Cognitive Operations: Models that Open the Black Box and Predict our Decisions 3031319966, 9783031319969

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Cognitive Operations Models that Open the Black Box and Predict our Decisions Konstantinos V. Katsikopoulos

Cognitive Operations

Konstantinos V. Katsikopoulos

Cognitive Operations Models that Open the Black Box and Predict our Decisions

Konstantinos V. Katsikopoulos University of Southampton Business School Southampton, UK

ISBN 978-3-031-31996-9 ISBN 978-3-031-31997-6 (eBook) https://doi.org/10.1007/978-3-031-31997-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Palgrave Macmillan imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

To Özgür

Acknowledgments

This book benefited greatly from the input and support provided by a number of people. I am grateful to Robert Aumann, Elliot Bendoly, Craig Carter, Stephanie Eckerd, Alberto Franco, Gerd Gigerenzer, Paul Goodwin, Werner Güth, Ça˘grı Haksöz, Raimo Hämäläinen, Stefan Herzog, Martin Kunc, Stephen Leider, Gilberto Montibeller, Jon Malpass, Laura Martignon, Thorsten Pachur, Fotios Petropoulos, Jochen Reb, Hersh Shefrin, Enno Siemsen, Leonidas Spiliopoulos, Aris Syntetos, Özgür Sim¸ ¸ sek, Riccardo Viale, Jyrki Wallenius, and Rosanna Arquette. I would also like to thank the organizers and participants of the First and Second Summer Schools on Behavioural Operational Research at respectively Aalto and Radboud Nijmegen Universities, and the First Innsbruck Workshop on Behavioral Operations and Supply Chain Management, as well as the students of the postgraduate module Behavioural Operations at the University of Southampton. I am more than indebted to Juan Pablo Fernández for preparing graphics, performing computational analyses, and offering writing suggestions. Finally, a big thanks goes to Alec Selwyn, Jessica Harrison, and Abarna Antonyraj, my editorial support at Palgrave Macmillan and Springer Nature.

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Contents

1

What Is Cognitive Operations? 1.1 Behavioral Operations 1.2 Cognitive Operations

1 2 3

Part I A Cognitive Perspective 2

Optimization and Simple Heuristics 2.1 When Do People Take Risks? 2.2 The Distinction Between Risk and Uncertainty 2.3 Expected Utility Theory 2.4 Minimax and Maximax 2.5 Two Approaches to Modeling Human Behavior 2.6 The Kind of Studies in This Book 2.7 Summary

13 14 14 16 18 21 25 28

3

Decision Under Risk 3.1 Empirical Phenomena 3.2 Prospect Theory 3.3 Priority Heuristic 3.4 Predictive Power 3.5 Cognitive Processes 3.6 Transparency 3.7 Usefulness of Output 3.8 Summary and Resources

35 36 39 42 46 50 53 56 61

ix

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CONTENTS

4

Strategic Interaction 4.1 Giving and Receiving Ultimatums: Theory and Data 4.2 Inequity Aversion 4.3 Fast-and-Frugal Trees 4.4 Predicting Response Time Patterns 4.5 Cognitive Processes and Transparency 4.6 Theory Integration: Behavioral Outcomes 4.7 Beyond Bargaining Games 4.8 Summary and Segue

75 77 80 83 87 91 93 94 95

Part II Benefits of Cognitive Modeling 5

Inventory Control 5.1 The Newsvendor Problem: Theory and Data 5.2 Optimization 5.3 Anchoring and Adjustment Heuristic 5.4 Correction Heuristic 5.5 Predictive Power 5.6 Assessment and Integration of Models 5.7 Bounded Rationality and AI in Operations 5.8 Summary

105 107 110 114 116 121 125 128 131

6

Decision Under Uncertainty 6.1 A Peace-Keeping Operation: Compliance Heuristic 6.2 Making Supply Chains Flexible and Robust 6.3 Ecological Rationality 6.4 Summary and a Guide

143 145 151 154 161

7

Behavioral and Cognitive Interventions 7.1 Behavior with AI 7.2 Nudge and Boost 7.3 Summary

171 172 174 178

8

Lessons Learned and a Positive Look Ahead

183

Appendix

187

Bibliography

199

Author Index

225

Subject Index

231

About the Author

Konstantinos V. Katsikopoulos is Professor of Behavioral Science at the University of Southampton, where he is also the director of research for the Business School. He has been a visiting assistant professor at the Naval Postgraduate School and the Massachusetts Institute of Technology, as well as a senior research scientist and deputy director at the Max Planck Institute for Human Development. Konstantinos is the first author of Classification in the Wild: The Science and Art of Transparent Decision Making (MIT Press). He has received a German Science Foundation fellowship for young researchers, is a fellow of the Psychonomics Society, an associate editor of the Journal of Mathematical Psychology and Judgment and Decision Making, and chair of the Behavioural OR special interest group of the OR Society.

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List of Figures

Fig. 2.1 Fig. 2.2

Fig. 2.3

Fig. 3.1

Fig. 3.2

√ √ The utility function u(x) = x for x ≥ 0 and −2 −x for x < 0 Graphical representation of the minimax heuristic for the choice between an option X with minimum outcome x min and an option Y with minimum outcome y min . For simplicity we assume that x min / = y min Graphical representation of the maximax heuristic for the choice between an option X with maximum outcome x max and an option Y with maximum outcome y max . For simplicity we assume that x max / = y max Prospect theory’s utility function u(x) = x 0.88 for x ≥ 0 and −2.25(−x)0.88 for x < 0, as estimated by Tversky and Kahneman Prospect theory’s probability-weighting functions w( p) = and

Fig. 3.3

p 0.61 1

[ p 0.61 +(1− p)0.61 ] 0.61 p 0.69 1

[ p 0.69 +(1− p)0.69 ] 0.69

17

20

20

41

for p corresponding to x ≥ 0

for p corresponding to x < 0,

as estimated by Tversky and Kahneman Representation of the priority heuristic for gains as a fast-and-frugal tree. To simplify the last step we assume that xmax / = ymax

42

45

xiii

xiv

LIST OF FIGURES

Fig. 3.4

Fig. 3.5

Fig. 3.6

Fig. 3.7

Representation of the priority heuristic for losses as a fast-and-frugal tree. To simplify the last step we assume that xmin / = ymin Median response times (in seconds) of participants in the experiment by Brandstätter et al., when the priority heuristic would lead to a choice at its Step 1 or Step 3, for gambles with two or four outcomes The utility function u(x) = x 0.82 for x ≥ 0 and −1.37(−x)0.82 for x < 0, characterizing the priority heuristic in the cognitive psychometrics exercise by Pachur et al., where prospect theory was fitted to the heuristic’s choices The probability-weighting functions,

45

53

58

0.05 p 0.17 for p corresponding 0.05 p 0.17 +(1− p)0.17 0.62 p 0.17 for p corresponding to x ≥ 0 and 0.62 p 0.17 +(1− p)0.17

w( p) =

to x < 0, characterizing the priority heuristic in the cognitive psychometrics exercise by Pachur et al.,

Fig. 3.8

Fig. 4.1

Fig. 4.2

Fig. 4.3

Fig. 4.4 Fig. 4.5

where prospect theory was fitted to the heuristic’s choices The probability-weighting function wpriority ( p) = 0.05 + 0.5 p, for p < 0.1, p for 0.1 ≤ p ≤ 0.9, and 0.45 + 0.5 p for p > 0.9, that can be mapped to the priority heuristic based on the threshold value of 0.1 in its Step 2 Proportions of participants making various ultimatum-game offers, and of rejecting each offer, in the experiment by Güth and Sutter Inequity-aversion theory’s utility function u(x) = 3x − 1 for 0 ≤ x ≤ 0.5 and −0.2x + 0.6 for 0.5 < x ≤ 1, proposed by Fehr and Schmidt as characterizing 30% of the population Inequity-aversion theory’s utility function u(x) = 2x − 0.5 for 0 ≤ x ≤ 0.5 and 0.5x + 0.25 for 0.5 < x ≤ 1, proposed by Fehr and Schmidt as characterizing 30% of the population A mini-ultimatum game and its four, offered and foregone, payoffs The mirror tree of Hertwig et al., for predicting whether the responder to the mini-ultimatum game accepts or rejects an offer of Ro

59

60

80

82

83 85

86

LIST OF FIGURES

Fig. 4.6

Fig. 4.7 Fig. 4.8

Fig. 4.9

Fig. 5.1

Fig. 5.2

The priority tree of Hertwig et al., for predicting whether the responder to the mini-ultimatum game accepts or rejects an offer of Ro . The proposer’s payoff equals Po and the foregone payoff of the responder is R f Example of a screen shown to responders in the experiment by Hertwig et al.; adapted from Fischbacher et al. Median response times (in seconds) of participants in the Hertwig et al. mini-ultimatum game experiment, for participants classified as users of the selfish tree and all other participants Median response times (in seconds) of participants in the Hertwig et al. mini-ultimatum game experiment, when the priority tree leads to a choice at its Step 2 or Step 3 Mean orders q placed in the Bolton et al. experiment by students and practitioners, given sample and distribution information about demand The equation of Ockenfels and Selten’s impulse balance equilibrium model, q =

Fig. 5.3

Fig. 5.4

Fig. 5.5

Fig. 5.6

Fig. 6.1

1 1−q ∗ )(2−q ∗ ) ( 1+ q∗ √

Illustration of the anchoring and adjustment heuristic for w = 0.33, which means q = 0.67q ∗ + 0.17; w = 0.5, which leads to q = 0.5q ∗ + 0.25; and w = 0.67, which means q = 0.33q ∗ + 0.33 Illustration of the correction heuristic for t = 0.33, which means q = 0.5q ∗ + 0.17 for q ∗ < 0.33, q ∗ for 0.33 ≤ q ∗ ≤ 0.67, and 0.5q ∗ + 0.33 for q ∗ > 0.67; for t = 0.5 which leads to q = 0.5q ∗ + 0.25; and for t = 0.67, which means that q = 0.5q ∗ + 0.33 for q ∗ < 0.33, 0.5 for 0.33 ≤ q ∗ ≤ 0.67, and 0.5q ∗ + 0.17 for q ∗ > 0.67 The performance of the two heuristics and the two benchmarks as a function of the training set size. The curves for the heuristics are identical Histograms of best-fitting parameter estimates for the two heuristics when the training set has six data points; each bin has a width of 0.02 The compliance heuristic represented as a fast-and-frugal tree

xv

87 88

90

91

109

112

115

119

123

125 150

xvi

LIST OF FIGURES

Fig. 6.2

Fig. 6.3

Fig. 7.1

Fig. 7.2

Fig. A.1

A fast-and-frugal tree for classifying vehicles approaching a checkpoint as civilian or hostile (Adapted from Keller and Katsikopoulos 2016) A fast-and-frugal tree that puts together the three simple rules discussed in this section, for describing and prescribing successful practice in supplier sourcing (Adapted from Haksöz et al.). It is assumed that supply chain managers go through the tree repeatedly until the bottom-left exit is reached Mean completion times of a manufacturing production task, when instructions were readily available (guided learning) and when instructions were not available (free recall); in both cases instructions were provided by an AI system or on paper (Adapted from Wuttke et al.) Mean rates of compliance with a hand hygiene hospital protocol, when a nudge was presented and when a boost was provided; in both cases participants were tested immediately after the intervention and then a second time with a delay of one week (Adapted from Roekel et al.) A game tree model of the checkpoint problem

151

154

174

177 194

List of Tables

Table 2.1 Table 2.2

Table 3.1 Table 3.2

Table 3.3 Table 4.1

Table 4.2 Table 5.1 Table 5.2

Table 5.3

Summary of the comparative analysis of expected utility theory and the minimax/maximax heuristics When a fair coin is flipped three times, the average probability that heads follow heads is counted to be 2.5 = 41.7% 6 Estimates of the parameters of prospect theory from two datasets Proportion of people’s majority choices predicted correctly by prospect theory and the priority heuristic in four datasets Summary of the comparative analysis of prospect theory and the priority heuristic The 24 decision scenarios in the Hertwig et al. mini-ultimatum game experiment, and the observed rejection rates Summary of the comparative analysis of inequity-aversion theory and fast-and-frugal trees Summary of the theoretical results on how the models presented in the chapter can describe the empirical data Mean size of the pull-to-center effect s from empirical studies where demand is uniformly distributed, high ∗ = 0.75 and low profit case q ∗ = 0.25 profit case q H L (from Zhang and Siemsen, 2018, Table 2) Summary of the analyses of optimization and heuristic models for describing people’s newsvendor behavior

25

27 47

48 62

89 95 120

121 132

xvii

xviii

LIST OF TABLES

Table 6.1

Table 6.2 Table 8.1 Table A.1

Analysis of the soldier classifications in non-routine encounters at Afghanistan checkpoints between 2004 and 2009 (from Keller and Katsikopoulos 2016) Best-performing family of methods for each type of task Lessons from research on models of and interventions for human decision making The payoff matrix of the checkpoint problem, where the numbers are expected payoffs based on the information in the game tree of Fig. A.1

147 161 184

195

CHAPTER 1

What Is Cognitive Operations?

The American classic Cheaper by the Dozen is the story of a family of twelve children and their parents Frank and Lillian Gilbreth, pioneers of quantitative management in the early twentieth century. At one point, Frank goes on a rant about surgeons1 : Surgeons really aren’t much different from skilled mechanics, except that they’re not so skilled. If I can get to study their motions, I can speed them up. The speed of an operation often means the difference between life and death.

Frank studied the physical movements of surgeons performing abdominal operations and redesigned them so that patient time under ether was reduced by 15%. Encouraged by this success, Frank wanted to repeat the study for his children’s removal of tonsils. In doing so, Lillian and he considered the psychology of the doctors and the children. They ascertained that the doctors would not get nervous and underperform when they were observed. In addition, Frank offered moral support to the children by volunteering to have his tonsils taken out as well. The operations were successful, even though the father had a longer recuperation period than the children.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6_1

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1.1

Behavioral Operations

Operations management and operations, or operational, research2 are prescriptive sciences. They aim at suggesting what customers, retailers, suppliers, managers, and other decision makers should do, and at supporting them in doing so. As Frank Gilbreth’s rant says, the improvement of an operation is easier to accomplish when the behavior of the people involved in it is well understood. In order to prescribe what decisions one should make, it is important to first describe what decisions one actually does make.3 This approach is taken in the fields of behavioral operations management and behavioral operational research,4 or as referred to jointly here, behavioral operations. In a handbook edited by Karen Donohue and her colleagues, behavioral operations is defined as the ‘study of how individuals behave and make decisions within operational settings’.5 For example, behavioral operations studies under which conditions customers choose to pay a fixed price now or an uncertain price later, to what extent inventory orders are calibrated to demand, or how retailers bargain with suppliers. Human behavior can be described in various ways. Observational studies, lab experiments, case studies, and secondary data sources can all help build a base of empirical knowledge. A standard method of summarizing knowledge on human behavior is by representing it formally. This method also allows for deducing clear and precise predictions about future behavior. A review of 238 behavioral operations articles published in five leading journals between 2012 and 2017 found that formal modeling was the most prevalent method, employed in 44% of the articles.6 This book presents models that describe mathematically how practitioners and laypeople make decisions under risk and uncertainty. Such descriptive models can be plugged into and expand the scope of existing prescriptive models. For instance, modeling how people experience and react to waiting in a queue can be used to revise standard queueing theory.7 Behavioral modeling is critical in the operation of systems during a crisis such as a pandemic, by helping estimate the impact of behavioral interventions (e.g., quarantine rules) and resource management strategies (e.g., hospital admission rules) within epidemiological and simulation approaches.8 An important part of the science of crisis management is behavioral science.

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3

Some of the descriptive models in this book are well known in behavioral operations, while others are little or not at all known to the field and are imported from core behavioral sciences such as psychology and economics, and yet other models are developed for the first time here. The selection of models presented serves three goals. The first goal is, as suggested by Stephanie Eckerd and Elliot Bendoly,9 to enhance pluralism in the study of behavioral operations and to ensure the openness of the field to new points of view. As we will see, most models in the field to date come from a single approach to descriptive modeling. The book introduces an alternative approach as well. The second goal is to support readers in selecting a modeling approach that suits the decision problem at hand. The third goal is to point out cases where the approaches have been integrated, and show the benefits that integration brings. These goals are achieved by introducing a spectrum of modeling ideas that have been used fruitfully in disciplines such as cognitive psychology, behavioral economics, and machine learning,10 and by applying these ideas to the study of operations.

1.2

Cognitive Operations

Most modeling in behavioral operations follows the approach of optimization. For example, take prospect theory that is often used to describe people’s decisions under risk.11 This theory proposes that people maximize the expectation of a utility function that includes not only money but also other factors such as loss aversion and the non-linear perception of probability. Given that operations research and operations management have been employing optimization for developing prescriptive models— despite criticism by leading figures such as Russell Ackoff—it is perhaps not surprising that behavioral operations embraced optimization for developing descriptive models as well.12 But note that optimization in prescriptive models is performed by computers. It is less clear how people could be processing information optimally. Economics, a source of inspiration for behavioral operations, is of little help on this issue which it traditionally circumvents by suggesting that people behave ‘as if’ they optimize a utility function, and pronouncing irrelevant the study of how they do so.13 An alternative approach to describing human behavior is based on Herbert Simon’s14 idea that people do not optimize but satisfice 15

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For example, a retailer can choose a particular supplier without evaluating other suppliers, as long as the price and delivery schedule are deemed acceptable.16 Such simple ways of processing information might be more psychologically plausible than postulating that people are able to compute and integrate probabilities and utilities, deduce strategic equilibria, or calculate expected revenues and costs. One approach to formally modeling the information processing that underlies people’s non-optimizing behavior is that of simple heuristics 17 sometimes also called simple rules 18 two terms that will be used interchangeably here. Models of simple heuristics have received scarce attention in the behavioral operations literature, and the presentations mostly referred to their prescriptive, not descriptive, use.19 This notion of heuristics is related, but distinct, from other notions of heuristics used in the operations literature. Unlike purely computational shortcuts developed in ‘hard’ operations research, simple heuristics are derived from human psychology. And, unlike verbal heuristics and biases studied in ‘soft’ operations research or behavioral operations, simple heuristics are formally modeled. Cognitive Operations studies in-depth models of human behavior based on optimization as well as simple heuristics. The book puts emphasis on clarifying the differences and similarities between these two approaches, and the opportunities for their integration. In order to better understand models and support the choice of a modeling approach for a particular situation, the models are analyzed on the following criteria: Are the cognitive processes underlying behavior specified in the model? Are decisions predicted or fitted by the model? How transparent is the model? How can the output of the model be used?

Cognitive processes. Cognitive Operations is inspired by the ‘cognitive revolution’ of the 1960s, which was launched, among others, by Simon (again). This revolution proclaimed that researchers should specify the mental processes leading to an agent’s, human or artificial, observed behavior.20 In other words, researchers should open the black box. Specifying the underlying processes improves the understanding of

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5

why a behavior was observed. For example, it is insightful to know that a retailer chose a supplier because the proposed price and delivery schedule met her aspirations. The models presented in this book are assessed on the degree to which they specify cognitive processes. Predictive power. The Gilbreths did not just assume that Frank’s method for reducing the duration of abdominal operations would necessarily succeed for tonsil operations as well. Rather, they tested this proposition empirically. Statistics and machine learning place a premium on testing models according to their power to perform well in new tasks, which are different from the tasks in which the models were trained.21 In other words, predicting future observations is more valuable than fitting past ones. In operations, retailers need to predict future, not past, demand. In their 20-year retrospective of research on behavioral operations, Karen Donohue, Özalp Özer, and Yanchong Zheng point out the importance of prediction and how it can enhance the understanding of processes: ‘Prediction-focused research helps separate out which behavioral theories are robust to different situations and, in the process, often identifies a new attribution that provides a deeper understanding of the underlying mechanisms’.22 The present book measures quantitatively how well models predict unknown, rather than fit known, human behavior. Transparency. Cognitive Operations aims at building mathematical models that are transparent to their users. A model is transparent to someone when she can understand, apply, and explain it to other people. This definition includes components of transparency commonly put forth in computer science, such as usability and explainability.23 Transparent models facilitate the development of narratives and stories. Operational research can be viewed as a process-based practice of storytelling, where the purpose of model-based stories is to bring positive change.24 With the increasing use of data-driven analytics in sensitive domains such as wealth, health, and justice, stakeholders such as citizens, practitioners, and lawmakers deserve access to transparent models. Usefulness of output. Finally, the book focuses on the kind of output provided by various models. Optimization models such as prospect theory provide a numerical valuation of each decision option, whereas satisficing models typically just state which option is preferred (although, as we will see, sometimes they can also be augmented to make valuations). In which contexts is one kind of output more useful than the other? One should not rush to assume that the more complex or quantitatively sophisticated the output of a model is, the more useful it is for the model users. If you

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own a chain of restaurants and you are trying to gauge customer satisfaction across different locations in the UK based on TripAdvisor reviews, how seriously would you take the difference between a rating or estimate of 4.48 for Southampton and a rating or estimate of 4.24 for Bath? In an experiment on resource utilization for an ambulance service, users of complex models which fully represented the task demonstrated a worse understanding of the problem than others who used a simpler model that had less detail.2526 This book presents models of human behavior in four fundamental types of operational decisions: decision under risk, strategic interaction, inventory control, and decision under uncertainty. Decision under risk and strategic interaction have been treated extensively in the literature, and form building blocks for studying inventory control, whereas decision under uncertainty is more uncharted territory, presenting novel challenges. The selection of these decision types aims at explaining general principles of cognitive modeling in operations, in order to help readers customize and apply those principles to more specific situations. Each decision type forms a separate chapter, where multiple models are developed formally, tested with data (from the lab or the field), analyzed conceptually, and integrated with each other. The two modeling approaches of optimization and simple heuristics are introduced and sketched in the next chapter, and shown in action in the chapters after that, with some technical material relegated to an Appendix. The exposition is example-based and assumes little a priori knowledge, developing slowly and reaching the state of the art. There is a substantial amount of cross-referencing and cross-fertilizing across chapters. Besides this introductory chapter and a concluding one, the book consists of two parts. Part I (Chapters 2–4) focuses on a cognitive perspective on operational decision making, introducing ideas and tools that cognitive psychology, behavioral economics, and machine learning, have offered to model decisions. Part II (Chapters 5–7) looks at and further develops these ideas and tools in richer operational contexts, also discussing benefits that can be expected from suitable cognitive modeling in operations. The last chapter of this part also makes a connection with approaches to behavioral change that are related to models but go beyond them,27 focusing on ideas such as nudge and boost.28 Chapter 8 concludes by summarizing the lessons learned in the book and offering a positive look ahead.

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Notes 1. Frank B. Gilbreth Jr. and Ernestine Gilbreth Carey, Cheaper by the Dozen (New York: Thomas Y. Crowell, 1994): Ch. 10. 2. The term “operations research” is used more in North America whereas the term “operational research” is used more in Europe. In this book, I use the term that seemed most appropriate for each context. 3. David E. Bell, Howard Raiffa and Amos Tversky, eds., Decision Making: Descriptive, Normative, and Prescriptive Interactions (Cambridge, UK: Cambridge University Press, 1988). 4. Examples of foundational work in these fields are: Pekka J. Korhonen, Herbert Moskowitz and Jyrki Wallenius, “Choice Behavior in Interactive Multiple-Criteria Decision Making,” Annals of Operations Research 23, no. 1 (1990): 161–179; Neil J. Bearden and Amnon Rapoport, “Operations Research in Experimental Psychology,” Tutorials in Operations Research (2005): 213–236; Craig R. Carter, Lutz Kaufmann and Alex Michel, “Behavioral Supply Management: A Taxonomy of Judgment and Decision-Making Biases,” International Journal of Physical Distribution and Logistics Management 37, no. 8 (2007): 631–669; Christoph H. Loch and Yaozhong Wu, Behavioral Operations Management (Norwell, MA: Now Publishers, 2007); Raimo P. Hämäläinen, Jukka Luoma and Esa Saarinen, “On the Importance of Behavioral Operational Research: The Case of Understanding and Communicating about Dynamic Systems,” European Journal of Operational Research 228, no. 3 (2013): 623–634; Elliot Bendoly, Wout van Wezel and Daniel G. Bachrach, eds., The Handbook of Behavioral Operations Management: Social and Psychological Dynamics in Production and Service Settings (New York: Oxford University Press, 2015); Martin H. Kunc, Jonathan Malpass and Leroy White, eds., Behavioral Operational Research: Theory, Methodology and Practice (London: Palgrave Macmillan, 2016); Karen Donohue, Elena Katok and Stephen Leider, eds., The Handbook of Behavioral Operations (Hoboken, NJ: John Wiley and Sons, 2018); Leroy White, Martin H. Kunc, Katharina Burger and Jon Malpass, eds., Behavioral Operational Research: A Capabilities Approach (London: Palgrave Macmillan, 2020). 5. Donohue et al., The Handbook of Behavioral Operations, xxi. For other definitions and discussion on definitions, see Rachel Croson, Kenneth Schulz, Enno Siemsen and M. Lisa Yeo, “Behavioral Operations: The State of the Field,” Journal of Operations Management 31, nos. 1–2 (2013): 1–5; Behnam Fahimnia, Mehrdokht Pournader, Enno Siemsen, Elliot Bendoly and Charles Wang, “Behavioral Operations and Supply Chain Management–A Review and Literature Mapping,” Decision Sciences 50, no. 6 (2019): 1127–1183.

