for post-accession period 2004 – 2015), Scientific Conference 25.06.2002, www.prezydent.pl. Nowak, A.Z., Ste˛pniak, A. (eds.) (2003) Strefa euro – wyzwanie dla Polski (The euro-zone – a challenge for Poland). Wydawnictwo Naukowe Wydziału Zarza˛dzania Uniwersytetu Warszawskiego, Warszawa 2003. Waluta biurokratów (The currency of bureaucrats). Interview with G.S. Becker by L.M. Bednarz, Wprost Nr 19 (14 May 2006 r.), p. 48.

Chapter 11

The Conflict Between China and Taiwan

1 Introduction A long-festering problem now threatens the peace and stability of the Asia–Pacific region. As Assistant Secretary of State for East Asian and Pacific Affairs Stanley Roth warned Congress on March 25, 1999, the Taiwan issue—or, as we prefer to say, the ‘‘Divided China’’ problem—has become ‘‘one of the United States most complex and important foreign policy challenges for many years to come.’’ Most of countries are concerned that the crisis has arrived. The origins of today’s divided China problem go back some sixty years ago to a very different time and place. At that time, two political parties, the Kuomintang (KMT) and the communist party of China (CPC), and their armies fought each other while both tried to win over the Chinese people to their ideals. As the Chinese civil war seemed to be ending in early 1950, one of those unusual historic turning points took place: The U.S. government intervened in the Chinese civil war by allying with the Republic of China (ROC) to counter the People’s Republic of China (PRC). In so doing, the ‘‘divided China’’ situation turned out to be a source of instability in Asia.

2 Possible Alternatives Since the two parties introduced different ideals, Democracy (Taiwan) and Communism (mainland China), into the government system, there were two Chinese regimes opposing each other across the Taiwan Strait. The possible options for them to end the long lasting Chinese civil war and resolve the divided China problem are: • • • •

Peaceful unification Stay as in the present Independence of Taiwan China armed takeover of Taiwan.

T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_11,  Springer Science+Business Media New York 2013

255

256

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The Conflict Between China and Taiwan

The goal is to develop a Super decisions ANP model to determine what Taiwan and China should do to resolve the separated China situation. The benefits, opportunities, costs, and risks (BOCR) networks are created and each has a subnet. The benefits network indicates the alternative that yields the most benefit and the opportunities network indicates the alternative that offers the most opportunities. The costs and risks networks indicate the alternative that is the most costly or poses the greatest risk to the Taiwan–China decision.

3 BOCR Model 3.1 Strategic Criteria In pursuit of this decision, we consider five strategic control criteria: China Government, International Political Power, Taiwan Economy Power, Taiwan Government, and Taiwanese. These five strategic control criteria influence the weight of the BOCR. They were used to implement a rating system in the ANP program in order to prioritize the BOCR (see Fig. 1).

Fig. 1 BOCR model and strategic criteria

3 BOCR Model

257

Fig. 2 Control criteria

3.2 Control Criteria Under the benefits, opportunities, costs, and risks models, different clusters define the interactions with respect to the control criteria. Each subnet under the BOCR has the same control criteria. They are Political, Social, and Economic (see Fig. 2). The same control criteria were considered for all BOCR networks.

3.3 Benefits Subnet under Political 1. Stability of international relations cluster—This cluster represents the serious concern of other countries about the four alternatives. Especially Japan and the United States, have closest relationship with divided China. It includes: US Pacific Defense System and Japan’s concern about National Security. 2. Security cluster—This cluster defines how Taiwan would defend its territory in terms of four alternatives, involving two powers: US Army’s Support and National Defense, ROC. 3. China cluster—This cluster shows that three influences from mainland China could interact with the four alternatives. It includes: China Political Influence, China Attacks, and Vision of One China. 4. Taiwan’s Vision cluster—This cluster represents two main voices from inside Taiwan, One Side, One Country and We are a Family. 5. National System cluster—This cluster indicates the difference between two ideals in the struggle across the Taiwan Strait. It includes: Democracy and Communism (see Fig. 3).

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Fig. 3 Subnet under political benefits

Subnet Under Social 1. Social System cluster—This cluster represents the different social structures started and developed by the opposing ideals, Democracy and Communism. 2. Culture Difference cluster—This cluster represents the different Standard of Living and the different point of view of Human Rights as issues evaluated in terms of the four alternatives (see Fig. 4). Subnet Under Economic 1. Business cluster—This cluster represents the factors of running businesses that could be influenced differently in terms of the four alternatives. It includes: Transportation Cost, Labor Cost, Market Entry Barriers, Labor Quality, and Management Expertise. 2. Individual cluster—This cluster identifies the new situation that an individual might need to face, in terms of the four alternatives. It includes: Fierce Job Competition and Price Level (see Fig. 5).

3 BOCR Model

Fig. 4 Subnet under social benefits

Fig. 5 Subnet under economic benefits

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3.4 Opportunities Subnet Under Political 1. International Relations cluster—This cluster represents the opportunities afforded for international relations in terms of the four alternatives. It includes: Increase Political Power, and International Recognition (see Fig. 6). Subnet Under Social 1. Social Issue cluster—This cluster represents the opportunities related to social issues in China and Taiwan in terms of the four alternatives. It includes: More Education Resources, Improve Quality of Life in China, Improve Human Rights in China, and Higher Social Status (see Fig. 7). Subnet Under Economic 1. Taiwan cluster—This cluster identifies the opportunities to Taiwan in terms of the four alternatives. It includes: Greater Market Openness, Access to Natural

Fig. 6 Subnet under political opportunities

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Fig. 7 Subnet under social opportunities

Fig. 8 Subnet under economic opportunities

Resources, More Job Opportunities for Taiwanese, and Increase Taiwan’s Economic Power. 2. China cluster—This cluster identifies the opportunities to China in terms of the four alternatives. It includes: More Job Opportunities for the Chinese People, and More Investment Opportunities in Taiwan (see Fig. 8)

3.5 Costs Subnet Under Political 1. Taiwan to International cluster—This cluster represent the costs that Taiwan needs to incur to get international support in terms of the four alternatives. It includes: Lobby costs and International support.

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Fig. 9 Subnet under political costs

2. Taiwan cluster—This cluster identifies the costs to Taiwan domestically in terms of the four alternatives. It includes: Autonomy, High National Defense Budget, and Voter Support. 3. China cluster—This cluster identifies the costs to China in terms of the four alternatives. It includes: Tangible Costs to get Taiwan back and Intangible Costs to get Taiwan back (see Fig. 9). Subnet Under Social 1. China cluster—This cluster identifies the cost to China in terms of the four alternatives. It includes: Tangible Costs to get Taiwan back and Intangible Costs to get Taiwan back. 2. Blue Taiwanese cluster—This cluster identifies the cost to Taiwan in terms of the four alternatives. It includes: Fears, Uncertain Society, Casualties and People Movement (see Fig. 10). Subnet Under Economic 1. International cluster—This cluster identifies the costs that both China and Taiwan would have to incur in the international arena in terms of the four alternatives. It includes: Hobbling Global Economy, Capital Fleeing and Losing Investors’ confidence. 2. Taiwan cluster—This cluster identifies the cost to Taiwan domestically in terms of the four alternatives. It includes: Currency Depreciation, Damage to Domestic Economy and Price Fluctuation.

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Fig. 10 Subnet under social costs

3. China cluster—This cluster identifies the cost to China in terms of the four alternatives. It includes: Tangible costs to get Taiwan back and Intangible Costs to get Taiwan back (Fig. 11).

Fig. 11 Subnet under economic costs

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3.6 Risks Subnet Under Political 1. International cluster—This cluster represents the risks to global and international relations in terms of the four alternatives. It includes: Alliance between US and China, China’s growing power, and Stability of Asia–Pacific. 2. Taiwan cluster—This cluster identifies the risks to the Taiwanese and to the Taiwan Government in terms of the four alternatives. It includes: Threat of China attack, The Government’s decision, and Budget crow-out effect. 3. China cluster—This cluster represents what risks to China in terms of the four alternatives. China has been saying it will prohibit Taiwan from independence from China regardless of all risks. Again this cluster simply includes Tangible Risks to China and Intangible Risks to China (see Fig. 12). Subnet Under Social 1. Social Risks cluster—This cluster stands for the risks to both China’s and Taiwan’s societies with regard to the four alternatives. It includes: (1) Birth rate, (2) Crime rate, (3) Irreconcilable, (4) Refugees issues, and (5) Ideology (see Fig. 13). Subnet Under Economic 1. International cluster—This cluster represents the economic risks the global market would take in terms of the four alternatives. The risks include Damage international logistic network, Trade sanctions against China, and Damage the global supply chain.

Fig. 12 Subnet under political risks

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Fig. 13 Subnet under social risks

Fig. 14 Subnet under economic risks

2. Domestic cluster—This cluster identifies the risks to Taiwan’s domestic economy and market. It includes the risks of GDP slips, Exhausted resources in Taiwan, and Economic isolation (see Fig. 14).

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Table 1 Alternatives priorities wrt the control criteria and synthesis Political Social Economic Alternatives 0.6250 0.1365 0.2385 Benefits 1. Peaceful unification 2. Status Quo 3. Independence of Taiwan 4. China armed takeover of Opportunities 1. Peaceful unification 2. Status Quo 3. Independence of Taiwan 4. China armed takeover of Costs 1. Peaceful unification 2. Status Quo 3. Independence of Taiwan 4. China armed takeover of Risks 1. Peaceful unification 2. Status Quo 3. Independence of Taiwan 4. China armed takeover of

Synthesis

Taiwan

1.0000 0.7723 0.5992 0.6484

0.7285 1.0000 0.5245 0.5245

1.0000 0.7436 0.4864 0.7039

0.9629 0.7965 0.5621 0.6447

Taiwan

0.9915 1.0000 0.7155 0.6019

0.8353 1.0000 0.9039 0.7232

1.0000 0.8333 0.6401 0.7767

0.9722 0.9602 0.7232 0.6601

Taiwan

0.4988 0.6861 0.9843 1.0000

0.4029 0.4729 0.8385 1.0000

0.3921 0.4117 0.8140 1.0000

0.4603 0.5915 0.9238 1.0000

Taiwan

0.4199 0.4477 0.8611 1.0000

0.6187 0.5804 0.9312 1.0000

0.4411 0.4213 0.7284 1.0000

0.4521 0.4595 0.8390 1.0000

4 Overall Synthesized Results Each of the subnets under the control criteria for the benefits, opportunities, costs and risks yields priorities for the alternatives. These priorities in ideal form are synthesized to obtain the overall priorities of the alternatives with respect to the benefits, opportunities, costs and risks (Table 1). To synthesize the results, first the benefits, opportunities, costs and risks are rated according to the strategic criteria using the best ranked alternative as the norm under each of the merits. Table 2 gives the normalized priorities of the benefits, opportunities, costs and risks. The priorities of the alternatives are obtained by combining the results from the benefits, opportunities, costs and risks models using a multiplicative (BO/CR) and an additive negative (bB ? oO-cC-rR) composition principle (see Table 3). The results indicate that Peaceful Unification is the best scenario for the future relationship of China and Taiwan.

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Table 2 BOCR ratings and intensity scale Int’l China Government Political Power 0.292707 0.203558 Benefits

Medium

Very Strong

Opportunities Medium

Weak

Costs

Strong

Medium

Risks

Weak

Strong

Intensities:

Very Strong Strong 1.0000 0.5684

Taiwan Economy Power 0.098507

Taiwanese Normalized Taiwan Government Priorities 0.212643

0.192585

Very Strong Very Strong Very Strong Very Strong Medium 0.3026

Medium

Very Strong Very Strong Medium

0.2821

Very Strong Very Strong Weak 0.1595

0.2902

Medium Strong

Table 3 Multiplicative and additive syntheses of BOCR results Benefits Opportunities Costs Risks

0.2075 0.2202

Multiplicative Additive

Alternatives

0.2821

0.2075

0.2202 0.2902 BO/CR

1. Peaceful Unification 2. Status Quo 3. Independence of Taiwan 4. China armed takeover of Taiwan

0.9629 0.7965 0.5621

0.9722 0.9602 0.7233

0.4603 0.4521 4.4988 0.5915 0.4595 2.8140 0.9238 0.8390 0.5246

bB ? oOcC-rR 0.2408 0.1604 -0.1382

0.6447

0.6601

1.0000 1.0000 0.4256

-0.1915

5 Sensitivity Analysis The following graphs show sensitivity analysis of the four alternatives for the relationship between China and Taiwan (Figs. 15, 16, 17, 18).

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Fig. 15 Sensitivity analysis under benefits

BENEFITS Alternatives 1. Peaceful Unification 2. Status Quo 3. Independence of Taiwan 4. China Armed Takeover of Taiwan

0.5 0.421 0.331 0.122 0.125

Fig. 16 Sensitivity analysis under opportunities

1 2

3

4

OPPORTUNITIES Alternatives 1. Peaceful Unification 2. Status Quo 3. Independence of Taiwan 4. China Armed Takeover of Taiwan

0.5 0.407 0.376 0.095 0.009

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Fig. 17 Sensitivity analysis under costs

1 2 3 4

COSTS Alternatives 1. Peaceful Unification 2. Status Quo 3. Independence of Taiwan 4. China Armed Takeover of Taiwan

0.5 -0.122 -0.166 -0.332 -0.379

Fig. 18 Sensitivity analysis under risks

RISKS Alternatives 1. Peaceful Unification 2. Status Quo 3. Independence of Taiwan 4. China Armed Takeover of Taiwan

0.5 -0.12 -0.138 -0.334 -0.408

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6 Conclusions 1. No one wants to fight Based on the synthesized results, one clearly sees that Peaceful Unification is the ideal scenario among all the alternatives followed by the Status Quo alternative. The other two alternatives (Independence of Taiwan and China Armed Takeover of Taiwan) are far behind in the overall result. This provides the favorable conclusion that war is never a desired option for China and Taiwan. 2. Status Quo will NOT be a permanent situation Before developing the model, it was thought that Status Quo would be the best option because it was basically more favorable to Taiwan and overall perhaps also to China. However, by doing this model, it was realized that Status Quo, in the long run, would keep Taiwan under great pressure from China’s threats and thus would hurt Taiwan’s society and economy. That is why Status Quo does not come out to be the ideal solution. 3. Go Independent = War + Loss Undoubtedly, by becoming independent Taiwan would be a shame for China. China has been announcing publicly that, once Taiwan goes independent, it would launch a war to take it over at any cost. According to the sensitivity analysis under benefits, the China Armed Takeover of Taiwan would surpass the Independence of Taiwan alternative as more weight is assigned to benefits. This is understandable because, as Taiwan becomes independent, it would lose international support since not many countries support its independence. Moreover, Taiwan would lose economic advantage because China would block Taiwan’s business and trade. The foregoing shows that the independence option would bring more costs than benefits, and more risks than opportunities. It is thought that this model is both realistic and reliable in portraying the current situation between China and Taiwan. The authors are very confident about the outcome and conclusions as they mirror many studies made about the subject. While the criteria and priorities may change with the passage of time the ideal solution is likely to remain for reasons given above.

Chapter 12

U. S. Response to North Korean Nuclear Threat

1 Introduction As more and more countries around the world begin to develop nuclear weapons, the threat of a nuclear attack against the United States increases. In addition to the threat directly posed by these countries, there is also the threat that nuclear weapons could be sold or given to other hostile countries or to terrorists. North Korea is one country whose development of nuclear weapons represents a threat to the United States, somewhat aggravated by the confrontational attitude of its leader, Kim Jong-un. The purpose here is to determine what best action the United States can take in response to the potential nuclear threat from North Korea. The current United States policy is to only deal with North Korea through sixnation talks involving the United States, North Korea, China, Russia, Japan, and South Korea. Some economic sanctions are in place. The United States has not ruled out using incentives, but would not talk about them unless North Korea first agrees to abandon its nuclear program.

2 Alternative Courses of Action 1. Attack on Facilities: This alternative involves an attack whose purpose would be to take out North Korea’s nuclear facilities. Advantages: Using this alternative has the advantage of not having to deal with Kim Jung Il. Since he has not been very responsive to talks up to this point, there may be no way to achieve a satisfactory solution by dealing with him. In addition, this alternative would involve using less troops and resources than a full scale attack.

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Disadvantages: Hostile response from North Korea and other countries, damage to U.S. reputation, and the chance that some facilities may be missed and the threat would remain with the certainty of escalating the conflict. 2. Full Scale Attack: This alternative involves a full scale attack on the North Korean soil. Advantages: A full scale attack could ensure that North Korea’s weapon facilities are destroyed. Also, it would send a sobering message to other countries that are possibly developing nuclear weapons such as Iran. Disadvantages: Given the large presence of U.S. troops in other countries, such as Iraq, Afghanistan and the Balkans, it might be difficult to gather enough forces for a full scale assault without adequate preparation for a major war. Such a war would undoubtedly create major diplomatic problems with East Asian countries and could damage U.S. credibility in the region. It could also affect the political stability of the region. 3. Economic Sanctions: This involves using economic sanctions to punish North Korea until it agrees to give up its nuclear program. Advantages: This strategy has not had any negative results so far. It is not as costly as some of the other alternatives. Disadvantages: Economic sanctions have failed to eliminate the threat of North Korea’s nuclear weapons. Its leadership does not seem to care about the people’s well-being. 4. Remove Sanctions, No Other Action: This involves removing all sanctions and not pursuing any other course of action such as using incentives or attacking North Korea. Advantages: Removing sanctions could make the U.S. appear to be fair in the eyes of some hostile countries. There are minimal direct economic costs to this alternative. Disadvantages: The U.S. might seem weak in the eyes of some enemy countries, and upset allies that continue to use sanctions. In addition, if North Korea’s borders were more open to trade, this could make it easier for nuclear weapons to leave the country and get into the hands of terrorists or enemy countries. 5. Negotiate with Incentives: This involves negotiating by tempting North Korea with positive offers that can serve as incentives. Advantages: The use of incentives could make the U.S. appear fair to other countries. North Korea might be more responsive to this approach than to less friendly alternatives. Disadvantages: This could make the U.S. appear weak. Providing incentives would only encourage other countries to act as North Korea has acted. Incentives have a direct economic cost.

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6. Combination: This involves negotiating with North Korea by using both sanctions and incentives as bargaining tools (the carrot and the stick approach). Advantages: In addition to making the U.S. appear fair while not looking as weak as with some of the alternatives, it would also provide North Korea with the most reasons to agree to U.S. demands. Disadvantages: Incentives have costs and may encourage other countries to act like North Korea. 7. Take out Kim Jong-un: This involves eliminating/deposing the leader of North Korea, Kim Jong-un as with Saddam Hussein. Advantages: Removing Kim Jong-un may result in a new leader who is more responsive to U.S. demands. This would show other enemy countries that the U.S. is serious in dealing with dictators. Disadvantages: There is a strong possibility that this would lead to an attack from North Korea and create further hostility from enemy countries and terrorists. It could also damage the U.S. image in the eyes of ally countries.

3 Benefits, Opportunities, Costs and Risks The alternative courses of action model need to be evaluated according to their merits based on benefits, opportunities, costs and risks (BOCR). The merits in turn are evaluated in terms of the strategic criteria depicted in Fig. 1. Before the BOCR model is evaluated with respect to the strategic criteria we need to identify the best alternative course of action in each of the merit categories.

3.1 Benefits Subnet The benefits subnet consisted of three criteria (see Fig. 2). Each of these criteria also had subcriteria. To determine which subcriteria were important enough to have their own subnets, subcriteria were selected when they accounted for at least 75 % of the importance of the benefits subnet. These relative priorities were found by multiplying the priority of each criterion by the priority of each subcriterion within the corresponding subcriteria cluster. For example, among the criteria, National Security had a priority of 0.637, Economic had a priority of 0.105, and Political had a priority of 0.258. In the National Security Subcriterion cluster, Eliminate Potential Nuclear Threat had a priority of 0.8, and Anti-Terrorism had a priority of 0.2. Therefore, the relative priority of Eliminate Potential Nuclear Threat was 0.637 9 0.8 = 0.51. This method for determining which criteria and subcriteria

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Fig. 1 Hierarchy of strategic criteria and BOCR model

274

require subnets was used for the costs and risks subnets as well. Table 1 shows all the criteria and subcriteria along with their relative priorities. The subcriteria that have subnets are highlighted.