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6. Karen Donohue and Kenneth Schulz, “The Future is Bright: Recent Trends and Emerging Topics in Behavioral Operations,” in The Handbook of Behavioral Operations, 622, Figure 18.2. 7. Yina Lu, Andrés Musalem, Marcelo Olivares and Ariel Schilkrut, “Measuring the Effect of Queues on Customer Purchases,” Management Science 59, no. 8 (2013): 1743–1763; Gad Allon and Mirko Kremer, “Behavioral Foundations of Queueing Systems,” in The Handbook of Behavioral Operations, 325–366. 8. Christine S. M. Currie et al., “How Simulation Modelling Can Help Reduce the Impact of COVID-19,” Journal of Simulation 14, no. 2 (2020): 83–97. 9. Stephanie Eckerd and Elliot Bendoly, “The Study of Behavioral Operations,” in The Handbook of Behavioral Operations Management, 3–23. 10. Gerd Gigerenzer, Peter M. Todd and the ABC Research Group, Simple Heuristics that Make Us Smart (New York: Oxford University Press, 1999); Colin F. Camerer, George Loewenstein and Matthew Rabin, eds., Advances in Behavioral Economics (Princeton: Princeton University Press, 2004); Konstantinos V. Katsikopoulos, Özgür Sim¸ ¸ sek, Marcus Buckmann and Gerd Gigerenzer, Classification in the Wild: The Science and Art of Transparent Decision Making (Cambridge, MA: MIT Press, 2020). 11. Daniel Kahneman and Amos Tversky, “Prospect Theory: An Analysis of Decision Under Risk,” Econometrica 47, no. 2 (1979): 263–291; Amos Tversky and Daniel Kahneman, “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Risk and Uncertainty, 5, no. 4 (1992): 297–323. 12. For example, see Karen Donohue, Özer Özalp and Yanchong Zheng, “Behavioral Operations: Past, Present, and Future,” Manufacturing and Service Operations Management 22, no. 1 (2020): 197, who write: “… it is natural, or perhaps, even necessary to begin exploration by crafting a normative [optimization] model as a benchmark for comparison against actual behavior”. 13. Milton Friedman, Essays in Positive Economics (Chicago: University of Chicago Press, 1953). 14. Herbert Simon was a polymath, who in the second half of the twentieth century made lasting contributions to the behavioral, management and computational sciences, some of which are key to this book. 15. Herbert A. Simon, “A Behavioral Model of Rational Choice,” The Quarterly Journal of Economics 69, no. 1 (1955): 99–118; Herbert A. Simon, “Rational Choice and the Structure of the Environment,” Psychological Review 63, no. 2 (1956): 129–138. 16. For example, a quantitative analysis of 628 German used car dealers found that 97% of them relied on satisficing; see Florian M. Artinger and Gerd

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17. 18. 19.

20. 21. 22.

23.

24.

25.

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Gigerenzer, “Adaptive Heuristic Pricing,” in Academy of Management Proceedings, 2016. Gigerenzer et al., Simple Heuristics that Make Us Smart. Donald N. Sull and Kathleen M. Eisenhardt, Simple Rules: How to Thrive in a Complex World (Boston: Houghton Mifflin Harcourt, 2015). For some exceptions, see Sven Bertel and Alex Kirlik, “Fast and Frugal Heuristics,” in Wiley Encyclopaedia of Operations Research and Management Science, ed. James J. Cochran (Hoboken, NJ: John Wiley and Sons, 2010); Manel Baucells and Konstantinos V. Katsikopoulos, “Descriptive Models of Decision Making,” Wiley Encyclopaedia of Operations Research and Management Science, ed. James J. Cochran (Hoboken, NJ: John Wiley and Sons, 2010); Konstantinos V. Katsikopoulos and Gerd Gigerenzer, “Behavioral Operations Management: A Blind Spot and a Research Program,” Journal of Supply Chain Management 49, no. 1 (2013): 3–7; Ian N. Durbach et al., “Fast and Frugal Heuristics for Portfolio Decisions with Positive Project Interactions,” Decision Support Systems 138 (2020): 113399. For an innovative perspective, see Suzanne de Treville et al., “Toyota Production System Practices as Fast-and-Frugal Heuristics,” Journal of Operations Management 69, no. 4 (2023): 522–535. Herbert A. Simon, The Sciences of the Artificial (Cambridge, MA: MIT Press, 1968). Leo Breiman et al., Classification and Regression Trees (Boca Raton, FL: CRC Press, 1984). Donohue et al., “Behavioral Operations: Past, Present, and Future”, 197. Woodside makes this point forcefully for business and management research more generally, in his “Seating Gigerenzer, Gladwin, McClelland, Sheth and Simon at the Same Table: Constructing Workbench Theories of Decision Processes That Predict Outcomes Accurately,” in Handbook of Advances in Marketing in an Era of Disruptions: Essays in Honour of Jagdish N. Sheth, eds. Atul Parvatiyar and Rajendra Sisodia (New Delhi, India: Sage, 2019), 445–480. Terms such as transparency, explainability, interpretability, trustworthiness, simulability, and so on, are often conflated and can mean different things to different people. See Zachary C. Lipton, “The Mythos of Model Interpretability: In Machine Learning, the Concept of Interpretability is Both Important and Slippery,” ACM Queue 16, no. 3 (2018): 31–57. Jonathan H. Klein, N. A. D. Connell and Edgar Meyer, “Operational Research Practice as Storytelling,” Journal of the Operational Research Society 58, no. 12 (2007): 1535–1542. Antuela A. Tako, Naoum Tsioptsias and Stewart Robinson, “Can We Learn From Simplified Simulation Models? An Experimental Study On User Learning,” Journal of Simulation 14, no. 2 (2020): 130–144;

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for further discussion and evidence see Pekka J. Korhonen and Jyrki Wallenius, Making Better Decisions (Berlin: Springer 2020): 118–119. 26. The above four criteria can be mapped to the different kinds of studies of models in behavioral operational research. Martin Kunc and his colleagues (see Behavioral Operational Research: Theory, Methodology and Practice) suggest that one may study how human behavior is incorporated in various models (criteria of cognitive processes and predictive power) or study how people interact with those models (criteria of transparency and usefulness of output). 27. Ibid.; the study of behavior beyond models is the third—besides behavior in and with models—kind of study of models in behavioral operational research. 28. Richard H. Thaler and Cass R. Sunstein, Nudge: Improving Decisions about Health, Wealth, and Happiness (New York: Penguin, 2009); Bond, Michael. “Risk School: Can the General Public Learn to Evaluate Risks Accurately, or Do Authorities Need to Steer it Towards Correct Decisions? Michael Bond Talks to the Two Opposing Camps.” Nature 461, no. 7268 (2009): 1189–1193; Gerd Gigerenzer, “On the Supposed Evidence for Libertarian Paternalism,” Review of Philosophy and Psychology 6, no. 3 (2015): 361–383; Ralph Hertwig and Till Grüne-Yanoff, “Nudging and Boosting: Steering or Empowering Good Decisions?,” Perspectives on Psychological Science 12, no. 6 (2017): 973–986.

PART I

A Cognitive Perspective

CHAPTER 2

Optimization and Simple Heuristics

The Drosophila Melanogaster, or as it is more commonly known the fruit fly, has about 75% of the genes known to cause human diseases. This makes it a great model organism for the basic study of human disease and the affordable and efficient testing of medical drugs, as pointed out by Christiane Nüsslein-Vollhard in her 1995 Nobel Prize in Physiology or Medicine lecture: The three of us have worked on the development of the small and totally harmless … Drosophila. This animal has been extremely cooperative in our hands and has revealed to us some of its innermost secrets and tricks for developing from a single celled egg to a complex living being of great beauty and harmony … None of us expected that our work would be so successful or that our findings would ever have relevance to medicine.

The drosophila is a workhorse of medical genetics. All scientific fields have their workhorses. People’s choices from a menu of options that exhibit different levels of risk is a drosophila of the study of decision making. Such choices are analyzed in this chapter and the next one. The present chapter introduces this work by focusing on people’s choices between a guaranteed outcome and an option that has some risk.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6_2

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2.1

When Do People Take Risks?

Modern probability theory was developed in the sixteenth and seventeenth centuries in Italy and France to support the business of life insurance, measure the reliability of eyewitness testimony, and win in games of chance with coins, dice, cards, and fortune wheels.1 In such games, people bet on outcomes and it is possible to calculate the probabilities of these outcomes. For example, when two people bet on the flip of a fair coin, the probability that it lands tails is 0.5,2 and the same for heads. Consider now a slightly more complicated bet where a generous friend gives you the following choice: Do you want 50 dollars or do you prefer a risky option? The risky option is that she will flip a fair coin, and if the coin lands tails, you will receive 100 dollars; but if it lands heads, you will receive nothing. The two options have an equal expected value of 50 dollars. Will you go for the certainty of the 50 dollars or will you gamble for double or nothing? Researchers routinely ask such questions, for example about how people choose between one job that has a practically certain salary and another job that provides uncertain income. Alfred Marshall speculated that ‘as a rule the certainty of moderate success attracts more than the expectation of an uncertain success that has an equal actuarial value’.3 Indeed most people prefer 50 dollars for sure to an even chance of 100 dollars or nothing.4 They avoid the risk in this context. Let us now say that your friend is not quite as generous. Your choice is the following: Do you accept a sure loss of 50 dollars or do you prefer a risky option? The option is that she will flip a fair coin, and if the coin lands tails, you would lose 100 dollars; but if it lands heads, you would lose nothing. The options again have the same expected value, − 50 dollars. Would you again go for certainty or would you now gamble? Most people prefer the even chance of losing 100 dollars or nothing to losing 50 dollars for sure.5 They now take the risk. Behavior changes between the two contexts of gaining and losing money.

2.2

The Distinction Between Risk and Uncertainty

Decisions such as the ones presented above, where all possible outcomes and their probabilities are known, are called decisions under risk. Frank Knight, a founder of the Chicago School of Economics, used the term

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decisions under uncertainty to distinguish situations where probabilities are not known.6 A more radical version of uncertainty is when some of the possible outcomes are also unknown, including the cases where the decision maker does not know that they do not know some possible outcomes.7 Operational decisions are typically made under some degree of uncertainty. For example, a retailer must approve or reject an offer without knowing the supplier’s probability of timely delivery. And a customer has to decide whether to buy a product online now without knowing whether the product might be offered at a discounted price in the future, the magnitude of the discount, and how probable the event of a discount is. In Chapter 6, decision making under radical uncertainty is analyzed in the two contexts of peace-keeping operations and the sourcing of supply chains during a disruptive crisis. Is the study of decisions under risk useful to behavioral operations? In some parts of the literature, especially in behavioral operational research8 and in qualitative, experiential approaches to behavioral operations management9 people’s decisions under risk are not discussed much. The present book is aligned with quantitative approaches to behavioral operations management10 which view people’s decisions under risk as a core of the empirical base of behavioral operations.11 There are at least two arguments for investigating decisions under risk. First, there are contexts in which probabilities can be estimated with good precision. In healthcare, for instance, extensive randomized controlled trials have measured the survival probability with and without screening for breast and prostate cancer in Europe and North America.12 Second, consider those contexts in which it might be challenging to estimate probabilities accurately. This does not preclude that practitioners do use probabilities to make decisions. In fact, this seems to often be the case. For example, in inventory control, archival data is fed into forecasting software which estimates probabilities of customer demand; subsequently, practitioners might adjust these estimates, which are finally used to place orders and make other decisions.13 Granted, it might not always be sound to force a decision under uncertainty into the form of a decision under risk14 but in many situations, this is what people do. Research has to acknowledge and work with this reality.

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Unlike the 75% overlap between the genes of fruit flies and humans, one cannot know the extent to which real-world operational decisions are ultimately made as decisions under risk. As others,15 I hold that being aware of interesting regularities in people’s decisions under risk will inform behavioral operations. It is interesting that people avoid risks when making choices for gains but take risks for losses. Can we understand how such changes in behavior occur? Can we model them?

2.3

Expected Utility Theory

Optimization principles are often used to summarize the behavior of physical objects. For example, the principle of least action says that objects, when allowed to move freely, tend to minimize the amount of energy they expend.16 Similarly, when economics and psychology started becoming rapidly mathematized in the middle decades of the twentieth century, some behavioral theorists proposed that human beings might make decisions in optimal ways.17 This development paralleled the bloom of optimization in operations research,18 with the difference that the latter was meant to prescribe, not describe, human behavior. Expected utility theory 19 is a prime example of how the optimization approach can be used to describe human decisions. This theory holds that people choose an option that maximizes their expected utility which is a measure of the ‘worth’ of an option to a person. Economists such as Milton Friedman and Harry Markowitz suggested general forms that people’s utility function should have in order for expected utility theory to be able to capture some phenomena in decision making under risk.20 Based on the subsequent work of psychologists Daniel Kahneman and Amos Tversky21 here I consider a particular form of the utility function, and apply it to the two choice problems discussed in this chapter. For a monetary amount x, the utility u(x) to a decision maker is given by the following equation, which is graphed in Fig. 2.1. ⎧ √ x, x ≥ 0 √ (2.1) u(x) = −2 −x, x < 0 First, consider the choice between x = 50 dollars for sure and the gamble which offers x = 100 dollars with probability p = 0.5 and x = 0 dollars with probability 1− p = 0.5. The utility of the sure thing is u(50) = 7.07. The expected utility of the gamble equals 0.5u(100) + 0.5u(0) = 5.

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u(x)

x 0

Fig. 2.1 The utility function u(x) =

√

100

√ x for x ≥ 0 and −2 −x for x < 0

According to expected utility theory, the decision maker would avoid risk and choose the sure thing. Second, consider the choice between x = −50 with certainty and the gamble offering x = −100 with probability p = 0.5 and x = 0 with probability 1 − p = 0.5 (all amounts are in dollars). The utility of the sure thing is u(−50) = −14.14. The expected utility of the gamble equals 0.5u(−100) + 0.5u(0) = −10. The decision maker would now maximize expected utility by taking the risk and choosing the gamble. Thus, expected utility theory can capture the switch from risk aversion in the domain of gains to risk taking in the domain of losses. To be able to accomplish this, the utility function must be chosen appropriately. Not all utility functions would do; for example, u(x) = x 2 for gains and u(x) = −x 2 for losses does not reproduce the observed behavior. The utility function needs to exhibit diminishing sensitivity, which means that it is convex for gains and concave for losses. In Fig. 2.1, diminishing sensitivity is illustrated by the phenomenon that, the further away x is from the origin, the changes in u(x) decrease as x increases by a constant amount; for instance, the difference |u(x + 1) − u(x)| decreases as x increases.

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Furthermore, the utility function presented above is designed to capture another key aspect of people’s decisions under risk. Aversion to a particular loss is stronger than attraction to a gain of equal magnitude. For example, 92% of the participants in a classic lab experiment chose to gamble in the domain of losses, whereas 80% of participants chose the sure thing in the domain of gains.22 This phenomenon is called loss aversion. It has been observed for centuries; in the words of Adam Smith in The Theory of Moral Sentiments: ‘Pain … is, in almost all cases, a more pungent sensation than the opposite and correspondent pleasure’.23 In the above utility function, loss aversion is expressed by using the factor of 2 for losses. This factor results in the absolute difference in utilities between the sure thing and the gamble being double for losses compared to gains, 4.14 versus 2.07. In Fig. 2.1, loss aversion is illustrated by the curve for losses being steeper than the curve for gains. In sum, as long as the utility function incorporates diminishing sensitivity and loss aversion, expected utility theory can accommodate the basic evidence on people’s choices between a sure thing and a risky option discussed in this chapter. Tversky and Kahneman proposed a generalization of Eq. 2.1: u(x) = x α for x ≥ 0 and −λ(−x)β for x < 0. This model has three free parameters, α, β and λ, and it can capture the evidence discussed above as long as α, β < 1 and λ > 1. We will discuss it further in Chapter 3. A sufficient amount of quality data should be gathered in order to be able to precisely estimate this model’s parameters. In practice, valid and reliable parameter estimates are not always straightforward to obtain.24 The following approach provides a simpler and parameter-free alternative.

2.4

Minimax and Maximax

For some time, biologists have been discovering that animals use simple rules of thumb.25 For example, the ant Leptothorax albipennis uses an ingenuous rule to estimate the size of a candidate nest site.26 A nest site is usually a cavity on a rock. First, the ant explores the cavity by moving around it and producing a pheromone trail. Later on, the ant returns and moves around the cavity but on a different path. The frequency of encountering its previous pheromone trail can be used by the ant to estimate nest size. The rule is surprisingly accurate: nests half the area of others yield reencounter frequencies 1.96 times greater.

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Simple rules have a long history in the study of human psychology too.27 The Gestalt school in Germany identified heuristics that people use to organize sensory input, according to properties such as proximity, closure, and similarity, in order to facilitate the perception of objects.28 Gestalt researchers viewed heuristics as informed guesses that in general yield accurate perceptions, although occasionally they produce illusions. Gerd Gigerenzer and his colleagues at the Max Planck Institute for Human Development developed models of simple heuristics for how people make inferences and choices, and delineated conditions under which those models are accurate and under which they lead to errors.29 In the field of strategic management, Kathleen Eisenhardt and her colleagues ‘… highlight[ed] a positive view of heuristics as rational ’.30 What do these researchers mean by heuristics? Consider the development of a strategy for capturing business opportunities in a new international market. In-depth interviews with six successful entrepreneurial firms from the information-technology industry have revealed simple rules such as ‘enter one continent at a time’ and ‘use a direct-sales approach’.31 Brilliant mathematician John von Neumann, who provided axiomatic foundations for expected utility theory, also proposed two simple rules for choosing among options with different possible outcomes. These rules can be used in individual decision making or strategic interaction32 Von Neumann’s two heuristics are called minimax and maximax and they apply to gains and losses, respectively. Minimax (for gains): Step 1. For each option, determine its minimum outcome. Step 2. Choose an option that yields the largest outcome determined in Step 1. Maximax (for losses): Step 1. For each option, determine its maximum outcome. Step 2. Choose an option that yields the largest outcome determined in Step 1. For both heuristics, if Step 2 leads to a tie, a choice is made randomly. Figures 2.2 and 2.3 provide graphical representations of the heuristics for choices between two options X and Y. These representations are extremely simple decision trees 33 Decision trees are a great help in

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building transparent models of human cognition, as we shall see in detail in Chapters 3, 4, and 6. Because minimax and maximax do not rely on probabilities to make a decision, the heuristics apply to decisions under uncertainty as well as risk. For risky decisions, minimax and maximax are simple models. This is so because the two heuristics (i) ignore most of the available information, that is, all probabilities and all but one outcome, and (ii) do not transform the outcome they do use by employing, say, a utility function. These features (i) and (ii) contrast with expected utility theory which uses all available information and transforms outcomes. There is no diminishing sensitivity or loss aversion embodied in von Neumann’s simple rules. A similarity between the two approaches is that, just as expected utility theory uses one form of the utility function for gains and another one for losses, there is one simple rule for gains and another one for losses. Let us apply the heuristics to the two choices discussed previously. First, consider the choice between x = 50 with certainty and the gamble

Fig. 2.2 Graphical representation of the minimax heuristic between an option X with minimum outcome x min and an minimum outcome y min . For simplicity we assume that x min / =

for the choice option Y with y min

Fig. 2.3 Graphical representation of the maximax heuristic for the choice between an option X with maximum outcome x max and an option Y with maximum outcome y max . For simplicity we assume that x max / = y max

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which offers x = 100 with probability p = 0.5 and x = 0 with probability 1 − p = 0.5. The minimum outcome for the gamble is 0, whereas the minimum (actually, the only) outcome for the sure thing is 50. Thus, according to the minimax rule, the decision maker would choose the sure thing. Second, consider the choice between x = −50 for sure and the gamble offering x = −100 with probability p = 0.5 and x = 0 with probability 1 − p = 0.5. The maximum outcome for the gamble is 0, whereas the maximum outcome for the sure thing is −50. According to the maximax rule, the decision maker would now choose the gamble. In sum, the pair of simple heuristics, minimax and maximax, can capture the switch from risk aversion in the domain of gains to risk taking in the domain of losses. But so can expected utility theory. How are these two approaches different?

2.5 Two Approaches to Modeling Human Behavior Expected utility theory and the minimax/maximax rules illustrate how the modeling approaches of optimization and simple heuristics differ. Chapters 3–6 will explore these differences in depth, presenting more sophisticated optimization and heuristic models, and applying these models to the study of more intricate behaviors than those in the present chapter. For now, here is a first comparative analysis of the two approaches in this chapter’s context. Cognitive processes. The modeling of the cognitive processes that lead to observed behaviors is a crux of the differences between the two approaches. Expected utility theory does not aim at specifying such processes and opening the black box. Economist Milton Friedman together with statistician Jimmie Savage—who developed the Bayesian approach of subjective expected utility theory—set the ground rules of this methodology34 : Consider the problem of predicting … the direction of travel of a billiard ball hit by an expert billiard player. It would be possible to construct … mathematical formulas that would give the directions of travel that would score points and, among these, would indicate the one (or more) that would leave the balls in the best positions … It seems not at all unreasonable that excellent predictions would be yielded by the hypothesis that the

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billiard player made his shots as if he knew the formulas, could estimate accurately by eye the angles describing the location of the balls etc., could make lightning calculations from the formulas, and could then make the ball travel in the direction indicated by the formulas.

Friedman and Savage are clear about their lack of interest in how the billiard player could do what is required by the optimization hypothesis. More specifically, they do not ask how the player knows formulas, perceives the state of play in the table, makes calculations, or executes the shot. Friedman and Savage skip questions about process and directly hypothesize that behavior is optimal. This methodology is followed in the application of optimization to people’s choices between a sure thing and a monetary gamble. The thesis is that people behave as if they optimize their expected utility. In Eq. 2.1 there is no specification of how exactly utilities are estimated and how they are combined with probabilities. Is the utility of the best outcome estimated first? If yes, is it then multiplied with its probability, or is the utility of the worst outcome estimated before this multiplication takes place? We do not know. But if we do not know the answers to such questions, how well can we understand the decision maker’s behavior? Recall the well-known saying attributed to W. Edwards Deming: If you can’t describe what you are doing as a process , you don’t know what you’re doing. Specifying the processes underlying behavior can also be important for predicting it. For example, if there is time pressure, and a decision maker is known to first attend to the best outcome (e.g., estimating its utility and multiplying it with its probability), then it can be expected that he might not have the time to estimate accurately the utility of the worst outcome. The minimax and maximax rules specify the process of the decision maker. In minimax, the decision maker first determines the minimum outcome for each option and then chooses an option with the largest minimum outcome. Further detail could also be provided as, for example, in what order are the outcomes of the options searched to determine their minimum outcomes? Such detail might not always be necessary for behavioral operations. I believe that it suffices to distinguish between models that specify some underlying processes, as in minimax and maximax, versus none at all, as in expected utility theory. In a considered synthesis of debates on what constitutes a process model,35 a process model is defined as one that includes at least one information processing stage that

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transforms input to output. According to this definition, minimax and maximax are process models whereas expected utility theory is not. Transparency. The emphasis of minimax and maximax on processes, together with the simplicity of these heuristics, contributes to their transparency. The two heuristics use easily understandable concepts: minimum outcome, maximum outcome, and an outcome being larger than another one. It is easy to execute the two heuristics, by performing the elementary operations of comparing one number to another and picking the larger number of the two. On the other hand, the concept of ‘utility’ has a quite technical ring to it, and understanding the reasons for its multiplication with probability, and then performing the multiplication, are even more demanding. To be fair, fields such as decision analysis36 have helped in making the ingredients of subjective expected utility theory easier to understand for some decision makers. It is ultimately an empirical question of which decision model, under which conditions, is more transparent to a given practitioner, layperson, or academic.37 In the upcoming chapter, quantitative measures of transparency will be put forth and calculated for optimization and heuristic models. Usefulness of output. Another dimension on which expected utility theory and the minimax/maximax pair differ is the kind of output they provide. In the examples of choosing between a sure thing and a gamble, expected utility theory provides a numerical valuation for each option, such as a utility of 7.07 for the sure gain of 50 dollars. These valuations can be used to construct an index of the strength of the decision maker’s preference, as when the difference in utilities between the sure thing and the gamble is 2.07 in the domain of gains. Because utilities can be scaled so that they range between 0 and 1, it is possible to interpret such numbers as representing a particular proportion, says 2%, of one’s maximum utility. On the other hand, minimax outputs simply that, for gains, the decision maker would choose the sure thing over the gamble. No quantitative statements are made about the worth of the options to the decision maker or the strength of the preference. This is less information than what utility theory provides. Which kind of information is more useful? Well, more information would be more useful, assuming that it is valid. But is it? Is it realistic to expect that people can tell by how much they prefer one option to another,38 or are people only able to say which option they prefer?

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Such questions have been debated at length,39 and the answer might depend on the domain. Experts often avoid quantitative information that appears to be overly precise and instead rely on qualitative approaches that may lead to more robust outcomes. Trader and author Nassim Taleb has strongly argued that systemic financial risks cannot be predicted by mathematical models,40 but instead can only be managed by principles such as ensuring that decision makers have ‘skin in the game’.41 And here are economists Mervyn King, governor of the Bank of England from 2003 to 2013, and John Kay, the first dean of Oxford’s Saïd Business School and director of several public companies42 : Good strategies for a radically uncertain world acknowledge that we do not know what the future will hold. Such strategies identify reference narratives, visualise alternative future scenarios, and ensure that plans are robust and resilient to a range of plausible alternatives43 … And the relevant reference narrative for a bank is—fundamentally—that it can continue to operate as a bank, meeting its obligations as they fall due. The banks of [the financial crisis of] 2008 were not within miles of being either robust or resilient, whatever their elaborate calculations of value at risk and risk weighted capital told them and their supervisors.

In Chapter 1, four criteria were put forth for the comparative analysis of models: specification of cognitive processes, transparency, usefulness of output, and predictive power. Here, I compared expected utility theory and the minimax/maximax heuristics on the first three criteria. The results of the analysis are summarized in Table 2.1. The predictive power of expected utility theory and the minimax/ maximax heuristics were not evaluated. Rather, we saw that they can both fit the known switch of most people’s attitude towards risk, from risk averse for gains to risk taking for losses. More sophisticated experimental designs are needed to test the predictions of these models on unknown data. Such studies are presented in Chapters 3–6. Before proceeding to these chapters, I explain the rationale for the kind of studies discussed in this book.

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Table 2.1 Summary of the comparative analysis of expected utility theory and the minimax/maximax heuristics Cognitive processes

Transparency

Expected utility theory

Not modeled; makes the hypothesis of as-if behavior

Might appear quite technical to decision makers without a quantitative background

Minimax/maximax heuristics

Modeled with information processing stages that transform input to output

2.6

Usefulness of output

Able to valuate options; though unclear how useful this output is because it may not be valid Uses easily Statements are made understandable concepts, about the choice such as minimum/ between options, but maximum outcome, and not their valuations is easy to execute

The Kind of Studies in This Book

There are plenty of empirical studies on human reasoning and decision making in operational settings.44 This book focuses on studies that present evidence that is quantitative and has been described by mathematical models. For example, I do not consider qualitative studies in the fields of project management and product development. And I also do not consider studies that investigate models of human decision making which have not been formalized, such as the affect heuristic45 Furthermore, I do not discuss studies where formal models for describing human behavior have been presented, but they are only of one type. This is the case in forecasting, where descriptive models include simple rules but not optimization46 Other work, such as in transportation studies of people’s route choices and parking strategies,47 has employed paradigms that are special cases of fields of study treated in this book such as decision under risk and strategic interaction, and is mentioned in the respective chapters. Behavioral evidence can have issues with data quality and analysis. The empirical findings modeled in this book have been chosen so that they meet two criteria: (i) the data quality has been verified through experimental replication or another kind of triangulation and (ii) the data has been analyzed and interpreted in a statistically sound way. The replication crisis in the behavioral sciences refers to failures in obtaining the same finding when the same behavioral experiment is

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repeated.48 The importance of experimental replication in behavioral operations management has also been pointed out in a 2015 entry in the blog of the journal Manufacturing and Service Operations Management, authored by Gary Bolton and Elena Katok49 Reasons for the failure to replicate include selective reporting, the lack of hypotheses before the data is analyzed, and insufficient theoretical specification of the conditions necessary for the finding. Social psychology is one field that has been criticized for lack of replicability. For instance, research on power posing initially showed that after people stood or sat in poses such as placing their legs astride, they exhibited improved physiological measures of testosterone and stress,50 but subsequently, these effects were not replicated with a larger group of participants.51 The Open Science Collaboration attempted to replicate the results of 100 psychological studies. Based on criteria such as p values and effect sizes, the conclusion was that only one-third to one-half of the original findings could be replicated.52 In management, triangulation is a research strategy often employed for validating empirical findings.53 Triangulation of data means gathering data based on different methods (e.g., experiments, surveys, interviews, and ethnographic studies), at different places and times, and sometimes also from various target populations. Now, even if an empirical finding has been validated, this does not mean that the data has been analyzed and interpreted soundly. A case of incorrect application of statistics in the study of human behavior, which went unnoticed for decades, is in the analysis of the so-called ‘hot hand fallacy’. Let us think about a game of basketball. If Giannis has made three shots in a row, does it make sense to believe that he has a hot hand? In other words, does the existence of Giannis’ streak of hits make it more probable that his next shot will also be a hit? It depends on who you ask. Players, coaches, and spectators believe in hot hands. This is much to the chagrin of behavioral scientists, based on a landmark paper54 that argued against the existence of hot hands. It has also been hypothesized that beliefs in hot hands might lead to biased decisions in operational settings.55 But Joshua Miller and Adam Sanjurjo took a fresh look at the analysis of the data, and vindicated the hot hand.56 Consider first the usual test of the existence of a hot hand: Over a basketball season, identify all of Giannis’ streaks of three hits and all of his streaks of three misses. Then, calculate the percentage of hits following three hits and the percentage of hits following three misses. If the two percentages are equal, there is no hot hand. In an experiment with college

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basketball players each taking 100 shots under controlled conditions (not during a game), the success percentages were 49% after hitting streaks and 45% after misses streaks, and this difference of 4% was found to not be statistically significant.57 There is a problem with the logic of this test. It is incorrect to assume that, if there is no hot hand, then the success percentages after hits streaks and after misses streaks are equal (assuming, as it is reasonable, that there is a finite sequence of shots). Miller and Sanjurjo showed that when a fair coin is flipped a finite number of times, the probability of heads following three heads is smaller than 50% and conversely the probability of heads following three tails is larger than 50%. Table 2.2 demonstrates this surprising result in a smaller context. For the case of flipping a fair coin three times, straightforward counting shows that the probability of heads following heads is 41.7%. The general claim can be proven analytically for any number of flips and any length of the streak of heads. The reason is that the particular streak of heads considered is more likely to be identified when the next flip is tails because then there are fewer heads’ streaks; and this fact makes it more probable that the next flip is tails. If a fair coin is flipped 100 times, the difference between the probability of heads in the cases that the three previous flips are tails and heads turns out to be 8%.58 In the basketball data used to originally argue for the hot hand fallacy48 , there is a discrepancy of 8% plus 4%, or 12%, between shooting randomly (as when flipping a fair coin) and having a hot Table 2.2 When a fair coin is flipped three times, the average probability that heads follow heads is counted to be 2.5 6 = 41.7% Possible outcome of flipping a fair coin three times (T = tails, H = heads)

Probability that heads follow heads in each outcome

TTT TTH THT HTT THH HTH HHT HHH

not defined not defined 0 0 1 0 0.5 1

Average probability, across outcomes, that heads follow heads

2.5 6

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hand. The 12% advantage is large and might equal the difference between the success percentage of the best and average three-point shooter in the NBA.59 Other seemingly well-established behavioral findings have been questioned as well, either in terms of replicability or in terms of analysis. Examples include the negative effects of having too many choices60 and one’s overconfidence in their own judgment.61 Statistician and political scientist Andrew Gelman runs the blog https://statmodeling.stat.columb ia.edu which discusses practices of gathering, analyzing, and reporting data in the behavioral sciences. For issues and guidance more specific to behavioral operations, see a piece by Stephanie Eckerd and her colleagues.62

2.7

Summary

The workhorse of the behavioral study of decision making is people’s choices from a menu of options that manifest different levels of risk. This chapter introduced this work by discussing choices between a guaranteed outcome and an option with some risk. A key finding is that most people avoid risks when choices refer to gains but take risks when choices refer to losses. We saw that an optimization model, expected utility theory, as well as a pair of much simpler rules, minimax and maximax—interestingly, both approaches proposed by the same person, John von Neumann—can, after the fact, capture the switch. This result raises the question of how complex does a model of human decision making under risk need to be. The next chapter provides a more detailed answer, focusing on the a priori prediction of behavior, along with our three other criteria for operational decision modeling.

Notes 1. Lorraine Daston, Classical Probability in the Enlightenment (Princeton, NJ: Princeton University Press, 1988); Ian Stewart, Do Dice Play God?: The Mathematics of Uncertainty (London: Hachette, 2019). 2. In this book, non-integer numbers are represented in decimal form, and rounding to the nearest 10 is used as needed. 3. Alfred Marshall, Principles of Economics (London: Macmillan, 1920), 554. 4. Ward Edwards, “The Theory of Decision Making,” Psychological Bulletin 51, no. 4 (1954): 380–417; Daniel Kahneman and Amos Tversky,

2

5. 6. 7. 8.

9.

10.

11.

12.

13. 14.

15.

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29

“Prospect Theory: An Analysis of Decision Under Risk,” Econometrica 47, no. 2 (1979): 263–291. Harry S. Markowitz, “Portfolio Selection,” The Journal of Finance 7, no. 1 (1952): 77–91; Kahneman and Tversky, “Prospect Theory”. Frank H. Knight, Risk, Uncertainty and Profit (Boston: Houghton Mifflin, 1921). Donald P. Rumsfeld, U.S. Department of Defense News Briefing (Washington, DC: February 12, 2002). Martin H. Kunc, Jonathan Malpass and Leroy White, eds., Behavioral Operational Research: Theory, Methodology and Practice (London: Palgrave Macmillan, 2016); Leroy White, Martin H. Kunc, Katharina Burger and Jon Malpass, eds., Behavioral Operational Research: A Capabilities Approach (London: Palgrave Macmillan, 2020). Elliot Bendoly, Wout van Wezel and Daniel G. Bachrach, eds., The Handbook of Behavioral Operations Management: Social and Psychological Dynamics in Production and Service Settings (New York: Oxford University Press, 2015). Christoph H. Loch and Yaozhong Wu, Behavioral Operations Management (Norwell, MA: Now Publishers, 2007); Karen Donohue, Elena Katok and Stephen Leider, eds., The Handbook of Behavioral Operations (Hoboken, NJ: John Wiley and Sons, 2018). Tony H. Cui and Yaozhong Wu, “Incorporating Behavioral Factors into Operations Theory,” in The Handbook of Behavioral Operations, 89– 119; Andrew M. Davis, “Biases in Individual Decision-Making,” in The Handbook of Behavioral Operations, 151–198. For breast cancer, see https://www.hardingcenter.de/en/early-detectionof-cancer/early-detection-of-breast-cancer-by-mammography-screening. For prostate cancer, see https://www.hardingcenter.de/en/early-detect ion-of-cancer/early-detection-of-prostate-cancer-with-psa-testing. Paul Goodwin, Brent Moritz and Enno Siemsen, “Forecast Decisions,” in The Handbook of Behavioral Operations, 433–458. Goodwin et al., “Forecast Decisions”; Ralph Hertwig, Timothy J. Pleskac, Thorsten Pachur and the Center for Adaptive Rationality, Taming Uncertainty (Cambridge, MA: MIT Press, 2019); Konstantinos V. Katsikopoulos, Özgür Sim¸ ¸ sek, Marcus Buckmann and Gerd Gigerenzer, “Transparent Modeling of Influenza Incidence: Big Data or a Single Data Point from Psychological Theory,” International Journal of Forecasting 38, no. 2 (2022): 613–619. Loch and Wu, Behavioral Operations Management; Cui and Yu, “Incorporating Behavioral Factors into Operations Theory”; Davis, “Biases in Individual Decision-Making”.

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16. Richard P. Feynman, Matthew Sands and Robert B. Leighton, The Feynman Lectures on Physics: The New Millennium Edition (New York: Basic Books, 2015). 17. Milton Friedman and Leonard J. Savage, “The Utility Analysis of Choices Involving Risk,” Journal of Political Economy 56, no. 4 (1948): 279–304; Edwards, “The Theory of Decision Making”. 18. Ding-Zhu Du, Panos M. Pardalos and Weili Wu, “History of Optimization,” in Encyclopedia of Optimization, eds., Christodoulos A. Floudas and Panos M. Pardalos (New York: Springer Science and Business Media, 2008): 1538–1542. 19. John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior (Princeton: Princeton University Press, 1944); Leonard J. Savage, The Foundations of Statistics (New York: John Wiley and Sons, 1954). 20. Friedman and Savage, “The Utility Analysis of Choices Involving Risk”; Markowitz, “Portfolio Selection”. 21. Kahneman and Tversky, “Prospect Theory”; Amos Tversky and Daniel Kahneman, “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Risk and Uncertainty 5, no 4 (1992): 297–323. 22. Kahneman and Tversky, “Prospect Theory”, 268, table 1, problem 3. 23. Adam Smith, An Inquiry into the Nature and Causes of the Wealth of Nations (London: W. Strahan and T. Cadell, 1776), 176. 24. George Wu and Richard Gonzalez, “Curvature of the Probability Weighting Function,” Management Science 42, no. 12 (1996): 1676– 1690; William Neilson and Jill Stowe, “A Further Examination of Cumulative Prospect Theory Parameterizations,” Journal of Risk and Uncertainty 24, no. 1 (2002): 31–46; Pavlo R. Blavatskyy, “Back to the St. Petersburg Paradox?,” Management Science 51, no. 4 (2005): 677–678; Konstantinos V. Katsikopoulos and Gerd Gigerenzer, “One-Reason Decision-Making: Modeling Violations of Expected Utility Theory,” Journal of Risk and Uncertainty 37, no. 1 (2008): 35–56; Håkan Nilssom, Jörg Rieskamp and Eric-Jan Wagenmakers, “Hierarchical Bayesian Parameter Estimation for Cumulative Prospect Theory,” Journal of Mathematical Psychology 55, no. 1 (2011): 84–93. 25. Gottfried S. Fränkel and Donald L. Gunn. The Orientation of Animals: Kineses, Taxes and Compass Reactions (Oxford: Oxford University Press, 1940); Thomas D. Seeley, The Wisdom of the Hive: The Social Physiology of Honeybee Colonies (Cambridge, MA: Harvard University Press, 2009). 26. Eamonn B. Mallon and Nigel R. Franks, “Ants Estimate Area using Buffon’s Needle,” Proceedings of the Royal Society of London. Series B: Biological Sciences 267, no. 1445 (2000): 765–770.

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27. Ralph Hertwig and Thorsten Pachur, “Heuristics, History of,” in International Encyclopedia of the Social and Behavioral Sciences, ed., James D. Wright (Amsterdam, Netherlands: Elsevier, 2015): 829–835. 28. Max Wertheimer, “Studies on the Theory of Gestalt II,” Psychological Research 4 (1923): 301–350. 29. Gerd Gigerenzer, Peter M. Todd and the ABC Research Group, Simple Heuristics that Make us Smart (New York: Oxford University Press, 1999); Gerd Gigerenzer, Ralph Hertwig and Thorsten Pachur, eds., Heuristics: The Foundations of Adaptive Behavior (New York: Oxford University Press, 2011); Peter M. Todd, Gerd Gigerenzer and the ABC Research Group, Ecological Rationality: Intelligence in the World (New York: Oxford University Press, 2012); Konstantinos V. Katsikopoulos et al., Classification in the Wild: The Science and Art of Transparent Decision Making (Cambridge, MA: MIT Press, 2020). 30. Christopher B. Bingham and Kathleen M. Eisenhardt, “Rational Heuristics: The ‘Simple Rules’ that Strategists Learn from Process Experience,” Strategic Management Journal 32, no. 13 (2011), 1458 (emphasis in the original). 31. Ibid., table 3. 32. Von Neumann and Morgenstern, Theory of Games and Economic Behavior. These authors proposed minimax and maximax as formal models. There is also empirical research that has tested whether and when people use them—see Thorsten Pachur, Ralph Hertwig and Roland Wolkewitz, “The Affect Gap in Risky Choice: Affect-Rich Outcomes Attenuate Attention to Probability Information,” Decision 1, no. 1 (2014): 64–78. 33. Leo Breiman et al., Classification and Regression Trees (Boca Raton, FL: CRC Press, 1984). 34. Friedman and Savage, “The Utility Analysis of Choices Involving Risk”, 298 (emphasis in the original). 35. Jana B. Jarecki, Jolene H. Tan and Mirjam A. Jenny, “A Framework for Building Cognitive Process Models,” Psychonomic Bulletin and Review (2020): 1–12. 36. Detlof von Winterfeldt and Ward Edwards, Decision Analysis and Behavioral Research (Cambridge, UK: Cambridge University Press, 1986); Gilberto Montibeller and Detlof von Winterfeldt, “Cognitive and Motivational Biases in Decision and Risk Analysis,” Risk Analysis 35, no. 7 (2015): 1230–1251; Konstantinos V. Katsikopoulos and Barbara Fasolo, “New Tools for Decision Analysts,” IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 36, no. 5 (2006): 960–967. 37. There is not much empirical research answering questions such as what types of models people judge to be transparent, under what conditions they do so, and what are the effects of these judgments on how people interact with models. For exceptions, see Johan Huysmans et al., “An

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38. 39.

40. 41. 42. 43.

44.

45. 46.

47.

Empirical Evaluation of the Comprehensibility of Decision Table, Tree and Rule Based Predictive Models,” Decision Support Systems 51, no. 1 (2011): 141–154; and Forough Poursabzi-Sangdeh et al., “Manipulating and Measuring Model Interpretability,” In Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems (2021): 1–52. Expected utility theory needs to ask people to make such choices in order to elicit their utility function. Alfred Marshall, Principles of Economics; Vilfredo Pareto, Manual of Political Economy (Milan: Bocconi University, 1906); Edwards, “The Theory of Decision Making”. Nassim Nicholas Taleb, Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets (New York: Random House, 2005). Nicholas Nassim Taleb, Skin in the Game: Hidden Asymmetries in Daily Life (New York: Random House, 2020). Mervyn King and John Kay, Radical Uncertainty: Decision-Making for an Unknowable Future (London: Hachette, 2020): 424 (footnote added). For similar ideas, see Paul J. H. Schoemaker, “Scenario Planning: A Tool for Strategic Thinking,” Sloan Management Review 36, no. 2 (1995): 25–50. Loch and Wu, Behavioral Operations Management ; Bendoly et al., The Handbook of Behavioral Operations Management; Kunc et al., Behavioral Operational Research: Theory, Methodology and Practice; Donohue et al., The Handbook of Behavioral Operations; White et al., Behavioral Operational Research: A Capabilities Approach. Paul Slovic et al., “The Affect Heuristic,” European Journal of Operational Research 177, no. 3 (2007): 1333–1352. Mirko Kremer, Brent Moritz and Enno Siemsen, “Demand Forecasting Behavior: System Neglect and Change Detection,” Management Science 57, no. 10 (2011): 1827–1843; Goodwin et al., “Forecast Decisions”. See for example Song Gao, Emma Frejinger and Moshe Ben-Akiva, “Adaptive Route Choices in Risky Traffic Networks: A Prospect Theory Approach,” Transportation Research Part C: Emerging Technologies 18, no. 5 (2010): 727–740; Konstantinos V. Katsikopoulos, “Advanced Guide Signs and Behavioral Decision Theory,” in Donald L. Fisher et al., eds., Handbook of Driving Simulation for Engineering, Medicine, and Psychology: An Overview (Boca Raton, FL: CRC Press, 2011): 371–378; Merkouris Karaliopoulos, Konstantinos V. Katsikopoulos and Lambros Lambrinos, “Bounded Rationality can Make Parking Search More Efficient: The Power of Lexicographic Heuristics,” Transportation Research Part B: Methodological 101 (2017): 28–50; Amnon Rapoport and Vincent Mak, “Strategic Interactions in Transportation Networks,” in The Handbook of Behavioral Operations (2018): 557–586.

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33

48. The discussion that follows does not refer to the replicability of the results of formal models used in operational research. For such discussions, see John E. Boylan et al., “Reproducibility in Forecasting Research,” International Journal of Forecasting 31, no. 1 (2015): 79–90 in forecasting; Graham Kendall et al., “Good Laboratory Practice for Optimization Research,” Journal of the Operational Research Society 67, no. 4 (2016): 676–689 in optimization, and Thomas Monks et al., “Strengthening the Reporting of Empirical Simulation Studies: Introducing the STRESS Guidelines,” Journal of Simulation 13, no. 1 (2019): 55–67 in simulation. 49. See https://www.informs.org/Blogs/M-SOM-Blogs/From-M-SOMJournal-Editor/The-Importance-of-Replication-in-Behavioral-OperationsManagement. 50. Dana R. Carney, Amy J. C. Cuddy and Andy J. Yap, “Power Posing: Brief Nonverbal Displays Affect Neuroendocrine Levels and Risk Tolerance,” Psychological Science 21, no. 10 (2010): 1363–1368. 51. Eva Ranehill et al., “Assessing the Robustness of Power Posing: No Effect on Hormones and Risk Tolerance in a Large Sample of Men and Women,” Psychological Science 26, no. 5 (2015): 653–656. 52. Open Science Collaboration, “Estimating the Reproducibility of Psychological Science,” Science 349, no. 6251 (2015): aac4716. 53. Uwe Flick, “Triangulation in Qualitative Research,” in Uwe Flick, Ernst von Kardoff and Ines Steinke, eds., A Companion to Qualitative Research (Thousand Oaks, CA: Sage, 2004): 178–183. 54. Thomas Gilovich, Robert Vallone and Amos Tversky, “The Hot Hand in Basketball: On the Misperception of Random Sequences,” Cognitive Psychology 17, no. 3 (1985): 295–314. 55. Davis, “Biases in Individual Decision-Making”; Goodwin et al., “Forecast Decisions”. 56. Joshua B. Miller and Adam Sanjurjo, “Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers,” Econometrica 86, no. 6 (2018): 2019–2047. 57. Gilovich et al., “The Hot Hand in Basketball”; Miller and Sanjurjo, “Surprised by the Hot Hand Fallacy?”. 58. Miller and Sanjurjo, “Surprised by the Hot Hand Fallacy?”. 59. Joshua B. Miller and Adam Sanjurjo, “Momentum Isn’t Magic—Vindicating the Hot Hand With the Mathematics of Streaks”, The Conversation (March 28, 2018). 60. Benjamin Scheibehenne, Rainer Greifeneder and Peter M. Todd, “Can There Ever Be Too many Options? A Meta-Analytic Review of Choice Overload,” Journal of Consumer Research 37, no. 3 (2010): 409–425.

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61. Robyn M. Dawes and Matthew Mulford, “The False Consensus Effect and Overconfidence: Flaws in Judgment or Flaws in how We Study Judgment?,” Organizational Behavior and Human Decision Processes 65, no. 3 (1996): 201–211. 62. Stephanie Eckerd, Scott DuHadway, Elliot Bendoly, Craig R. Carter and Lutz Kaufmann, “On Making Experimental Design Choices: Discussions on the Use and Challenges of Demand Effects, Incentives, Deception, Samples, and Vignettes,” Journal of Operations Management 67, no. 2 (2021): 261–275.

CHAPTER 3

Decision Under Risk

Fruitless discussions about the relative merits of the ‘hard’ and the ‘soft’ sciences abound. But John Maynard Keynes brought these two bodies of knowledge beautifully together1 : Professor Planck, of Berlin, the famous originator of the quantum theory, once remarked to me that in early life he had thought of studying economics, but had found it too difficult! Professor Planck could easily master the whole corpus of mathematical economics in a few days. He did not mean that! But the amalgam of logic and intuition and the wide knowledge of facts most of which are not precise, required for economic interpretation… is, quite truly, overwhelmingly difficult…

Science is able to predict the behavior of physical objects with greater precision than it can predict the behavior of sentient beings. It is challenging to anticipate human decision making because there can be large differences between people as well as irreducible intra-individual noise in each person’s behavior.2 Furthermore, models of human behavior should do more than predict. As Keynes pointed out, and historian Mary Morgan has emphasized,3 behavioral models should also provide coherent and insightful stories. Such stories can be used by citizens and policymakers as platforms for discussion. How can one build predictive and insightful models of people’s decisions under risk? This is the topic of the present chapter. I first present the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6_3

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web of empirical phenomena in risky decision making. Then, I cover the optimization model of prospect theory 4 and a simple rule called priority heuristic 5 for describing people’s decisions under risk. In such research, it is common to focus on capturing the choice of the majority because it averages out individual differences. The same approach is taken in modeling work in behavioral operations6 and this chapter as well.7 I also analyze these two models on the criteria of predictive power, cognitive processes, transparency, and usefulness of output. I mention related research on decisions under risk in more specific contexts, such as transportation and logistics. Along the way, I will be making connections to the modeling of decisions in machine learning.