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Fig. 2 Hierarchy of benefits control criteria

3 Benefits, Opportunities, Costs and Risks

Table 1 Benefits criteria and subcriteria Criteria Subcriteria Economic National Security Political

Defense industry Stable environment for global trading Anti-terrorism Eliminate potential nuclear threat Improve U.S. influence in Asia Positioning For future negotiations Stable global political environment

Relative priority 0.0209 0.0838 0.1274 0.5096 0.1033 0.0517 0.1033

Each of the most important subcriteria (in bold letters in Table 2) contains a subnet. Figure 3 is the subnet containing the alternatives and actors involved and the potential interactions.

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Relative priority

Improve U.S. trading relationships Improve U.S. image Step towards world peace Enhance political alliances

0.1143 0.2802 0.4699 0.1356

Fig. 3 Subnet under benefits—antiterrorism/eliminate potential nuclear threat/stable global political environment

Table 2 Opportunities criteria Criteria

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Fig. 4 Hierarchy of opportunities control criteria

3.2 Opportunities Subnet Unlike the benefits subnet, there were no subcriteria in the opportunities subnet (see Fig. 4). Therefore, determining which criteria needed subnets required only looking at the priorities of each criterion. Table 2 shows the opportunities criteria and the priorities of the two criteria that have subnets (highlighted). Figures 5 and 6 contain the subnets under the opportunities criteria.

3.3 Costs and Risks Subnets The relative priorities under the costs (Fig. 7) and risks (Fig. 8) control hierarchies were determined in the same manner as they were under the benefits and opportunities hierarchies. Tables 3 and 4 show the criteria, subcriteria, and priorities in these subnets. The subcriteria that have subnets are highlighted. Figures 9, 10, 11, and 12 show the subnets under the costs control hierarchy. Figures 13, 14, 15, and 16 show the subnets under the risks control hierarchy.

4 Rating Benefits, Opportunities, Costs and Risks Three strategic criteria were used in the model (See Fig. 1) to rate the benefits, opportunities, costs and risks. Two of them were broken down into subcriteria. We have: Economic Political: With two subcriteria • World Reaction • Political Stability of Region Social: With two subcriteria • Effect on U.S. Citizens • Effect on Citizens of Other Nations.

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Fig. 5 Subnet under opportunities—improve US image

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Fig. 6 Subnet under opportunities—step toward world peace

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Fig. 7 Hierarchy of costs control criteria

280

281

Fig. 8 Hierarchy of risks control criteria

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Table 3 Costs criteria and subcriteria Relative Criteria National security Economic

Political

Subcriteria Diversion of security forces Loss of life Immediate cost Ongoing cost Opportunity cost Foreign relations Public concern

Table 4 Risks criteria and subcriteria Criteria Subcriteria National security Economic Political Social

Increased terrorism Nuclear war Destabilized trading environment Damage to trade relationships U.S. reputation Damage to existing alliances Unrest over war Anxiety over nuclear threat

Priority 0.1342 0.1342 0.1825 0.3315 0.1004 0.0879 0.0293

Relative priority 0.0910 0.4552 0.0279 0.0558 0.0459 0.0918 0.0774 0.1549

Table 5 shows the ratings and priorities of benefits, opportunities, costs and risks. Under each criterion, there were five possible ratings: • • • • •

Extremely Low Low Medium High Extremely High.

It should be noted that the priorities for costs and risks were much higher than the priorities for benefits and opportunities leading to negative outcomes. This makes sense given that the goal of dealing with the North Korean nuclear weapons threat is more about avoiding bad consequences than it is about achieving positive results.

5 Results and Sensitivity Analysis Under both the benefits and opportunities subnets, Combination was the alternative that ranked highest. Under costs and risks, Full Scale Attack was the alternative that ranked the highest. Table 6 show the results of each subnet.

Fig. 9 Subnet under costs—diversion of security forces

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Fig. 10 Subnet under costs—loss of life

284

Fig. 11 Subnet under costs—immediate costs

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Fig. 12 Subnet under costs—ongoing costs

286

Fig. 13 Subnet under risks—increased terrorism

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Fig. 14 Subnet under risks—nuclear war

288

Fig. 15 Subnet under risks—damage to existing alliances

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Fig. 16 Subnet under Risks—anxiety over nuclear threat

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Table 5 BOCR priorities Economic World Political reaction stability of region

Effect on US citizens

Effect on citizens Normalized of other countries priorities

0.4000 Benefits Medium Opportunities Medium Costs Extremely High Risks High

0.3000 High Medium High

0.1000 High High High

0.1500 Low Low Medium

0.0500 Medium Low Low

0.1959 0.1519 0.3484

High

High

Medium

0.3037

Intensities:

High

Extremely high Medium

0.5574

0.2963

0.1564

Extremely High 1.0000

LOW

Table 6 Benefits subnet results Alternatives

Benefits

Opportunities

Costs

Risks

1 2 3 4 5 6 7

0.5277 0.3011 0.7038 0.3891 0.7401 1 0.4446

0.3277 0.1919 0.5685 0.4096 0.9052 1 0.3774

0.5953 1 0.1188 0.1231 0.1810 0.1527 0.6278

0.6599 1 0.1774 0.2346 0.1700 0.1685 0.5889

Attack on facilities Full scale attack Economic sanctions Remove sanctions, no other action Negotiation with incentives Combination Take out Kim Jung Il

Table 7 Results found using additive negative formula Alternatives BO/CR

bB ? oO–cC–rR

1 2 3 4 5 6 7

-0.2546 -0.5640 0.1290 0.0243 0.1678 0.2435 -0.2531

Attack on facilities Full scale attack Economic sanctions Remove sanctions, no other action Negotiate with Incentives Combination Take out Kim Jung Il

0.4402 0.0578 18.9827 5.5171 21.7717 38.8732 0.4539

The overall results were calculated using two different formulas. Table 7 shows the results obtained using the multiplicative and additive negative formulas. Since the additive negative formula allows for negative results, Take Out Kim Jung Il, Attack Facilities, and Full Scale Attack all had negative values.

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Both approaches gave the same results showing the alternatives ranked from best to worst as follows: • • • • • • •

Combination Negotiate with Incentives Economic Sanctions Remove Sanctions, No Other Action Take Out Kim Jong-un Attack on Facilities Full Scale Attack.

6 Sensitivity Analysis Sensitivity analysis was performed to determine how sensitive the results were to changes in the priorities of benefits, opportunities, costs, and risks. Looking at benefits, no matter what value they had, the results still indicated that the best course of action was Combination. When sensitivity analysis was done on opportunities, Combination was also found to be the best alternative regardless of the priority of opportunities. Looking at costs, Combination was found to be the best alternative as long as costs had a priority less than 76 %. Looking at risks, Combination was the best alternative regardless of the priority of risks. Figures 17, 18, 19, and 20 show the sensitivity analysis graphs for benefits, opportunities, costs, and risks.

Fig. 17 Sensitivity analysis for benefits 1. 2. 3. 4. 5. 6. 7.

6

5 4 3

1 2

7

Attack on facilities Full scale attack Economic Sanctions Remove sanctions. No other action Negotiate with incentives Combination Take out Kim Jung Il

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Fig. 18 Sensitivity analysis for opportunities

1. 2. 3. 4. 5. 6. 7.

6

Attack on facilities Full scale attack Economic Sanctions Remove sanctions. No other action Negotiate with incentives Combination Take out Kim Jung Il

5 4

3

7

1 2

Fig. 19 Sensitivity analysis of costs 1. 2. 3. 4. 5. 6. 7.

3

6

5

4 7

1 2

Attack on facilities Full scale attack Economic Sanctions Remove sanctions. No other action Negotiate with incentives Combination Take out Kim Jung Il

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Fig. 20 Sensitivity analysis of risks 1. 2. 3. 4. 5. 6. 7.

3

Attack on facilities Full scale attack Economic Sanctions Remove sanctions. No other action Negotiate with incentives Combination Take out Kim Jung Il

6

5

4 7

1 2

7 Conclusion Current United States policy towards North Korea has so far not been successful in eliminating the nuclear threat. To resolve the problem, the United States may need to take a more active role in dealing with North Korea. When weighting all of the factors, it appears that the best option for dealing with North Korea is to negotiate using both the threat of sanctions and the offering of incentives.

Chapter 13

Criteria for Evaluating Group Decision-Making Methods

1 Introduction In this chapter we are concerned with the development of criteria for evaluating different methods of group decision-making that range from the strictly technical, to the psychophysical and social, and finally, to the logical and scientific. Our purpose is to identify similarities and differences with the aim of showing from such wide consideration which method is more attractive, and is likely to gain greater attention both in academia and in practice. Its outcome would survive outside influences because it makes possible incorporating such influences in its structures, and assessing their relative impact on the outcome in a way that does not tax one’s intelligence to accept its procedures, nor do these procedures alienate the user. Needless to say, all users are born, potentially expert, decision-makers. Eventually all MCDM methods need to be extended to allow for dependence of criteria on alternatives so that the user is not forced to cast her/his problems and think in ways that may seem artificial because of strong assumptions about independence that cannot be adhered to strictly. Urli and Nadeau (1999) have observed that the future of MCDM is ‘‘subject to questions and debate among its researchers: what is the evolution of the field? What is its structure? Is it integrating new topics?’’ thus giving us a slant on the possibility of an evolving set of criteria for evaluation as well. In this regard, Corner et al. (2001) have talked about dynamic interaction between criteria and alternatives that can lead to expanding the structure of a decision with increased understanding. Da Costa and Buede (2000) have written about dynamic decision-making and how to deal with optimizing decisions in the framework of dynamic decision networks, again taking a long time horizon in thinking about decision making. The main object of this work is not so much about identifying and exhaustively summarizing all MCDM methods as it is about developing a way of examining, with a broad set of criteria, what to look for in judging the merit of a decision making approach. Undoubtedly, what we have here needs to be altered and further expanded to take into consideration factors that deal with interaction between user and method, outcome and method, and user and outcome. A scientific undertaking

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of this kind may be helpful in improving and expanding MCDM research thrusts to deal with complex decisions. One can delve into a diversity of ramifications involved in decision- making. Such ramifications may deal with intellectual, psychological, or environmental effects regarding the comfort of a decision maker when making a decision for example. They can also deal with improving intuitive understanding and practice as appropriately pointed out by Wierzbicki (1997). Here we have to confine our attention to general criteria concerning the technical merits of MCDM methods and how well they address their subject matter. ‘‘Should a decision analyst primarily support a client’s decision process as it is or should he reshape it and teach the client how to make a decision in another way? Which is the proper balance between the two in different situations? Perhaps it does not matter if the input from a client to a multi-criteria decision model is compatible with that model or not?’’ writes Svenson (1998) adding further complexity to the idea of evaluation methods. A client may be pleased with a simple method because he is unaware of the complexity involved in the process of eliciting and synthesizing judgments and may even strongly advocate the best outcome unaware that a richer structure and better knowledge and interaction can produce a better decision. This further adds to the difficulty of choosing additional criteria to compare methods. There are numerous useful criteria proposed in the literature to judge group decision-making. We use them as a basis for establishing new criteria for judging group decision support methods. We identify and briefly describe several of the well-known methods in decision-making. We define various intensity measures on each of the new criteria. We then evaluate each of these methods by assigning it the intensity that describes it best on each criterion, explaining briefly why that intensity is appropriate for the method. In this manner, the methods are compared and contrasted with respect to each criterion, and for lack of a better and more general way to structure the problem, a table is developed that can be used to obtain an overall rating of the methods, although we have refrained from doing it here as we do not wish to offend the developers and the users of one or the other of these methods.

2 Criteria for Group Decision Making Methods Rubin (Swap and associates 1984) proposed six quality indicators for group decision making that address both achievement and maintenance goals (Brightman 1980, 1988): efficiency, careful development and analysis of alternatives, fairness, member satisfaction and morale, leadership effectiveness, and growth over time. These indicators are developed from a group process point of view, and need to be translated into another set of indicators before they can be used as criteria for evaluating the methodologies that facilitate for a group to excel on those quality indicators. We exclude efficiency from our analysis because it is highly dependent

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on the way the group is organized and led. We perceive growth over time as learning. We assume that a method that addresses group maintenance (leadership effectiveness and learning) would also ensure member satisfaction and morale; hence we do not consider the latter as a criterion explicitly. First, a general method for group decision-making must provide a facilitator with the means to lead the group to achieve and maintain its goals. The method must also assist the facilitator in enhancing individual and group learning, both single loop or small ‘‘l’’ learning and double loop or big ‘‘L’’ learning (Argyris 1977, 1994; Pascale 1991). It addresses the first if it enables the group to solve problems of implementing organizational policies and achieving the goals of the organization through incrementally, based on past performance and knowledge. It addresses the second if it facilitates questioning the underlying assumptions of those policies and goals through breakthrough shift of knowledge. Systematic and comprehensive development of alternatives means that the group must not view a problem from a scope too narrow to ensure a meaningful solution or too broad to ensure controllable actions. It also means that the group must be able to identify a set of distinct alternatives from a level of abstraction that is adequate for the group. For example, a group of top executives would view a problem from a higher level of abstraction than would a group of operational managers because they have a much wider choice space from which to draw controllable alternative courses of actions. Careful analysis of alternatives requires the group to work with a model/ structure (Reagan-Cirincione 1994) with the appropriate breadth (for relevance) and depth (for precision). A successful analysis depends on faithfulness of judgment elicitation, psychophysical applicability, and the depth of the analysis. For example, in some methods one must first accept the premise that eliciting judgment by comparing two alternatives with respect to a certain property would produce the most faithful representation of one’s tacit preference relations. Faithful judgment can be obtained if: (1) it is expressed directly by the decision maker, rather than derived from some other form of judgments, (2) it is not clear to the decision maker as to how that particular judgment would ultimately affect the outcome and hence would not play games with it to influence the outcome, thus preventing strategic judgment (Dummett 1984), and (3) the decision maker has the choice to express preference relations numerically (as a minimum for representing objective measurement) or verbally (for representing perception or feeling), or even graphically. Interestingly, Larichev and Brown (2000) have examined the merit of making decision approaches to improvise ways to create a new alternative that is better than the existing ones. Depth of analysis means how well an analytical method provides the means to guide a decision-makers’ thinking to ensure the validity of the outcome. It includes, for example, having a feedback mechanism for making changes and adjustments or directing the decision-maker to an expert or looking for specific information. Fairness is addressed both during group interaction, and when the variety of information or judgments from individuals must be mathematically aggregated into one judgment for the group. For this criterion, we are only concerned with the method of aggregation, since group discussion is likely to be controlled by the

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facilitator. A strong condition for a successful decision theory with regard to resource allocation is that it often needs to make it possible to separate the alternatives with cardinal numbers than simply order them. The group members themselves may need to be weighted as to the reliability of their opinions. Other actors or stakeholders who may be affected by the implementation of the decision often need to be considered, and a successful method needs to have a way to include their judgments. Most significantly we add, a method must be generally applicable, valid (can be scientifically validated), and reflects the truth advocated by those who provide the judgments. From such considerations, one would be concerned with such issues as: (1) Is the method applicable to conflict resolution? (2) Does it apply to intangibles in the same way it does to tangibles? (3) Does it have mathematical validity and generality, and is it supported with axioms and theorems? (4) Can the method be applied to psychophysical measurement? and (5) Is the outcome valid, ensuring, for example, reliability in prediction? Applicability to conflict resolution means that the method must provide a way for each conflicting party to evaluate the costs and the benefits of giving up some of what it has, in return for getting what it wants from the other party. Applicability to intangibles involves inclusion, and measurement of, the multidimensionality of the factors involved. Mathematical validity and generality calls for formal mathematical representation of the logic and reasoning behind a theory and the economy of additional assumptions required for its generalization. Psychophysical applicability means that an analytical method must deal with the measurement of relationships between the physical attributes of stimuli and the resulting sensation reflecting diminishing response to increasing stimulus such, for example, as that described by the Weber-Fechner law. Validity of the outcome involves the accuracy of the outcome in predicting situations. One needs to be careful, however, to define what constitutes a prediction situation. In an experimental study, Schoemaker and Waid (1982) showed that guesswork with direct estimation of the rank of multi-criteria objects produces a very different ordinal ranking than the cardinal ranking produced by another method. The following 16 criteria are used to compare and contrast the various methods:

2.1 Group Maintenance: Leadership Effectiveness We assume that all group methods enhance leadership effectiveness. We use a democratic leader’s characteristics as criteria for leadership effectiveness, assuming that the group mostly works in moderate situational control in terms of leadermember relations, task clarification, and position power (Lewin et al. 1939; Fiedler 1973). A method is rated low if it is highly technical or does not involve much interaction and where leadership is of a little concern, medium if it provides no more than structure to facilitate group leadership, and high if it also provides other collaborative tools and the necessary control mechanism to guide the facilitator’s leadership actions in pursuing the group’s achievement and maintenance goals.

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2.2 Group Maintenance: Learning It is assumed that objective knowledge that is widely accepted and agreed upon, is considered less important by the people involved in the group than what they know from their experience relevant to the issues and what they learn by problem solving within the group. A method is rated low if it advances technical learning that has little to do with the group member’s subjective values, medium if it improves understanding with regard to cause-effect relations in a problem (but actions may not be clear, single loop or small ‘l’ learning only, or, it does not provide clear evaluation of alternatives), high if it facilitates both single and double loop learning, or small ‘‘l’’ and big ‘‘L’’ learning (leading to action), and very high if it also enables one to produce the necessary material to facilitate learning beyond the membership of the group.

2.3 Problem Abstraction: Scope The need for problem abstraction or definition is inherent in any decision-making, therefore this indicator is assumed to be addressed by all methods. The question is whether a method explicitly addresses this issue or not. Voting is an exception for which alternatives are always given, hence problem abstraction is not applicable and this method is rated NA. A method is rated low if it does not propose a specific technique and does not involve problem analysis that enhances the scope of abstraction, medium if its technique creates boundaries that limit group thinking, or, if it does not propose a specific technique but involves problem analysis that serves as feedback to broaden problem abstraction, and high if double loop learning is explicitly addressed.

2.4 Problem Abstraction: Development of Alternatives It is generally assumed that the alternatives are not given to the group; hence any method involving problem structuring must go through a process of identifying alternatives. It is assumed that multi-criteria methods require a process of generating alternatives that allows a certain degree of interaction among group members. It is also assumed that a method for enhancing problem abstraction leads to a set of alternatives. Again, voting is an exception because a set of alternatives is always given. A method is rated NA if the alternatives must be given, low if it does not provide a specific technique for identifying alternatives, medium if it ensures a free wheeling environment without group interaction, or, if it generates incremental alternatives (it is assumed that innovative change is more preferred to incremental change), high if it ensures a free wheeling environment as well as group interaction

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but no requirement that the alternatives selected satisfy certain properties or requirements (e.g., distinct or independent), very high if it is also based on challenged assumptions, if it systematically generates alternatives, or, if it requires the alternatives to satisfy certain properties to ensure the validity of the outcome.

2.5 Structure: Breadth A structure is said to be broad if it has many distinct elements (criteria) that are assumed to be independent of each other. A problem that is modeled by more than one such structure is considered to be even broader. A method is ranked NA (not applicable) if it does not involve problem structuring, low if the method allows only one element (direct comparison), medium if the method creates a constraint with respect to the number of elements, and high if there is no such constraint.

2.6 Structure: Depth A structure is said to be deep if each element is broken down into sub-elements, each sub-element into sub-sub-elements and so on down to the most detailed elements. A method is ranked NA if it does not involve structuring, low if it allows only one element, medium if it creates a constraint with respect to the number of elements, and high if there is no such constraint.

2.7 Analysis: Faithfulness of Judgments A method is rated NA if it does not involve problem analysis, low if it does not include intensity of preferences, medium if it involves direct assignment of numbers to represent intensity on an scale that is assumed but not derived from more basic and common understanding, high if it is derived from some other judgments carefully elicited, very high if it is elicited in the most elementary way (pairwise comparison with respect to a property), expressed in a way that fits the decision maker best (numerically, verbally, or graphically), or, if it is by design an objective method, or, if it is continuously improved.