3.1

Empirical Phenomena

In order to describe the behavioral evidence, I use the following notation. Monetary outcomes are denoted by symbols such as x or y and the probabilities of such outcomes are denoted by symbols such as p or q. The expression (x, p; y, 1 − p) represents the gamble which pays off x with probability p and y with probability q, where p + q = 1. For example, a gamble that pays 10 euros when a fair coin lands heads and zero euros when the coin lands tails can be written as (10, 0.5; 0, 0.5). An outcome x which is received with certainty is denoted by (x, 1). Gambles are denoted by symbols such as G and G ∗ . For any gamble G, its opposite gamble −G obtains the outcome −x if G obtains x, and with the same probability. For example, if G = (10, 0.5; 0, 0.5), then −G = (−10, 0.5; 0, 0.5). A gamble can be compound, which means that it includes another gamble as an outcome. For instance, we may flip a fair coin and receive 5 euros immediately if it lands heads; but if it lands tails, we flip the coin again. If now it lands heads, the payoff is 10 euros, otherwise there is a zero payoff. This gamble G is a compound one, with G = (5, 0.5; G ∗ , 0.5), where G ∗ = (10, 0.5; 0, 0.5). Compound gambles can be simplified by multiplying the probabilities along the path leading to an outcome. In this example G = (5, 0.5; 10, 0.25; 0, 0.25). Below I present three types of key behavioral phenomena, which build on the empirical evidence discussed in Chapter 2. There exist other behavioral phenomena,8 including two classics, the Saint Petersburg paradox9 and the equity premium puzzle,10 as well as the theoretically important common ratio effects.11 I present these other phenomena and results on

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37

how prospect theory and the priority heuristic can explain and predict them in the Appendix. Reflection effects. Markowitz12 discussed extensively how people’s choices change between gains and losses, and his speculations have been borne out.13 In the lab, Kahneman and Tversky found that people’s majority choices are reversed when gambles are substituted by their opposites. That is, if G is chosen to G ∗ , then −G ∗ is chosen to −G. These findings are called reflection effects . The risk attitude reversal discussed in Chapter 2 is a reflection effect with G = (50, 1) and G ∗ = (100, 0.5; 0, 0.5). Reflection effects have also been observed in tasks where both gambles include risk or differ in expected value.14 Four-fold pattern of risk attitude. The reversal of choice between gains and losses is part of a more complicated pattern of human attitude to risk.15 People are generally risk averse in the domain of gains, but there is an exception: when the probability of the gain is ‘small’, people are risk seeking. For example, the gamble (100, 0.05; 0, 0.95) was deemed by 50% of experimental participants16 to be equally worth a certain outcome of at least 14, which is better than 5, the gamble’s expected value. A common instance of risk seeking behavior for gains with small probabilities is the purchase of lottery tickets. In this case, the probability of some of the gains is very small whereas these gains themselves are very large, a pattern which often occurs in lab experiments and in the field.17 Similarly, whereas people are generally risk seeking in the domain of losses, there is an exception: when the probability of the loss is ‘small’, people are risk averse. For instance, the gamble (−100, 0.05; 0, 0.95) was deemed by 50% of experimental participants18 to be equally worth a certain outcome of at best –8, which is worse than –5, the gamble’s expected value. People routinely buy insurance policies against adverse events that have low probabilities. The above set of findings comprises the four-fold pattern of risk attitude, which Amos Tversky and Daniel Kahneman saw as distinctive and characteristic of human decisions under risk. The whole pattern can be written as follows, where it is assumed that x > 0. ( px, 1) is chosen to (x, p; 0, 1 − p) if and only if p is ‘large’ and (−x, p; 0, 1 − p) is chosen to (− px, 1) if and only if p is ‘large’ (RA)

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The above two types of effects refer to opposite gambles. The last type of effects discussed below refers to compound gambles. Common consequence effects. Paris, May of 1952, at an international conference on risk. Iconoclast physicist and economist Maurice Allais performed an early experiment in human decision making, featuring the cream of academic economics as participants.19 Among them, Milton Friedman questioned what could be learned from the experiment, whereas Jimmie Savage engaged with it and provided an answer. Savage’s response, shared by most people who have participated in such behavioral studies,20 has been labeled the Allais paradox. It is not a logical paradox, but ironically it contradicts Savage’s own Bayesian expected utility theory,21 which was and is a reigning idea in decision making. Allais’ experiment requires making the following two choices, where ‘m’ refers to millions of francs. Case A (100m, 1) or (500m, 0.10; 100m, 0.89; 0, 0.11)? Case B (100m, 0.11; 0, 0.89) or (500m, 0.10; 0, 0.90)? The vast majority of people choose (100m, 1) in case A and (500m, 0.10; 0, 0.90) in case B. This pattern of choices is inconsistent with having a utility function u(x) and choosing the gamble that optimizes one’s expected utility. This is so because, assuming without loss of generality that u(0) = 0, the A choice implies u(100m) > 0.10u(500m) + 0.89u(100m) whereas the B choice implies 0.10u(500m) > 0.11u(100m), and these two statements contradict each other. The Allais paradox is a special case of common consequence effects .22 For the two gambles in case A, the common consequence is the outcome of 100m with a probability of 0.89. For the two gambles in case B, the common consequence is the outcome of 0 with also a probability of 0.89. Because expected utility theory combines probabilities and utilities linearly, the actual value of the common consequence should not affect one’s choice, according to the theory. But in practice, changing the common consequence often changes the choices people make. Common consequence effects can be written as follows.

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39

(x, 1) is chosen to (G, p; x, 1 − p) and (G, p; 0, 1 − p) is chosen to (x, p; 0, 1 − p); where G = (y, q; 0, 1 − q) and y > x > 0

(CC)

The common consequence is x in the top choice and 0 in the bottom choice, both occurring with probability 1 − p. In the Allais paradox, x = 100m, p = 0.11, y = 500m, and q = 0.10. Common consequence effects have been key in the evolution of the modeling of human decision under risk.23 They violate the independence axiom which is a core axiom of expected utility theory. That is, independence, together with some more technical axioms, is logically equivalent to the theory; therefore, if one does not conform to the axiom, they should logically not conform to the theory.24 The independence axiom says that a choice between two gambles remains the same if both gambles are augmented by another gamble; formally, if G is chosen to G ∗ , then   (G, p; G , 1− p) is chosen to (G ∗ , p; G , 1− p). This seems intuitive. It says that you would choose to spend a day in the sea to a day in the mountain if you would choose the sea when it is sunny and you may walk and if you are indifferent between sea and mountain when it rains and you have to drive. But human reasoning is more subtle than that, and the overall choice can reflect an interaction between the choice when it is sunny and the choice when it rains. How can one capture such subtlety? Should they make the modeling more complex? Or make it simpler? Prospect theory and the priority heuristic respectively illustrate a complex and a simple approach.

3.2

Prospect Theory

Prospect theory proposes that people choose a gamble that has maximum ‘worth’ among all available options. The differences to standard expected utility theory are in how values are transformed and probabilities are

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weighted. The original version of prospect theory25 by Daniel Kahneman and Amos Tversky dates back to 1979, and there have been many variants and extensions since, notably including cumulative prospect theory,26 and they are reviewed thoroughly in a textbook by Peter Wakker.27 To ease the exposition, I will use the term prospect theory to include all of these versions. Choosing an implementation of prospect theory for a particular application is not always straightforward because its utility function (also called its value function) and probability-weighting functions can combine in ways that complicate theoretical interpretation28 and empirical estimation of parameters.29 Here I present functions suggested and estimated by Tversky and Kahneman, and used in empirical comparisons of prospect theory with other optimization models and a number of simple heuristics.30 The utility function of prospect theory u(x) is given by the equation below, where r stands for the monetary reference point employed by the decision maker. An interpretation of the reference point is that it is the decision maker’s current wealth. In lab experiments as the ones discussed here, it is commonly assumed that r = 0, which means that the participant focuses on the choices she is facing in the experiment, without being influenced by her financial situation outside the lab. This assumption can be debated of course, but it does not alter the gist of the analyses presented in this chapter, so I make it as well.31  (x − r )α , x ≥ r (3.1) u(x) = −λ(r − x)β , x < r The free parameters of this utility function are α, β, and λ. Tversky and Kahneman32 provided the estimates α = 0.88, β = 0.88, and λ = 2.25. Equation 3.1 with these parameters, and r = 0, is graphed in Fig. 3.1. This function exhibits diminishing sensitivity and loss aversion, which are characteristic of optimization models for decision under risk (Chapter 2). The probability-weighting function of prospect theory w( p) is given by the following Eq. 3.2. In this equation, it is assumed that the outcome with value x is obtained with probability p. ⎧ pγ ⎪ 1 ,x ≥ r ⎨ γ p)γ ] γ w( p) = [ p +(1− (3.2) δ p ⎪ ⎩ 1 ,x < r [ p δ +(1− p)δ ] δ

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41

u(x)

x 0

100

Fig. 3.1 Prospect theory’s utility function u(x) = x 0.88 for x ≥ 0 and −2.25(−x)0.88 for x < 0, as estimated by Tversky and Kahneman

The free parameters of the probability-weighting function are γ and δ. According to Tversky and Kahneman,33 they can be estimated as γ = 0.61 and δ = 0.69. Equation 3.2 with these parameters, and r = 0, is graphed in Fig. 3.2. This function exhibits a pattern of over-weighting small probabilities and under-weighting large probabilities. This pattern is characteristic of prospect theory and it is used by the theory to capture the four-fold pattern of risk attitude.34 Like standard expected utility theory, prospect theory postulates that the decision maker chooses a gamble G that maximizes worth, which is the sum of probability-weighted value across all possible outcomes in each gamble. For the case where the gamble provides one gain or loss x which is obtained with probability p (and the zero outcome with probability 1 − p), the worth of the gamble equals w( p)v(x). For example, prospect theory with the utility and probability-weighting functions in Eqs. 3.1 and 3.2 predicts that the gamble (5, 1) would be chosen over the gamble (10, 0.5; 0, 0.5) because the worth of the former is 50.88 = 4.12, and this is larger than

0.50.61 1 (0.50.61 +0.50.61 ) 0.61

10

0.88

= 3.19, which is the worth of the latter.

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w(p)

1

Gains (x 0) Losses (x < 0)

0 0

1

p

Fig. 3.2 Prospect p 0.61 1

[ p 0.61 +(1− p)0.61 ] 0.61

theory’s

probability-weighting

functions

for p corresponding to x ≥ 0 and

w( p)

p 0.69

= 1

[ p 0.69 +(1− p)0.69 ] 0.69

for p corresponding to x < 0, as estimated by Tversky and Kahneman

3.3

Priority Heuristic

The priority heuristic was developed in 2006 by Edouard Brandstätter, Gerd Gigerenzer, and Ralph Hertwig.35 As is often the case with simple heuristics, it consists of a short sequence of easy steps. At each step, a question is asked about one attribute of the options, and depending on the answer, the decision maker will either choose a gamble or continue to the next step where a question about another attribute is asked and so on (except for the last step where a choice will always be made, if necessary by guessing). There is one version of the priority heuristic for gains and another for losses, and both are spelled out below. For brevity, it is assumed here that there are two gambles, G and G ∗ , with one or two possible outcomes each. That is, G = (xmin , pmin ; xmax , pmax ) and G ∗ = (ymin , qmin ; ymax , qmax ), with xmin ≤ xmax and ymin ≤ ymax , 0 ≤ pmin , q min , p max, qmax , and pmin + q min = p max +

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qmax = 1. These kinds of choices cover the bulk of the available empirical evidence. Extensions of the priority heuristic for choices among more than two gambles, which may also have more than two outcomes, are straightforward.36 Priority heuristic for gains ( xmin , ymin ≥ 0) Step 1. If the difference between the minimum outcomes |xmin − ymin | exceeds the threshold 0.1 max{xmax , ymax }, then choose the gamble with the larger minimum outcome; otherwise continue. Step 2. If the difference between the probabilities of minimum outcomes | pmin − qmin | exceeds the threshold 0.1, then choose the gamble with the smaller probability of minimum outcome; otherwise continue. Step 3. Choose the gamble with the larger maximum outcome; if those are equal, then choose a gamble randomly. For example, consider the choice between (5, 1) and (100, 0.05; 0, 0.95). Step 1 does not lead to a choice because the difference between the minimum outcomes equals 5 − 0 = 5, which is smaller than the threshold 0.1(100) = 10. Step 2 also does not lead to a choice because the difference between the probabilities of minimum outcomes equals 1 − 0.95 = 0.05, which is smaller than the threshold 0.1. Step 3 leads to the choice of (100, 0.05; 0, 0.95) because its maximum outcome, 100, is larger than 5, the maximum outcome of (5, 1) Priority heuristic for losses ( xmax , ymax ≤ 0) Step 1. If the difference between the maximum outcomes |xmax − ymax | exceeds the threshold 0.1 max{|xmin |, |ymin |}, then choose the gamble with the larger maximum outcome; otherwise continue. Step 2. If the difference between the probabilities of maximum outcomes | pmax − qmax | exceeds the threshold 0.1, then choose the gamble with the larger probability of maximum outcome; otherwise continue. Step 3. Choose the gamble with the larger minimum outcome; if those are equal, then choose a gamble randomly. .

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For instance, consider the choice between (−5, 1) and (−10, 0.5; 0, 0.5). Step 1 leads to the choice of (−10, 0.5; 0, 0.5) because the difference between the maximum outcomes equals 0 − (−5) = 5, which is larger than the threshold 0.1(10) = 1, and the larger maximum outcome is 0. Fast-and-frugal trees. Figures 3.3 and 3.4 provide graphical representations of the two versions of the priority heuristic as fast-and-frugal trees .37 Fast-and-frugal trees are a special case of decision trees, where it is always possible to make a decision each time a question is asked. Such trees are easy to apply and be understood by practitioners without quantitative backgrounds, such as medical doctors and legal experts, while also competing very well on performance with less transparent models commonly used in operations research or machine learning.38 Fast-andfrugal trees are instances of lexicographic heuristics wherein decisions are made by ordering attributes and deciding based on the first attribute that discriminates between the available options.39 Such heuristics are commonly employed systems in practice, as for example in ranking countries in the Olympic games—the first attribute is the number of gold medals, followed by the number of silvers, and finally bronze ones. Lexicographic heuristics are non-compensatory in that there is no way to change the choice suggested by the first attribute based on the subsequent attributes. That is, in the priority heuristic for losses, the choice suggested by the maximum outcome cannot be changed by the minimum outcome. In terms of theory, Arch Woodside has argued strongly for the usefulness of lexicographic heuristics across the business and management sciences,40 and pointed out early applications of fast-and-frugal trees.41 Fast-andfrugal trees are an instance of asymmetrical cognitive modeling, wherein the processes leading to one decision might be qualitatively different from those leading to another decision42 (unlike in linear models such as regression). Both versions of the priority heuristic start by inspecting one of the outcomes in each gamble. For gains, this is the minimum outcome. This is the worst-case scenario considered by the minimax heuristic discussed in Chapter 2, and it expresses people’s risk aversion for gains. For losses, the outcome inspected by the priority heuristic is the maximum outcome. This is the best-case scenario considered by the maximax heuristic (Chapter 2), and it expresses people’s risk taking for losses. Like von Neumann’s two heuristics, the priority heuristic does not embody diminishing sensitivity or loss aversion.

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Fig. 3.3 Representation of the priority heuristic for gains as a fast-and-frugal tree. To simplify the last step we assume that xmax  = ymax

Fig. 3.4 Representation of the priority heuristic for losses as a fast-and-frugal tree. To simplify the last step we assume that xmin  = ymin

The priority heuristic goes beyond the minimax and maximax heuristics in two ways. First, it evaluates how large the difference is between the minimum, respectively maximum, outcomes (Step 1). Second, if this difference is not sufficiently large, another attribute is considered, the probability of the minimum, respectively maximum, outcome, where a similar rule to the rule for outcomes is employed (Step 2), and this process might continue (Step 3). The reasons for ordering the attributes

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of gambles in this way are discussed in Sect. 3.5. Deciding whether a difference in outcomes or probabilities, is sufficiently large is done by comparing the difference with a threshold. In both cases, the threshold is 0.1, with the caveat that this threshold might need to be scaled appropriately. For outcomes, this is done by multiplying the threshold with a factor equal to the most extreme outcome of either gamble in the choice scenario under consideration. There is no need for using a scaling factor for probabilities since the upper bound for probabilities is 1. The priority heuristic has zero free parameters.43 In order to fix the value of the thresholds, the authors made an educated guess based on what is known from psychology. The idea is that people often tend to use prominent numbers such as powers of 10, their halves, doubles, and so on44 ; thus decision makers might use 10% of the upper bound of the scale as a threshold.45 The approach of using fixed parameters, such as fixed thresholds, is a common one in the heuristics approach because it enhances simplicity. For example, a simple way of diversifying funds over a financial portfolio is the 1/N heuristic, where funds are split equally to the N assets being considered. Under some conditions, parameter-free heuristics, such as 1/N , perform competitively in terms of profit with optimization models such as Markowitz’s mean–variance analysis.46 This heuristic is also discussed in Chapter 6, for sourcing in supply chains. The priority heuristic is simpler than prospect theory in that it (i) may ignore some of the available outcomes and probabilities (if the choice is made in Steps 1 or 2), and (ii) does not transform the outcomes or probabilities that are actually used, by employing a utility or a probabilityweighting function. A similarity between the models is that, just as prospect theory uses one form of the utility and probability-weighting functions for gains and another form for losses, there is one version of the heuristic for gains and another version for losses. People can adapt their decision strategy from one task to another, and modeling has to reflect this versatility.

3.4

Predictive Power

The pioneering studies of Kahneman and Tversky on prospect theory up to the early 1990s focused on demonstrating that it can fit behavioral effects. For example, a set of parameter values would be identified so that prospect theory could reproduce the Allais paradox or common ratio effects.47 A few years later it was recognized in psychology that it is key

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to go beyond fitting and assess how well does a model predict.48 To do so, one should estimate the parameters of a model in a dataset and then test the fixed model in other datasets. Furthermore, a test dataset should not refer to a single effect, but it should represent a range of empirical evidence. Finally, the performance of any model should be benchmarked against that of other models. Such features of model validation studies are standard in statistics and machine learning. They were employed in the study by Brandstätter and his colleagues. Brandstätter and colleagues used four test datasets.49 Two were from Kahneman and Tversky50 —in the original data used to test prospect theory, there are 14 choices between gambles with at most two outcomes and equal or similar expected value, and in a latter test of cumulative prospect theory, there are 56 choices which are inferred by using the certainty equivalents of two gambles (i.e., the monetary amount that should be received for sure so that a participant is indifferent between this amount and the gamble).51 In the third dataset, the data is people’s 90 choices between two gambles with five outcomes each and equal expected value.52 The fourth dataset had human data from another 100 choices between two gambles with two outcomes which were randomly generated. A total of 14 models were tested. Optimization models included prospect theory and the transfer-of-attention-exchange model,53 a probability-weighted utility model designed to enhance prospect theory by formally specifying the behavioral effects of changes in how choices are described and presented to people. Simple heuristics included the priority heuristic as well as the minimax and maximax rules. The authors used the estimates of the parameters of prospect theory produced in two of the four datasets, as shown in Table 3.1. On average, prospect theory and the priority heuristic were the most accurate models. Table 3.2 shows the proportion of majority choices that were predicted correctly by these two models in the four datasets Table 3.1 Estimates of the parameters of prospect theory from two datasets

Certainty equivalents Five outcomes

α

β

γ

δ

λ

0.88 0.57

0.88 0.97

0.61 0.70

0.69 0.99

2.25 1.00

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described above. In the table, for each of the two outcomes studies, the accuracy of prospect theory is the average produced by using the two parameter sets. For each of the five outcomes and certainty-equivalents studies, the parameter set estimated in the other study was used so as to avoid mere fitting. Recall that the priority heuristic does not have any free parameters, and thus it fits and predicts the data with the same accuracy. In all datasets, the priority heuristic predicted better than prospect theory. Interestingly, prospect theory fit as well or better than the priority heuristic in the two studies in which its parameters were estimated, achieving an accuracy of 87% in the five outcomes study (using the parameter estimates from this study) and 91% in the certainty-equivalents study (using the estimates from it). That is, there is an average loss of accuracy of 16% from fitting to prediction for prospect theory. In a study where prospect theory was used to fit and predict individual choices, the loss of accuracy from fitting to prediction ranged between 2 and 8%, depending on the number of free parameters used.54 Such results underscore the importance of differentiating between fitting and prediction when assessing behavioral models. Robustness. At first glance, the results of Table 3.2 might seem surprising. How can it be that a model without free parameters, employing simple arithmetic comparisons without transforming or combining outcomes and probabilities, predicts more accurately than a multi-parameter model which combines non-linearly transformed outcomes and probabilities? Actually, such results are not uncommon. In areas such as multi-attribute choice, probabilistic inference, time-series forecasting, and games of strategic interaction, it has been empirically Table 3.2 Proportion of people’s majority choices predicted correctly by prospect theory and the priority heuristic in four datasets

Prospect theory Priority heuristic

Two outcomes; equal (approx.) expected value (%)

Two outcomes; random values (%)

Five outcomes; equal expected value (%)

Certainty equivalents (%)

68

82

67

80

100

85

87

89

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found that simple models can predict as well as or better than more mathematically complex ones.55 This evidence can be explained by the theory of ecological rationality 56 that comprises mathematical analyses identifying structural and statistical conditions under which it pays to go simple and under which it does not.57 Ecological rationality is discussed more deeply in Chapter 6. More specifically to decision making under risk, the lack of robustness of the parameter values of prospect theory has been pointed out in the economics literature. This means that prospect theory parameters fit to one behavioral effect are unlikely to predict other effects. For example, none of the theory’s estimated sets of parameters can simultaneously account for buying lottery tickets, buying insurance policies, the Allais paradox, and other behavior observed in the literature.58 And wellknown estimates of the utility and probability-weighting functions imply that people will purchase neither lottery tickets nor insurance policies.59 The lack of robustness in parameters is consistent with the observed lack of robustness in the accuracy of prospect theory, expressed by the loss from fitting to predictive accuracy.60 On the other hand, the priority heuristic is robust. The heuristic’s robustness comes exactly from the fact that it has no free parameters. It has been proven analytically61 that it logically implies reflection effects, the four-fold pattern of risk attitude, and common consequence effects at the same time. For example, the four-fold pattern of risk attitude is predicted by the heuristic when a ‘large’ probability in the statement of the pattern (Sect. 3.1), p, is interpreted to mean p > 0.1. That is, consider the pattern for gains: According to the priority heuristic, ( px, 1) is chosen to (x, p; 0, 1 − p) if and only if p > 0.1. As two examples, the heuristic chooses (5, 1) over (10, 0.5; 0, 0.5) and (100, 0.05; 0, 0.95) over (5, 1). The comparative robustness of the priority heuristic and prospect theory help explain the results in Table 3.2. For more details on the formal properties of the priority heuristic see the Appendix, which also includes analyses of the heuristic, as well as of prospect theory, in the contexts of the Saint Petersburg paradox and the equity premium puzzle. Such analyses and the empirical results presented above suggest a bold hypothesis: Modeling diminishing sensitivity, loss aversion, and probability weighting might not be necessary for explaining and predicting human behavior in decision under risk.62

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Other model competitions and machine learning. Statistician George Box famously said that all models are wrong, but some are useful. With regard to the first part of Box’s quote, both prospect theory and the priority heuristic systematically lead to choices that people do not make.63 This suggests that it may be possible to improve their accuracy. Indeed, consider a competition where researchers were invited to submit models for predicting 750 choices made by each one of 125 participants, encompassing 14 behavioral effects, including some that were discussed in this chapter.64 The winning model, while incorporating aspects of prospect theory and the priority heuristic, differs from both in sampling the realizations of gambles and computing expected values. The model is so involved that the competition organizer and first author Ido Erev and his colleagues wittingly named it BEAST (best estimate and sampling tools). Subsequently, machine learning researchers leveraged BEAST to produce an even more accurate, and also even more complex, model.65 First, synthetic data, generated by BEAST, was used to train a neural network. This training set consisted of 185,000 data points. Second, the neural network was fine-tuned by using human data. The resulting neural network predicted human data from the Erev and colleagues study better than BEAST, almost halving the mean squared error (0.0053 versus 0.0099). Cognitive Operations takes seriously the second part of Box’s quote. I do not believe that the point of behavioral modeling is a race where the aim is to increase accuracy and to do so at any cost. Rather, behavioral models that are operational must achieve predictive power while at the same time providing useful insights into how people think.

3.5

Cognitive Processes

Greek astronomer Ptolemy tried to explain the periodic but irregular motions of the sun, moon, and other planets by postulating that the earth is in the center of the universe and does not move, while the planets move in epicycles (a small circle whose center moves on the circumference of a larger circle). For centuries, Ptolemy’s framework could fit the available observations because it is mathematically flexible, meaning that any periodic motion can be approximated arbitrarily well by constructing iterations of epicycles.66 But the framework was eventually abandoned because it became too cumbersome and most importantly because its

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postulates do not reflect the real processes underlying the workings of the earth and the other planets.67 Ptolemy’s approach to theory development resonates with the as-if approach of Milton Friedman and Jimmie Savage (Chapter 2). In as-if modeling, the processes underlying how a person makes decisions may be neglected as long as the data can be captured well. But philosopher of science Clark Glymour criticized what he called Ptolemaic psychology: ‘If one wants to understand what is going on, it doesn’t help much.’68 What does it mean to understand what is going on? For Glymour, it means to understand how the human brain produces thought, emotion, and action.69 When the Bank of England’s monetary policy committee members discuss ‘what is going on here’ in the economy, they ponder questions such as how would a particular setting of the interest rate affect market sentiment and financial investment, and then they act on the basis of this discussion.70 In their concluding chapter on future work in behavioral operations, Elliot Bendoly and Daniel Bachrach (emphasis in the original) suggest analyzing the ‘dialogue that emerges across processes in which actions are decided upon and executed.’71 Do prospect theory and the priority heuristic support discussion about human decision processes? Do they help open the black box? Part of the answers has been provided in Chapter 2, where I analyzed expected utility theory and the minimax/maximax rules on this dimension. Below I recap and extend that analysis. Prospect theory. In expected utility theory, there is no specification of how exactly utilities are estimated and how they are combined with probabilities. For example, in Eq. 3.1 we do not know if the utility of the best outcome is estimated first, if it is then multiplied with its probability, or if the utility of the worst outcome is estimated before this multiplication takes place. Expected utility theory, and more generally optimization models, do not typically specify information processing stages that transform input to output. Hence, optimization models are typically not process models.72 This analysis applies to the evaluation phase of prospect theory. This phase is the one explicated in Sect. 3.2 for evaluating the worth of a gamble. In this phase, there is no specification of how utility and probability-weighting functions can be computed by people. Prospect theory also includes an editing phase, which outlines a number of operations that people are assumed to perform in order to process information in gambles before they evaluate these gambles.73 For

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instance, dominated gambles are detected and eliminated. The editing phase provides a description of the cognition underlying people’s decision making. An issue is that the order in which the editing operations are performed has not been specified. This limits the degree to which prospect theory may be viewed as a process model. On the other hand, one can imagine that prospect theory can be turned into a process model by adding reasonable auxiliary assumptions. In fact, such work has been done for another optimization model, used to model strategic interaction,74 and is discussed in Chapter 4. Priority heuristic. As in the case of the minimax/maximax heuristics, the priority heuristic specifies the order in which attributes are inspected, as well as how the attribute values are processed. There is a clear sequence of three steps that transforms input (two gambles and their attributes) to output (choice of one gamble). In this sense, the priority heuristic is a process model. Process-related investigations of the priority heuristic have focused on why this particular sequence of steps is assumed in the heuristic and if it is empirically valid. On the first issue, Brandstätter and his colleagues point out that the literature and common experience suggest that people tend to pay more attention to outcomes than probabilities. For example, an Enlightenment classic on the art of thinking asserts this point.75 And it is evident that all of us who buy lotteries and insurance focus on outcomes. On the second issue, there has been a number of lab tests. One basic test utilized the response time of participants, which is the time they take to make a choice.76 If the priority heuristic is employed to make a choice, then one would expect that it would take longer to respond to choices made in Step 3 compared to choices made in Step 1. Figure 3.5 shows that this prediction was borne out in an experiment with 121 participants. The median response time was 9.3 seconds when the priority heuristic would choose at Step 1 and 10.1 seconds when the heuristic would choose at Step 3, in both cases for gambles with two outcomes. For choices between gambles with five outcomes, the respective median response times were 10.3 and 11.8 seconds. More sophisticated tests compare the process predictions of the priority heuristic with those of optimization models. The empirical results can be complicated to interpret77 or paint a mixed picture.78 For instance, the patters of search for attribute values seem to agree more with the predictions of the priority heuristic for ‘difficult’ choices and more with the predictions of optimization models for ‘easy’ choices.79

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11.8 10.1

10.3

Response time (sec)

9.3

Step 1 Step 3 Two outcomes

Step 1 Step 3 Five outcomes

Fig. 3.5 Median response times (in seconds) of participants in the experiment by Brandstätter et al., when the priority heuristic would lead to a choice at its Step 1 or Step 3, for gambles with two or four outcomes

3.6

Transparency

A model is transparent to someone when she can understand, apply, and explain it to other people. Conceptual analyses suggest that understandability, applicability (which is similar to usability), and explainability are all closely related to simplicity.80 The thesis is that simpler models tend to be more transparent. This thesis might not seem very surprising, and possibly because of that, there has been little empirical testing of it in operations research or operations management. A few experiments with human participants, in Loughborough University’s School of Business and Economics, have focused on models for simulation81 and multi-attribute/criteria decision under certainty.82 The decision-making experiments showed that simple heuristics, such as lexicographic ones, are easier than optimization models for people to understand and apply. Computational complexity. Another stream of empirical work on the transparency of decision-making models has studied the simplicity of models per se, rather than from the point of view of people. This stream takes a computer science approach. In computer science, models and algorithms83 are often assessed on their computational complexity.

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This can be done empirically by first identifying all elementary operations (e.g., logical, arithmetic) that a computer performs in order to apply the model or algorithm to a dataset, and then counting the total number of these operations. To illustrate, assume that the dataset consists of a single choice, between (5, 1) and (10, 0.5; 0, 0.5). In the only step the priority heuristic will use, Step 1, it performs the following 7 operations: 1. Identify the minimum outcome of the first gamble (5) 2. Identify the minimum outcome of the second gamble (0) 3. Compute the difference between the minimum outcomes (5–0 = 5) 4. Identify the maximum outcome across gambles (10) 5. Compute the threshold [0.1(10) = 1] 6. Compare the difference with the threshold (5 > 1) 7. Choose the gamble (5, 1). By the same token, prospect theory performs the following 30 operations: 1. Identify the outcome of the first gamble (5) 2. Compute the value of the outcome of the first gamble (50.88 = 4.12) 3–8. Identify the probability and compute its weight for the outcome of the first gamble   (

10.61 1 0.61 (1 +00.61 ) 0.61

=1 )

9. Compute the worth of the first gamble (1 × 4.12 = 4.12) 10 and 11. Identify the outcomes of the second gamble (10 and 0) 12 and 13. Compute the values of the outcomes of the second gamble (100.88 = 7.59 and 00.88 = 0) 14–19 and 20–25. Identify the probabilities and compute their weights for  the outcomes of the second  gamble 

0.50.61

1 (0.50.61 +0.50.61 ) 0.61

0.50.61

1 (0.50.61 +0.50.61 ) 0.61



= 0.32

= 0.32

and

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26–28. Compute the worth of the second gamble (0.32 × 7.59 + 0.32 × 0 = 2.43) 29. Compare the worth of the two gambles (4.12 > 2.43) 30. Choose the gamble (5, 1). Such numerical measures of complexity/simplicity are often used in the psychology of judgment and decision making in order to compare optimization and heuristic models. This is the case in research programs that postulate that people may, depending on the situation, use either kind of model; see work in the adaptive decision maker 84 and the adaptive toolbox.85 As in the above illustration, in these studies, optimization models are found to be more complex than heuristics. For example, in a landmark study by John Payne, James Bettman, and Eric Johnson, the computational complexity of lexicographic heuristics for multi-attribute choice was between 30 and 50% of the complexity of a model that weighted and added attributes.86 Such analyses are typically based on assumptions about the human brain’s computational architecture. In the previous illustration, all computations were assumed to be performed serially. If the values and weights of outcomes, as well as the operations in computing the worth of a gamble, were assumed to be performed in parallel,87 then the complexity of prospect theory would equal 25. In specific families of models, such as decision trees, however, it is possible to construct measures of computational complexity that do not seem to make brain architecture assumptions. Together with my colleagues, we defined the simplicity of a decision tree to be the number of questions it includes, and also identified this as a measure of transparency.88 The idea is that, given a tree structure, this measure gives a good indication of how much information needs to be understood, memorized, or taught to someone else. Across 64 real-world datasets from fields such as medicine, business, law, and the arts, the mean number of questions was 5.3 in fast-and-frugal trees and 24.0 in classification-and-regression trees,89 a family of machine learning models especially designed to be transparent. As seen in Figs. 3.3 and 3.4, the priority heuristic has three questions. Other machine learning models, which are not designed with transparency in mind, such as random forests, have worse transparency by one or two orders of magnitude.90 Explainability. There are many efforts to make machine learning models more transparent by making them more explainable.91 For

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instance, the researchers who developed the neural network for predicting people’s choices under risk (Sect. 3.4) recognized this need and suggested that relating their neural network to BEAST could help, although they did not spell out how exactly. A common approach to making a model explainable is to construct a new model that approximates the predictions of the original one and is designed to be easier to explain to stakeholders.92 There are a number of issues with this approach.93 First, it decouples explanation and prediction because each function is performed by a different model. Because of that, data scientists themselves may have trouble understanding the exact relationship between the two models, and this problem is compounded for other stakeholders, which may undermine the value of both models and the whole enterprise.94 Second, as behavioral finance pioneer Hersh Shefrin has pointed out, even if the predictions of two models are similar their underlying processes can be very different, and it may thus make little sense to explain one model’s processes in terms of the other’s processes. In fact, as Shefrin discusses in a report for the Professional Risk Managers’ International Association, companies such as ZestFinance have spotted inaccuracies and inconsistencies in the practical application of popular explainability protocols.95 It is curious how research focuses on developing techniques to explain the predictions of complex, black-box models, rather than developing simple, transparent models in the first place, especially given that transparent models can be as, or more, accurate, and the behavioral sciences provide resources for doing just that.96

3.7

Usefulness of Output

The multi-parameter functions used in prospect theory decrease its robustness and transparency but at the same time allow it to produce more granular output, in two ways. First, prospect theory can produce a valuation for a decision option since it can compute the worth of a gamble. Second, it can capture individual differences between decision makers by estimating their different utility and probabilityweighting functions.97 In contrast, the more robust and transparent priority heuristic can only output that one decision option is chosen to another, and this choice is predicted to be the same for all decision makers.

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As discussed in Chapter 2, it is not clear whether attempts at quantifying and personalizing human preferences and choices to date are always valid and useful. For example, the 2008 financial crisis has been partially attributed to individual investors and banks placing too much confidence in tailored but inaccurate valuation instruments.98 And it has been estimated that personalized online advertising has led companies such as eBay to lose money.99 The results of Table 3.2 show the limits of prospect theory in predicting decisions under risk, although it should be noted that more quantitatively sophisticated models such as BEAST and neural networks have been found to perform better.100 Let us assume for the sake of the argument that it is possible, in valid and useful ways, to generate option valuations and capture individual differences. Below we explore how simple heuristics, such as the priority heuristic, can also be used to do so. Cognitive psychometrics. One can employ an approach similar to the one used in machine learning for making complex models explainable. Thorsten Pachur and his colleagues carried out an exercise in cognitive psychometrics .101 The idea is to first generate choices by the priority heuristic and to use those choices to estimate the parameters of prospect theory. Then, if the fit is satisfactory, one can map a person who uses the priority heuristic to the estimated utility and probabilityweighting functions, which in turn allows generating valuations and capturing individual differences. The utility and probability-weighting functions characterizing the priority heuristic—in a study where prospect theory was fit to 180 priority heuristic choices between two-outcome gambles—are shown in Figs. 3.6 and 3.7, respectively. In this exercise, different probability-weighting functions were fitted for gains and losses. All estimated functions are piecewise linear. It is interesting to note here that the inverse procedure, where parameterized lexicographic heuristics (e.g., allowing the order of attributes and the value thresholds to vary)102 would be estimated by prospect theory simulated choices, could be used to explain prospect theory as simple heuristics. This kind of exercise can help integrate103 prospect theory and the priority heuristic, and more generally the approaches of optimization and simple heuristics. Chapter 4 describes such work in the study of strategic interaction. It is also interesting that such exercises allow the priority heuristic to be applied to celebrated behavioral phenomena that involve valuation, such as the St. Petersburg Paradox and the equity premium puzzle (see Appendix).

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u(x)

x 0

100

Fig. 3.6 The utility function u(x) = x 0.82 for x ≥ 0 and −1.37(−x)0.82 for x < 0, characterizing the priority heuristic in the cognitive psychometrics exercise by Pachur et al., where prospect theory was fitted to the heuristic’s choices

An alternative approach does not go through prospect theory or any other optimization model, but rather studies directly the workings of the priority heuristic. The idea is to examine if any of the steps of the heuristic can be mapped to weighting probabilities or calculating values. Interestingly, one may again argue that the priority heuristic can be mapped to piecewise linear functions. Consider probability weighting. In Step 2 of the heuristic, a probability p is considered indistinguishable from all other probabilities q such that | p − q| ≤ 0.1. One can say that p is ‘weighted’ to be the arithmetic mean of all theseq. For example, if p = 0.05, then the interval of q is [0, 0.15], and the weighted value of p is 0.075. Similarly, if p = 0.95, the interval of q is [0.85, 1], and the weighted value of p is 0.925. This calculus reproduces Tversky and Kahneman’s proposal of under-weighting of small probabilities and under-weighting of large probabilities. For intermediate values of p, the weighted value is p (e.g., if p = 0.5, the range of q is [0.4, 0.6] which is centered around 0.5). Overall, the priority heuristic can be

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1

w(p)

Gains (x 0) Losses (x < 0)

0 0

1

p

Fig. 3.7 The probability-weighting functions, w( p) = corresponding to x ≥ 0 and

0.05 p 0.17 for p 0.05 p 0.17 +(1− p)0.17

0.62 p 0.17 for p corresponding to x < 0, 0.62 p 0.17 +(1− p)0.17

characterizing the priority heuristic in the cognitive psychometrics exercise by Pachur et al., where prospect theory was fitted to the heuristic’s choices

mapped to the probability-weighting function provided below, which is graphed in Fig. 3.8. ⎧ ⎨ 0.05 + 0.5 p, p < 0.1 wpriority ( p) = (3.3) p, 0.1 ≤ p ≤ 0.9 ⎩ 0.45 + 0.5 p, p > 0.9 It is not clear how to map the priority heuristic to a utility function. But it is possible to provide a closed-form expression for the certainty equivaoutcome c is chosen

lent of the heuristic,104 C E priority . Note that a certain by the priority heuristic over the gamble xmin , pmin ; xmax , 1 − p min where xmin < c < xmax if and only if it is chosen in Step 1 where it has to hold that c − x min > 0.1x max . This fact implies the following equation. C E priority = xmin + 0.1x max

(3.4)

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w(p)

1

0 0

1

p

Fig. 3.8 The probability-weighting function wpriority ( p) = 0.05 + 0.5 p, for p < 0.1, p for 0.1 ≤ p ≤ 0.9, and 0.45 + 0.5 p for p > 0.9, that can be mapped to the priority heuristic based on the threshold value of 0.1 in its Step 2

Research in more specific contexts. People have to make decisions under risk in a number of contexts, such as transportation and logistics. For example, when going to stores, consumers choose driving routes and parking lots, and managers solve vehicle routing problems in order to dispatch goods to destinations. In such applications, where the objective is to analyze and improve system efficiency, behavioral models must output the proportion of people that make each choice, rather than just the choice of the majority. Optimization models, such as prospect theory, can do this by transforming the worth of a gamble into its choice probability. For example, for a choice between gambles G and G ∗ with worth w(G) and w(G ∗ ) respectively, the probability of choosing G is often computed ek·w(G) as the ratio ek·w(G) ∗ , where the parameter k > 0 controls the sensi+ek·w(G ) tivity of choice probability on differences in worth (e.g., if k is very large, it is basically certain that the gamble with the higher worth is chosen).

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Simple models such as the priority heuristic cannot be readily combined with this approach; rather, more complex heuristics would be needed.105 Amnon Rapoport and his colleagues have investigated individual route choices from a game-theoretic perspective,106 not of decision under risk, and this work is described in Chapter 4. Behavioral research on vehicle routing has focused on deterministic problems and uncovered heuristics, such as visuospatial ones, which are distinct from the cognitive heuristics discussed in this book.107 Studies of individual routes and parking choices that compared heuristic and optimization models of behavior have been performed by the group of Don Fisher at the University of Massachusetts driving simulation lab.108 These studies asked participants to make decisions under uncertainty. For example, a task was to choose between staying on the highway interstate I-93 which would reach downtown Boston in 100 minutes for sure, or to divert to the local Route 28 which could take from 70 to 120 minutes. Some behavioral effects were replicated, such as attitude reversals from gains to losses, and also tested in novel situations, as when the reference point, route I-93, also had a range of travel times.109 The conclusion from these studies is that heuristics capture people’s choices more accurately than optimization models. For scenarios as the one described above, a successful heuristic postulated that people estimate the travel time of an uncertain route by taking a random sample from the range provided.110 This idea is reminiscent of BEAST, but the heuristic is more frugal in using only one piece of information.

3.8

Summary and Resources

The comparative analysis of prospect theory and the priority heuristic in the preceding four sections are summarized in Table 3.3. In one sentence, one can say that because of its simplicity, the priority heuristic is more robust, process-oriented, and transparent than prospect theory, whereas prospect theory can directly provide more granular and quantitatively sophisticated output than the priority heuristic. The approach of building simple models of people’s bounded rationality that process attributes sequentially or use numerical thresholds, is not unique to the priority heuristic, but comes from a long tradition in behavioral modeling.111 The short book Modeling Bounded Rationality

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Table 3.3 Summary of the comparative analysis of prospect theory and the priority heuristic

Prospect theory

Priority heuristic

Predictive power

Cognitive processes

Transparency

Usefulness of output

Lower than the heuristic in predicting the majority choice; higher in fitting. Can be applied to individual choice. Cannot predict response time patterns Higher than prospect theory in predicting majority choice; lower in fitting. Cannot be applied to individual choice. Can predict response time patterns

Not modeled in the evaluation phase; outlined—but not precisely specified—in the editing phase

High computational complexity; no simple representation of the model; though a cognitive psychometrics exercise could lead to one

Able to valuate options and characterize individual differences; though unclear how valid or useful this output is

Modeled precisely with zero free parameters: fixed attribute order and fixed thresholds for comparing attribute values

Low computational complexity; simple graphical representation of the model as a fast-and-frugal decision tree

Unable to evaluate options or characterize individual differences; the heuristic can be mapped to (piece-wise) linear functions in prospect theory

by economist Ariel Rubinstein provides a view of such work, and also includes a discussion with the ‘father’ of bounded rationality, Herbert Simon.112 A more recent and comprehensive introduction to bounded rationality is provided by Clement Tisdell.113 Systematic methods for statistically inducing and testing fast-and-frugal trees, of which the priority heuristic is an instance, have been developed and are available to execute through publicly available online resources, including the R packages ffcr 114 and FFTrees.115 Machine learning approaches to inducing simple heuristics, often from large datasets, are studied by a number of groups, such as the lab of Tom Griffiths at Princeton University116 ; see https:// cocosci.princeton.edu/people.php.

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Notes 1. John M. Keynes, Essays in Biography (London, UK: Palgrave Macmillan, 2010), 158. 2. R. Duncan Luce, “Four Tensions Concerning Mathematical Modeling in Psychology,” Annual Review of Psychology 46 (1995): 1–26; Kenneth R. Hammond, Human Judgment and Social Policy: Irreducible Uncertainty, Inevitable Error, Unavoidable Injustice (Oxford: Oxford University Press, 1996); Alan A. Stocker and Eero P. Simoncelli, “Noise Characteristics and Prior Expectations in Human Visual Speed Perception,” Nature Neuroscience 9, no. 4 (2006): 578–585. 3. Mary S. Morgan, “Models, Stories and the Economic World,” Journal of Economic Methodology 8, no. 3 (2001): 361–384; Mary S. Morgan and Till Grüne-Yanoff, “Modeling Practices in the Social and Human Sciences: An Interdisciplinary Exchange,” Perspectives on Science 21, no. 2 (2013): 143–156; Konstantinos V. Katsikopoulos, “Bounded Rationality: The Two Cultures,” Journal of Economic Methodology 21, no. 4 (2014): 361–374. 4. Daniel Kahneman and Amos Tversky, “Prospect Theory: An Analysis of Decision Under Risk,”Econometrica, 47, no. 2 (1979): 263–291. 5. Edouard Brandstätter, Gerd Gigerenzer and Ralph Hertwig, “The Priority Heuristic: Making Choices Without Trade-Offs,” Psychological Review 113, no. 2 (2006): 409–432. 6. Christoph H. Loch and Yaozhong Wu, Behavioral Operations Management (Norwell, MA: Now Publishers, 2007); Tony H. Cui and Yaozhong Wu, “Incorporating Behavioral Factors Into Operations Theory,” in The Handbook of Behavioral Operations, eds. Karen Donohue, Elena Katok and Stephen Leider (Hoboken, NJ: John Wiley and Sons, 2018), 89–119; Andrew M. Davis, “Biases in Individual Decision-Making,” in The Handbook of Behavioral Operations, 151–198; Gary E. Bolton and Yefen Chen, “Other-Regarding Behavior: Fairness, Reciprocity, and Trust,” in The Handbook of Behavioral Operations, 199–235. 7. More mathematically sophisticated approaches to modeling people’s reasoning and decision making use Bayesian and quantum probability—see respectively Nick Chater and Mike Oaksford, eds., The Probabilistic Mind: Prospects for Bayesian Cognitive Science (New York: Oxford University Press, 2008); Jerome M. Busemeyer and Peter D. Bruza. Quantum Models of Cognition and Decision (Cambridge, MA: Cambridge University Press, 2012). 8. A number of phenomena have been replicated in a large international study by Kai Ruggeri et al., “Replicating Patterns of Prospect Theory

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9.

10.

11.

12. 13.

14. 15.

16. 17.

18. 19. 20.

21. 22. 23. 24.

for Decision Under Risk,” Nature Human Behaviour 4, no. 6 (2020): 622–633. Gerárd Jorland, “The Saint Petersburg Paradox 1713–1937,” in The Probabilistic Revolution: Ideas in History Vol 1, eds. Lorenz Krüger, Lorraine J. Daston and Michael Heidelberger (Cambridge, MA: MIT Press, 1987), 157–190. Shlomo Benartzi and Richard H. Thaler, “Myopic Loss Aversion and the Equity Premium Puzzle,” The Quarterly Journal of Economics 110, no. 1 (1995): 73–92. Chris Starmer, “Developments in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice Under Risk,” Journal of Economic Literature 38, no. 2 (2000): 332–382. Harry S. Markowitz, “Portfolio Selection,” The Journal of Finance 7, no. 1 (1952): 77–91. Peter C. Fishburn and Gary A. Kochenberger, “Two-Piece von Neumann-Morgenstern Utility Functions,” Decision Sciences 10, no. 4 (1979): 503–518. Kahneman and Tversky, “Prospect Theory,” 268, table 1. Amos Tversky and Daniel Kahneman, “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Risk and Uncertainty 5, no. 4 (1992): 297–323. Amos Tversky and Craig R. Fox, “Weighing Risk and Uncertainty,” Psychological Review 102, no. 2 (1995): 269–283. Timothy J. Pleskac et al., “The Ecology of Competition: A Theory of Risk-Reward Environments in Adaptive Decision Making,” Psychological Review 128, no 2 (2020): 115–135. Tversky and Fox, “Weighing Risk and Uncertainty”. Floris Heukelom, “A History of the Allais Paradox,” The British Journal for the History of Science (2015): 147–169. Kenneth R. Maccrimmon, “Descriptive and Normative Implications of the Decision-Theory Postulates,” in Risk and Uncertainty, eds. K. Borch and J. Mossin (International Economic Association Conference, London: Palgrave Macmillan, 1968), 3–32. Leonard J. Savage, The Foundations of Statistics (New York: John Wiley and Sons, 1954). Starmer, “Developments in Non-Expected Utility Theory”. Ibid. The equivalence of optimization models, such as expected utility theory and prospect theory, to sets of apparently reasonable axioms (see Savage, The Foundations of Statistics and Tversky and Kahneman, “Advances in Prospect Theory” respectively) is often employed as an argument for prescribing the use of such models. Simple heuristics have also

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25. 26. 27. 28.

29.

30. 31. 32. 33. 34. 35. 36.

37.

38.

39.

40.

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been axiomatized, including the priority heuristic; see Mareile Drechsler, Konstantinos V. Katsikopoulos and Gerd Gigerenzer, “Axiomatizing Bounded Rationality: The Priority Heuristic,” Theory and Decision 77, no. 2 (2014): 183–196. Kahneman and Tversky, “Prospect Theory”. Tversky and Kahneman, “Advances in Prospect Theory”. Peter P. Wakker, Prospect Theory For Risk and Ambiguity (Cambridge, UK: Cambridge University Press, 2010). For instance, see Menahem E. Yaari, “The Dual Theory of Choice Under Risk,” Econometrica (1987): 95–115, for a discussion of how the elevation of the probability weighting function reflects the degree of risk aversion. George Wu and Richard Gonzalez, “Curvature of the Probability Weighting Function,” Management Science 42, no. 12 (1996): 1676– 1690. Brandstätter et al., “The Priority Heuristic”. The assumption has been relaxed in describing inventory decision making; see Chapter 5. Tversky and Kahneman, “Advances in Prospect Theory”. Ibid. Ibid. Brandstätter et al., “The Priority Heuristic”. See Brandstätter et al., “The Priority Heuristic” and Marc O. Rieger and Mei Wang, “What is Behind the Priority Heuristic? A Mathematical Analysis and Comment on Brandstätter, Gigerenzer, and Hertwig (2006),” Psychological Review 115, no. 1 (2008): 274–280. Laura Martignon, Konstantinos V. Katsikopoulos and Jan K. Woike, “Categorization With Limited Resources: A Family of Simple Heuristics,” Journal of Mathematical Psychology 52, no. 6 (2008): 352–361; Shenghua Luan, Lael J. Schooler and Gerd Gigerenzer, “A SignalDetection Analysis of Fast-and-Frugal Trees,” Psychological Review 118, no. 2 (2011): 316–338. Konstantinos V. Katsikopoulos et al., Classification in the Wild: The Science and Art of Transparent Decision Making (Cambridge, MA: MIT Press, 2020). For a review, see Peter C. Fishburn, “Lexicographic Orders, Utilities and Decision Rules: A Survey,” Management Science 20, no. 11 (1974): 1442–1471. Note that the trees in Figs. 2.2 and 2.3 are also (trivial) fast-and-frugal trees. Arch G. Woodside, “Seating Gigerenzer, Gladwin, McClelland, Sheth and Simon at the Same Table: Constructing Workbench Theories of Decision Processes That Predict Outcomes Accurately,” in Handbook of Advances in Marketing in an Era of Disruptions: Essays in Honour of

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41.

42.

43.

44.

45.

46.

47.