2.8 Analysis: Breadth and Depth of Analysis (What If) A method is rated NA if it does not involve problem analysis, low if it allows judgment, but not analysis, medium if the depth of analysis is constrained by the

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method’s structure, high if it provides the means for careful thinking (but it is difficult to review previous analysis), and very high if it facilitates careful thinking and review.

2.9 Fairness: Cardinal Separation of Alternatives This indicator is applicable only to methods that involve aggregation of judgments of individual members. Alternatives can only be treated either fairly (high) or not fairly (low). A method is evaluated according to its consistency with the impossibility problem intrinsic in ordinal group aggregation. An aggregation method is rated low if it uses an ordinal scale of measurement and high if it uses an interval, a ratio, or an absolute scale. A method is rated NA if it does not involve judgment aggregation.

2.10 Fairness: Prioritizing of Group Members This indicator is also applicable only to methods that involve aggregation of individual judgments. Voting theories usually operationalize fairness as equal treatment of the voters. With group decision-making, there may be circumstances in which the group may want to apply the concept of fairness with unequal treatment of the individuals involved. For example, weights may need to be assigned to the members according to the relevance of their expertise or to their known previous contribution to the goal. A method is rated NA if it does not involve judgment aggregation, low if individual preferences are represented on an ordinal scale, medium if the preferences are represented on an interval or ratio scale, or an absolute (but the individuals must carry the same weight), high if it also provides a group with an option to treat group members unequally (but the weights are assigned arbitrarily), and very high if it provides a method to determine the weights as appropriately as the group wishes.

2.11 Fairness: Consideration of Other Actors and Stakeholders This criterion is applicable only to methods that involve problem analysis. A method is rated NA if it does not involve problem analysis, low if addressing fairness to other actors that might be possible (but it is not yet made explicit in the method), medium if it addresses the issue explicitly but qualitatively, and high if it addresses the issue both explicitly and quantitatively.

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2.12 Scientific and Mathematical Generality A method is rated NA if it does not involve problem analysis, low if it does not involve any mathematics, medium if it involves mathematics that is not axiomatized, or, it involves multidimensional concepts that may be axiomatized differently by different researchers leading to a diversity of theorems, high if it is axiomatized with more or less unified conceptualization (but its generalization has considerable mathematical rigor), and very high if its theorems are axiomatized and generalizable in a natural and less taxing way by not requiring many new assumptions.

2.13 Applicability to Intangibles A method is rated NA if it does not involve problem analysis, low if it does not involve quantification of intangibles, or, simply assigns arbitrary ordinal numbers to intangibles, medium if it involves measuring intangibles on an interval or a ratio scale or an absolute (but must be represented by tangibles or intensities in absolute terms with no assigned priority, high if it involves measuring intangibles on an interval or a ratio scale or an absolute, but must be represented by tangibles or intensities in absolute terms with assigned priority), and very high if its measurement is applicable to intangibles and gives an assessment of their relative importance, both absolutely or relatively, as the user wishes.

2.14 Psychophysical Applicability A method is rated NA if it does not involve problem analysis, low if it does not address issues of stimulus-response so it appears relevant and not arbitrary, medium if it could but requires a complex model that may not be practical to develop or to apply, and high if it is psychophysically applicable.

2.15 Applicability to Conflict Resolution A method must have an approach and perhaps also normative standards for best solution of a group conflict that is understandable, acceptable, practical, flexible, and has been demonstrated to work well in practice. Such a method would be rated high. However, secrecy makes it hard to use such an approach in a clear step-bystep fashion, and hence people often resort to less structured and less explicit methods. For this reason, an analytical method for dealing with conflict resolution is rated medium. A method that enables the conflicting parties to structure a comprehensive model and quantify the payoffs accurately is rated high.

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2.16 Validity of the Outcome (Prediction) A method is rated NA if it does not involve problem analysis, low if it uses ordinal measurement with no structural representation of a problem, medium if it uses cardinal measurement, but its main concern is computation, or, if it uses ordinal measurement with some problem representation, or, if it provides a rigorous model without measurement, high if it uses cardinal measurement, but mathematical validity sets limits on the structural representation of a problem, and very high if it uses cardinal measurement and no theoretical limit with respect to the structural representation of the problem.

3 Group Decision Making Methods Couger (1995) provides a summary of most of the methods.

3.1 Structuring Analogy and attribute association are methods for gaining fresh perspective on a problem to create an alternative space from which meaningful and controllable distinct alternatives are likely to be identified. They involve the use of key words from the original formulation of a problem as the means to identify relations between the otherwise unrelated analogy/association and the original problem. Boundary examination is a conscious effort to openly challenge and restructure the underlying assumptions that prevent one from seeing a problem from a broad perspective. The progressive abstraction method increases problem abstraction implied in the goal step by step. This, along with the first, differs in technique but their purpose is so similar that we do not consider them as different methods. Brainstorming (Osborne 1957) is based on the premise that deferred judgments enhance creativity and that oral communication diminishes it. Its modification includes, e.g., brainwriting (generating ideas in writing), bug list and negative brainstorming (generating complaints to identify weaknesses), the Crawford blue slip method (independently brainstorms in response to a number of questions that are related to a problem), and discussion among group participants as long as it is not judgmental. Morphological connection is an attempt to broaden the space of alternatives not through problem abstraction, but from different combinations of problem attributes as in a hierarchy. Despite what the term may imply, this method is not designed for connecting or structuring different ideas related to a problem to make a decision. Why-What’s Stopping is proposed for formulating ill-structured problems (Basadur et al. 1994). It consists of a series of diverging and converging ideas by

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seeking responses to the questions: ‘‘How might we…’’ (to elicit ideas on alternative solutions) ‘‘What’s stopping us…’’ (to provide narrower sub-problems for each response to the ‘‘How might we…’’ query), and ‘‘Why would we need to…’’ (to ensure that we work on the right problem as stated in the ‘‘How might we…’’ query). The outcome of this process is a big picture of a problem, indicating relationships among problems and sub-problems; to help decision makers select the most meaningful problem area to work on.

3.2 Ordering and Ranking Voting, as has been discussed at length in the previous chapters, elicits ordinal judgments and mathematically aggregates them into a group judgment. It is considered as a single criterion analysis since the individuals compare alternatives directly. For our purpose, interaction among members is considered irrelevant. The Nominal Group Technique (NGT) (Delbecq et al. 1975) takes advantage of the positive aspects of brainstorming and brainwriting and structured communication that improves alignment of group members’ perception of the problem without working towards consensus. The Delphi method (Turoff 1970; Linstone and Turoff 1975; Gustafson et al. 1973) is similar to NGT except that the group members do not meet face to face. A great deal of preparation is required due to the nature of written communication. Disjointed incrementalism is a method to select the best policy based on its incremental consequences. This method was proposed to deal with complex policy decisions, typically in the government, in which a holistic approach for policy decisions is either impossible or impractical. It has been argued that muddling through is a science. Matrix evaluations refer to methods for presenting information to facilitate the evaluation of alternatives. It may describe factors and sub-factors involved in a problem with their ranking scores, or by providing the relative overall positions of alternatives in a multidimensional space. For example, various company products may be evaluated with respect to their market share and growth (BCG matrix) or various organizational improvements with respect to their importance and imminence (Camillus and Datta 1991). These methods, however, do not provide a methodological way to arrive at a decision. Goal programming is an approach to optimize a set of objective functions subject to constraints. However, it does not necessarily suggest decisions that optimize the objective functions (Ching and Ming 1987). It only yields decisions that ‘‘satisfice’’ (Simon 1957). The outcome is perceived as indicating trade offs that need to be made in terms of reducing a certain objective in return for an increase in some other objectives. Conjoint measurement is concerned with predicting the values of a dependent variable by combining a set of independent variables in some functional form. The coefficients of the function are usually estimated by regression techniques.

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A conjoint analysis measure has been suggested for use as a numerical basis for estimating the priorities of a goal-programming problem (O’Leary and O’Leary 1984). The concept of outranking was developed by Bernard Roy based on Multiattribute Utility Theory (MAUT) principles with the motivation to improve efficiency without affecting the outcome while considering less information. The idea is to see whether there are enough arguments to decide that an alternative Ai is at least as good as Aj, while there is no essential reason to refute that statement. Researchers in this area have worked toward the satisfactory axiomatization of the concept, in which criterion prioritization has been their major preoccupation (Roy and Bouyssau 1985; Vincke 1982). In the meantime, ten different methods have been developed to apply the concept. They differ in how the reason is formalized that leads to refuting the statement that Ai is at least as good as Aj, the type of decision problem (choice, scoring, or ranking) they address, the preference model they adopt (whether or not Weber-Fechner’s psychophysical law is to be embraced), whether or not the concept of probability is used, and the way criteria weights are determined. A concern has been voiced about how the method combines concordance and discordance that leaves one in doubt about the accuracy of its outcome.

3.3 Structuring and Measuring Bayesian analysis is a popular statistical decision making process which provides a paradigm for updating information in the form of probabilities. It is based on the premise that decisions involving uncertainty can only be made with the aid of information about the uncertain environment in which the decision is made. Bayesian theory updates information by using Bayesian theorem, a statement in conditional probabilities relating causes (states of nature) to outcomes. Outcomes are results of experiments used to uncover the causes. Bayesian theory revises initial or prior probabilities of causes, known from a large sample of a population, into posterior probabilities by using the outcome of an experiment or test with a certain probability of success. Prior probabilities are obtained either subjectively or empirically by sampling the frequency of occurrence of a cause in a population. Posterior probabilities are those based on the prior probabilities and on both the outcome of the experiment and on the observed reliability of that experiment. Bayesian analysis often makes heavy use of probability trees and that is why we have included them in this section. Multiattribute Utility (Value) Theory (MAUT/MAVT) (Luce and Suppes 1964) attempts to maximize a decision maker’s utility (under uncertainty) or value (preference) which is represented by a function that maps an object measured on a ratio scale into the decision maker’s utility or value relations. The function is constructed by, for example in the case of MAUT, asking lottery questions involving probability to articulate decision makers’ value trade-offs among the

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conflicting attributes. Preferences are used in MAVT. The functional representation of a multicriteria problem is obtained by aggregating the different single attribute functions, each representing a different attribute, by taking into consideration the relative weights of the attributes. The use of objective measurement leads to a complex functional representation if the Weber–Fechner law is to be embraced. The law suggests that the relation between a stimulus and an individual’s response is not as smooth as may be indicated by a continuous utility function. Maintaining that ‘‘it is now firmly established that expected utility (EU) theory and subjective expected utility (SEU) theory are descriptively invalid,’’ Miyamoto (1992) proposes a generic utility theory, designed as a general framework for descriptive multiattribute utility modeling. A group utility or value function that takes the diversified evaluations of its individual members into consideration, can be obtained either by aggregating individual functions or by partial identification of the group function (Seo 1985). Recent versions of MAUT/ MAVT have tended to look at the broad complexity of a problem within a structured framework and not simply as criteria and alternatives. The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP) (Saaty 1990, 2001) use both paired comparisons and ratings to prioritize or rate alternatives one by one on a set of criteria arranged in a hierarchic or in a network structure in the process of developing measurements for intangibles. Tangibles are dealt with directly by using their measurements or indirectly through preference. Priorities are obtained as the principal right eigenvector of a paired comparison reciprocal matrix whose entries belong to a fundamental scale used to express the dominance of each member of a ‘‘homogeneous’’ pair over the other with respect to a common property or criterion. The priorities with respect to each criterion are weighted by the priority of their parent criterion and appropriately summed to obtain the overall priority of each alternative. In more recent extensions of the subject (Saaty 2001) has used benefits, opportunities, costs and risks to analyze decisions and then combine the outcome for the overall outcome for the alternatives. In the AHP/ANP rank preservation and reversal (subjects of considerable debate in the literature early in the history of the method) are allowed to take place depending on whether the alternatives are assumed to be independent both functionally and structurally or not. Paired comparisons always imply structural dependence among the alternatives according to quality and number present. By using the ratings mode or by creating an ideal and preserving that ideal in making comparisons after the initial set of alternatives, the AHP/ANP always preserves rank when it is assumed that the criteria are independent from the alternatives and alternatives are independent among themselves. The ANP measures and combines the outcome of influence with respect to various criteria: economic, social, political and the like known as control criteria and combines the outcomes for the alternatives by prioritizing the importance of these criteria. Saaty (2003) has generalized AHP/ANP to capture dynamic judgments both mathematically and by using scenarios to project ahead.

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4 Evaluation of the Methods on the Criteria Comparison of the group decision-making methods is presented in Table 1.

4.1 Group Maintenance: Leadership Effectiveness Analogy/association, brainstorming, morphological connection, voting, goal programming, and conjoint analysis are rated low because the methods are highly technical. Boundary examination, why-what’s stopping, NGT, Delphi, disjointed incrementalism, matrix evaluation, outranking, Bayesian analysis and MAUT/ MAVT are rated medium because they provide nothing more than simple structures to assist a facilitator. AHP is rated high because it provides collaborative tools to enhance communication effectiveness, inconsistency and incompatibility measures that provide feedback to the group members to ensure validity of the outcome, structure to facilitate task division, and the means to balance consensus and voting to obtain group judgments.

4.2 Group Maintenance: Learning Brainstorming, voting, goal programming, and conjoint analysis are rated low because they involve highly technical knowledge. Brainstorming excludes member interaction because of its requirement that there be no discussion or criticism of ideas proposed. Analogy/association, boundary examination, morphological connection, why-what’s stopping, NGT, Delphi, and matrix evaluation are rated medium because they improve understanding of the problem, but actions to take from them may not be readily clear. Disjointed incrementalism, outranking, Bayesian analysis and MAUT/MAVT are rated high because it is assumed that their outcomes provide learning that leads to action. Research indicates, however, that despite group satisfaction, study participants rated the combination of NGT and MAUT as low in improving knowledge about the content of the issue (Thomas et al. 1989). AHP is rated very high because it provides a highly summarized description of the problem that facilitates learning beyond membership of the group. Participants in an experimental study ranked the AHP as the least difficult and the most trustworthy method among those studied (Schoemaker and Waid 1982). It is assumed that the easier to apply and the more trustworthy a method is, the more one learns from its application.

Structuring Analogy, Association Boundary Examination Brainstorming/ Brainwriting Morphological Connection Why-what’s stopping Ordering and ranking Voting Nominal group Technique Delphi Disjointed Incrementalism Matrix evaluation Goal programming Conjoint analysis Outranking

Methods

Medium Medium Low Medium Medium Low Medium Medium High Medium Low Low High

Low Medium Low

Low

Medium

Low Medium

Medium Medium

Medium Low Low Medium

Medium Medium Medium Medium

Medium Medium

NA Medium

High

High

Medium High Low

Low Low Low High

High Medium

NA High

Very high

Very high

Low Low Medium

Development of alternatives

Scope

Leadership effectiveness

Learning

Problem abstraction

Group maintences

Table 1 Comparison of group decision making methods

High High Low High

Low High

Low Low

High

NA

NA NA NA

Breadth

Structure

Low Low Low Low

Low Low

Low Low

High

NA

NA NA NA

Depth

Medium Very high Very high Medium

Low Medium

Low Low

NA

NA

NA NA NA

Faithfulness of judgments

Analysis

Medium Medium Medium High

Low Medium

Low Low

NA

NA

NA NA NA

(continued)

Breadth and depth of analysis (what if)

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Structuring Analogy, association Boundary examination Brainstorming/ Brainwriting Morphological connection Why-what’s stopping

Methods

Structuring and measuring Bayesian analysis MAUT/MAVT ANP ANP

Table 1 (continued) Methods

High High Very high Very high

Learning

Medium Medium Medium Medium

Scope

Low High High High

Breadth

Structure

Low Low High Very high

Depth

Applicability, validity, and truthfulness

Low High Very high Very high

Development of alternatives

Problem abstraction

Very high High Very high Very high

Faithfulness of judgments

Analysis

Medium High Very high Very high

Breadth and depth of analysis (what if)

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA‘

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

NA

(continued)

Consideration Cardinal separation Prioritizing Scientific Applicability Psychophysical Applicability Validity group members of other actors and mathematical to intangibles applicability of alternatives to conflicy of the outcome and stakeholders geneality resolution (prediction)

Fairness

Medium Medium High High

Leadership effectiveness

Group maintences

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NA not applicable

Ordering and ranking Voting Nominal group technique Delphi Disjointed incrementalism Matrix evaluation Goal programming Conjoint Analysis outranking Structuring and measuring Bayesian analysis MAUT/MAVT ANP ANP

Applicability, validity, and truthfulness

Low NA

NA NA

NA NA NA High

NA High Very high Very high

Low NA

NA NA

NA High High High

High High High Very high

Low Medium High High

Medium Low NA Low

NA Medium

NA NA

High High High High

Low Medium Medium Medium

Medium Low

Medium Medium

Medium Medium Very high Very high

Low Medium Medium Medium

NA Low

NA NA

Low Medium Very high Very high

Low NA NA Medium

NA Low

NA NA

NA Medium High High

NA NA NA NA

NA NA

NA NA

Medium Medium High High

Medium Low Low Medium

Low Medium

Low Low

Consideration Scientific Cardinal separation Prioritizing Applicability Psychophysical Applicability Validity to conflicy of the outcome group members of other actors and mathematical to intangibles applicability of alternatives resolution and stakeholders geneality (prediction)

Table 1 (continued) Methods Fairness

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4.3 Problem Abstraction: Scope Voting is rated NA because a group does not generally generate alternatives, and thus broaden the scope, but is somehow given a set of alternatives. Brainstorming does not involve a specific technique to enhance problem abstraction and does not involve problem analysis, and so it is rated low. The use of key words from the original formulation of a problem in analogy and attribute association, which ensures some relations between the analogy or association problem with the original problem, at the same time sets perceptual boundaries. For example, an analogy to a difficulty is usually another difficulty (as opposed to an opportunity) and a spatial problem is likely to generate attributes that direct thinking to increasing the productivity of the space given the same demand, rather than reducing the demand itself. For this reason, these methods are ranked medium. Nominal Group Technique and Delphi are also rated medium because they include careful preparation of a questionnaire for the group to respond to which implies the development of problem abstraction. Disjointed incrementalism, matrix evaluation, goal programming, conjoint analysis, outranking, Bayesian analysis and MAUT/MAVT, and AHP/ANP do not involve a technique to broaden problem abstraction, but since analysis enhances problem abstraction, they are rated medium. Also outranking, Bayesian analysis, MAUT/MAVT, and AHP/ANP are rated medium because they are assumed to apply techniques such as NGT or Delphi that are rated medium. Morphological analysis is rated high because of its systematic search for combinations of attributes that produce candidates for alternatives. Why-what’s stopping is also rated high because its why’s questions uncover the assumptions underlying the difficulties in implementing the suggested solutions identified by the what’s (how’s) questions. Structuring the responses to the repeated questions provides highly comprehensive relationships among problems, subproblems, and alternative courses of action. Boundary examination systematically challenges the underlying assumptions regarding the problem, hence it is also rated high.

4.4 Problem Abstraction: Development of Alternatives Analogy and attribute association, boundary examination, matrix evaluation, goal programming, conjoint analysis and Bayesian analysis are rated low because identifying alternatives is not an explicit part of the method. Brainstorming/ brainwriting is rated medium because it ensures a free-wheeling environment but does nothing to take advantage of the positive aspects of interaction among group members. This method assumes that an alternative ranked high by the group is the most relevant solution to the problem, which may not be generally true because the group does not get to bring out possible disadvantages to the suggested alternatives. This weakness is inherent in brainstorming as well as in its modifications,

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e.g., brainwriting (generating ideas in writing), bug list and negative brainstorming (generating complaints to identify weaknesses). Crawford’s blue slip method (independently brainstorming in response to a number of questions that are related to a problem) does not tell one how to organize the information. Brainstorming addresses the negative aspect of communication by removing interaction from the decision process, at the cost of taking advantage of its positive aspects. This may be the reason why this popular method is observed as the least effective technique (Couger 1995). Disjointed incrementalism is also rated medium, but because it generates incremental alternatives rather than distinct ones. Nominal Group Technique (NGT) and Delphi are rated high because a certain degree of alignment of group member’s perceptions takes place. Outranking and MAUT/MAVT are also rated high, the same as NGT and Delphi, because the complexity of the problem approached using these methods is assumed to require an application of either one of the two alternative generating methods. Morphological connection is mostly useful for new product or new system development, and is rated very high under development of alternatives. Why-what’s stopping is also rated very high because the outcome of this method is a highly comprehensive view of the problem and its subproblems, with alternative courses of action included. One potential problem may be that presenting such a broad and detailed analysis may be quite a challenge. AHP is rated very high because, although it may begin with brainstorming as to what alternatives should be located at the bottom of the hierarchy, the level of problem abstraction represented by its hierarchy of criteria provides the opportunity to question whether or not the alternatives that are known indicate appropriate breadth for that level of abstraction.

4.5 Structure: Breadth This indicator does not apply to analogy/association, boundary examination, brainstorming/brainwriting, and morphological connection, voting, conjoint analysis and Bayesian analysis. NGT and Delphi are rated low because they are direct comparison methods. Why-what’s stopping, disjointed incrementalism, matrix evaluation, outranking, MAUT/MAVT, and AHP are rated high because they do not limit the number of criteria or factors considered in the analysis.

4.6 Structure: Depth This indicator does not apply to analogy/association, boundary examination, brainstorming/brainwriting, morphological connection, voting, conjoint analysis and Bayesian analysis. NGT and Delphi are rated low because they are direct comparison methods. Lack of measurement and of theoretical foundation for disjointed incrementalism and matrix evaluation prevent them from constructing a

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deep structure, hence they are rated low. Goal programming, outranking, and older MAUT are rated low because they have no provision for subcriteria. Why-what’s stopping and AHP are rated high because they do not limit the level of detail of the analysis with respect to breaking down criteria into subcriteria, sub-subcriteria and so on.

4.7 Analysis: Faithfulness of Judgments This indicator, and all others here, do not apply to analogy/association, boundary examination, brainstorming/brainwriting, morphological connection, and whywhat’s stopping. NGT and Delphi include a voting process to determine which alternative is preferred by the majority of the group members. However, there is an opportunity to use them together with a ratio or an absolute scale evaluation method like the AHP. Voting is rated low because it uses an ordinal scale. Disjointed incrementalism, matrix evaluation, and outranking are rated medium because they involve assigning numbers which can be assumed to represent intensity of importance better than the ordinal rating of voting, for example. MAUT/MAVT is rated high because intensity of preference is derived from lottery judgments which are once removed from direct elicitation of preferences, and AHP is rated very high because it elicits elementary judgments.

4.8 Breadth and Depth of Analysis (Analysis) Voting is rated low because it involves judgment, but not analysis. Disjointed incrementalism, matrix evaluation, goal programming, conjoint analysis and Bayesian analysis are rated medium because they are structurally constrained. MAUT/MAVT is rated high because they provide more structural flexibility but it is difficult to go back and review previous analysis. The AHP is rated very high because its structural flexibility facilitates in-depth analysis of a problem. It also provides inconsistency and incompatibility measures to indicate if some improvement in judgments, and some effort to align perceptions among group members are required. Its supporting software provides the information as to where the sources of inconsistency and incompatibility are.

4.9 Fairness: Cardinal Separation of Alternatives This indicator is applicable only to voting, outranking, MAUT/MAVT, and AHP. Voting is rated low because it uses an ordinal scale, and the others are rated high because they use cardinal scales. ANP is rated very high because feedback

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improves accuracy of the outcome. Arrow’s theorem indicates that any ordinal preference relation, be it expressed as a set of pairwise comparisons or point allocations, does not treat the alternatives fairly.

4.10 Fairness: Prioritizing Group Members This indicator is also applicable only to voting, outranking, MAUT/MAVT, and AHP/ANP. Voting is rated low because fairness is operationalized using head counting with no regard to intensity of preference, which has been argued as unsatisfactory (Dummett 1984). Outranking and MAUT/MAVT treat individual members of the group equally. They may in fact, implicitly give them unequal weights, as for example, by giving the boss’s opinion greater accord than that of other members of the group in constructing their measures, but the lack of method requires that the relative weights can only be assigned rather arbitrarily. Hence they are rated high. With the AHP/ANP, it is at the decision-maker’s discretion to determine what concept of fairness is appropriate, and hence, they are rated very high. A hierarchy can be structured, with the different individuals at the bottom of the hierarchy. The criteria levels may include area of responsibilities or expertise that can be used to prioritize the individuals.

4.11 Fairness: Consideration of Other Actors and Stakeholders This indicator is not applicable to analogy/association, boundary examination, brainstorming/brainwriting and morphological connection because they do not involve problem analysis. It is unlikely that this indicator would be applicable to Bayesian analysis because of its complex cause-effect relationship with the states of nature, hence it is rated low. Conjoint analysis is rated low because it may be possible for a creative user to represent other actor’s concerns in its model. NGT and Delphi are rated low because they do not make explicit this concern, which might be made implicit by individual members of the group. Matrix evaluation is rated low because of its highly constrained structural representation and nonquantifiable analysis. Outranking is rated low because it obtains a decision with incomplete information, and its theoretical foundation is not yet settled even for the most fundamental issues, making it unlikely that this concern would be addressed and settled once and for all. MAUT/MAVT is rated low because, although it may incorporate this concern as one of its criteria, its limited structural representation makes it difficult to address the possible diversity of actors. Whywhat’s stopping and disjointed incrementalism may address the issue explicitly, but qualitatively, and are rated medium. It appears that the AHP is the only method that facilitates for a group to explicitly include other actor’s concerns in detail as parts of the problem structure, and quantify them, hence it is rated high.

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4.12 Scientific and Mathematical Generality This indicator is not applied to analogy/association, boundary examination, brainstorming/brainwriting, morphological connection, why-what’s stopping, NGT, Delphi, because they do not involve problem analysis. Disjointed incrementalism and matrix evaluation are rated low because they do not involve mathematics. Voting is rated medium because there are many procedures proposed for aggregating ordinal votes, with or without axiomatization. The ones that are axiomatized are usually mathematically complex to deal with the impossibility inherent in ordinal group aggregation. Goal programming and conjoint analysis are rated medium because they do not involve axiomatization. Outranking is rated medium because it is not yet axiomatized. Bayesian Analysis, and MAUT/MAVT are rated high because they are axiomatically solid but their generalization’s have considerable mathematical difficulties. The AHP is rated very high because its mathematical foundation is generalizable without additional assumptions.

4.13 Applicability to Intangibles This indicator is not applied to analogy/association, boundary examination, brainstorming/brainwriting, morphological connection, why-what’s stopping, NGT, Delphi and voting because they do not involve problem analysis. Disjointed incrementalism and matrix evaluation are qualitative methods and are rated low. Goal programming and conjoint analysis may incorporate intangibles in their model, but they must be represented by tangibles with absolute measurement, hence they are rated medium. Outranking and MAUT/MAVT are rated medium because they must use absolute measurement. Medium is probably a generous judgment because MAUT is riddled with unresolved paradoxes and problems and ‘‘the standard theory is being challenged on several grounds from both within and outside economics (Machina 1987).’’ Bayesian analysis deals with the probability of events, and is rated medium because it often contrives and guesses at its prior probabilities without adequate scientific justification. AHP is rated very high because its fundamental measurement ensures its applicability to intangibles naturally, that gives discretion to the user whether to use relative, ideal or absolute measurement (Saaty 1990).

4.14 Psychophysical Applicability Psychophysical applicability does not apply to voting, goal programming and conjoint analysis. Disjointed incrementalism, matrix evaluation and Bayesian analysis are rated low because psychophysical law is irrelevant. Outranking and

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MAUT/MAVT are rated medium because they generally do not incorporate the psychophysical phenomenon. If they do, it would complicate the mathematical representation of the theory considerably. AHP is rated high because in many examples, its priority scales approach has produced measurement of responses to physical stimuli that corresponded closely to the normalized values of physical measurement of those stimuli in the homogeneous ranges in which they were examined.

4.15 Applicability to Conflict Resolution There are only two theories applicable to conflict resolution, game theory that is based on the utility theory, and the AHP/ANP. AHP/ANP is rated high because it allows a wide range of structure from a simple one to a set of benefits-opportunities-costs-risks models with feedback for improvements.

4.16 Validity of the Outcome (What If) This indicator is not applied to analogy/association, boundary examination, brainstorming/brainwriting, morphological connection, why-what’s stopping, NGT and Delphi because they do not involve problem analysis. Voting is rated low because it uses ordinal measurement with no problem representation, Disjointed incrementalism and matrix evaluation are rated medium because they are limited in terms of measurement and model representation, Goal programming, conjoint analysis, and Bayesian analysis are rated medium because their main concern is with computation, not with problem representation. Outranking and MAUT/MAVT are rated medium because they use cardinal measurement with a relatively simplified model representation. AHP is rated high because its reliance on absolute scales derived from paired comparisons, enabling one to model a problem by ordering its elements and levels in a fine, structured way to legitimize the meaningfulness of the comparisons, and also because different ratio scales can be multiplied and divided to obtain an outcome from hierarchies of benefits, costs, risks, and opportunities. Research indicates that sometimes a method does not perform as intended. For example, instead of directing decision makers to profitable investment, a series of experiments indicate that the use of the Boston Consulting Group (BCG) matrix increases the subject’s likelihood of selecting less profitable investment (Armstrong and Brodie 1994) due to misuse of the method (Wensley 1994).

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5 Conclusion This chapter has brought many criteria and many methods under one umbrella. We believe that our schematization is a good start and may eventually be improved upon in subsequent revisions and extensions of the criteria used and in debating the importance of these criteria and the accuracy with which they are used to evaluate the methods of MCDM.

References Argyris, C. (1977, Sept-Oct). Double loop learning in organizations. Harvard Business Review. 115–125. Argyris, C. (1990). Integrating the Individual and the Organization. New York: John Wiley and Sons. Armstrong, J. S. & Brodie R. J. (1994). Effects of portfolio planning methods on decision making: experimental results. International Journal of Research in Marketing 11, 1, 73–84. Basadur, M., Ellspermann, S. J. & Evans, G. W. (1994). A new methodology for formulating illstructured problems. Omega. (22)6. 627–645. Brightman, H. J. (1980). Problem Solving: A logical and creative approach, Business Publishing Division, College of Business Administration, Georgia State University, Atlanta, Georgia. Brightman, H. J. (1988). Group Problem Solving: An improved managerial approach. Atlanta, GA: Business Publishing Division, Georgia State University. Camillus, J. C. & Datta, D. K. (1991, April). Managing strategic issues in a turbulent environment. Long Range Planning, (24)2. 67–74. Ching, Lai Wang and Ming Jeng Lin. (1987). Group Decision Making under Multiple Criteria: Methods and Applications (Lecture Notes in Economics and Mathematical Systems. no.281). Beckmann, M. & Krelle, W. (eds.). Springer-Verlag. Corner, J., Buchanan, J. & Henig, M. (2001, May-June). Dynamic Decision Problem Structuring. Journal of Multi-Criteria Decision Analysis. 10(3). Couger, J. D. (1995). Creative Problem Solving and Opportunity Finding. Boyd & Fraser Publishing Company, An International Thomson Publishing Company. Da Costa, P.C.G. & Buede D.M (2000). Dynamic decision making: a comparison of approaches. Journal of Multi-criteria Decision Analysis 6, 6, 243–262. Delbecq, A. l., Van de Ven, A. H. & Gustafson, D. H. (1975). Group Techniques for Program Planning: a guide to nominal group and delphi process. Scott, Foresman and Company. Dummett, M. (1984). Voting Procedures. Clarendon Press. Fiedler, F. E. (1973). The trouble with leadership is that it doesn’t train leaders. Psychology Today. 92. 23–29. Gustafson, D. H., Shukla, R. M., Delbecq, A. L. & Walster, G. W. (1973). A comparative study of differences in subjective likelihood estimates made by individuals, interacting groups, Delphi groups, and Nominal groups. Organizational Behavior and Human Performance. 9. 280–291. Larichev, Oleg I. & Brown, Rex V. (2000). Numerical and Verbal Decision Analysis: Comparison on Practical Cases. Multi-Criteria Decision Analysis. Vol. 9, Issue 6. Nov. 2000. Lewin, K., Lippitt, R. & White, R. K. (1939). Patterns of aggressive behavior in experimentally created ‘‘social climate. Journal of Social Psychology. 10. 271–299. Linstone, H. A. & Turoff, M. (eds.). (1975). The Delphi Method: Techniques and applications. Reading, Mass: Addison-Wesley Pub. Co., Advanced Book Program. Luce, R.D. & Suppes, P. (1964). Preference, Utility and Subjective Probability.’’ In Handbook of Mathematical Psychology Vol. 3, New York. Wiley.

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Machina M. J. (1987, Summer). Choice under uncertainty: Problems solved and unsolved. Economic Perspectives. (1)1. 121–154. Miyamoto, J. M. (1992). Generic analysis of utility models, in Edwards, N. (ed.). Utility Theories: Measurements and Applications. Kluwer Academic Publishers. O’Leary, D. H. & O’Leary, J. H. (1984). The use of conjoint analysis in the determination of goal programming weights for a decision support system, in Y. Y. Haimes and Chankong, V. (eds.) Decision Making with Multiple Objectives. Springer-Verlag. Osborne, A. F. (1957). Applied Imagination. Scribners. Pascale, R. T. (1991, March), ‘‘The Two Faces of Learning,’’ Modern Office Technology, (36)3, 14, 16. Reagan-Cirincione, P. (1994). Improving the accuracy of group judgment: A process intervention combining group facilitation, social judgment analysis, and information technology. Organizational Behavior and Human Decision Processes. 58. 246–270. Roy, B & Bouyssau, D. (1985). Comparison of multiattribute utility and an outranking model applied to a nuclear power plant siting example. Haimes and Chankong (eds.). Decision Making with Multiple Objectives. Springer-Verlag. Saaty, T. L. (1990). The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, and (2001). Decision Making with Dependence and Feedback: The Analytic Network Process. Pittsburgh, PA: RWS Publications. Saaty, T. L. (2001). The Analytic Network Process. Pittsburgh, PA, RWS Publications. Saaty, T. L. (2003). Time Dependent Decision-Making; Dynamic Priorities In AHP/ANP Generalizing From Points To Functions And From Real To Complex Variables. Proceedings of the 7th International Symposium on the Analytic Hierarchy Process, Bali, Indonesia. Schoemaker, P. J. H. and Waid, C. C. (1982, February). An experimental comparison of different approaches to determining weights in additive utility models. Management Science. (28)2. 182–196. Seo, F. (1985). Multiattribute utility analysis and collective choice: A methodological review. Haimes and Chankong (eds.). Decision Making with Multiple Objectives. Springer-Verlag. Simon, H. (1957). Models of Man. New York: John Wiley. Svenson, O. (1998, Nov.). Letter to the Editor. Multi-criteria Decision Aids and Human Decision making: Two Worlds?. Journal of Multi-Criteria Decision Analysis. 7(6). Swap, W.C. & Associates (1984). Group Decision Making. Beverly Hills: Sage Publications. Thomas, J. B., McDaniel, Jr., & Dooris, M. J. (1989). Strategic issue analysis: NGT ? decision analysis for resolving strategic issues. The Journal of Applied Behavioral Science. (25)2. 189–200. Turoff, M. (1970). The design of a policy Delphi. Technological Forecasting and Social Change. 2. Urli, B. & Nadeau, R. (1999, Jan.). Evolution of Multi-criteria Analysis: A Scientometric Analysis. Journal of Multi-Criteria Decision Analysis. 8(1). Vincke, P. (1982). Multicriteria Decision Aid. New York: John Wiley and Sons. Wensley, R. (1994, January). Making better decisions. International Journal of Research in Marketing. (11)1. 85–90. Wierzbicki, A. (1997, March). On the Role of Intuition in Decision Making and Some ways of Multicriteria Aid of Intuition. Journal of Multi-Criteria Decision Analysis. 6(2).

Chapter 14

An Innovative Orders-of-Magnitude Approach to AHP-Based Multicriteria Decision Making: Prioritizing Divergent Intangible Humane Acts

1 Introduction The past we inherit; the future we create, the saying goes. To create a credible future that is founded on our global values and priorities we need to learn how to deal with the immense variety of factors and with the expanse of the many dimensions of this variety. Our progress depends on our ability to make effective decisions that depend on one another in their causes and effects, on inputs and outputs and on being able to reach out to the smallest and largest causes and effects of which we are aware. Phenomena we are creating now that will have significant influence on the future are already happening. We are currently witnessing intersecting revolutions in biotechnology, nanotechnology, molecular electronics, computation, artificial intelligence, pattern recognition, virtual reality, human brain reverse engineering, brain augmentation and robotics. Undeniably, knowledge and technology have in general expanded consciousness far beyond what we could imagine only a little while ago, and such knowledge and information would ultimately alter the nature of what it means to be human. To date our decision making has not attained its maximum potential and success, especially those decisions that require a comprehensive global view (Ozdemir and Saaty 2006). One reason may be because such decisions are many and diverse, and are separated in time and space. Their interactions and their consequences are hard to contemplate concurrently, as exemplified by the excerpt from the Economist (Oct 9, 2010, p. 30) with regard to the very slow recovery from the greatest economic recession since the great depression of the 1930s: ‘‘The economic case for a growth strategy that combines hefty fiscal cuts with timid structural reform is not obvious especially when private demand is likely to stay weak. In the long run bold productivity enhancing reforms would do more….’’ The sheer volume of information on the Internet shows that we all need to accelerate the process of learning to become more creative and have courage to use our creativity in many different sometimes wild and fast moving technological ways. The renowned futurist Kurzweil (2005) writes that ‘‘technological change is exponential, contrary to the common-sense ‘‘intuitive linear’’ view. So our society T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_14,  Springer Science+Business Media New York 2013

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won’t experience 100 years of progress in the 21st century—it will be more like 20,000 years of progress (at today’s rate). The ‘‘returns’’, such as chip speed and cost-effectiveness, will also improve exponentially. There’s even exponential growth in the rate of exponential growth. Within a few decades, machine intelligence is likely to surpass human intelligence, leading to The Singularity—technological change so rapid and profound it represents a rupture in the fabric of human history. The implications include the merger of biological and nonbiological intelligence, immortal software-based humans, and ultra-high levels of intelligence that expand outward in the universe at the speed of light.’’ Knowledge in different fields must be creatively integrated and structured to facilitate making complex decisions that are interdependent (Saaty and Takizawa 1986). How do we prioritize the building blocks (Millet and Saaty 2000) whose importance will vary by many orders of magnitude? What we need is to learn about how to deal with the problem of the diversity of alternatives (and when needed also of criteria) that are too far flung to assign them numbers from a scale without a questionable outcome of priorities. We must compare them to determine their relative magnitudes. That is our concern for the rest of this paper. The wellknown hierarchical multi-criteria decision making aid—the Analytic Hierarchy Process (AHP) offers a practical tool for decision makers facing such prioritization problems. The AHP has been applied to diverse applications; see examples in Shang and Sueyoshi (1995), Sueyoshi et al. (2009), and Tjader et al. (2010). This research advances the current AHP literature (Saaty 1996, 2003) by addressing the need of prioritizing numerous alternatives of substantial heterogeneity. In what follows, we first discuss the need for considering many orders of magnitude difference in the priorities of decisions. Our main thrust is to develop an example based on the contribution of people to society, and on the need to reward some people with such recognition that today has no direct bearing on enhancing people’s economic wellbeing. Thus developing a way to evaluate the significance of all such acts looms high in these considerations. Criteria and alternatives are identified and then integrated in the improved AHP model in which priorities are developed for all acts, whose importance is eventually separated by ten orders of magnitude.