Jagdish N. Sheth, eds. Atul Parvatiyar and Rajendra Sisodia (New Delhi, India: Sage, 2019), 445–480. Christina H. Gladwin, Ethnographic Decision Tree Modeling (Newbury Park, CA: Sage, 1989). For empirical evidence on the use of fast-andfrugal trees for describing human decision making, see Shenghua Luan and Jochen Reb, “Fast-and-Frugal Trees as Non-Compensatory Models of Performance-Based Personnel Decisions,” Organizational Behavior and Human Decision Processes 141 (2017): 29–42, and references therein. Arch G. Woodside, “Moving Beyond Multiple Regression Analysis to Algorithms: Calling for Adoption of a Paradigm Shift from Symmetric to Asymmetric Thinking in Data Analysis and Crafting Theory,” Journal of Business Research 66, no. 4 (2013): 463–472. Not everyone agrees that the parameters of the priority heuristic have been fixed independently of data. For example, Werner Güth (personal 1 is the result of a communication) suggested that “in all likelihood, 10 systematic fitting exercise [by a user of the heuristic]”. See the remaining of the paragraph for counterpoints to Güth’s view. Walter Albers, “Prominence Theory as a Tool to Model Boundedly Rational Decisions,” in Bounded Rationality: The Adaptive Toolbox, eds. Gerd Gigerenzer and Reinhard Selten (Cambridge, MA: MIT Press, 2001), 297–317. It is of course possible to regard these thresholds as free parameters and attempt to estimate their values empirically, as done in Jörg Rieskamp, “The Probabilistic Nature of Preferential Choice,” Journal of Experimental Psychology: Learning, Memory, and Cognition 34, no. 6 (2008): 1446–1465. Victor De Miguel, Lorenzo Garlappi and Raman Uppal, “Optimal Versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?,” The Review of Financial Studies 22, no. 5 (2009): 1915– 1953. There are other simple, parameter-free heuristics for financial investment, as the following, apparently used by three behavioral operations researchers: “allocate 80% of retirement savings to stocks and 20% to bonds”; see Karen Donohue, Özalp Özer and Yanchong Zheng, “Behavioral Operations: Past, Present, Future,” Manufacturing and Service Operations Management 22, no. 1 (2020): 191. A number of fast-and-frugal heuristics for making portfolio decisions are studied by Ian N. Durbach et al., “Fast and Frugal Heuristics for Portfolio Decisions With Positive Project Interactions,” Decision Support Systems 138 (2020): 113399. Kahneman and Tversky, “Prospect Theory”; Tversky and Kahneman, “Advances in Prospect Theory”.

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48. See for example the special issues on model selection in the Journal of Mathematical Psychology, edited by In Jae Myung, Malcolm Forster and Michael W. Browne (January 2000), and by Lourens Waldorp and EricJan Wagenmakers (April 2006), as well as Gerd Gigerenzer, Peter M. Todd and the ABC Research Group, Simple Heuristics that Make Us Smart (New York: Oxford University Press, 1999). 49. Brandstätter et al., “The Priority Heuristic”. 50. Kahneman and Tversky, “Prospect Theory”; Tversky and Kahneman, “Advances in Prospect Theory”. 51. Ido Erev et al., “Combining a Theoretical Prediction With Experimental Evidence to Yield a New Prediction: An Experimental Design With a Random Sample of Tasks” (Columbia University and Technion: Unpublished Manuscript, 2002). 52. Lola L. Lopes and Gregg C. Oden, “The Role of Aspiration Level in Risky Choice: A Comparison of Cumulative Prospect Theory and SP/A Theory,” Journal of Mathematical Psychology 43, no. 2 (1999): 286–313. 53. Michael H. Birnbaum and Alfredo Chavez, “Tests of Theories of Decision Making: Violations of Branch Independence and Distribution Independence,” Organizational Behavior and Human Decision Processes 71, no. 2 (1997): 161–194. 54. Andreas Glöckner and Thorsten Pachur, “Cognitive Models of Risky Choice: Parameter Stability and Predictive Accuracy of Prospect Theory,” Cognition 123, no. 1 (2012): 21–32. 55. For probabilistic inference, see for example Robyn M. Dawes and Bernard Corrigan, “Linear Models in Decision Making,” Psychological Bulletin 81, no. 2 (1974): 95–106; Hillel J. Einhorn and Robin M. Hogarth, “Unit Weighting Schemes for Decision Making,” Organizational Behavior and Human Performance 13, no. 2 (1975): 171–192; and reviews by Peter M. Todd, “How Much Information Do We Need?,” European Journal of Operational Research 177, no. 3 (2007): 1317–1332 and Konstantinos V. Katsikopoulos, “Psychological Heuristics for Making Inferences: Definition, Performance, and the Emerging Theory and Practice,” Decision Analysis 8, no. 1 (2011): 10–29; for multi-attribute choice see for example Robin M. Hogarth and Natalia Karelaia, “Simple Models for Multi-Attribute Choice With Many Alternatives: When It Does and Does Not Pay to Face Trade-Offs With Binary Attributes,” Management Science 51, no. 12 (2005): 1860–1872; Ian N. Durbach and Theodor J. Stewart, “Using Expected Values to Simplify Decision Making Under Uncertainty,” Omega 37, no. 2 (2009): 312–330; for forecasting see for example Spyros Makridakis and Michele Hibon, “Accuracy of Forecasting: An Empirical Investigation,” Journal of the Royal Statistical Society: Series A (General) 142, no. 2 (1979): 97–125; Spyros Makridakis, Rob J. Hyndman and Fotios Petropoulos,

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K. V. KATSIKOPOULOS

56.

57.

58.

59.

60.

“Forecasting in Social Settings: The State of the Art,” International Journal of Forecasting 36, no. 1 (2020): 15–28; for a synthesis across these three fields see Konstantinos V. Katsikopoulos, Ian N. Durbach and Theodor J. Stewart, “When Should We Use Simple Decision Models? A Synthesis of Various Research Strands,” Omega 81 (2018): 17– 25; and for games of strategic interaction, see Leonidas Spiliopoulos and Ralph Hertwig, “A Map of Ecologically Rational Heuristics for Uncertain Strategic Worlds,” Psychological Review 127, no. 2 (2020): 245–280. For perspectives of machine learning on simple models, see Pedro Domingos, “A Few Useful Things to Know about Machine Learning,” Communications of the ACM 55, no. 10 (2012): 78–87. Gigerenzer et al., Simple Heuristics that Make Us Smart; Peter M. Todd, Gerd Gigerenzer and the ABC Research Group, Ecological Rationality: Intelligence in the World (New York: Oxford University Press, 2012); Katsikopoulos et al., Classification in the Wild. See for instance Laura Martignon and Ulrich Hoffrage, “Fast, Frugal, and Fit: Simple Heuristics for Paired Comparison,” Theory and Decision 52, no. 1 (2002): 29–71; Konstantinos V. Katsikopoulos and Laura Martignon, “Naive Heuristics for Paired Comparisons: Some Results on Their Relative Accuracy,” Journal of Mathematical Psychology 50, no. 5 (2006): 488–494; Manel Baucells, Juan A. Carrasco and Robin M. Hogarth, “Cumulative Dominance and Heuristic Performance in Binary Multi-Attribute Choice,” Operations Research 56, no. 5 (2008): 1289–1304; Gerd Gigerenzer and Henry J. Brighton, “Homo Heuristicus: Why Biased Minds Make Better Inferences,” Topics in Cognitive Science 1, no. 1 (2009): 107–143; Konstantinos V. Katsikopoulos, “Psychological Heuristics for Making Inferences”; Özgür Sim¸ ¸ sek, “Linear Decision Rule as Aspiration for Simple Decision Heuristics,” Advances in Neural Information Processing Systems 26 (2013): 2904–2912. William Neilson and Jill Stowe, “A Further Examination of Cumulative Prospect Theory Parameterizations,” Journal of Risk and Uncertainty 24, no. 1 (2002): 31–46. Colin F. Camerer and Teck-Hua Ho, “Violations of the Betweenness Axiom and Nonlinearity in Probability,” Journal of Risk and Uncertainty 8, no. 2 (1994): 167–196; George Wu and Richard Gonzalez, “Curvature of the Probability Weighting Function,” Management Science 42, no. 12 (1996): 1676–1690. Andreas Glöckner and Thorsten Pachur in their article “Cognitive Models of Risky Choice” (footnote no. 49) measured the correlation between the parameter values of prospect theory as estimated on the same individuals making choices in two instances one week apart. The values of these correlations ranged from 0.03 to 0.61. It is unclear how

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61.

62.

63. 64.

65.

66.

67.

68. 69. 70.

71.

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such changes in parameter values affect choices. For a broad empirical examination of whether utility-based optimization models, including prospect theory, can predict human behavior, see Daniel Friedman, R. Mark Isaac, Duncan James and Shyam Sunder, Risky Curves: On the Empirical Failure of Expected Utility (Milton Park, UK: Routledge, 2014). Konstantinos V. Katsikopoulos and Gerd Gigerenzer, “OneReason Decision-Making: Modeling Violations of Expected Utility Theory,” Journal of Risk and Uncertainty 37, no. 1 (2008): 35–56. For a critical view of the evidence for loss aversion, see Eldad Yechiam, “Acceptable Losses: The Debatable Origins of Loss Aversion,” Psychological Research 83, no. 7 (2019): 1327–1339. Konstantinos V. Katsikopoulos and Gerd Gigerenzer raise concerns for the evidence for probability weighting in their article “One-Reason Decision-Making” (footnote no. 56). Michael H. Birnbaum, “New Paradoxes of Risky Decision Making,” Psychological Review 115, no. 2 (2008): 463–501. Ido Erev et al., “From Anomalies to Forecasts: Toward a Descriptive Model of Decisions Under Risk, Under Ambiguity, and From Experience,” Psychological Review 124, no. 4 (2017): 369–409. David D. Bourgin et al., “Cognitive Model Priors for Predicting Human Decisions,” in International Conference on Machine Learning (Long Beach, CA, 2019), 5133–5141. Clark Glymour, “Bayesian Ptolemaic Psychology,” in Probability and Inference: Essays in Honour of Henry E. Kyburg Jr. (London: King’s College Publications, 2007). The heliocentric model of Nicolaus Copernicus, as in On the Revolutions of the Heavenly Spheres (1543; New York: Prometheus, 1995, translated by Charles Glenn Wallis) has been anticipated in the ancient times by Aristarchus of Samos. Glymour, “Bayesian Ptolemaic Psychology”. Clark Glymour, “Osiander’s Psychology,” Behavioral and Brain Sciences 34, no. 4 (2011): 199. “What is going on here” is one of the most often repeated phrases in Mervyn King and John Kay’s Radical Uncertainty: Decision-Making for an Unknowable Future (London: Hachette, 2020). Elliot Bendoly and Daniel G. Bachrach, “Behavioral Operations in Practice and Future Work”, in The Handbook of Behavioral Operations Management: Social and Psychological Dynamics in Production and Service Settings, eds. Elliot Bendoly, Wout van Wezel and Daniel G. Bachrach (New York: Oxford University Press, 2015), 408.

70

K. V. KATSIKOPOULOS

72. Jana B. Jarecki, Jolene H. Tan and Mirjam A. Jenny, “A Framework for Building Cognitive Process Models,” Psychonomic Bulletin and Review (2020): 1–12. 73. Kahneman and Tversky, “Prospect Theory”, 274–275. 74. Urs Fischbacher, Ralph Hertwig and Adrian Bruhin, “How to Model Heterogeneity in Costly Punishment: Insights From Responders’ Response Times,” Journal of Behavioral Decision Making 26, no. 5 (2013): 466. 75. Antoine Arnauld, Pierre Nicole and John Ozell, Logic or the Art of Thinking (Cambridge, UK: Cambridge University Press, 1996; original work published in 1662). 76. Brandstätter et al., “The Priority Heuristic”. 77. Eric J. Johnson, Michael Schulte-Mecklenbeck and Martijn C. Willemsen, “Process Models Deserve Process Data: Comment on Brandstätter, Gigerenzer, and Hertwig (2006),” Psychological Review 115, no. 1 (2008): 263–272; Eduard Brandstätter, Gerd Gigerenzer and Ralph Hertwig, “Risky Choice With Heuristics: Reply to Birnbaum (2008), Johnson, Schulte-Mecklenbeck, and Willemsen (2008), and Rieger and Wang (2008),” Psychological Review 115, no. 1 (2008): 281–289. 78. Thorsten Pachur et al., “Testing Process Predictions of Models of Risky Choice: A Quantitative Model Comparison Approach,” Frontiers in Psychology 4 (2013), and references therein. 79. Ibid. 80. Stewart Robinson et al., “Facilitated Modelling With DiscreteEvent Simulation: Reality or Myth?,” European Journal of Operational Research 234, no. 1 (2014): 231–240; Katsikopoulos et al., “When Should We Use Simple Decision Models?”; Konstantinos V. Katsikopoulos, “The Merits of Transparent Models,” in Behavioral Operational Research: A Capabilities Approach, eds. Leroy White et al. (London: Palgrave Macmillan, 2020), 261–275; Christine S. M. Currie et al., “How Simulation Modelling Can Help Reduce the Impact of COVID-19,” Journal of Simulation 14, no. 2 (2020): 83–97; Antuela A. Tako, Naoum Tsioptsias and Stewart Robinson, “Can We Learn From Simplified Simulation Models? An Experimental Study On User Learning,” Journal of Simulation 14, no. 2 (2020): 130–144. 81. Tako et al., “Can We Learn From Simplified Simulation Models?”. 82. Götz Giering, Process-Tracing Choice Quality in Riskless MultiAttribute Decisions (Loughborough University: Ph.D. dissertation, 2021); Shashwat M. Pande, Nadia Papamichail and Peter Kawalek, “Compatibility Effects in the Prescriptive Application of Psychological Heuristics: Inhibition, Integration and Selection,” European Journal of Operational Research 295, no. 3 (2021): 982–995.

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83. Strictly speaking, when an algorithm is calibrated on a training set, the result is a model for the test set (these sets are more precisely defined in Chapter 5). Sometimes, also in this book, the two terms are used interchangeably. 84. John W. Payne, James R. Bettman and Eric J. Johnson, The Adaptive Decision Maker (Cambridge, UK: Cambridge University Press, 1993). 85. Gigerenzer et al., Simple Heuristics that Make Us Smart. 86. Payne et al., The Adaptive Decision Maker, Figure 1. For an application of this method to strategic interaction (Chapter 4), see Leonidas Spiliopoulos, Andreas Ortmann and Le Zhang, “Complexity, Attention, and Choice in Games Under Time Constraints: A Process Analysis,” Journal of Experimental Psychology: Learning, Memory, and Cognition 44, no. 10 (2018): 1609–1640. 87. The two operations 12 and 13 would run in parallel, the two sets of operations 14–19 and 20–25 would run in parallel and each would require four steps, and operations 26–28 would require two steps. 88. Katsikopoulos et al., Classification in the Wild. 89. Breiman et al., Classification and Regression Trees (Boca Raton, FL: CRC Press, 1984). 90. Katsikopoulos et al., Classification in the Wild. 91. Cynthia Rudin, “Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead,” Nature Machine Intelligence 1, no. 5 (2019): 206–215. For an example of the common assumption that more transparent or explainable algorithms are less accurate, see https://www.darpa.mil/attachments/ DARPA-BAA-16-53.pdf (Figure 5, p. 14). 92. Scott M. Lundberg and Su-In Lee, “A Unified Approach to Interpreting Model Predictions,” Advances in Neural Information Processing Systems (Long Beach, CA, 2017), 4765–4774; Christoph Molnar, Interpretable Machine Learning (Lulu. com, 2020). 93. Rudin, “Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead” and Dimitris Bertsimas and Jack Dunn, “Optimal Classification Trees,” Machine Learning 106, no. 7 (2017): 1039–1082; Konstantinos V. Katsikopoulos and Marc C. Canellas, “Decoding Human Behavior With Big Data? Critical, Constructive Input From the Decision Sciences, AI Magazine 43, no. 1 (2022): 1–13. Interestingly, whereas all three pieces agree in their favoring interpretable heuristics over black-box models, they propose different methods for inducing such heuristics. Rudin and Bertsimas’ group suggest setting up and solving an optimization problem, whereas Canellas and I put forth (meta)heuristic methods such as empirically harvesting the practitioners’ intuition and knowledge by using qualitative

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94.

95.

96.

97. 98.

99.

or quantitative data (see Chapter 6), or theoretically deriving heuristics by leveraging facts from cognitive psychology. Samir Passi and Steven J. Jackson, “Trust in Data Science: Collaboration, Translation, and Accountability in Corporate Data Science Projects," Proceedings of the ACM on Human–Computer Interaction 2, no. CSCW (2018): 1–28; Harmanpreet Kaur et al., “Interpreting Interpretability: Understanding Data Scientists’ Use of Interpretability Tools for Machine Learning,” in Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems (Hawaii, 2020), 1–14; Elizabeth I. Kumar et al., “Problems with Shapley-Value-Based Explanations as Feature Importance Measures,” in International Conference on Machine Learning (Vienna, 2020), 5491–5500. Hersh Shefrin, Explainable AI As a Tool for Risk Managers (Northfield, MN: Professional Risk Managers’ International Association Institute, 2021), 19. See for example Thomas L. Griffiths, “Manifesto For a New (Computational) Cognitive Revolution,” Cognition 135 (2015): 21–23; Pantelis Pipergias Analytis, Daniel Barkoczi and Stefan M. Herzog, “Social Learning Strategies for Matters of Taste,” Nature Human Behaviour 2, no. 6 (2018): 415–424; Tim Miller, Piers Howe and Liz Sonenberg, “Explainable AI: Beware of Inmates Running the Asylum or: How I Learnt to Stop Worrying and Love the Social and Behavioural Sciences,” arXiv preprint arXiv:1712.00547 (2017); Katsikopoulos and Canellas, “Decoding Human Behavior With Big Data?”; Konstantinos V. Katsikopoulos, Özgür Sim¸ ¸ sek, Marcus Buckmann and Gerd Gigerenzer, “Transparent Modeling of Influenza Incidence: Big Data or a Single Data Point from Psychological Theory,” International Journal of Forecasting 38, no. 2 (2022): 613–619. Wu and Gonzalez, “Curvature of the Probability Weighting Function”. Nicholas Nassim Taleb, Skin in the Game: Hidden Asymmetries in Daily Life (New York: Random House, 2020); Mervyn King and John Kay, Radical Uncertainty: Decision-Making for an Unknowable Future (London: Hachette, 2020). For example, see Thomas Blake, Chris Nosko and Steven Tadelis, “Consumer Heterogeneity and Paid Search Effectiveness: A Large-Scale Field Experiment,” Econometrica 83, no. 1 (2015): 155–174; Jesse Frederik and Maurits Martijn, “The New Dot Com Bubble is Here: It’s Called Online Advertising,” The Correspondent (6 November, 2019)—see https://thecorrespondent.com/100/the-new-dot-com-bubble-is-hereits-called-online-advertising/13228924500-22d5fd24 and references therein.

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100. Big data analytics promises a lot in predicting human behavior, but a closer look suggests that it might not have yet delivered as much—for example, see Katsikopoulos and Canellas, “Decoding Human Behavior with Big Data?”; Gerd Gigerenzer, How to Stay Smart in a Smart World (London, UK: Penguin, 2022), and references in both sources. 101. Thorsten Pachur, Renata S. Suter and Ralph Hertwig, “How the Twain Can Meet: Prospect Theory and Models of Heuristics in Risky Choice,” Cognitive Psychology 93 (2017): 44–73; David M. Riefer et al., “Cognitive Psychometrics: Assessing Storage and Retrieval Deficits in Special Populations With Multinomial Processing Tree Models,” Psychological Assessment 14, no. 2 (2002): 184–201. The term “cognitive psychometrics” appears to have been coined by Bill Batchelder. 102. Rieskamp, “The Probabilistic Nature of Preferential Choice”. 103. Gerd Gigerenzer, “A Theory Integration Program,” Decision 4, no. 3 (2017): 133–145. 104. Rieger and Wang, “What is Behind the Priority Heuristic?”. 105. Rieskamp, “The Probabilistic Nature of Preferential Choice”. 106. For a review and references, see Amnon Rapoport and Vincent Mak, “Strategic Interactions in Transportation Networks,” in The Handbook of Behavioral Operations (2018), 557–586. 107. Genovefa Kefalidou and Thomas C. Ormerod, “The Fast and the not-So-Frugal: Human Heuristics for Optimization Problem Solving,” in Proceedings of the Annual Meeting of the Cognitive Science Society, vol. 36, no. 36 (Quebec City, 2014). 108. For reviews, see Konstantinos V. Katsikopoulos, “Advanced Guide Signs and Behavioral Decision Theory,” in Handbook of Driving Simulation for Engineering, Medicine, and Psychology: An Overview, eds. Donald L. Fisher et al. (Boca Raton, FL: CRC Press, 2011), 371–378; Konstantinos V. Katsikopoulos and Ana Paula Bortoleto, “Congestion and Carbon Emissions,” in Handbook of Human Factors for Automated, Connected, and Intelligent Vehicles, eds. Donald L. Fisher et al. (Boca Raton, FL: CRC Press, 2020), 441–453. 109. Konstantinos V. Katsikopoulos, Yawa Duse-Anthony, Donald L., Fisher and Susan A. Duffy, “Risk Attitude Reversals in Drivers’ Route Choice When Range of Travel Time Information Is Provided,” Human Factors 44, no. 3 (2002): 466–473. 110. Ibid. 111. R. Duncan Luce, "Semi-Orders and a Theory of Utility Discrimination," Econometrica (1956): 178–191; Amos Tversky, “Choice by Elimination," Journal of Mathematical Psychology 9, no. 4 (1972): 341– 367; Ariel Rubinstein, “Similarity and Decision-Making Under Risk (Is There a Utility Theory Resolution to the Allais Paradox?," Journal of

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112.

113. 114. 115.

116.

Economic Theory 46, no. 1 (1988): 145–153; Jonathan W. Leland, “Generalized Similarity Judgments: An Alternative Explanation for Choice Anomalies,” Journal of Risk and Uncertainty 9, no. 2 (1994): 151– 172; Ariel Rubinstein, Modeling Bounded Rationality (Cambridge, MA: MIT Press, 1998). Rubinstein, Modeling Bounded Rationality. See also Riccardo Viale (Ed.) Routledge Handbook of Bounded Rationality (Milton Park, UK: Routledge, 2020). Clement A. Tisdell, Advanced Introduction to Bounded Rationality (Cheltenham, UK: Edward Elgar, 2022). Katsikopoulos et al., Classification in the Wild. Nathaniel D. Phillips et al., “FFTrees: A Toolbox to Create, Visualize, and Evaluate Fast-and-Frugal Decision Trees,” Judgment and Decision Making 12, no. 4 (2017): 344–368. See for example Paul M. Krüger et al., “Discovering Rational Heuristics for Risky Choice” (working paper, Princeton University, Princeton, NJ, 2022).

CHAPTER 4

Strategic Interaction

Consider two takes on the Cold War, the first by actor and activist Rosanna Arquette in a 1985 TV interview and the second in Robert Aumann’s 2005 Nobel prize in economics lecture: Rosanna Arquette: If I could have anything I wanted in the world, what would I like? Nuclear disarmament. Robert Aumann: You want to prevent war. To do that, obviously you should disarm, lower the level of armaments. Right? No, wrong. You might want to do the exact opposite. In the long years of the cold war between the U.S. and the Soviet Union, what prevented ‘hot’ war was that bombers carrying nuclear weapons were in the air 24 hours a day, 365 days a year. Disarming would have led to war.

The scientific study of strategic interaction thrived during the beginning of the Cold War, in the 1950s and 1960s. At that time, there was an overwhelming sense of distrust in the world leaders’ motives and skills for keeping the world from blowing up. To help, operations researchers and quantitatively minded social scientists developed models of ‘rational’ interaction between people, organizations, and nations. But what is the rational way of interacting with others? Difficult to say. Arquette offered the straightforward approach of trusting one’s enemies as well as one’s

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6_4

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own self. Aumann used analytical reasoning to argue that we and our enemies need to be incentivized in order to behave trustworthily. In war and in peace, it is hard to know whether one should follow Arquette’s or Aumann’s approach. A tool in the study of strategic interaction is game theory 1 It started as a formal study but soon developed an empirical branch as well.2 Operations management often relies on game theory, for example, in the design of contracts governing the operation of supply chains. This chapter focuses on behavioral game theory 3 It takes a similar approach to the behavioral study of decision under risk, by focusing on a drosophila—bargaining games. The caveats discussed in Chapters 2 and 3 apply: Yes, the games are somewhat basic for capturing the full richness of interactions among clients, suppliers, and retailers.4 On the plus side, the games constitute building blocks of complex interactions and have provided interesting facts about human nature. The study of these games forms an empirical basis for building behavioral models and designing mechanisms for managing interactions.5 A distinguishing aspect of the present chapter is that it assesses predictive power by employing the response times of experimental participants.6 The chapter is structured as follows. I first define the so-called ultimatum and dictator bargaining games, present the predictions of game theory, and contrast these predictions with the empirical evidence on human behavior. In the next two sections, I present two behavioral models—an optimization model where inequity aversion 7 forms a major input to a utility function, and simple heuristics, in particular, fast-andfrugal trees that employ a small number of social motives 8 I then analyze these two models on the criteria of predictive power, cognitive processes, and transparency. Non-bargaining games are also discussed. Importantly, this chapter consolidates the integration of the optimization and simple-heuristics approaches. We will see that, with some reasonable auxiliary assumptions, inequity-aversion theory can be used to theorize and make predictions about processes in transparent ways, as fast-and-frugal trees do. And as in Eqs. 3.3 and 3.4 for the priority heuristic for decision under risk, we will see that the fast-and-frugal trees for strategic interaction can be mapped to linear models at the level of behavioral outcomes. This chapter concludes the first part of the book that develops a cognitive perspective on decision modeling. In this chapter, I will also comment on the relationship between how decision making is studied in behavioral

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economics and cognitive psychology on the one hand, and in operations research and operations management on the other. As such, the chapter serves as a segue from the first to the second part of the book, Chapters 5–7, which take a more operational perspective.