2 Decision Making Using the New Orders-of-Magnitude AHP Model There are many factors that influence outcomes in decision making and these factors may straddle the spectrum of possibilities from the very low to the very high priorities. We often impatiently assume that we can reduce the diversity of factors into only a few—what we at a given time consider to be the important ones. But in real life, there may be numerous not-so-important determinants of an outcome, and these low-priority determinants could be collectively very influential

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in shaping a decision. A serious weakness in decision making to date is the mixing and reduction of all factors into few that one habitually assumes to be the important ones. An essential difference between what we do in this paper and what one does using traditional measurement is that in the latter, in some way, a number from a scale is assigned to each element once and for all. In our case, measurements of objects are derived from gradual relative comparisons with respect to properties that can change from instant to instant as behavior often does, and also from problem to problem. Applying a once and for all measurement from a scale to properties that remain the same or about the same is justified for events in which the elements do not change their properties over time. However, this is not the way to do it in the measurement of multi-faceted (dynamic and transient) behavior. Thus unlike the use of traditional measurement, we need to derive measurements for not so durable objectives. As a consequence, solving a problem with relative measurement requires greater effort to lay out the structure and to perform relative measurement comparisons for that problem. One has to do much more thinking to make pairwise comparisons and justify that analysis than one does when one has readymade scales with arbitrary units used uniformly to measure everything. As in any physical science, the concern is that the resulting numbers do not correspond to some meaning for the contexts in which they are used, but need judgment by knowledgeable persons to interpret their significance. Interpretation of the meaning and significance of numbers is at the heart of all theories and formulas used in science. Thus science is subjective because it needs personal interpretation that also becomes group interpretation. This observation is particularly relevant for our consideration in this paper. Because multiple factors are often inhomogeneous (Saaty 1994a, b), it is essential to organize them carefully into different homogeneous clusters and then deal with the linkage among these clusters in the process of relating them and then deriving priorities for their measurement. As we shall see later, by using an example, we take the step to group the homogeneous activities first in separate clusters, and then prioritize them within each cluster and finally combine the different cluster measurements by using a pivot element from a cluster to an adjacent cluster. If the clusters are arranged in ascending order, when the priority derived for an element exceeds (is dominated by) the other elements by more than an order of magnitude, then that element is moved to the cluster that follows (precedes) the given cluster.

2.1 A New AHP Model for Comparing Heterogeneous Elements Traditional multi-criteria decision making methods evaluate all alternatives in a single level, which inadvertently restricts the simultaneous comparison of numerically heterogeneous alternatives. For dealing with the comparison of

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homogeneous elements, it is known that one cannot usually compare more than about seven homogeneous elements without increasing the overall inconsistency of the judgments. The scale used for comparing homogeneous elements in the AHP is restricted to the absolute numbers 1–9 and their reciprocals and perturbations when evaluating the relative importance of one element against another element (Saaty 1990a, b). When one has more than seven homogenous elements to compare, one links them with a common element that is called ‘‘a pivot’’, and uses its measurement in both clusters to combine the measurements in the two clusters. That is also what one does to extend the use of the scale for the measurement of elements in heterogeneous clusters. By grouping alternatives into different comparison matrices and linking them through pivot alternatives, numerous alternatives in different clusters are linked together through their priorities. As a simple example we compare a cherry tomato with a watermelon according to size as in Fig. 1. We use a process of clustering with a pivot from one cluster to an adjacent cluster that is one order of magnitude larger or smaller than the given cluster, and continue to use the 1–9 scale within each cluster to make the comparisons, and in doing that, the scale is extended as far out as desired. What determines the clusters is the proximity of the relative value of the priorities of the elements in each. Figure 2 shows the orders-of-magnitude AHP schema produced in the process. As usual, at the top of the model it includes a goal, followed with criteria and sub-criteria. In contrast with current AHP

.07 Unripe Cherry Tomato

.28 Small Green Tomato

.08 Lime

.22

.22 = 2.75 .08 2.75 × .65= 1.79

.10

.70 Honeydew

Grapefruit

.08 =1 .08 1x .65=.65

.65 Lime

.70 = 8.75 .08 8.75x.65 =5.69

.30

.60

Honeydew

Sugar Baby Watermelon

Oblong Watermelon

.10 =1 .10 1 × 5.69 = 5.69

.30 =3 .10 3× 5.6917.07

.60 =6 .10 6 × 5.6934.14

This means that 34.14/.07 = 487.7 unripe cherry tomatoes are equal to the oblong watermelon

Fig. 1 Clustering to compare non-homogeneous objects

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structures, in the second half of Fig. 2, the proposed AHP schema allows for multicluster of alternatives. If the priority of an alternative differs by an order of magnitude, it is moved to the appropriate cluster. To do that one simply compares it with the largest priority element in that cluster and if its priority is close in magnitude, it is kept in that cluster. Otherwise it is moved to a cluster below or above it. Note that many elements may be homogeneous but still need to be grouped in clusters to make the comparisons conform to the requirement of consistency. In general, hypothetical elements may have to be introduced to make the transition from cluster to cluster a well-designed operation. The entire process stretches the imagination to deal with magnitudes and dimensions. To address the difficulty of dealing with this subject, we elaborate the procedure of the proposed AHP model by using the example of generous and caring activities contributed by people to society. An interesting example can be found in comparing a small gesture of kindness with the large donations made by Bill Gates. To illustrate our model, we discuss the heterogeneous undertakings in the following section.

GOAL

Criteria

Sub-Criteria

… . Pivot

Pivot Alternatives A1

.

A2 A3 A4 A5 A6 A7

A7 A8 A9 A10 A11 A12 A13 .

. . A*

pivot A*=B1 B2 B3 B4 B5 B6 B7

B7 B8 B9 B10 B11 B12 B13 .

. . B*

pivot B*=C1 C2 C3 C4 C5 C6 C7 C7 C8 C9 C10 C11 C12 C13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . .

pivot Y*=Z1 Z2 Z3 Z4 Z5 Z6 Z7

. .

Z7 Z8 Z9 Z10 Z11 Z12 Z13 .

. C* . . . . . .

Z*

Fig. 2 The orders-of-magnitude AHP schema to mutli-criteria decision making: multi-level of criteria and sub-criteria, with multi-level of alternatives. Note The rightmost alternative with superscript ‘‘9’’ is the pivot alternative, which reappears as the first alternative in the next cluster

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3 The Importance of Valuing Activities Contributed by People Unemployment brings sharp decline in income and laid-off workers suffer the worst and join the ranks of the impoverished in negative economic climates. Economic suffering appears to be an inevitable consequence of economic cycles. It shows that a society focused on monetary value alone is not designed to ensure citizens’ happiness; happiness is not easily pursued by those who must worry about their next meal and about paying the rent and sending children to school. On the other hand, the unemployed have ample time and abilities to make contributions to enrich society. Society is shaped by numerous contributions and activities people make to enrich it, but currently there is a lack of an established means to recognize and include these contributions in a compensation system. Often, acts of helpfulness are rewarded with words of praise and gestures of appreciation, certificates and mementos, and sometimes with acclamation in the media. ‘‘Thank you’’ is often the only recognition and appreciation they receive. Doing favors inevitably involves time and labor. Under different circumstances, such effort is compensated with money. At times, the individuals who perform acts of kindness do not need monetary payment or recognition. But more often, the person doing a worthwhile favor is not so fortunate economically. Thus, an act of kindness may provide an opportunity for compensation, either directly from others or from society. Recognition of people’s good acts should put society at a higher level of sensitivity to individual needs. Many acts of kindness can be done by temporarily laid-off workers who are very eager to contribute to the society. This area of human activity has not been examined and worth study in the context of multi-criteria decision making.

3.1 Need Rating Intangible Contribution to Improve Life Quality The UN Human Development Program (Gaye 2007) reports that only half of the world’s time spent on ‘‘productive activities’’ was reported in the GDP. Meanwhile, numerous endeavors that are critical to the survival of modern society are unpaid. When only paid work is considered ‘‘real’’ work, the connective tissue that holds society together—trust, reciprocity, and civic engagement—are simply unaccounted for. We believe active contributions should earn contributors a new kind of credit, translatable to satisfying their basic needs and improving their wellbeing. Recognizing and rewarding people’s efforts with social units could also help society encourage more people to perform humane acts. The social units they earn might be exchanged for favors from others when the need arises. By assigning fair market values to benevolent acts, we foresee more people being motivated to contribute to society actively and more well-being created and devoted to the

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society. The potential monetary conversion scheme offers a promising way to motivate more people to commit and more research in this direction. Taking the economy of large unemployment as an opportunity to develop a more compassionate society would ensure that the world functions humanely beyond money and behaves consistently with cherished principles. The new system should explicitly include normative values—family, neighborhood, community, city, country, and the entire world which drives the creation of diverse intangible values. Compensating people for contributions that are not strictly economic but humane and intangible would benefit society. The proposed model can formally prioritize all criteria and activities in a scientific and systematic way. It determines the worth of the service people offer and the potential for exchange to enrich ordinary citizens’ life. Pursuit of happiness along with life and liberty are inalienable rights. Britain is planning to introduce a ‘‘happiness index’’ to measure the nation’s psychological and environmental wellbeing (Yahoo 2010), and employing a happiness index for future policy-making and prepare methods to assess the ‘‘general wellbeing’’. Canada and France are also taking on a similar initiative. Kostigen (2009) maintains that there are various reasons for happiness: health, welfare, prosperity, leisure, family, and social connections. In this paper, we look at activities from different angles and concentrate on existing acts that increase wellbeing of others. We are now facing a choice between a society where people accept some sacrifices for the common good or a divided society where groups focusing on protecting their own interests. Appeals to the common good are frequently heard when discussing business’ social responsibility, health care systems, environmental pollution, education, crime, and poverty (Velasquez et al. 1992). We believe that a community where people reach out and help each other would be a happier one.

3.2 On Quantifying the Relative Value of Altruistic Acts The idea of measuring the worth of intangible acts in relative terms is quite new. However, people’s activities vary with circumstances and do not have the permanence of objects manufactured by industries that consume resources in the form of materials and overheads. Therefore, we cannot hope to ascribe to them a constant (absolute) value, as we do with objects. We can only measure them in terms relative to: similar acts with which they are compared; the amount of effort and time needed to complete them; and, perhaps the impact they produce. Thus, we need to perform comparisons with a variety of other actions to develop value permanence for acts within a group of categorized situations. The question is: How to perform comparisons to produce meaningful and useful ways to measure intangibles and convert those measurements into social units or dollars? To derive the significance (priorities) of the benefits of intangibles that are important to people, we demonstrate the order-of-magnitude AHP model in a hierarchy where these factors are incorporated into a formal evaluation system. Our model will

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show that different types of service have different value. For that reason, the amount of ‘‘value’’ exchanged in any transaction should not be arbitrary or negotiable but carefully planned. Our model can help to (1) determine exchange standards for benevolent acts in more diverse communities where products or services may encompass a variety of skills, experience, training, equipment, or risk, and (2) reduce uncertainty in the evaluation process and outcome. In equilibrium, all prices are known to all traders, thus eliminating price uncertainty as a rationale for unacceptability in trade (Starr 1972). When a society suffers from severe recession or hyperinflations, and currency is unreliable, exchange provides an acceptable alternative to increase individual and community wellbeing. The proposed AHP model could help provide an objective worth and a common medium of exchange to store values. When benevolent activities and random acts of kindness are acknowledged, dormant social potential is awakened for further development. Historically, the multi-criteria facets of human activities have been difficult to quantify in objective terms. Our model which allows for the exchange of intangibles (social units) in the free market may help reduce the anguish of people who have little monetary wealth. We feel that it could also raise awareness of how to live an ‘‘affluent’’ life without money. Another reason we must create ‘‘social units’’ is because some people often feel unappreciated for all that they do and may in time feel unfairly treated for all the meaningful effort they provide, if society does not get around to recognize their contributions. There is of course the danger that people may collude to earn credit in a fraudulent way. Safeguards need to be examined following better understanding of the idea and of its implementation. Intangibles and their measurement are at the heart of all pursuit, especially socio-economic endeavors. Hubbard (2007) writes that it is important to develop a method to explain, measure, value, and manage intangibles. In the following section we explore a society’s valuation system where, besides currency, people may enumerate and acquire credits for their services.

3.3 Non-monetary Units Already Used in Parts of Our World A very useful alternative for the disadvantaged is to equate people’s acts into money as done in Yufuin, Japan. Yufuin has suffered economic difficulties with low-paying and seasonal tourism-related jobs. To resolve this predicament, residents print their own currency to solve a chronic yen-flow problem. Using the locally printed notes, yufu, residents enjoy their own wealth and are not subject to what the national government does. In addition the Yufu has been converted to the Yen through general agreement. Our model could give yufu scrip a publicly agreed-upon value when the pairwise comparisons are made through group decision making of that society. Residents of Yufuin could offer services to exchange for yufu freely. Villagers with little cash can trade labor for life’s necessities and improve living standard (Larimer 2006).

3 The Importance of Valuing Activities Contributed by People

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Another example is Local Exchange Trading Systems (LETS 2011). LETS was established in 1983 by Michael Linton in British Columbia, Canada. It is a local, non-profit exchange network where goods and services are exchanged without using national currency. Members in LETS earn credits from any member and spend them with anyone else in the system. An individual may work on job A for person X and spend it later on job B with person Y. Under such a system, people can build houses using LETS in place of a bank mortgage, freeing owners from onerous interest payments. LETS revitalizes communities by allowing individuals, small businesses, local and voluntary groups to cooperate and to extend purchasing power. It stimulates the economies of financially depressed community that have goods and services, but scarce of currency. LETS are also present in South Africa, New Zealand, Australia, Israel, USA, Norway, United Kingdom, Europe, Japan, South Korea. The AHP model proposed in the paper could be applied to Yufuin and LETS systems to develop standards for exchange. In short, the values of rewards are often forgotten and people have nothing tangible to show for them. By creating equivalence with money, we offer an opportunity to reward people with something tangible and useful. Clearly, Bill Gates does not need this kind of compensation, yet a dedicated, conscientious but economically poor individual may appreciate such monetary equivalence that could enhance his living style as no other kind act would do for him. This would be one instance where money is not the root of all evil, but it is the sustenance of a lot of good.

4 Identifying Criteria and Alternatives for the Proposed AHP Model The AHP makes use of the principles of decomposition, comparative judgments, and synthesis (Saaty 2001). Decomposition involves constructing a hierarchy which puts the goal of the problem at the top and places the criteria, sub-criteria, and alternatives at descending order of the hierarchy. For comparative judgments, a comparison matrix is arranged at each level to compare pairs of (sub) criteria or pairs of alternatives. The fundamental scale of absolute numbers used to represent dominance with regard to a common property by using pairwise comparisons ranges from 1 (indifference) to 9 (extreme importance, preference or likelihood). The complete pairwise comparison-matrices are synthesized to estimate the relative priorities for all alternatives. In the end, the AHP provides rank order and relative value on an absolute scale for each alternative (Saaty 2006). Conventionally, the presence of intangibles adds new dimensions of complexity to decision problems. Due to subjectivity, evaluating intangible contributions to society is a difficult task to perform. Without a systematic approach, decision makers may deal with the problem using knowledge, experience and intuition. The process may entail a level of bias, inexactness, and inconsistency. Nevertheless, it must be

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done. A systematic way of doing the evaluation like the AHP offers a safe valuable tool to deal with qualitative and intangible issues, because it makes the problem more transparent, comprehensive and provides the means to check on each judgment and where bias may be involved. The composite views in this paper are drawn from a three-member committee’s personal observations and experience, including information from multi-media and discussions with other colleagues. The values assigned to the variables are intended to be illustrative, not final, because they need greater public participation. Still we have provided a structure with the factors and alternatives properly arranged. The judgments in the model work as a foundation, guiding the reader to recognize the value of important contributions made by people throughout the world and to understand the structure to deal with them. It is common for people to believe that in general diamonds are more valuable than water, but in particular situations where a person may die of thirst water becomes the most precious substance for life. This implicitly proves that the existing market does not necessarily reflect human value fairly—socially, ecologically, or politically because it does not include all the necessary criteria to evaluate things comprehensively. We propose a way of thinking that is different from our familiar imbalanced system—a system that is too heavily relied upon in our current society.

4.1 The Evaluation Criteria People have several basic needs. In Fig. 3, we modify Maslow’s (1943) hierarchy of needs to derive criteria for evaluating activities through which people make a contribution. These criteria are shown in the second level of Fig. 3, and are further broken down into 12 sub-criteria, shown in the third level of the hierarchy.

Contribution to the Wellbeing of the Society

Physical Needs (.398)

Food (.373) .112

Clothing Shelter (.168) (.127) .051 .038

Emotional Needs (.285)

Medical (.333) .010

Esteem (.4) .076

SelfActualization (.6) .114

Social Needs (.206)

Safety Needs (.714) .168

Environmental Needs (.111)

Belonging needs (.286) .067

Water Air Waste Nature (.282) (.434) (.107) (.177) .063 .097 .024 .040

Fig. 3 The AHP criteria and sub-criteria and their corresponding weights for evaluating the contribution of the altruistic acts to the wellbeing. Note that: the values inside the parentheses in the sub-criteria level are local weights. Those under them are the global weights

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Physical needs (the 1st criterion) are those necessary for maintaining body strength, including food, clothing, shelter, and medical. Emotional needs are the desire of people to gain respect from others and feel powerful. Through selfactualization, people achieve individual potential and operate at higher personal capacity. Social needs are those that make people feel safe and draw a sense of belonging. Safety keeps people from harm. A person with a strong social network and support feels safer. Belonging needs are related to affection and being a part of a group. A helpful group member feels more integrated with society. Finally, environmental needs center on protecting the earth and its ecosystems. This includes protecting nature to maintain fresh air, clean water, and ensuring that garbage and other wastes are removed and processed in a timely manner. After identifying these pertinent evaluation criteria, we proceed to assess different types of altruistic contributions.

4.2 Categorization of Clusters Table 1 lists multiple clusters of altruistic activities under the evaluation criterion social needs. In order to arrive at a logical categorization of alternatives under each criterion, the team members with their diverse backgrounds took on the role of critical evaluators and explored each alternative’s contribution to achieve the overall goal under the particular criterion. The group was introduced to the nominal group technique (NGT), under which individuals work alone but in a group setting (Delbecq et al. 1975). There are four steps involved: (1) Generating ideas. Each participant silently writes down his judgments for 5–10 min. (2) Recording ideas. The coordinator collects the judgment by letting participants share them round-robin fashion (one response per person each time). (3) Discussing ideas. The leader asks if there are questions, interpretations, or explanations. (4) Voting on ideas. Assuming that the alternatives are homogeneous, each participant privately rates each alternative from no importance ‘‘0’’ to top priority ‘‘9’’. The cumulative ratings are computed and announced. Next, these approximate values were arranged in an ascending order. Members of the committee then worked through a similar procedure again to determine where the pivot alternative from one cluster to the next one should be. That is, the committee determined an initial cluster categorization so that pairwise comparisons within each cluster can be carried out. After the pairwise comparisons, if the priority derived for an alternative exceeds the priorities of the other alternatives by more than an order of magnitude, the larger-priority alternative is moved to a cluster that follows the given cluster (proceeding from small to large) and conversely if the alternative is more than an order of magnitude smaller. The process is continued with care using calculations along with discussion. Basically, users need to assume a tentative order first and perform pairwise comparisons in small group of elements. Note that there is no definite way to be

16. Long-term help nursing home

20. Adopt disabled children 23. Run for political office

Intermediate acts cluster 1 (M2)

Intermediate acts cluster 1 (M3) Big acts cluster 1 (LI)

3. Gratitude thankfulness, and honoring 6. Help in library

4. Surprise people w/generosity

(continued)

7. Allow children to shadow your job 9. Work at food 10. Cleaning and 11. Volunteer at bank caring homeless shelter environment 15. Hosp ital C are 16. Long-term 13. Community 14. Organize program for blood drive community help children’s ward service nursing home 17. Social work and 18. Donate moderate 19. Community 20. Adopt disabled giving advice amount of money fund raising children (e.g. United way, event red cross) 21. Habitat for humanity 22. Moderate micro 23. Run for political lending office 24. Military, police, 25. Peace corp 26. Breakthrough or fire service invention (sacrifice)

Modest acts cluster 1 1. Compliment people 2. Acts of courtesy (SI) and agreeableness (e.g. open) Modest acts cluster 2 4. Surprise people 5. Keep company and (S2) w/generosity comfort people Modest acts cluster 3 7. Allow children to 8. Offer help to (S3) shadow and learn unpleasant tasks about your job at work Intermediate acts 11. Volunteer at 12. Teaching, cluster 1 (Ml) homeless shelter educating community

Table 1 Clustering the altruistic acts under the social needs criterion Clustering the altruistic acts under the social needs criterion Altruistic acts cluster type

330 14 An Innovative Orders-of-Magnitude Approach

Big acts cluster 3 (L4)

Big acts cluster 3 (L3)

28. Life time humanity devotion (Mother Teresa) 30. Individual 28. Life time humanity 29. Sizable (tens of Sacrifice life to $billion) money devotion (Mother save others donation Teresa) 30. Individual sacrifice 31. International conflict 32. Humanity relief 33. Global disease cure life to save others mediation rescue (e.g. medical)

27. Large micro lending

Big acts cluster 2 (L2)

26. Breakthrough invention (sacrifice)

Clustering the altruistic acts under the social needs criterion

Table 1 (continued) Altruistic acts cluster type

4 Identifying Criteria and Alternatives for the Proposed AHP Model 331

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sure about the order of the alternatives at the very beginning. So the committee needed to work using careful observation and experiment iteratively; bringing about refinements, until in the end they came up with a consistent and agreeable order.

4.3 Altruistic Alternatives In ascending order of these alternatives’ importance to the chosen criterion of social needs, we divide them into three levels that contain 10 clusters. They are: (1) Level 1—Modest acts, e.g. kind gestures and small help; (2) Level 2—Intermediate acts, e.g. sacrificing career, considerable time, and material wealth; and, (3) Level 3—Big acts, e.g. devoting significant portions of one’s life or money, and taking greater risks to serve. We divide small acts into three clusters, medium acts into three clusters, and large acts into four clusters. We label them as S1–S3, M1–M3, and L1–L4, respectively and list them on the leftmost column in Table 1. (A) Level 1—Modest acts: Modest acts are performed to enliven others and make people happy. The small kind acts given in cluster S1 are complimenting people, acts of courtesy and agreeableness, gratitude, etc. Modest acts encourage the positive, caring side of human nature. Gratitude, thankfulness and honoring acknowledge other’s value, while surprising people with covert and hidden generosity is love given with thoughtfulness. The modest acts in cluster S2 include keeping company and comforting people for physical and emotional connection, helping in library and allowing youngsters to shadow work. One can find that activity #4 (i.e. surprising people with generosity) is repeated and shown in Cluster 2 again, due to the need to use it to link the two clusters: S1 and S2. Similar repetition can be found in activities 7, 11, 16, etc. Helping the needy and the poor at a food bank and homeless shelter (see S3) shows the caring and willingness to serve. Compassion can also be extended to include animals and nature. Environmental disasters, green house effects, and climate change make cleaning and caring for the environment important. Teaching and educating community opens the door for people to learn and appreciate the world’s beauty and complexity. (B) Level 2—Intermediate acts: Some of the activities in this level include organizing community service to bring people together (act #14). Providing social work and giving advice (#17), donating moderate amounts of money (act #18), and occasional fund raising (#19) provide opportunities to change society on a larger scale. Giving USA (2009) reports that donation to charitable causes in the US reached $307.65 billion in 2008. As recession continues, the amount declines. In M3, moderate micro lending (#22) provides small loans to poor people who have no collateral and do not qualify for conventional bank loans. Beyond money, one may choose to give time to serve the public office (#23). (C) Level 3—Big acts: Innovation and creativity are essential for a better and brighter future. Breakthrough inventions are important in driving technological

4 Identifying Criteria and Alternatives for the Proposed AHP Model

333

and social progress. The Peace Corp promotes world peace and friendship. Besides the Peace Corp, one may sacrifice for values and beliefs to work in the military, the police and fire departments, or sacrifice their lives to provide service and ask for nothing in return. Sizable monetary donations are a way of giving meaning to wealth and allowing others to ‘‘live on’’ through socially conscious munificence. Donors often experience personal rewards by seeing others’ well-being enhanced. Society can show appreciation and gratitude for these altruistic contributions. Finally, curing global disease contributes to society on a large scale and deserves the highest kind of recognition.

5 Applying the New AHP Model For each subcriterion (e.g. foods, safety, esteem needs) as listed in Fig. 3, we need to identify appropriate group clusters similar to those listed in Table 1. For the sake of simplicity and clarity, we only illustrate the proposed AHP model methodology using the four main criteria in the paper. Detailed hierarchies for the whole model using all of the 12 subcriteria are available online as supplements titled ‘‘Complete Model with 12-Subcriteria’’. In Fig. 4 we display the ten clusters of alternatives under the Social Needs criterion. Table 2 gives the pairwise comparison matrices with the local priorities of the alternatives shown in the rightmost column of each matrix, which can also be found in the 1st row of each cluster. In Fig. 4 we show that we can use the results from pairwise comparisons, and divide them by the weight of the pivot in that cluster, and, finally, multiply them by the pivot’s weight from the previous less important group to connect the different levels of importance. Eventually, the smallest acts, such as compliment people, end up indirectly compared with the biggest acts, such as curing global disease.

5.1 Pairwise Comparison The comparisons in Table 2 are made by first comparing compliment people with all the modest acts in the same cluster S1, such as acts of courtesy and agreeableness, gratitude thankfulness and honoring, etc. The act of surprising people with covert and hidden generosity is used again as the pivot in cluster S2, which includes keeping company and comforting people, helping in library, etc. Copy all ratings derived in Table 2 to Fig. 4 as local priorities (note however that in S1 the rating is shown as global priority since it’s the base for all transformations). Next, we divide all the local priorities in cluster S2 by the local priority of surprising people with covert & hidden generosity (0.08), and multiply all the resulting local

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idealized priorities (1, 1.732, 3.206, 6.412) in this cluster by the global priority in cluster S1 of surprising people with covert and hidden generosity (0.55) to arrive at the global priority. In the same manner, the priorities of the intermediate acts in M1, M2 and M3 are derived. Similarly, we include the M3 act of running for political office in the big acts cluster L1. We pairwise compare and synthesize the matrix in Table 2 to find the local priorities (0.096, 0.161, 0.277, 0.466) for all cluster L1 acts. Next, in Fig. 4, cluster L1 we derive the local ideals by dividing every local priority by the smallest local priority, 0.096. Multiplying the local ideals (1, 1.678, 2.888, 4.854) by the global priority of running for political office (45,080) in the intermediate acts Level M3, we obtain the global priorities for all cluster L1 acts. Similarly, we obtain the global priorities of the cluster L4 acts as 5,384,577; 10,832,968; 26,533,253, and 68,755,097. In the end, we normalize all acts in S1 by dividing each act by the global priority of the smallest act, 0.06 (acts of complimenting people in S1). Link them group by group. Eventually, global ideals are obtained for modest acts S1 = (1.00, 1.7, 5.07, 9.39), S2 = (9.39, 16.266, 30.115, 60); and S3 = (60, 110, 203, 306, 595). For intermediate acts M1 = (595; 1,125; 1,934; 3,619; 5,028; 7,376), M2 = (7,376; 18,446; 29,728; 46,115; 78,890), and M3 = (78,890; 169,003; 365,185; 773,639). For big acts L1 = (773,639; 1,298,430; 2,234,102; 3,755,093), L2 = (3,755,093; 7,840,304; 17,124,874), L3 = (17,124,874; 33,345,464; 92,406,497), and L4 = (92,406,497; 185,908,141;

Fig. 4 The AHP model to prioritize the benevolent acts under the social needs

5 Applying the New AHP Model

M1 Local Priority Local Ideal Global Priority Global Ideal

335

11.Voluntee 14.Organize 15.Hospital Care 12.Teaching, r at 16.Long-term Help 13.Community Educating Program for Community Blood Drive Homeless Nursing Home Children's Ward Service Community Shelter 0.02 0.03 0.06 0.10 0.14 0.21 1.000 1.890 3.249 6.080 8.446 12.391 34.687 66 113 211 293 430 595 1,125 1,934 3,619 5,028 7,376

18.Donate 16.LongModerate 17.Social Work 19.Community term Help Amount 20.Adopt & Giving Fund Raising Nursing Money (e.g. Disabled Children Advice Event Home United Way, M2 Red Cross) 0.03 0.07 0.11 0.16 0.28 Local Priority 1.000 2.501 4.030 6.252 10.695 Local Ideal 430 1,075 1,732 2,687 4,597 Global Priority 7,376 18,446 29,728 46,115 78,890 Global Ideal

M3 Local Priority Local Ideal Global Priority Global Ideal

20.Adopt 21.Habitat for 22.Moderate 23.Run for Disabled Humanity Micro Lending Political Office Children 0.057 0.122 0.263 0.558 1.000 2.142 4.629 9.807 4,597 9,848 21,280 45,080 78,890 169,003 365,185 773,639

L1 Local Priority Local Ideal Global Priority Global Ideal

L2 Local Priority Local Ideal Global Priority Global Ideal

L3 Local Priority Local Ideal Global Priority Global Ideal

L4 Local Priority Local Ideal Global Priority Global Ideal

Fig. 4 continued

24.Military, 23.Run for Police, or Fire Political Office Service 0.096 0.161 1.000 1.678 45,080 75,660 773,639 1,298,430 26.Breakthroug 27.Large h Invention Micro Lending (sacrifice) 0.108 1.000 218,811 3,755,093 28.Life Time Humanity Volunteering (Mother Teresa) 0.094 1.000 997,876 17,124,874

0.226 2.088 456,859 7,840,304

25.Peace Corp 0.277 2.888 130,182 2,234,102

26.Breakthrough Invention (sacrifice) 0.466 4.854 218,811 3,755,093

28.Life Time Humanity Volunteering (Mother Teresa) 0.494 4.560 997,876 17,124,874

29.Sizable (tens of 30.Individual $Billion) Sacrifice life to Money save others Donation 0.182 0.505 1.947 5.396 1,943,058 5,384,577 33,345,464 92,406,497

30.Individual 31.Internationa l Conflict Sacrifice life to Mediation save others 0.048 0.097 1.000 2.012 5,384,577 10,832,968 92,406,497 185,908,141

32.Humanity 33.Global Disease Relief Rescue Cure (e.g. Medical) 0.238 0.617 4.928 12.769 26,533,253 68,755,097 455,345,908 1,179,928,909

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Fig. 5 The final priorities of all studied benevolent acts

8. Offer help to unpleasant tasks at work 1/3 1 3 4 5

1

3

4 5

6

7. Allow children to shadow your job 8. Offer help to unpleasant tasks at work 9. Work at food bank 10. Cleaning and caring environment 11. Volunteer at homeless shelter

3

1

1/6 1/4

4

1 2

1/3

1/4

1 2

1/2

3

1/2 1

1/4

1/5

1

1/3

1/7 1/5

4. Surprising people w/generosity

1/2 1

1/4

1

1/4 1/3

1/5

1/6

11. Volunteer at homeless shelter

7. Allow children to shadow your job 1/6

10. Cleaning and caring environment

6. Volunteer in library 1/3

3. Gratitude, thankfulness, and honoring

9. Work at Food bank

2 4

3 6

7. Allow children to shadow your job

1

2

Social needs (S3)

4. Surprising people w/generosity 5. Keep company and comfort People 6. Volunteer in library 7. Allow children to shadow your job

5. Keep Company and comfort People 1/2

5

7

4. Surprising people w/generosity 1

4

6

Social needs (S2)

1/2 1

1 2

1. Compliment people 2. Acts of courtesy and agreeableness (e.g. open) 3. Gratitude, thankfulness, and Honoring 4. Surprising people w/generosity

2. Acts of courtesy and Agreeableness (e.g. open)

1. Compliment people

Social needs (SI)

Table 2 The pairwise comparisons and local priorities of the altruistic acts under social needs criterion

0.467

0.159 0.240

0.086

0.047

Rating

0.260 0.519

0.140

0.081

Rating

0.547

0.295

0.058 0.099

Rating

5 Applying the New AHP Model 337

3 5

5 7

20. Adopt disabled children 1 3 5 7

1 2

3 4

Social needs (M3) 20. Adopt disabled children 21. Habitat for humanity 22. Moderate micro lending 23. Run for political office

1/3

9

1

7

8

16. Long-term help nursing home 17. Social work and giving advice 18. Donate Moderate amount of money (e.g. United way, red cross) 19. Community fund raising event 20. Adopt disabled children

4

3 7

4

3

1 2

1/2

1/3

3

2

1/2 1

1/3

14. Organize community service 1/7

21. Habitat for humanity 1/3 1 3 5

2 4

1/2 1

2

1

1/3 1/2

1/4

1/8

1 2

1/3 1/2

1/5

1/2 1

1/5 1/4

1/7

20. Adopt disabled children

23. Run for political office 1/7 1/5 1/3 1

19. Community fund raising event

1

1/2

1/4 1/3

1/7

1/9

15. Hospital care program for 16. Long-term help children’s ward nursing home

22. Moderate micro lending 1/5 1/3 1 3

18. Donate moderate amount of money (e.g. United way, red cross) 1/4

13. Community blood drive

17. Social work and giving advice

2 3

2

16. Long-term help nursing home

1

1

11. Volunteer at homeless shelter 12. Teaching, educating community 13. Community blood drive 14. Organize community service 15. Hospital Care program for children’s ward 16. Long-term help nursing home

Social needs (M2)

12. Teaching, educating community 1/2

11. Volunteer at homeless shelter

Social needs (Ml)

Table 2 (Continued)

Rating 0.057 0.122 0.263 0.558

0.165 0.282

0.066 0.106

0.026

Rating

0.212

0.144

0.056 0.104

0.032

0.017

Rating

338 14 An Innovative Orders-of-Magnitude Approach

30. 31. 32. 33.

Individual sacrifice life to save others International Conflict Mediation Humanity relief rescue (e.g. Medical) Global disease cure

Social needs (L4)

28. Life time humanity humanity devotion (Mother Teresa) 29. Sizable (tens of $Billion) money donation 30. Individual sacrifice life to save othersBig

Social needs (L3)

26. Breakthrough invention (sacrifice) 27. Large micro lending 28. Life time humanity humanity devotion (Mother Teresa)

Social Needs (L2)

31. International conflict mediation 1/3 1 4 7

1/3 1/2 1 2

26. Breakthrough invention (sacrifice) 1/4 1/3 1/2 1

1

1/3

1/9 1/7 1/4 1

33. Global disease cure

30. Individual sacrifice life to save othersBig 1/5

28. Life time humanity devotion (Mother Teresa) 1/5 1/2 1

25. Peace corp

32. Humanity relief rescue (e.g. Medical) 1/5 1/4 1 4

3

5

30. Individual sacrifice life to save 1 3 5 9

1

2

1/2 1 2

27. Large micro lending

29. Sizable (tens of $Billion) money donation 1/2

1/2 1 2 3

24. Military. police, or fire service

28. Life time humanity devotion (Mother Teresa) 1

26. Breakthrough invention (sacrifice) 1 2 5

1 2 3 4

23. 24. 25. 26.

Run for political office Military. police, or fire service Peace corp Breakthrough invention (sacrifice)

23. Run for political office

Social Needs (LI)

Table 2 (Continued)

0.048 0.097 0.238 0.617

Rating

0.505

0.182

0.094

Rating

0.108 0.226 0.494

Rating

0.096 0.161 0.277 0.466

Rating

5 Applying the New AHP Model 339

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14 An Innovative Orders-of-Magnitude Approach

455,345,908; 1,179,928,909). For the other three criteria listed in Fig. 3, we have built the similar sub-structures with different cluster membership, depending on their similarity in contributing to the goal of the criterion. By multiplying the global ideal priorities with the corresponding criterion weights and summing over the criteria, we are able to determine the overall final scores for each of the 33 activities. For example, the global disease cure is of 1,140,230,056 (1,183,020,799 9 0.398 ? 1,179,928,909 9 0.206 ? 1,115,698,094 9 0.285 ? 976,112,301 9 0.111). In this way, we have created a comparison between the smallest act compliment people and the biggest act of global disease cure; correspondingly extending the scale beyond 9 to 1,140,230,056. Figure 5 gives the final score of each act, e.g. the final synthesized value of global disease cure is at 1,140,230,056 times more important relative to compliment people in terms of satisfying human needs. The grouping or clustering approach adopted here is critical. In most decision problems, there may be two or three groups that differ by orders of magnitude from one another. The AHP scale does not limit us in comparing alternatives if we cluster similar objects into groups and use for a pivot the largest element in one group as the smallest element in the next group. The priorities in two adjacent groups should be sufficiently different, each being one order of magnitude smaller than the other. As a result, the ratings of the smaller set have some impact on the judgment of the larger set. Using this method, comparing a modest act with a highly respectable and noble act becomes possible. Note that the clusters of alternatives under each criterion differ since they depend on where an alternative stands respect to that criterion. This rearrangement of the alternatives has to be done several times, once for each of the criteria.

5.2 Results: The Value of Benevolent Acts Although humaneness, international disaster relief, and community help are familiar concepts, there has been no openly accepted standard for appraising the value of these benevolent acts. Without an objective means to determine the monetary equivalence of intangibles, society cannot appreciate their true worth. By the proposed AHP model, we uncover a better approach to assign values to altruistic deeds taking place all over the world. Through our method, acts of charity can be valued for the psychological satisfaction they bring to the individuals performing the acts and they can also be assigned significance based on their level of social contribution. Here we show how benevolent acts can be converted into explicit value. At its extreme, we may equate dollars to priorities, or some similar variant, and then assign a relative fair market price to an act. For example, acts of a lifetime commitment to humanity, e.g., that of Mother Teresa, would be worth $40– $50 million dollars or $45,721,297 according to our account (see Fig. 5, act #28). Investing in the cure of global disease, such as the development of a vaccine for

5 Applying the New AHP Model

341

H1N1 flu or AIDS would be worth $1,140,230,056 as suggested by the global weighted score derived in our model (act #33 in Fig. 5). This value is a composite of the values derived under each criterion in which this alternative falls in a higher range of values. We must admit that this is only an illustrative example that may not be perfect, and needs judgment from many more experts in this domain of knowledge and experience (Saaty and Peniwati 2007). When using greater effort to do the same evaluation in terms of the sub-criteria listed in the 3rd level of Fig. 3, we have obtained a comparable representation of this very large value with $1,190,691,853.

6 Conclusions If one were to use a scale to rate alternatives one at a time, one would have to make the values of that scale range from zero to 1010 in some cases and it would be extremely difficult to judge accurately where the value assigned to each alternative on that scale should fall. We must often guess as to the likely outcome resulting from our decisions. This is also illustrated by the example of our depressed economy. Comparing the many small actions taken to improve the economy through decisions at the local levels with those taken through decisions at the state or the national level, would be difficult and imprecise. To deal with intangibles scientifically, we have pairwise compared them to derive the relative priorities. Making comparisons is our biological heritage. It was there long before measurement scales were invented with their arbitrary units and gradually used in science to develop scientific theories about the physical universe. But our internal universe of values has been largely ignored. We need to identify the factors that play a significant role in shaping this internal universe to better identify their significance and determine the role it plays that leads us to the future. The application of the proposed AHP model may be extended to allocate the U.S. budget to federal programs, since the importance of all federal programs are significantly different. Our model could be useful for legislative acts that authorize the expenditure of a designated amount of federal funds for various programs of specific purpose. Please refer to Saaty and Peniwati (2007) for elaboration. In terms of business and education, the proposed AHP model could be applied to the evaluation of schools, supermarkets, and fast food chain stores, whose performance involves tangible and intangible criteria. For example, McDonald’s (WalMart) has a string of 32,000 restaurants (7,928 Wal-Mart stores) over different regions and countries in the world. By applying the proposed AHP model, corporate executives will have more a comprehensive view regarding the operations and effectiveness of all stores across the board. In the past four decades, multi-criteria decision modeling has attracted much attention. However, a distinctive area, dealing specifically with the presence of significantly heterogeneous data, has not been explored. The main contribution of this research is the enhancement of the AHP methodology where we illustrate an

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14 An Innovative Orders-of-Magnitude Approach

extensive system with heterogeneous elements. So far as the judgments used are concerned, it is not the measurement precision for a particular alternative that determines the validity of the evaluation results, but the importance we attach to the various criteria used to weight and synthesize those measurement that has greater impact on the outcome. Members of society need to participate in assigning importance to these factors in order to obtain the diversity of information needed to best differentiate among all acts.