4.1 Giving and Receiving Ultimatums: Theory and Data To specify a game, one must list the players, their options, and the payoffs the players would receive for each possible combination of options they might choose. In its basic form, the ultimatum game features two players who anonymously interact with each other once. One player has the role of the proposer and the other the role of the responder. The proposer offers an allocation of a fixed monetary pie, and the responder, who knows the size of the pie, has to decide whether to accept or reject the offer. In case of acceptance, the allocation is implemented, and in case of rejection both players leave empty-handed. For example, if the pie is 10 pounds and the proposer offers 4 pounds to the responder, which he accepts, then the proposer receives 6 pounds and the responder 4 pounds; but if the proposer offers 1 pound which the responder rejects, then both proposer and responder receive zero. To avoid extremes, it is often assumed that a zero offer is not allowed. The ultimatum game is an instance of a take-it-or-leave-it bargaining situation, with the important characteristic that if an agreement is not reached, all rewards will be lost to all parties. Such situations have been studied in sociology and social psychology and became widely known in the behavioral sciences and beyond through the work of economist Werner Güth and his colleagues.9 A second game discussed in the present chapter is the dictator game. The only difference from the ultimatum game is that the responder is obliged to accept all offers, and the proposer knows that. Game theory. The approach of game theory to predicting human behavior is based on the assumptions that players are (i) interested only in their own payoff and (ii) able to identify a game’s strategy equilibrium. What is a strategy? In the ultimatum game, the strategy for the proposer is the offer she makes; and for the responder, the strategy is the specification of which offers he accepts and which he rejects. And what is an equilibrium? An equilibrium is a set of strategies—one for each player10 — so that no player can improve their own payoff by changing their strategy

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given that the other players stick to their own strategies.11 The prediction of game theory is that people will play strategies in an equilibrium (although a common issue is that it is not clear how one equilibrium would be chosen if there are many as for example is the case in games played over a network structure). Early development of game theory is due to John von Neumann and Oskar Morgenstern, who also pioneered expected utility theory (Chapter 2). The two theories share some important aspects: First, they are optimization theories, in which individual payoff is predicted to be maximized in some well-defined sense which considers all available information. Second, both are as-if theories that shun away from opening the black box and specifying the psychological processes that would make it possible for people to carry out the computations necessary for optimizing payoffs, such as computing and combining probabilities and utilities or deducing and choosing equilibria.12 A third aspect is that neither theory can fully capture human behavior. To compare the empirical evidence with the predictions of game theory, let us first derive these predictions. Consider the responder in the ultimatum game. If he is only interested in optimizing his own payoff, then surely he will accept all offers. Given this strategy, the optimal strategy of the proposer is to make the smallest offer possible. Of course, it may also be that the responder is not only interested in optimizing his own payoff and that the proposer knows this; then, the proposer’s optimal strategy is to make the smallest possible offer that she knows would be accepted. Thus, game theory can capture any behavior by the proposer in the ultimatum game. For the dictator game, the prediction is that the proposer makes the smallest offer possible. For the responder in the ultimatum game, the prediction is that no responder rejects any offer. This last prediction of game theory is strong.13 A strong prediction of a theory is one that does not follow from most or all other competing theories; therefore, if a strong prediction is supported by the data, this would lend considerable unique support to the theory, and conversely one might expect that the prediction does not hold and the theory can be readily falsified. In other words, deriving and testing strong predictions may lead to the rejection of one’s pet theory but on the whole speeds up scientific progress. Is the prediction of no rejections in the ultimatum game true? Data. It has been empirically found that quite a few ultimatum-game offers are rejected by quite a few people.14 As in the case of choices

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between gambles, most experiments on bargaining games have taken place in a lab with university students as participants. But not all. For example, Werner Güth and Matthias Sutter15 recruited 1035 readers of the Berliner Zeitung —a newspaper tabloid which is not exactly known for being read by academic audiences—to play an ultimatum game. The size of the pie was 1000 German marks and the possible offers were 100, 200, …, 900 marks. Each participant had to specify their strategy both as proposer and responder. In order to incentivize participants, three randomly selected proposer-responder pairs were rewarded according to the rules of the game. Figure 4.1 shows the proportions of participants making each offer. Half of the participants offer the midpoint offer of 500 marks, with 400 marks being the second most prevalent offer (made by 22% of the participants), a considerable 11% of the participants make the ‘rational’ offer of 100 marks, and there are hardly any offers over 500 marks. The figure also shows the proportions of participants rejecting each offer. Only a tiny minority of participants (between 2 and 9%) reject offers equal to or above 500 marks. On the other hand, offers from 100 to 400 marks are rejected by up to 65% (for 100 marks) and not less than 21% (for 400 marks) of the participants. Such empirical results are common.16 The midpoint offer can be viewed as fair if one considers only that it is a 50–50 split and ignores the fact that the proposer has the power to propose any split they want. I asked Rosanna Arquette and Robert Aumann if, in the Berliner Zeitung vignette, their intuition tells them that the fair offer is 500 or not, requesting the answer that came immediately to their minds. Arquette said that 500 is fair and Aumann said that 300 is fair because the proposer has a distinct advantage.17 University of California anthropologist Joseph Henrich and a group of behavioral scientists have run many experiments with games outside what they call WEIRD (Western, educated, industrialized, rich, and democratic) societies, venturing into small-scale, non-market societies such as foragers in Africa and horticulturalists in South America.18 The results show that modelers should not take anything for granted about how people might interact strategically. For instance, it was found that some non-WEIRD people accept low offers or reject high offers. Such work might be particularly relevant as behavioral operations expand its scope to cross-cultural contexts.19 Research findings on the ultimatum game parallel findings on the choice between gambles. Standard ‘rationality’ does not capture human

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Making offer Rejecting offer

Proportion of participants (%)

59 50 43

2221

11

9

100

7

6

4

2

200

300

400

500

9

3 600

9 1

700

800

900

Possible offer (German marks)

Fig. 4.1 Proportions of participants making various ultimatum-game offers, and of rejecting each offer, in the experiment by Güth and Sutter

behavior and descriptive models must be more subtle. Researchers have proposed models to account for variables such as offers made, acceptance and rejection of offers, and the patterns of time taken to make these decisions. An optimization model and a simple heuristic are presented respectively in the next two sections.

4.2

Inequity Aversion

If you were considering how to respond to an ultimatum offer, would you think about the proposer’s payoff? If yes, what exactly would you think about it? Here are a couple of possibilities: Did she keep more money for himself than she gave you? Could she have offered more to you than she did? Perhaps you decide to accept only those offers that leave you as well off as the proposer. Or to accept all offers for which you believe that the proposer could not reasonably have offered you more.

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Deciding whether to accept or reject an ultimatum by considering the proposer’s payoff or his overall position are instances of other-regarding behavior 20 by the responder. Social preferences and social motives are two terms used in behavioral economics and psychology to denote reasons for other-regarding behavior.21 Inequity aversion is an example of a social preference, and it forms the core of an influential behavioral theory for strategic interaction, put forth by economists Ernst Fehr and Klaus Schmidt more than two decades ago.22 I outline it below. A person exhibits inequity aversion if she dislikes (i) being worse off than others, or (ii) being better off than others. Fehr and Schmidt proposed that a game player maximizes the sum of the utility received from their own payoff minus the disutility received from other-regarding inequity aversion. More precisely, for a two-player ultimatum game with a unit pie, the utility of a player who receives x (where 0 ≤ x ≤ 1) is given by the following equation. u(x) = x − α max{(1 − x) − x, 0} − β max{x − (1 − x), 0}

(4.1)

The first term in Eq. 4.1 represents the utility from the player’s own payoff, x. This kind of term is also assumed in standard game theory. The difference in the inequity-aversion theory is the subtraction of the second and third terms. These terms represent the disutility from the player being worse off than the other party (when 1 − x is larger than x) and from the player being better off than the other party (when x is larger than 1 − x). A similarity between the two theories is that people are assumed to maximize their utility. The second term in Eq. 4.1 model equals zero when the player receives at least as much as the intuitively fair offer, x > 0.5, and the third term equals zero when x ≤ 0.5. Thus utility can be calculated by the piece-wise linear function below.  (1 + 2α)x − α, x ≤ 0.5 u(x) = (4.2) (1 − 2β)x + β, x > 0.5 Parameter estimation. A challenge in inequity-aversion theory, as in prospect theory, is to estimate its parameters. The parameters α and β measure the impact of disadvantageous inequality and advantageous inequality on utility, and it is not clear how to estimate such effects directly. Indirect estimation from ultimatum-game data is also challenging, as a number of researchers have pointed out.23 To do so, the

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1 u(x)

x 0

1

Fig. 4.2 Inequity-aversion theory’s utility function u(x) = 3x − 1 for 0 ≤ x ≤ 0.5 and −0.2x + 0.6 for 0.5 < x ≤ 1, proposed by Fehr and Schmidt as characterizing 30% of the population

utility functions of the proposer and responder have to be mapped onto the theory’s predictions, that is, the strategy equilibria, and Fehr and Schmidt have analytically derived this mapping. But the problem is that this map does not allow making unique point estimates. For example, if a proposer has offered half of the pie, the only inference that can be made about their β value is that it exceeds 0.5 (see Appendix). A second issue is that it is necessary to have data where the same person has played both proposer and responder roles. In a fitting exercise,24 Fehr and Schmidt suggested that 30% of the population are characterized by α = 1 and β = 0.6, and another 30% by α = 0.5 and β = 0.25. The corresponding utility functions u(x) = 3x − 1 for x ≤ 0.5 and −0.2x + 0.6 for x > 0.5 and u(x) = 2x − 0.5 for x ≤ 0.5 and 0.5x + 0.25 for x > 0.5, are graphed in Figs. 4.2 and 4.3.25 These particular functions are presented for illustration and are not used in the empirical tests and other analyses reported in this chapter. Figure 4.2 shows that utility increases as the player’s own payoff increases until the

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1 u(x)

x 0

1

Fig. 4.3 Inequity-aversion theory’s utility function u(x) = 2x − 0.5 for 0 ≤ x ≤ 0.5 and 0.5x + 0.25 for 0.5 < x ≤ 1, proposed by Fehr and Schmidt as characterizing 30% of the population

midpoint offer, but then decreases with a smaller absolute slope; whereas in Fig. 4.3 utility is increasing with the player’s own payoff across the whole range, though with a smaller positive slope beyond the midpoint offer.

4.3

Fast-and-Frugal Trees

Recall that, in modeling decisions under risk, the priority heuristic uses the same attributes as prospect theory but processes the attributes in simpler ways and does not necessarily use all attributes to make decisions. Is this kind of approach viable for building heuristics describing people’s strategic interaction? To answer, psychologist Ralph Hertwig, who was involved in the development of the priority heuristic (Chapter 3), teamed up with economists Urs Fischbacher and Adrian Bruhin, who had worked on inequity-aversion theory, and they jointly developed and tested heuristics for strategic interaction.

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In choices between gambles, modelers focus on capturing the choice of the majority. In bargaining games, where individual differences can be substantial (Fig. 4.1), researchers have suggested the existence of different types of players. In inequity-aversion theory, each player type is characterized by a different utility function26 Hertwig, Fischbacher, and Bruhin put forth a number of fast-and-frugal trees for characterizing the different types of responders in the ultimatum game (the approach can also be used for modeling different proposers). There are four social motives, expressed by four binary attributes, employed in the trees. Three of these motives appear in optimization models as well, and the fourth motive is a novel one. Social motives and the mini-ultimatum game. The first attribute denotes whether the payoff offered to the responder, Ro , is positive. A second attribute indicates whether the responder’s payoff is at least as large as the payoff of the proposer, Po . These two motives are present in inequity-aversion theory as well. The third attribute is inspired by intention-based models27 of social preferences, where players are assumed to be inferring the intentions of the other party. For the responder in the ultimatum game, this might mean comparing the payoff actually offered to what could have been offered. To operationalize this attribute, Hertwig and his colleagues focus on the mini-ultimatum game, where there are two possible pie allocations,28 and hypothesize that the responder checks whether the payoff offered to her Ro is at least as large as her foregone payoff, R f . For example, say that the two possible allocations are (500, 500) and (200, 800) where the left payoff in each pair goes to the responder and the right payoff to the proposer. If the second allocation is offered, then Ro = 200, Po = 800, and R f = 500. One can also define the foregone payoff of the proposer, P f , which here equals 500. Figure 4.4 illustrates this mini-ultimatum game and its four payoffs. The last binary attribute asks whether the responder believes that she would have made the same offer as the proposer did. In general, the value of this attribute would be a function of all four offered and foregone payoffs. Hertwig and his colleagues did not specify a formula for this function but suggested that it can be estimated empirically by asking the responder to act as the proposer and make an offer in a dictator game with the same possible pie allocations. Building trees. Hertwig and colleagues suggested ways in which the attributes can be combined. These ways were produced by a mixedmethods approach, in two stages. In the first, data-fitting stage, a

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Fig. 4.4 A mini-ultimatum game and its four, offered and foregone, payoffs

finite-mixture statistical model was used to divide the 70 participants of a lab experiment (see Sect. 4.4) into four types according to their rejection patterns, so that the model maximized the likelihood of the obtained data.29 In the second, theorizing stage, the four participant types were mapped onto four fast-and-frugal trees, according to what is known from psychology about how people order attributes and use them to arrive at exits. One tree is extreme, using only the own-payoff attribute ‘Is Ro positive?’—if yes, the offer is accepted; if no, it is rejected. This selfish tree makes the same predictions as standard game theory. Another tree is also extreme in that it employs all four attributes listed above. In this chapter, I consider Hertwig and colleagues’ two fast-and-frugal trees of intermediate simplicity. Both trees start with the own-payoff attribute as one would expect that, for most people, this would be the most important criterion. The responder’s own payoff leads to an immediate rejection if it is zero, without

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looking at other attributes. If the responder’s payoff is positive, the two trees continue, and now diverge from each other. In the mirror tree (see Fig. 4.5), the intention attribute is consulted: ‘Would I have made the same offer?’—if yes, the offer is accepted; otherwise, rejected. In the priority tree (see Fig. 4.6), after the own-payoff question, first it is asked whether the own payoff is at least as large as the other’s payoff, and second it might be asked whether the own, actually offered payoff is at least as large as the foregone payoff—if either one of the two answers is yes, the offer is accepted; otherwise, it is rejected.30 By construction, the fast-and-frugal trees fit rejection data well. For example, consider a case where the allocation (200, 800) is offered instead of (500, 500). What is the prediction of the priority tree? Because Ro = 200 > 0 and Ro = 200 < 800 = Po , the third question of this tree is reached, where because Ro = 200 < 500 = R f , the prediction is to reject. Indeed, 89% of the participants of the type associated with the priority tree rejected that offer in an experiment by Hertwig and his colleagues.31 Inequity-aversion theory can also fit this data. For example, consider the utility function put forth by Fehr and Schmidt in Fig. 4.2. For a responder with u(x) = 3x −1, the utility of x = 0.2, which is the normalized value of the offer of 200, is –0.4, which is smaller than 0.5, the utility of x = 0.5 (the normalized value of the alternative offer of 500). Thus, the allocation

Fig. 4.5 The mirror tree of Hertwig et al., for predicting whether the responder to the mini-ultimatum game accepts or rejects an offer of Ro

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Fig. 4.6 The priority tree of Hertwig et al., for predicting whether the responder to the mini-ultimatum game accepts or rejects an offer of Ro . The proposer’s payoff equals Po and the foregone payoff of the responder is R f

(200, 800) would be rejected. The same result is obtained for u(x) = 2x − 0.5 (the function in Fig. 4.3). Thus, to assess the predictive power of inequity-aversion theory and the priority/mirror trees, one might want to move beyond the fitting accuracy of model choices, and utilize another dependent variable that can be genuinely predicted by the two approaches.32 Such empirical tests are described in the next section.

4.4

Predicting Response Time Patterns

In the experiment by Hertwig and colleagues, 70 Swiss students were presented with 12 mini-ultimatum games. Each game was presented twice, with each of the two possible allocations presented as an offer for the responder to consider. For example, if a game had Ro = 500, Po = 400, R f = 100, and P f = 600, then in its second presentation, it would have Ro = 100, Po = 600, R f = 500, and P f = 400. The 24 decision scenarios were presented in random order to the responder subject to the constraint that two scenarios from the same game were not presented back-to-back. Figure 4.7 shows an example screen presented to responders. After a responder made her 24 decisions, she was asked to make 12 offers as a dictator (with the same two possible pie allocations, and the

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Fig. 4.7 Example of a screen shown to responders in the experiment by Hertwig et al.; adapted from Fischbacher et al.

games presented in random order). Participants were incentivized by having one game where they acted as responders and one in which they acted as proposers randomly sampled and paired with another random proposer and responder respectively, and then paid accordingly. Table 4.1 shows the 24 decision scenarios, along with the observed rejection rates.33 Predictions. Consider two participants—one classified as using the selfish tree, and a second participant classified as using any other tree, say the priority tree. One can predict that the priority-tree participant will take longer to respond. Here is why: Because Ro > 0 for all decisions (Table 4.1), the priority-tree user will decide based on two or three attributes, requiring the processing of two or four payoffs, depending on the decision. But the selfish-tree participant will always process only one payoff (Ro ), and he will be faster. Using some reasonable auxiliary assumptions, the researchers showed that inequity-aversion theory leads to the same prediction as well. Notice first that in this theory participants differ only on their values of the parameters α and β. Then, some participants might have α and β (approximately) equal to zero, which can be taken to mean that they do not care about advantageous or disadvantageous inequality. Using the simpleheuristics lens, this class of participants are the ‘users’ of the selfish tree. In inequity-aversion terms, when computing their utility by using Eq. 4.1, these participants have fewer computations to make than the ‘users’ of

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Table 4.1 The 24 decision scenarios in the Hertwig et al. mini-ultimatum game experiment, and the observed rejection rates Ro

Po

Rf

Pf

Rejection rate (%)

500 800 800 500 500 300 400 500 600 400 800 800 500 500 200 600 200 200 200 200 200 200 200 200

400 800 400 800 500 500 600 200 400 800 200 100 200 200 200 100 200 800 800 800 800 800 800 800

600 500 500 200 200 200 200 800 200 200 200 500 800 800 200 500 400 200 300 800 400 600 500 500

100 200 200 800 800 800 800 100 800 200 800 200 800 400 800 400 800 200 500 200 600 400 500 800

0 0 0 1 1 3 3 3 3 4 4 4 6 7 9 9 11 17 26 29 29 31 33 34

the priority, or any other, tree, because the latter must calculate and subtract the dissutilities of advantageous or disadvantageous inequality. It is reasonable to assume that this extra work would take extra time.34 Fast-and-frugal trees and inequity-aversion theory also make contrasting predictions. For example, fast-and-frugal trees imply that response time might depend on the decision scenario encountered, since for different scenarios an exit might be reached at different levels of the tree. For example, consider the two scenarios with rejection rates of 1% in Table 4.1: Ro = 500, Po = 500, and R f = 200 in the fifth row, and Ro = 500, Po = 800, and R f = 200 in the sixth row. In the former case, the decision of the priority tree to accept will be made in the second step (Ro ≥ Po ), whereas the same decision in the latter case for the tree

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will be made in the third step (Ro ≥ R f ) and hence it will take longer. On the other hand, inequity-aversion theory suggests that all payoffs are always used for computing utility, and thus implies that response time does not depend on the decision scenario. How did these predictions fare? Fig. 4.8 shows that the median response time of participants classified as selfish-tree users is shorter than that of all other participants, 2.4 versus 4.3 sec. Additionally, the authors controlled for the fact that selfish-tree ‘users’ always accept an offer— note that, all else being equal, acceptances are quicker than rejections—by also computing the response time of other participants when accepting an offer, and this equals 4.1 sec. Figure 4.9 shows that the median response time of participants classified as priority-tree users is shorter when the tree decides in the second step, 2.5 sec (these are all acceptances) versus 3.8 for acceptances in the third step and 4.6 sec for rejections in the third step.35

4.3

Response time (sec)

4.1

2.4

Selfish accept

Other all

Other accept

Fig. 4.8 Median response times (in seconds) of participants in the Hertwig et al. mini-ultimatum game experiment, for participants classified as users of the selfish tree and all other participants

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4.6

Response time (sec)

3.8

2.5

Accept Step 2

Accept Step 3

Reject Step 3

Fig. 4.9 Median response times (in seconds) of participants in the Hertwig et al. mini-ultimatum game experiment, when the priority tree leads to a choice at its Step 2 or Step 3

The response-time analyses in this section corroborate the process predictions of the simple-heuristics approach. Furthermore, the analyses raise some interesting issues about how, like simple heuristics, optimization models can also be used to theorize about processes in a transparent way. These issues are explored in the next two sections.

4.5

Cognitive Processes and Transparency

Similar to expected utility theory and prospect theory, optimization models such as game theory and inequity-aversion theory do not spell out how people could be performing the necessary computations. As said in previous chapters, on this basis, such models would score lower in the criteria of specifying cognitive processes and providing explanatory power and transparency. In a personal review of research on ultimatum bargaining,36 Werner Güth puts forth such concerns:

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Doubtless a lot can be learned from such attempts to explain experimental phenomena, especially when they are based on well accepted motivational forces. Very often this kind of research resembles, however, a neoclassical repair shop in the sense that one first observes behavior for a certain environment and then defines a suitable optimization or game model which can account for what has been observed. In my view, additional arguments of utility functions like a desire for fairness, altruism, or envy… offer no really satisficing explanations, but shift only the problem to another level of research questions, namely why people have such utility functions and/ or beliefs.

The situation with inequity-aversion theory might be manageable, however. Its Eq. 4.1 is neatly decomposed into utility and disutility terms and, as we saw, can be used to make predictions about measures of cognitive processing such as response times. Additionally, the logic underlying the derivation of these predictions is straightforward. In this sense, we now have an optimization model that is theorizing about processes in a transparent way. In the words of Hertwig and colleagues37 : According to one view, classification trees are psychologically plausible implementations of the key selfish and social motives postulated by social preference models. Economic models traditionally focus on the behavioral outcome—in the present case, the decision to accept or reject a specific division of a monetary pie—without aspiring to capture the cognitive or affective processes that produce the decision… On this view, the heuristics are ancillary to the utility models in that they do not render choice predictions that differ from those of utility models, precisely because their sole task is to translate decisions derived from utility calculations into psychological processes.

Such applications of the theoretical thinking typical of the simpleheuristics approach can have far-reaching implications for the optimization approach. This strategy of marrying heuristics and optimization, wherein heuristics are enlisted to open the black box and explain how it can be that human brains can perform (exactly or approximately) optimization calculations that are in principle intractable, is not uncommon in modeling in the cognitive sciences.38 It is worth considering the development, application, and testing of a similar strategy of integration in economics and operations modeling.

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Theory Integration: Behavioral Outcomes

Simple heuristics and optimization models have been theoretically integrated at the level of behavior they output. Consider the scenario where the allocation (200, 800) is offered instead of (500, 500). What is the outcome of the priority tree (Fig. 4.6)? Because Ro = 200 > 0 and Ro = 200 < 800 = Po , the third question of this tree is reached, where because Ro = 200 < 500 = R f , the outcome is rejection. This outcome can be also produced by a linear model that uses the same binary attributes as the priority tree. Define a1 = 1 if Ro > 0 and 0 otherwise, a2 = 1 if Ro ≥ Po and 0 otherwise, and a3 = 1 if Ro ≥ R f and 0 otherwise. The model computes the score s = 4a 1 + 2a2 + a3 . If s is larger than 4, the model says that the offer is accepted, otherwise, the offer is rejected. In the example just above, a1 = 1, a2 = 0, and a3 = 0, and thus s = 4, and the model’s outcome is rejection. This result is not a fluke. It is a mathematical fact that the behavior of any fast-and-frugal tree with binary attributes and two categories (e.g., accept or reject an ultimatum) can be matched by a linear model that is chosen appropriately.39 More specifically, if the tree’s attribute values for a particular decision scenario are ai , , then this model is defined by the following rule (where wi , h ≥ 0).  If wi a i > h, accept offer; otherwise reject (4.3) i

The threshold h in Condition 4.3 is uniquely determined by the fastand-frugal tree40 and the attribute weights wi must be chosen so that they are non-compensatory which means that  wi ≥ wk for all i (4.4) k>i

Condition 4.4 is satisfied by the attribute weights w1 = 4, w2 = 2, and w3 = 1 used in the example. Some converse results also hold; for instance, given any linear model for classification that has non-compensatory weights (like the model in the example above), a fast-and-frugal tree can be constructed which matches the linear model’s outcomes. In other words, linear models and fast-andfrugal trees are able to fit each other’s behavior to some extent. This is an interesting connection, but it of course should caution one that, in order to meaningfully compare these two families of models, tests need to

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be carried out that measure predictive power or focus on the underlying processes. There are also deeper connections between lexicographic heuristics, of which fast-and-frugal trees are instances (Chapter 3), and optimization models. It has been proven analytically that a lexicographic heuristic for choosing one out of many alternatives41 is logically equivalent to a pair of standard axioms commonly used in ‘rational’ economic theory.42 Linearity features in this connection as well since one of these axioms43 is equivalent to the existence of an ordering of the alternatives on a line.