References A. Delbecq, A. Van de Ven, and D. Gustafson, Group Techniques for Program Planning: A Guide to Nominal Group and Delphi Processes. Glenview, IL: Scott, Foresman, 1975. Economist, 2010. A Better Way: The rich world should worry about growth-promoting reforms more than short-term fiscal austerity. Retrieved November 12, 2010 http://www.economist. com/node/17173919. Gaye, A. 2007/2008, Access to Energy and Human Development, Human Development Report 2007/2008. Fighting climate change: Human solidarity in a divided world, United Nations Development Program. Retrieved November 12, 2010. http://hdr.undp.org/en/reports/global/ hdr2007-2008/papers/gaye_amie.pdf. Giving USA 2009: The Annual Report on Philanthropy for the Year 2008, Retrieved Dec. 3, 2010, http://www.aafrc.org/gusa/gusa_order.cfm and http://www.philanthropy.iupui.edu/ News/2009/docs/GivingReaches300billion_06102009.pdf. Hubbard, D. W. 2007, How to Measure Anything: Finding the Value of ‘‘Intangibles’’ in Business, John Wiley & Son, Hoboken, NJ. Kurzweil, R (2005) The singularity is near. Penguin Books, New York. Kostigen, T. 2009, The happiest taxes on earth. Retrieved September 21, 2009, http:// www.marketwatch.com/story/the-happiest-places-on-earth-are-heavily-taxed. Larimer, T. 2006, No Yen? No Problem! Small town bartering, http://www.time.com/time/asia/ features/changed_japan/yufu.html. LETSystem Design Manual, http://www.gmlets.u-net.com/design/ Accessed on March 9, 2011. Maslow, A.H. 1943, A Theory of Human Motivation, Psychological Review, 50(4), 370-96. Millet, I. and Saaty, T.L. 2000, On the relativity of relative measures – accommodating both rank preservation and rank reversals in the AHP,’’ European Journal of Operational Research, 121(1), 205-212. Ozdemir, M.S. and T.L. Saaty, 2006, The Unknown in Decision Making: What to do about it? European Journal of Operational Research, 174 (1), 349-359. Saaty, T.L. and M. Takizawa, 1986, ‘‘Dependence and Independence: From Linear Hierarchies to Nonlinear Networks, European Journal of Operational Research, 26(2), 229-237. Saaty, T.L. 1990a, How to Make a Decision : The Analytic Hierarchy Process’’, European Journal of Operational Research, 48(1), 9-26. Saaty, T.L. 1990b, Physics as a Decision Theory, European Journal of Operational Research, 48(1), 98-104. Saaty, T.L. 1994a, Homogeneity and Clustering in AHP Ensure the Validity of the Scale’’, European Journal of Operational Research, 72(3), 598-601. Saaty, T.L. 1994b, Highlights and Critical Points in the Theory and Application of the Analytic Hierarchy Process’’, European Journal of Operational Research, 74(3), 426-447. Saaty, T.L. 1996, Decision Making with Dependence and Feedback, Pittsburgh: RWS Publications.

References

343

Saaty, T.L. 2001, Models, Methods, Concepts & Applications of the Analytic Hierarchy Process, with Luis G. Vargas, Kluwer Academic. Saaty, T.L. 2003, Decision-making with the AHP: Why is the principal eigenvector necessary, European Journal of Operational Research 145(1), 85-91. Saaty, T.L. 2006, Rank from comparisons and from ratings in the analytic hierarchy/network processes, European Journal of Operational Research 168(2), 557–570. Saaty, T.L. and Peniwati, K. 2007. Group Decision Making: Drawing Out and Reconciling Differences, Pittsburgh: RWS Publications. Shang, J. and T. Sueyoshi. 1995, A Unified Framework for the Selection of a Flexible Manufacturing System, European Journal of Operational Research. 85(2), 297-310. Starr, R.M. 1972, The Structure of Exchange in Barter and Monetary Economies, The Quarterly Journal of Economics, 86(2), 290-302. Sueyoshi, T., J. Shang, W. Chiang (2009), A Decision Support Framework for Internal Audit Prioritization in Rental Car Company: Combined Use between DEA and AHP’’, European Journal of Operational Research, 199(1), 219-231. Tjader, Y. J. Shang, L. Vargas 2010, Offshore Outsourcing Decision Making: A Policy-Maker’s Perspective, European Journal of Operational Research, 207(1), 2010, 434-444. Velasquez, M., Andre, C., Shanks, T. and Meyer, S.J. and M.J. 1992, The Common Good. Retrieved November 6, 2010, http://www.scu.edu/ethics/practicing/decision/Commongood. Yahoo, November 15, 2010, http://news.yahoo.com/s/afp/britainpoliticslifestylehappiness, access November 16, 2010.

Chapter 15

Sensitivity Analysis in the Analytic Hierarchy Process

1 Introduction In model building using the AHP, sensitivity analysis is a crucial step in determining if the solution is implementable and robust. For example, Zhong and Gu (2010) developed an AHP model to assess black-start schemes for fast restoration of a power system. They studied the impacts of the values and weights of indices on the ranking of the black-start schemes. Using sensitivity analysis, they proposed a model to help dispatchers with more comprehensive and accurate decisionmaking. Wu et al. (2007) used an AHP sensitivity analysis to construct an evaluation method that provides administrators of hospitals with a valuable reference for evaluating organizational performance. Here we present an approach to studying the sensitivity and stability of models based on the Analytic Network Process (ANP), the generalization of the Analytic Hierarchy Process (AHP) to systems with feedback and networks. Sensitivity analysis is a special case of stability analysis. In general, we believe that there are three ways of thinking about the stability of a solution from a model: (1) Core stability—finding the region of the solution space in which the solution remains most preferred; (2) Solution stability—finding the regions of the solution space in which different solutions are most preferred; and (3) Perturbation stability— understanding how perturbations in the model inputs change the most preferred solution or make the solution invariant. We show the first two types of stability analyses in this chapter Our methodology combines numerical perturbations of the ANP model with optimization modeling based on the results of those numerical perturbations. Because of the complex relationships between the nonzero entries in a supermatrix and the alternative recommended by the ANP model, it is impossible to describe analytically the sensitivity of the recommendation to perturbations in the numerical entries. We use linear optimization in our stability results so as to simplify the sensitivity analysis procedure. Further research is necessary to determine if a more sophisticated optimization approach could produce more precise sensitivity and stability outcomes.

T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7_15,  Springer Science+Business Media New York 2013

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2 Literature Review 2.1 Sensitivity Analysis of Judgments Parametric representations use the concept of interval judgments introduced by Saaty and Vargas (1987). Such representations are used to investigate the effect of uncertainty in judgments on the stability of the rank order of alternatives. The uncertainty is measured by associating with each judgment an interval of numerical values. This approach helps to estimate the probability that an alternative exchanges rank with other alternatives. The probabilities are used to calculate the odds that an alternative would change rank. The priority (importance) of each alternative is then combined with the probability that it does not change rank to obtain the final ranking. Arbel (1989) used a linear optimization model to find the priorities of alternatives when the judgments are intervals. His method does not always yield an optimal solution because the feasible region might be empty. Arbel and Vargas (2007) developed a necessary and sufficient condition for a feasible region not to be empty based on the concept of Euclidean centers. Aguaron and MorenoJimenez (2000) provide a sensitivity analysis of the judgments used in the AHP in two situations: the selection of the most preferred alternative, and the ranking of all the alternatives. In both cases, they use the geometric mean to compute the local priorities. They obtain, in the case of a single criterion, a local stability interval for each judgment that guarantees an alternative to be the most preferred one. Altuzarra et al. (2010) use a Bayesian approach to study the sensitivity of priorities to changes in judgments expressed as interval judgments in a group decision making environment. The first paper that treated judgments as random variables is due to Vargas (1982), who characterized the probability distribution of the eigenvector as a function of the judgments. Moreno-Jimenez and Vargas (1993) determined the ranking of the alternatives that one should infer when decision makers’ judgments are represented by random reciprocal uniform variables. They addressed: (1) How many rankings could be inferred from the matrix of random reciprocal uniform judgments, and (2) Which one is most likely to be selected? By assuming that the sole source of the uncertainty is the elements of the preference matrices, Paulson and Zahir (1995) found that ranking uncertainty decreases as the number of alternatives or the depth of the hierarchy increase. Mackay et al. (1996) developed a model, following Thurstone’s method (Thurstone, 1927), and assumed that judgments are folded normal random variables, i.e., the absolute value of normal variables. Lipovetsky and Tishler (1999) employed a Cauchy distribution to show how to modify comparison matrices of alternatives in order to handle random data, which often yields Saaty matrices reciprocally asymmetrical. They modified the AHP to deal with reciprocally asymmetric matrices, and to allow each priority estimate to be expressed on an interval of possible values, rather than as a single discrete point.

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347

2.2 Sensitivity Analysis of Priorities Masuda (1990) studied the effect that changes to entire vectors of the decision matrix may have on the ranking of the alternatives in hierarchies with multiple levels, but did not study the impact that changes to single criteria would have on the ranking of the alternatives. Huang (2002) pointed out some disadvantages of Masuda’s analysis, and suggested an alternative sensitivity coefficient. Triantaphyllou and Sánchez (1997) examined: (1) how critical each criterion is to the existing rank of the alternatives, i.e., they find what is the smallest change in the current weights of the criterion that would alter the existing ranking of the alternatives.; and (2) how critical the various performance measures of the alternatives (in terms of a single decision criterion at a time) are to the ranking of the alternatives. They defined a sensitivity coefficient of the weights and local priorities based on the minimum change in the current weight/local priority such that the ranking of two alternatives is reversed. Chen and Kocaoglu (2008) developed an algorithm to study the impacts of single and multiple changes to the local contribution vector/matrices at any level of a decision hierarchy. They defined the allowable range/region of perturbations and contribution tolerance to keep the ranking of interested decision alternatives unchanged. Sowlati et al. (2010) used mathematical programming to find the minimum required changes in the weights of criteria necessary to alter the ranking of the alternatives. They applied the approach to evaluate and select design and manufacturing software packages in a kitchen cabinet manufacturing facility in Canada. The results of sensitivity analysis were used to assess the robustness of the final decision.

3 Problem Complexity What makes the study of stability in the ANP difficult is the increasing number of results that need to be analyzed as the size of the network increases. For example, consider a hierarchy with H levels, where the ith level has ni elements. The priorities of the elements in the levels n2 ; . . .; nH1 can be changed either one at a time or in combination. If each weight can be perturbed to m other values, then the total number of perturbations to be considered is given by  N  X N mk ¼ ðm þ 1ÞN k k¼0

ð1Þ

where N¼

H X i¼2

ðni  1Þni1 :

ð2Þ

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The most preferred alternative is derived by determining the principal eigenvector of the supermatrix. Because there is no formulaic relationship between the relative sizes of the components of the principal eigenvector, which can be used to determine the most preferred alternative, and the perturbations, the impact of each perturbation has to be found separately and empirically. Now assume we have a network instead of a hierarchy. Then the supermatrix H H P P might contain up to ðni  1Þ  ni non-zero entries. For a network with i¼1

i¼1

H components, all of which could be interconnected, the supermatrix is given by L1 L2 L3 . W ¼ .. LH2 LH1 LH

0 L1 W1;1 B W2;1 B B W3;1 B B .. B. B B WH2;1 B @ WH1;1 WH;1

L2 W1;2 W2;2 W3;2 .. .

L3 W1;3 W2;3 W3;3 .. .

    .. .

LH2 W1;H2 W2;H2 W3;H2 .. .

LH1 W1;H1 W2;H1 W3;H1 .. .

WH2;2 WH1;2 WH;2

WH2;3 WH1;3 WH;3

  

WH2;H2 WH1;H2 WH;H2

WH2;H1 WH1;H1 WH;H1

LH W1;H W2;H W3;H .. .

1

C C C C C C C WH2;H C C WH1;H A WH;H

If all the entries could be perturbed to m other values, then the total number of results to be analyzed is given by ðm þ 1ÞN where N¼

H X

ðni  1Þ 

i¼1

H X

ni :

ð3Þ

i¼1

The most preferred alternative determination for an ANP model is similar to that of an AHP model, so the supermatrix would have to be calculated and analyzed empirically for each of the ðm þ 1ÞN perturbations.

4 Stability of the ANP Solution Our approach to stability analysis is based on the empirical perturbations of some of the entries of the rows of a supermatrix to create a space of perturbations. In that space, different regions are associated with different alternatives. That is, we can partition the space of perturbations into mutually exclusive regions such that all perturbations in a region yield the alternative associated with it as the most preferred one. Because the supermatrix may consist of a large number of entries, perturbing single entries may not lead to noticeable changes in the ranking of the alternatives. The most interesting case is to change all the entries of the row of the supermatrix. This allows us to study how one element influences all others at once, rather than how one element influences another. In this case the number of matrices to be analyzed is given by ðm þ 1ÞH  1:

4 Stability of the ANP Solution

Let X be the space of

H P

ni 

i¼1

349 H P

ni matrices of perturbations of the entries of a

i¼1

 be a nH  1 vector of limiting priorities of the alternatives supermatrix W. Let w resulting from the matrix W. A perturbation of the entries of W is given by the Hadamard elementwise product (Horadam 2007) of an element D 2 X and W, i.e., D  W; where D = (dij). Because the matrix W is column stochastic, the perturbations need to be made in such a way as to preserve stochasticity and the proportionality of the entries of the unperturbed entries in a column. Perturbations are created by increasing or decreasing the entries of a row by the same percentage. Because all the entries in a supermatrix must be between zero and one, perturbations that increase a value are based on a percentage of the distance between the entry’s original value and the distance to the upper bound of one; and perturbations that decrease a value are based on a percentage of the distance between the entry’s original value and the distance to the lower bound of zero. That is, given an entry wij ; a perturbation 1  dij  1 results in a new entry w0ij given by  wij þ dij wij if dij  0 0 wij ¼ : ð4Þ wij þ dij ð1  wij Þ if dij [ 0 The sets to be separated are created by selecting the points in the perturbation space and finding out which alternative has the largest limiting priority, as given by the supermatrix. Let XðiÞ be the subset of X for which the ith alternative is ranked first. Let Bði; jÞ be the boundary separating XðiÞ and XðjÞ: The boundary need not be linear but, in the analysis in this paper, we use linear boundaries because doing so reduces the amount of computation necessary and simplifies the interpretation of the results. Further research might identify hierarchies or networks for which the reduction in information loss resulting from estimating nonlinear boundaries for the partitions of the space X justifies the additional complications arising from using them.

4.1 Binary Classification The stability problem can be modeled as a set of binary classification problems. A binary classification problem consists of discriminating between two given point sets A and B, with m1 and m2 points, respectively, in the n-dimensional real space Rn ; by using as few of the n dimensions of the space as possible. Following Mangasarian (1997), geometrically our approach constructs a plane in Rn defined by P ¼ fxjx 2 Rn ; xT w ¼ cg with normal w 2 Rn and distance kwjckj to the origin ðkwk2 is the Euclidean norm of the 2 vector wÞ; while suppressing as many of the components of w as possible. In addition,

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the set A must lie, to the extent possible, in the open half space fxjx 2 Rn ; xT w [ cg and the set B in the open half spacefxjx 2 Rn ; xT w\cg: Let A and B denote the matrices representing the sets A and B; respectively, where A 2 Rm1 n and B 2 Rm2 n : The problem is to find variables w and c such that Aw [ c and Bw\c: Because strict inequalities are not possible in an LP formulation, the variables are rescaled by the positive constant  min Ai w  c; Bj w  c i¼1;...;m1 ;j¼1;...;m2

where Ai and Bj are the ith and jth rows of the corresponding matrices. To keep the notation simple, the variables are denoted the same as before the rescaling took place. Bennett and Mangasarian (1992) proposed the following robust, i.e., w ¼ 0 is excluded, linear programming formulation: Find w; c; y and z to Minimize Subject to

eT y eT z þ m1 m2 Aw þ ec þ e  y Bw  ec þ e  z y  0; z  0

where e ¼ ð1; . . .; 1ÞT : In our problem, instead of separating just two sets, we need to separate n sets. Then the robust linear programing formulation is given by: Find vectors wi ; i ¼ 1; . . .; n; yij ; i; j ¼ 1; . . .; n; i 6¼ j; and c to Minimize

n eT  P yij eT yji þ mj i;j¼1 mi i6¼j

Subject to Ai ðwi  wj Þ þ eðci  cj Þ þ e  yij Aj ðwj  wi Þ þ eðcj  ci Þ þ e  yji yij  0; i; j ¼ 1; . . .; n; i 6¼ j where mi ; i ¼ 1; . . .; n are the numbers of points in the sets. The result is a set of hyperplanes that separate the sets in pairs. For two sets i and j, the equation of the separating hyperplane is given by xT ðwi  wj Þ ¼ ci  cj : Thus, the boundary separating alternatives i and j is given by Bði; jÞ : xT ðwi  wj Þ ¼ ci  cj :

ð5Þ

If there are na alternatives, there may be as many as na(na–1)/2 distinct boundaries between pairs of alternatives. That bound requires that the space of perturbations for which an alternative is ranked first be connected. Otherwise, na(na–1)/2 is, at best, a lower bound. It might not even be a lower bound, because some alternatives may be dominated over the entire space.

4 Stability of the ANP Solution

351

It is easy to see that the region over which an alternative dominates is a connected region. First, it is known that a continuous function maps compact sets into compact sets. The set of perturbations is given by the product of [0, 1] intervals, as many as the number of perturbations studied. Thus, the perturbation space is compact. In addition, it is a connected space. Each perturbation induces a supermatrix W. By Perron-Froebenius theory (Keener 1993), because W is a stochastic matrix, there always exists a real positive eigenvalue equal to 1 and a corresponding real nonnegative eigenvector w. Wilkinson (1965) showed that small continuous perturbations of the entries of W induce small continuous perturbation of its eigenvectors, and specifically on w. Thus, the space of perturbations is mapped via a continuous function into the space of priorities represented by the principal eigenvector of the supermatrix W. In addition, the priorities add to unity. Hence, the space of perturbations is mapped via a continuous function into the hyperplane eT w ¼ 1: Because the image of a connected space via a continuous function is also connected, the space of priorities resulting from the space of perturbations is also connected.

4.2 Core Stability To study core stability, not all of the boundaries are required. What is required is (1) the solution to the original problem, and (2) the separating hyperplanes of the most preferred alternative from each of the other alternatives. Assume that the kth alternative is the most preferred alternative in the original study. In order to determine the region over which the kth alternative remains ranked first (or core stability), we first identify all the hyperplanes that separate the kth alternative from the other alternatives, i.e., Bði; kÞ : xT ðwi  wk Þ ¼ ci  ck ; i ¼ 1; 2; . . .; n; i 6¼ k; and then calculate the sphere of stability for the kth alternative. The spheres of stability for the other alternatives, the ones dominated by the kth alternative, can be used to identify the regions over which those dominated alternatives would become dominant and remain dominant. In perturbation space, the sphere of stability for the kth alternative is centered at 0 = (0,…, 0), the point at which no element in the supermatrix is perturbed away from its original value. The radius of that sphere is the distance from the origin to the nearest boundary. The distance from any point X to a hyperplane described by (5) is given by ci  cj  xT ðwi  wj Þ

dij ðxÞ ¼ ð6Þ

wi  wj 2 The region where the kth alternative is most preferred, XðkÞ; is defined by   1  xi  1 n ; i ¼ 1; . . .; n; i 6¼ k : XðkÞ ¼ x ¼ ðx1 ; . . .; xn Þ 2 R j T x ðwi  wk Þ  ci  ck

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Thus, the minimum distance from 0 = (0,…, 0) to the boundary where the kth alternative is the most preferred alternative is the largest radius of a hypersphere of perturbations centered at 0 = (0,…, 0), within which the solution remains the most preferred alternative. The equation of the hypersphere is given by   2 jci  ck j xT x ¼ ;1 min : ð7Þ 1  i  n;i6¼k kwi  wk k2 Hence, as long as a perturbation x ¼ ðx1 ; x2 ; . . .; xn ÞT satisfies    2 j ci  ck j xT x  min ;1 1  i  n;i6¼k kwi  wk k2 the kth alternative remains the most preferred alternative.

4.3 Solution Stability The spheres of stability for the dominated alternatives, that is, the regions in the perturbation space over which each of them becomes dominant and remains dominant, may be constructed using similar reasoning. For each alternative i, the center and the radius of the sphere of stability need to be determined. Because, by assumption, all of the boundaries of the partitions in perturbation space are linear, the problem of determining the spheres of stability for the dominated alternatives is known as the Euclidean center problem of a linear programming model (Dantzig and Thapa 1997). The spheres of stability are the largest spheres that can be inscribed in the regions XðhÞ; h ¼ 1; 2; . . .; n; h 6¼ k: Let yh ¼ ðyh1 ; . . .; yhn Þ denote the Euclidean center associated with the region XðhÞ: First, we need to find the distance from the Euclidean center to the boundaries. Using (6), the distance from the Euclidean center yh in the region XðhÞ to Bði; hÞ : xT ðwi  wh Þ ¼ ci  ch ; the boundary separating region h from region i, is given by ci  ch  yT ðwi  wh Þ h dih ðyh Þ ¼ : ð8Þ kwi  wh k2 Equation (8) implies that the boundary conditions may be written as yTh ðwi  wh Þ þ kwi  wh k2 dih ðyh Þ ¼ ci  ch if yTh ðwi  wh Þ  ci  ch and yTh ðwi  wh Þ  kwi  wh k2 dih ðyh Þ ¼ ci  ch if yTh ðwi  wh Þ  ci  ch : To find the Euclidean center we also need boundary conditions. In our case the perturbations fall between -1 and 1 [see Eq. (4)]. Thus, the constraints 1  yhi  1 are replaced by yhi þ di ¼ 1 if yhi  1 and yhi  di ¼ 1 if yhi   1: Because we want to find the largest inscribed circle in each of the regions XðhÞ; h ¼ 1; 2; . . .; n; h 6¼ k we solve the following problem:

4 Stability of the ANP Solution

353

Find yh ; dih ðyh Þ; di and a that Maximize Subject to

a

yTh ðwi  wh Þ þ kwi  wh k2 dih ðyh Þ ¼ ci  ch i ¼ 1; 2; . . .; n; i 6¼ h or yTh ðwi  wh Þ  kwi  wh k2 dih ðyh Þ ¼ ci  ch i ¼ 1; 2; . . .; n; i 6¼ h

if yTh ðwi  wh Þ  ci  ch ; if yTh ðwi  wh Þ  ci  ch ;

yhi þ di ¼ 1

if yhi  1; i ¼ 1; 2; . . .; n or yhi  di ¼ 1 if yhi  1; i ¼ 1; 2; . . .; n dih ðyh Þ  a; i ¼ 1; 2; . . .; n; i 6¼ h di  a; i ¼ 1; 2; . . .; n The equations of the spheres of stability for the dominated alternatives are given by ðx  yh ÞT ðx  yh Þ  a where a ¼

min

1  i  n;i6¼k

fdih ðyh Þ; di g:

5 An Example Consider the network in Fig. 1. As a hierarchy, there are three levels, with one element in the Goal level, two elements in the Criteria level, and three elements in the Alternatives level. Based on the notation of Sect. 3, the number of levels H ¼ 3; and the numbers of elements in each level are n1 ¼ 1; n2 ¼ 2; and n3 ¼ 3: If, for example, we consider m = 10 perturbations, for a hierarchy, from (2), N = 1 * 1 ? 2 * 2 = 5 and from (1), the number of matrices to be analyzed is given by 115. As a network, from (3), N = (0 ? 1 ? 2)*(1 ? 2 ? 3) = 18, and from (1), the number of matrices to be analyzed is given by 118. The four arcs (from the Goal to the Fig. 1 A simple example

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Criteria, from the Criteria to the Alternatives, from the Alternatives to the Criteria, and from the Alternatives to the Alternatives) cause the supermatrix for the network depicted in Fig. 1 to be of the form: 0 1 0 0 0 @ W21 0 W23 A: 0 W32 W33

For this example, we set the numerical values for the submatrices Wij as given in Table 1. We perturbed all the entries of rows 2 and 3 of the matrix W23 using m = 21 perturbation levels (-0.95, -0.9, -0.8, -0.7, -0.6, -0.5, -0.4, -0.3, -0.2, -0.1, 0, +0.1, +0.2, +0.3, +0.4, +0.5, +0.6, +0.7 +0.8, +0.9, +0.95), taking into account that the perturbed entries cannot go above 1 or below zero. The perturbation Dij was the same for every entry of a row. Every time the rows were perturbed, the limiting priorities of the supermatrix were computed and the alternative that dominated was associated with the perturbation vector (see Table 2). The resulting matrix of perturbations had 441 rows. Table 3 shows an example of the data generated in the experiment. The first two columns are the perturbations of the entries of rows 2 and 3 in the matrix of Table 1, and the third column gives the alternative whose limiting priority is the largest. Figure 2 shows the three regions in which the alternatives are most preferred. The perturbation space is partitioned into three regions, represented by the sets A1 ; A2 and A3 : Let Ai ; i = 1,2,3 be the matrices representing the sets Ai ; i ¼ 1; 2; 3; respectively. Using the robust linear programming formulation of Bennett Table 1 The supermatrix for the example Goal C1

C2

A1

A2

A3

Goal C1 C2 A1 A2 A3

0 0 0 0.1 0.4 0.5

0 0.07 0.63 0 0.18 0.12

0 0.35 0.35 0.18 0 0.12

0 0.63 0.07 0.12 0.18 0

Table 2 The limit matrix (The Cesaro Sum) Goal C1 C2

A1

A2

A3

Goal C1 C2 A1 A2 A3

0 0.203014 0.208747 0.184581 0.229314 0.174344

0 0.203014 0.208747 0.184581 0.229314 0.174344

0 0.203014 0.208747 0.184581 0.229314 0.174344

0 0.2 0.8 0 0 0

0 0.203011 0.208744 0.184583 0.229316 0.174346

0 0 0 0.5 0.4 0.1

0 0.203019 0.208752 0.184578 0.229309 0.174341

0 0.203019 0.208752 0.184578 0.229309 0.174341

5 An Example

355

Fig. 2 Regions of perturbations where the alternatives dominate

and Mangasarian (1992), we calculated the planes that best separated the regions represented by the Ai ; i ¼ 1; 2; 3 sets. We found the 2  1 vectors w1 ; w2 ; w3 ; the mi  1vectors yij ; i; j ¼ 1; 2; 3; i 6¼ j and the 3  1 vector c; to: Minimize eT y12 eT y21 eT y13 eT y31 eT y23 eT y32 þ þ þ þ þ m1 m2 m1 m3 m2 m3

Table 3 Example of the data generated in the perturbation experiment

Perturbation of C1

Perturbation of C2

Dominant alternative

0.4 0.4 0.5 0.5 0.5 … 0 0 0 0 0 … -0.2 -0.2 -0.3 -0.3 -0.3

-0.9 -0.95 -0.6 -0.7 -0.8 … 0 0.1 -0.1 0.2 -0.2 … 0.9 0.95 0.8 0.9 0.95

A1 A1 A1 A1 A1 … A2 A2 A2 A2 A2 … A3 A3 A3 A3 A3

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Fig. 3 Separating planes in the perturbation space

Subject to  A1 ðw1  w2 Þ þ eðc1  c2 Þ þ e  y12 A2 ðw2  w1 Þ  eðc2  c1 Þ þ e  y21  A1 ðw1  w3 Þ þ eðc1  c3 Þ þ e  y13 A3 ðw3  w1 Þ  eðc3  c1 Þ þ e  y31  A2 ðw2  w3 Þ þ eðc2  c3 Þ þ e  y23 A3 ðw3  w2 Þ  eðc3  c2 Þ þ e  y32 yij  0;

i; j ¼ 1; 2; 3; i 6¼ j

Alternative A1 was dominant for 47 perturbations, A2 for 354, and A3 for 40, so m1 = 47, m2 = 354 and m3 = 40. The points at which A2 dominated are not shown in Fig. 5 so that the other two partitions may be seen more clearly. The plane separating sets A1 and A2 is given by Bð1; 2Þ : 16x  12y ¼ 15:4 and the plane separating the sets A2 and A3 is given by Bð2; 3Þ : 4x  8y ¼ 7: Figure 3 shows the planes and the perturbation regions. The partition in Fig. 4 is based on a similar analysis, using a finer grid for the perturbations (increments of 0.002 instead of 0.1); the points shown are from the 0.1 grid. Note that the approximation of the boundaries of the three regions by hyperplanes misclassifies some perturbations along each hyperplane. The plot in Fig. 4 indicates that the actual boundaries of each region may be piecewise linear, and that the regions are not necessary convex, but they are connected. Figure 5 depicts the sphere of stability of alternative A2, the preferred alternative when the supermatrix entries are not perturbed. The equation of the sphere is xT x  ð0:77Þ2 : The implication of that equation is that alternative A2, the alternative that dominates when the supermatrix entries are not perturbed at all,

5 An Example

357

Fig. 4 A finer set of perturbations

Fig. 5 The largest sphere centered at the origin for which the alternative A2 is most preferred

remains the preferred alternative as long as p21 ? p22 is less than (0.77)2 = 0.5929, where p1 is the proportional perturbation of the Table 1 supermatrix entries in the row corresponding to A1, and p2 is the proportional perturbation of the Table 1 supermatrix entries in the row corresponding to A2. Figure 6 depicts the spheres of stability for alternatives A1 and A3. The inequality for the sphere of stability for alternative A1 is ðx1  0:7375Þ2 þ ðx2 þ 0:7375Þ2  ð0:2625Þ2 : The implication of that inequality is that alternative A1 is most preferred as long as p1 (the proportional perturbation of the Table 1 supermatrix entries in the row

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Fig. 6 The Euclidean centers spheres of dominated alternatives

corresponding to A1) is sufficiently close to 0.7375; and p2 (the proportional perturbation of the Table 1 supermatrix entries in the row corresponding to A2) is sufficiently close to -0.7375, such that (p1 - 0.7375)2 ? (p2 ? 0.7375)2 is no greater than 0.26252. The inequality for the sphere of stability for alternative A3 is given by ðx1 þ0:7613Þ2 þ ðx2  0:7613Þ2  ð0:2387Þ2 : Its interpretation is analogous to the interpretation of the sphere for A1.

6 Conclusions and Further Research W developed linear optimization models to study the sensitivity and stability of solutions of ANP models from two perspectives: Core stability—the region of the solution space in which the initial solution remains most preferred; and Solution stability—the regions of the solution space in which different solutions are most preferred. The primary contributions of our work are: (1) the structure of the methodology, (2) the use of a set of numerical experiments, and (3) the use of optimization to extract insight from those experiments. Further research might provide refinements to both the numerical experimentation component and to the optimization model used to define the boundaries. The first component of our approach is the numerical perturbations of the supermatrix entries. The more perturbations that are calculated, the more precise the optimization modeling may become. Perturbations require significant amount of computer resources, evidenced by the partitions depicted in Fig. 2 through Fig. 6. There, we found that the precision of the stability and sensitivity analysis is driven

6 Conclusions and Further Research

359

by fineness of the grid in the immediate neighborhood of the boundaries. A finer grid in the interior of each partition does not improve the model. Finding a way to increase the fineness of the grid in the neighborhood of the boundaries and to decrease the fineness of the grid in the interior of the partitions would decrease the amount of time necessary to gather the ANP perturbation results. It would also reduce the size of the linear programs necessary when applying our approach, because the size of the LP is based on the number of points in the total grid. It is important to note that the boundaries of the fine grid in Fig. 4 appear to be piecewise linear. If we can demonstrate that the boundaries are truly piecewise linear, then the perturbation part of the sensitivity analysis might be massively simplified when it is possible to determine the end points of each linear segment. The second component of our approach is the optimization models. We used LP for optimization because its results are simple to interpret. Linear approximation of the nonlinear boundaries introduces potential error into the analysis; the degree of error is a function of the nonlinearity of the true partition boundaries. Further research on the second component might proceed in several directions. For example, could we relate the degree of nonlinearity of the partition boundaries to the structure of the ANP supermatrix? What types of nonlinear optimization models would provide more precise boundary modeling, while permitting easy computation of the spheres of stability that are the basis for our results? ANP models, as with all management science methodologies, are of greater managerial value if their sensitivity can be determined and interpreted. The approach we introduced in this paper, and illustrated with a numerical example, should increase the value of ANP as a modeling tool. We believe that further extension and refinements of our work will continue to increase the utility of ANP.

References Aguaron, J. and J.M. Moreno Jimenez (2000). Local stability intervals in the Analytic Hierarchy Process. European Journal of Operational Research 125, 113-132. Altuzarra, A., J.M. Moreno-Jimenez, M. Salvador (2010). Consensus Building in AHP-Group Decision Making: A Bayesian Approach. Operations Research 58, 6, 1755-1773. Arbel, A. (1989). Approximate articulation of preference and priority derivation. European Journal of Operational Research 43, 317-326. Arbel, A. and L.G. Vargas (2007). Interval judgments and Euclidean centers. Mathematical and Computer Modeling 46, 976–984. Bennett, K. P. and O. L. Mangasarian (1992). Robust Linear Programming Discrimination of Two Linearly Inseparable Sets. Optimization Methods and Software 1: 23-34. Chen, H. and D. F. Kocaoglu (2008). A sensitivity analysis algorithm for hierarchical decision models. European Journal of Operational Research 185(1), 266-288. Dantzig, G. B. and M. N. Thapa (1997). Linear Programming 1: Introduction, Springer-Verlag. Huang, Y-F. (2002). Enhancement on sensitivity analysis of priority in Analytic Hierarchy Process. International Journal of General Systems 31, 5, 531–542. Horadam, K.J. (2007). Hadamard matrices and Their Applications, Princeton University Keener, J.P. (1993). The Perron-Frobenius Theorem and the Ranking of Football Teams, SIAM Review, Vol. 35, No. 1. (Mar., 1993), pp. 80-93.

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Lipovetsky, S. and A. Tishler (1999). Interval estimation of priorities in the AHP. European Journal of Operational Research 114, 153-164. Mangasarian, O. L. (1997). Mathematical Programming in Data Mining. Data Mining and Knowledge Discovery 1, 183-201. Masuda, T. (1990). Hierarchical sensitivity analysis of the priorities used in Analytic Hierarchy Process. International Journal of Systems Science 21, 2, 415-427. MacKay, D.B., W.M. Bowen and J.L. Zinnes (1996). A Thurstonian view of the Analytic Hierarchy Process. European Journal of Operational Research 89, 427-444. Moreno-Jimenez, J.M. and L.G. Vargas (1993). A probabilistic study of preference structures in the Analytic Hierarchy Process with interval judgments. Mathematical and Computer Modeling 17, 415, 73-81. Paulson, D. and S. Zahir (1995). Consequences of uncertainty in the analytic hierarchy process: A simulation approach. European Journal of Operational Research 87, 45-56. Saaty, T.L. and L.G. Vargas (1987). Uncertainty and rank order in the Analytic Hierarchy, European Journal of Operational Research 32, 107-117. Sowlati, T., P. Assadi, J.C. Paradi (2010). Developing a mathematical programming model for sensitivity analysis in analytic hierarchy process. Int. J. Mathematics in Operational Research 2, 3, 290–301. Thurstone, L. (1927). A law of comparative judgments. Psychological Review 34, 273–286. Triantaphyllou, E. and A. Sánchez (1997). A sensitivity analysis approach for some deterministic multi-criteria decision-making methods. Decision Sciences 28, 151–194. Vargas, L.G. (1982). Reciprocal Matrices with Random Coefficients. Mathematical and Computer Modeling 3, 69-81). Wilkinson, J.H. (1965). The Algebraic Eigenvalue Problem. Clarendon Press, Oxford. Wu, C.-R., C.-W. Chang and H.-L. Lin (2007). An organizational performance measurement model based on AHP sensitivity analysis. International Journal of Business Performance Management 9:1, 77-91. Zhong, H. and X. Gu (2010). Assessment of power system black-start schemes based on fuzzy analytic hierarchy process and its sensitivity analysis. Dianli Xitong Zidonghua/Automation of Electric Power Systems 34:16, 34-37.

Index

A Absolute Cardinal Preference Relations, 29 Alaska National Interest Conservation Act, 119 Analysis, 1 Arctic National Wildlife Refuge, 119 Arrow’s conditions, 26 Arrowvian social welfare function, 29

B Backtest ANP model, 89 Benefits, 12 BOCR model for ANWR, 120

C Cardinal Independence from Irrelevant Alternatives, 26 Cardinal Preference Relations, 27 Cesaro Sum, 15 CHINA and TAIWAN, 255 China armed takeover of Taiwan, 255 Comparative Advantage Approach, 199 Complete Energy Independence, 199 Consistency property, 30 Consistent, 25 Consistent profiles, 32 Control criteria, 11 Control hierarchy, 12 Core Stability, 351 Criteria for Group Decision Making Methods, 296 Cyclicity, 17

D DECISION-MAKING, 295 Distributive mode, 5 Divided China, 255

E Energy Independence Emphasis, 199 European Union, 239 Euro zone, 239 Evaluation of the Methods on the Criteria, 307

F Federal Insurance Contribution Act, 213 Feedback, 6 Financial crises types, 75 Financial-crisis human judgment, 87 signaling technique, 87 FINANCIAL-CRISIS FORECASTING, 75 Financial Crisis Model, 78 FORD EXPLORER CASE, 133 Forecast economic recovery, 75 financial crisis, 75 FORECASTING, 41 Forecast of the recovery, 49 Fundamental scale, 3

G Game theory, 160 Geometric mean, 26 GROUP, 295 Group Decision Making, 23 Group Decision Making Methods, 303

T. L. Saaty and L. G. Vargas, Decision Making with the Analytic Network Process, International Series in Operations Research & Management Science 195, DOI: 10.1007/978-1-4614-7279-7,  Springer Science+Business Media New York 2013

361

362 H Heuristics, 76, 91 Holarchy, 44 Homogeneity, 23

I Ideal mode, 5 Inconsistent profiles, 33 Independence of Taiwan, 255 Inner dependent, 9 INTANGIBLE HUMANE ACTS, 319 Intangibles, 2

L Limit matrix, 14 Logic deductive, 90 Long-Term Future Stability, 173

M Maastricht Treaty, 238 MIDDLE EAST CONFLICT RESOLUTION, 159 Mutual independence, 8

N National Energy Policy, 185 National Highway Safety Administration, 133 New Orders-of-Magnitude, 320 Non-Dictatorship, 26, 32 North Korean Nuclear Threat, 271 Nuclear threat, 294

O Of Judgment in Economic Forecasting, 41 Opportunities, 12 Ordering and Ranking, 304 ORDERS-OF-MAGNITUDE, 319 Outer dependent, 10 Outsourcing Information Technology, 93 Overall synthesis, 13

P Pairwise Dominance, 33 Pairwise preference, 25

Index Pareto Principle, 26 Peaceful unification, 255 Peace in Region, 173 POLAND, 235 Power conditions, 23

Q Quasitransitivity, 27

R Rating, 18 Rating Intangible Contribution, 324 Reciprocal pairwise profile, 25 Recognition of Defined Boundaries, 173 Relative Value of Altruistic Acts, 325 Retirement Risks, 13, 82

S SENSITIVITY ANALYSIS, 345 Sensitivity Analysis of Judgments, 346 Sensitivity Analysis of Priorities, 347 Separability, 23 Sink node, 7 SOCIAL SECURITY, 213 Social welfare function, 25 Social welfare mapping, 31 Solution Stability, 352 Source node, 7 Stability of the ANP Solution, 348 Status Quo Approach, 199 Stochastic matrix, 13 Structuring and Measuring, 305 SuperDecisions, 16 Supermatrix financial crisis, 77 financial crisis, construction, 82 Supermatrix, 9 Synthesis, 1

T Tangibles, 2 Technology and Resources, 97 The Value of Benevolent Acts, 340 Transient components, 9

Index U U.S. Banking Crisis 1991, 87 U.S. Energy Policy, 185 U.S. ENERGY SECURITY, 185 Unanimity, 23 Unrestricted Domain, 26 Utility theory, 160

363 W Weighted supermatrix, 14