4.7

Beyond Bargaining Games

Users of transportation networks, such as private and commercial drivers, interact strategically with each other, thus influencing the loading and delivery of first materials, commercial products, and other goods, and thus affecting the operation of supply chains. The behaviors of these users can be understood through the study of network games .44 These games can be modeled and analyzed similarly to bargaining games such as the ultimatum game, albeit in more complicated ways. In transportation network games in particular it is important to take account of external influences, such as traffic congestion. For example, route A that takes normally shorter to travel than route B and might end up taking longer if too many drivers switch to A from B. Furthermore, as can be the case in other games, the equilibrium strategy might not optimize social welfare: If route A takes 1 hour to travel independently of the number of drivers on it, and route B takes x hours when x drivers are on it (both of these times are per person), then the equilibrium strategy is that all drivers choose A, whereas a central planner can cut the average travel time from 1 to 0.75 hours by splitting traffic equally.45 Behavioral research has focused on creating lab versions of transportation networks and having groups of people play many iterations of the same game,46 as in the work of pioneer behavioral scientist Amnon Rapoport and his colleagues. Usually, the structure of the network and the formulas that govern the games (such as a linear function according to which the number of people on a road increases travel time) are made known to participants. Nevertheless, these situations still involve strategic uncertainty, as one cannot know the probability by which others would choose a route. A common question of this research is whether people, as a whole, can converge to an equilibrium. Often this is approximately

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the case on the aggregate although individuals may keep switching routes. Limitations of this work are the lack of testing of alternative descriptive models which might be more accurate than ‘rational’ game theory, and could also help shed light on how the observed behavior emerges.

4.8

Summary and Segue

As in previous chapters, I summarize in a table how the two models analyzed fare on the criteria of predictive power, cognitive processes, and transparency (no comments were made here on the usefulness of output, but the comments made in previous chapters apply)—see Table 4.2. Overall, the use of reasonable auxiliary assumptions for inequityaversion theory allows it to align with fast-and-frugal trees and make similar contributions in terms of the three criteria. As said in the text, this has led to progress in theory integration for the topic of strategic interaction. This chapter serves as the segue from Part I to Part II of this book. This first part focused on descriptive models employed in behavioral economics Table 4.2 Summary of the comparative analysis of inequity-aversion theory and fast-and-frugal trees

Inequity-aversion theory

Fast-and-frugal trees (selfish, mirror, and priority trees)

Predictive power

Cognitive processes

Transparency

Can fit offers and rejections (acceptances) in the ultimatum game. With reasonable auxiliary assumptions, it can predict response time patterns Can fit offers and rejections (acceptances) in the ultimatum game. It can predict response time patterns

Not explicitly modeled. Appropriate fast-and-frugal trees (those that match the theory’s outcomes), can be viewed as explicating processes Modeled precisely with zero free parameters

For the two-person ultimatum game, the utility function is easy to understand because the various terms are separate It also reduces to a piece-wise linear function Simple graphical representations, which are easy to understand and apply. Behavioral outcomes can be represented as the output of non-compensatory linear models

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and cognitive psychology. The models were inspired and induced by data designed to test ‘rational’, also called normative, optimization theories such as expected utility and game theory. As such, this literature can exhibit a strong concern with whether and the extent to which human behavior is ‘rational’ as measured by its adherence to conditions of internal logical consistency as the independence axiom or transitivity, or ‘optimal’ as measured by its closeness to a theoretical calculation. Such concerns are often carried over in the field of behavioral operations management, and to a lesser degree in behavioral operational research. Of course, to an extent this kind of carryover is natural.47 On the other hand, as Karen Donohue, Özalp Özer, and Yanchong Zheng have pointed out, ‘behavioral operations is a fundamental area of research, not just an application of behavioral economics or psychology’.48 In my view, the character of behavioral operations should be pragmatic, as intended by operations/operational research and operations management, and not worry too much about idealized conceptions of ‘rationality’ or ‘optimality’. It is noteworthy that there is no evidence of a positive link between people’s conformity to theoretical axioms and their performance in realworld tasks.49 Economics and psychology, as well as other behavioral sciences, can be very useful to behavioral operations50 by providing scientific tools for modeling the cognition underlying human decision making. Demonstrating how to do this was a principal goal of Part I. Part II will show more specifically how to reap the fruits of such modeling in operational contexts.

Notes 1. John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior (Princeton: Princeton University Press, 1944); Kenneth G. Binmore, Fun and Games: A Text on Game Theory (Lexington, MA: D. C. Heath, 1992). 2. For a historical analysis of formal and experimental approaches to studying rationality during the Cold War, see Paul Erickson et al., How Reason Almost Lost Its Mind: The Strange Career of Cold War Rationality (Chicago, IL: University of Chicago Press, 2013). 3. For a general perspective, see for example Colin F. Camerer, Behavioral Game Theory: Experiments in Strategic Interaction (Princeton: Princeton University Press, 2003); for an operations perspective see for example Christoph H. Loch and Yaozhong Wu, Behavioral Operations Management (Norwell, MA: Now Publishers, 2007); Gary E. Bolton and Yefen

4

4.

5.

6.

7.

8.

9.

10. 11.

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Chen, “Other-Regarding Behavior: Fairness, Reciprocity, and Trust,” in The Handbook of Behavioral Operations, eds., Karen Donohue, Elena Katok and Stephen Leider (Hoboken, NJ: John Wiley and Sons, 2018): 199–232; and Stephen Leider, “Behavioral Analysis of Strategic Interactions: Game Theory, Bargaining, and Agency,” in The Handbook of Behavioral Operations, 237–285. For strong arguments on this point, see Karen Donohue, Özer Özalp and Yanchong Zheng, “Behavioral Operations: Past, Present, and Future,” Manufacturing and Service Operations Management 22, no. 1 (2020): 199, including a reference to Camerer, Behavioral Game Theory, 115–117. For a general discussion of the merits of studying the ultimatum game, see Werner Güth and Martin G. Kocher, “More Than Thirty Years of Ultimatum Bargaining Experiments: Motives, Variations, and a Survey of the Recent Literature,” Journal of Economic Behavior and Organization 108 (2014): 396–409; and for an application to the design of the bargaining process in supply chains, see Ernan Haruvy, Elena Katok and Valery Pavlov, “Bargaining Process and Channel Efficiency,” Management Science 66, no. 7 (2020): 2845–2860. For an analysis of the benefits, challenges and desiderata of this approach, see Leonidas Spiliopoulos and Andreas Ortmann, “The BCD of Response Time Analysis in Experimental Economics,” Experimental Economics 21, no. 2 (2018): 383–433. Ernst Fehr and Klaus M. Schmidt, “A Theory of Fairness, Competition, and Cooperation,” The Quarterly Journal of Economics 114, no. 3 (1999): 817–868. Urs Fischbacher, Ralph Hertwig and Adrian Bruhin, “How to Model Heterogeneity in Costly Punishment: Insights From Responders’ Response Times,” Journal of Behavioral Decision Making 26, no. 5 (2013): 462–476; Ralph Hertwig, Urs Fischbacher and Adrian Bruhin, “Simple Heuristics in a Social Game,” in Ralph Hertwig, Ulrich Hoffrage and the ABC Research Group, Simple Heuristics in a Social World (Oxford, UK: Oxford University Press, 2013): 39–65. See respectively Gary E. Shapiro, “Effect of Expectations of Future Interaction on Reward Allocations in Dyads: Equity or Equality,” Journal of Personality and Social Psychology 31, no. 5 (1975): 873–880; and Werner Güth, Rolf Schmittberger and Bernd Schwarze, “An Experimental Analysis of Ultimatum Bargaining,” Journal of Economic Behavior and Organization 3, no. 4 (1982): 367–388. It is also possible that a player’s strategy is defined as a probability distribution over a set of strategies. For a discussion of the various types of equilibria, see Leider, “Behavioral Analysis of Strategic Interactions”.

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12. Ariel Rubinstein, “‘Economics and Psychology’? The Case of Hyperbolic Discounting,” International Economic Review 44, no. 4 (2003): 1207– 1216. 13. John R. Platt, “Strong Inference,” Science 146 (1964): 347–353. 14. Camerer, Behavioral Game Theory; Güth et al., “More Than Thirty Years of Ultimatum Bargaining Experiments”. 15. Werner Güth and Matthias Sutter, “Fairness in the Mail and Opportunism in the Internet: A Newspaper Experiment on Ultimatum Bargaining,” German Economic Review 4, no. 2 (2003): 243–265. 16. Güth et al., “More Than Thirty Years of Ultimatum Bargaining Experiments”. 17. Rosanna Arquette, June 18, 2021, personal communication; Robert Aumann, June 20, 2021, personal communication. Interestingly, they both went beyond the information given, in similar ways: Arquette suggested that one might also change the rules of the game and introduce the option “leave to charity of choice”, which resonates with Aumann’s ideas “… if [the proposer] wants to be pro-social, why doesn’t he take the entire endowment, then grant a part to a needy relative or a worthy cause or whatever he deems appropriate?”; see Robert J. Aumann, “A Synthesis of Behavioural and Mainstream Economics,” Nature Human Behaviour 3 (2019): 668–669. 18. Joseph Henrich et al., “In Search of Homo Economicus: Behavioral Experiments in 15 Small-Scale Societies," American Economic Review 91, no. 2 (2001): 73–78. 19. There is also work on the effects of one’s education on their behavior in bargaining games; see for example Malte Petersen et al., “Business Education: Does a Focus on Pro-Social Values Increase Student’s ProSocial Behavior?,” Mind and Society 18 (2019): 181–190, and references therein. 20. Other regarding does not necessarily mean altruistic. For a review of these concepts, see Bolton and Chen, “Other-Regarding Behavior”. 21. Hertwig et al., “Simple Heuristics in a Social Game”. 22. See Ernst Fehr and Klaus M. Schmidt, “A Theory of Fairness, Competition, and Cooperation,” Quarterly Journal of Economics 114, no. 3 (1999): 817–868. Influential behavioral game theories that incorporate social preferences include Matthew Rabin, “Incorporating Fairness Into Game Theory and Economics,” American Economic Review (1993): 1281–1302; and Gary E. Bolton and Axel Ockenfels, “ERC: A Theory of Equity, Reciprocity, and Competition,” American Economic Review 90, no. 1 (2000): 166–193. For a review, see Ernst Fehr and Klaus M. Schmidt, “The Economics of Fairness, Reciprocity and Altruism–Experimental Evidence and New Theories,” Handbook of the Economics of

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23.

24.

25.

26.

27. 28.

29.

30. 31. 32.

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Giving, Altruism and Reciprocity, eds., Serge-Christophe Kolm and Jean M. Ythier, 1 (2006): 615–691. See for instance Ken Binmore and Avner Shaked, “Experimental Economics: Where Next?,” Journal of Economic Behavior and Organization 73, no. 1 (2010): 87–100; and Mariana Blanco, Dirk Engelmann and Hans T. Normann, “A Within-Subject Analysis of Other-Regarding Preferences,” Games and Economic Behavior 72, no. 2 (2011): 321–338. Binmore and Shaked in “Experimental Economics” questioned the validity of this exercise; but see also Ernst Fehr and Klaus M. Schmidt, “On Inequity aversion: A Reply to Binmore and Shaked,” Journal of Economic Behavior and Organization 73, no. 1 (2010): 101–108. Another 30% of the population was suggested to have α = 0 and β = 0, thus u(x) = x, and the remaining 10%, α = 4 and β = 0.6, thus u(x) = 9x − 4 for x ≤ 0.5 and −0.2x + 0.6 for x > 0.5. See Fehr and Schmidt, “A Theory of Fairness, Competition, and Cooperation” (and also Figs. 4.2 and 4.3, and Footnote 23); and Blanco et al., “A Within-Subject Analysis of Other-Regarding Preferences”. Matthew Rabin, “Incorporating Fairness into Game Theory and Economics”. The mini ultimatum game is more restrictive than the typical ultimatum game because only two pie allocations are possible, but it is also more general because the size of the pie need not stay constant. For example, the two possible pairs of payoffs might be (300, 500) and (200, 800), where the first payoff in each pair goes to the responder and the second payoff to the proposer. For more details, see Urs Fischbacher, Ralph Hertwig and Adrian Bruhin, “How to Model Heterogeneity in Costly Punishment: Insights From Responders’ Response Times,” Journal of Behavioral Decision Making 26, no. 5 (2013): 468–469. Note that the order of the second and third attributes does not make a difference in the prediction of acceptance or rejection. Fischbacher et al., “How to Model Heterogeneity in Costly Punishment”, 470. There are other possibilities. One is to assess the predictive accuracy of the approaches across bargaining games, using the same participants. The study of Mariana Blanco et al., “A Within-Subjects Analysis of Other-Regarding Preferences” found that the parameter values of inequity-aversion theory for the same person had low correlations across different games. Wasilios Hariskos and I developed two parameterized heuristics that combined social motives in non-compensatory ways, and fitted them to two-player ultimatum data—we found that the fixed heuristics predicted behavior in three-person ultimatum games more accurately than compensatory models such as inequity-aversion theory; see Wasilios

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34.

35. 36.

37. 38.

39.

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Hariskos and Konstantinos V. Katsikopoulos, “A Heuristic Theory of Other Regarding Preferences,” Working paper (Erfurt, Germany: 2017). Another possibility is to focus on the different errors the two approaches make in fitting acceptances and rejections. Note, however, that these cases might be few, given the high fitting accuracy of the two approaches. For illustration, assume that the fitting accuracy of one approach is 90% and of the other 85%. Then, the maximum proportion of differing model choices is 2−(0.90 + 0.85) = 25%. Rejection rates vary considerably across types of participants. For example, for the decision in the penultimate row, the rejection rates associated with the four fast-and-frugal trees ranged from 0% (selfish tree) to 89% (priority tree), with an average of 33%. Similar to the computational-complexity analyses of prospect theory in Chapter 3, for the argument to go through, one must also assume that utility and disutility terms are not computed in parallel. Standard statistical tests found all of these differences to be significant. Werner Güth, “On Ultimatum Bargaining Experiments—A Personal Review,” Journal of Economic Behavior and Organization 27, no. 3 (1995): 329–344. Hertwig et al., “Simple Heuristics in a Social Game,” 63. For example, see the work by Nick Chater and his colleagues, as in Adam N. Sanborn and Nick Chater, “Bayesian Brains Without Probabilities,” Trends in Cognitive Sciences 20, no. 12 (2016): 883–893. Finding strategic equilibria can also be computationally intractable as shown by Constantinos Daskalakis, Paul W. Goldberg and Christos H. Papadimitriou, “The Complexity of Computing a Nash Equilibrium,” SIAM Journal on Computing 39, no. 1 (2009): 195–259. Laura Martignon, Konstantinos V. Katsikopoulos and Jan K. Woike, “Categorization with Limited Resources: A Family of Simple Heuristics,” Journal of Mathematical Psychology 52, no. 6 (2008): 352–361. Ibid., Result 2. In this formulation of lexicographic heuristics, attributes are framed so that they lead to the elimination of an alternative or not. Then, attributes are applied sequentially until one alternative is left, which is then chosen (if the last attribute applied eliminates more than one alternative, then one of these alternatives is chosen randomly). An example of such a heuristic is Tversky’s elimination-by-aspects; see Amos Tversky, “Elimination by Aspects: A Theory of Choice,” Psychological Review 79, no. 4 (1972): 281–299. For examples of deterministic versions of eliminationby-aspects which can be viewed as fast-and-frugal heuristics, see Robin M. Hogarth and Natalia Karelaia, “Simple Models for Multiattribute Choice With Many Alternatives: When It Does and Does Not Pay to Face Trade-Offs With Binary Attributes,” Management Science 51, no.

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44. 45.

46.

47. 48. 49.

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12 (2005): 1860–1872, and Konstantinos V. Katsikopoulos and Barbara Fasolo, “New Tools for Decision Analysts,” IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 36, no. 5 (2006): 960–967. Paola Manzini and Marco Mariotti, “Sequentially Rationalizable Choice,” American Economic Review 97, no. 5 (2007): 1824–1839. This axiom is the weak axiom of revealed preferences; see Paul A. Samuelson, “A Note on the Pure Theory of Consumer’s Behaviour,” Economica 5, no. 17 (1938): 61–71. Andrea Galeotti et al., “Network Games,” The Review of Economic Studies 77, no. 1 (2010): 218–244. For general analytical results see Tim Roughgarden, Selfish Routing and the Price of Anarchy (Cambridge, MA: MIT Press, 2005). Better system performance has also been demonstrated analytically in parking games where simple lexicographic heuristics that people use can do better than equilibrium strategies; see Merkouris Karaliopoulos, Konstantinos V. Katsikopoulos and Lambros Lambrinos, “Bounded Rationality Can Make Parking Search More Efficient: The Power of Lexicographic Heuristics,” Transportation Research Part B: Methodological 101 (2017): 28–50. For a review and references, see Amnon Rapoport and Vincent Mak, “Strategic Interactions in Transportation Networks,” in The Handbook of Behavioral Operations (2018): 557–586. Donohue et al., “Behavioral operations”, 197. Ibid., 192. See for example Peter C. Fishburn, “The Irrationality of Transitivity in Social Choice,” Behavioral Science 15, no. 2 (1970): 119–123; Hal R. Arkes, Gerd Gigerenzer and Ralph Hertwig, “How Bad is Incoherence?,” Decision 3, no. 1 (2016): 20–39; and Don P. Clausing and Konstantinos V. Katsikopoulos, “Rationality in Systems Engineering: Beyond Calculation or Political Action,” Systems Engineering 11, no. 4 (2008): 309–328. For a deep analysis of the more general relationship and cross-fertilization between operations/operational research and economics, see Philip Mirowski, “Cyborg Agonistes: Economics Meets Operations Research in Mid-Century,” Social Studies of Science 29, no. 5 (1999): 685–718.

PART II

Benefits of Cognitive Modeling

CHAPTER 5

Inventory Control

The pioneering motion studies of the Gilbreths in the early twentieth century (Chapter 1) employed arithmetic. The objective was to maximize the efficiency of operations. At about the same time, Ford Harris used algebra and calculus to determine the size of the order that minimizes the total inventory cost for replenishment and holding. The following quote shows Harris’ keen appreciation of how carefully such theories should be applied by practitioners on the job, and of the interaction between theory and practice1 : The writer… does not wish to be understood as claiming that any mere mathematical formula should be depended upon entirely for determining the amount of stock. This is a matter that calls… for a trained judgment, for which there is no substitute… In deciding on the best size of order, the [wo]man responsible should consider all the factors that are mentioned. While it is perfectly possible to estimate closely enough what effect these factors will have, the chances are many mistakes costing money will be made. Hence, using the formula as a check, is at least warranted. Given the theoretically correct result, it is easy to apply such correction factors as may be deemed necessary.

Like the Gilbreths, Harris too acknowledged the importance of the human factor in operations. It took a long time, however, before there

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6_5

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was systematic behavioral research on how people solve inventory problems. There are still only a few studies of retail orders in the context developed by Harris.2 Behavioral inventory control has been studied in another context, that of the so-called newsvendor problem.3 The newsvendor problem is possibly the drosophila of behavioral inventory control, and more generally a main experimental paradigm for behavioral operations management.4 It is the topic of the present chapter. The chapter is structured as follows. The first section introduces the newsvendor problem, presents the theoretically optimal solution, and contrasts it with observed human behavior. After that, two optimization interpretations of the idea that retailers exhibit bounded rationality are presented, and in the same section I also discuss prospect theory. The following two sections present two simple heuristics. Both heuristics can be viewed as instances of non-optimizing bounded rationality, and are true to the spirit of Ford Harris’ quote, wherein theory might need to be changed in order to be used on the job. But the departure from optimization has been interpreted and modeled differently in the two heuristics. I evaluate the predictive power of the two heuristics and of two benchmarks. To do so, I use a different testing method from the methods presented in Chapters 3 and 4. The chapter concludes with the assessment and integration of the various models discussed. There are bad news and good news. The bad news is that only the heuristics seem fit to describe the cognitive processes that underlie retail orders, and it is not clear how to do so for the optimization models. For the moment, theoretical integration appears challenging. The good news is that models, optimization as well as heuristic, can be viewed as quite similar in terms of transparency and output usefulness, and to an extent predictive power. I argue that all models can jointly help improve the practice of inventory control. That is, there is potential for practical integration. Along the way, I also reflect on the concepts of bounded rationality and AI in operations, bringing into the foreground the ideas of Herbert Simon, the renaissance figure of decision research who also sometimes wore the hat of an operations researcher.

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The Newsvendor Problem: Theory and Data

An inventory manager’s perennial challenge is to order the right number of units of a product. If she orders more than the demand some stock has to be disposed of at a loss, and if she orders less than the demand some profit is foregone. The newsvendor problem is a representation of this decision. In the vanilla version of the newsvendor problem, there is one selling period and one ordering point which occurs before selling starts. The manager purchases each unit with cost c and sells it at price p with p > c > 0. If q is the order quantity and D is the stochastic demand, then if q > D, the remaining units are salvaged at the end of the period at a price s with s < c. Hence, the profit equals π (q) = ( p − s)min{q, D}−(c − s)q. The objective of the manager is to maximize the expected profit where the expectation is taken with regard to the distribution of D. The cumulative distribution function of D is denoted by F. That is, the problem of inventory control is typically approached as a problem of decision under risk, where any aspects of uncertainty or strategic interaction are ignored. It turns out5 that the order quantity q ∗ that maximizes the expected profit is the solution to the equation F(q ∗ ) = p−c p−s . In most empirical studies, it has been assumed that s = 0 and that D follows a uniform distribution, and these assumptions are made in this chapter as well. Without loss of generality let us also say that the demand distribution is U (0, 1). Based on these assumptions the solution is the following. q∗ = 1 −

c p

(5.1)

If q ∗ > 0.5, then the product is classified as high profit , and if q ∗ < 0.5 as low profit . Typical high profit products are books and typical low profit products are personal computers and cell phones. Following the experiments of Maurice Schweitzer and Gérard Cachon in 2000,6 there has been a flurry of empirical studies on the quantity that laypeople and practitioners order when they are provided with a description of the problem and the values of its various characteristics.7 Long story short, actual orders deviate from the theoretically optimal solution. But how exactly? Are there interesting patterns in retailer behavior? The most prominent finding is the pull-to-center effect. Pull-to-center effect. This effect says that people’s departures from the theoretically optimal order mirror each other for high and low profit

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products. It is described by the following pair of inequalities, where q denotes people’s actual order. q < q ∗ when q ∗ > 0.5 and ∗

(PtC)

∗

q > q when q < 0.5 That is, (PtC) says that q is pulled away from the theoretical optimal q ∗ and towards the mean demand 0.5. In other words, q lies between q ∗ and 0.5. For instance, in their lab experiment, Schweitzer and Cachon found that for q ∗ = 0.75, q = 0.59, and for q ∗ = 0.25, q = 0.45. These values of q are means across 33 participants, who were told that D ∼ U ( 1, 300),8 p = 12, and c = 3 (high profit case) or c = 9 (low profit case), and each placed 15 orders per case. Ordering was incentivized by converting profit into cash which would be paid for one randomly selected participant. Subsequent studies showed that the effect might diminish but does not go away when participants are given the chance to learn, for example by placing multiple orders.9 As in behavioral research in the choice between gambles and bargaining games, one critique of most research in the newsvendor problem is that participants are University students. Can it be that practitioners, who by definition are better incentivized and more experienced, are less affected by mean demand and come closer to or even achieve the theoretical optimal? Gary Bolton, Axel Ockenfels, and Ulrich Thonemann checked this possibility.10 Bolton and his colleagues recruited 49 procurement managers, with experience ranging from 1 to 30 years, who had worked as buyers, team leaders, or vice presidents, and contrasted their inventory orders to those of undergraduate and graduate students at the University of Cologne. There were a number of experimental treatments, each with at least 20 participants in each of the three groups of participants. Figure 5.1 shows the mean order of the groups when the provided demand information referred to a sample or to the whole distribution. The orders of the three groups are close to each other, and lower than the theoretically optimal order q ∗ = 0.75.11

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Theoretical optimal order q* = 0.75 0.7

Order q

0.65 0.54

0.57

0.62

0.56

Undergrad GraduatePractitioner

Undergrad GraduatePractitioner

Sample demand information

Distribution demand information

Fig. 5.1 Mean orders q placed in the Bolton et al. experiment by students and practitioners, given sample and distribution information about demand

Asymmetry of effect for high and low profit products. The size s of the pull-to-center effect is given by12 s=

q∗ − q q ∗ − 0.5

(5.2)

If the pull-to-center effect, as stated in (PtC), holds then Eq. 5.2 implies s > 0. A larger s indicates a greater pull towards the center. In a meta-analysis of 24 studies by Yinhao Zhang and Enno Siemsen, the effect was found in 48 out of 54 comparisons, and its mean size s was 0.66 for high profit (H ) and 0.57 for low (L) profit products. Note that in these studies the optimal orders for the high and low profit cases ∗ = 0.75 sum to 1, as for example in the common experimental choice q H ∗ and q L = 0.25. The meta-analysis concluded that there was a statistically significant asymmetry (difference) in the size of the pull-to-center effect between the high and low profit products. The magnitude and sign of this difference appears to be strongly affected by the characteristics of the

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experimental design, such as the likelihood of financial loss or the offering of a decision support system.13 Individual differences. The findings presented above refer to people’s mean orders. Do all experimental participants place the same, or at least similar, orders? No. There are different types of participants—some tend to order the mean demand they have experienced previously, others order more or less randomly, and others in fact often order optimally. The proportion of participants whose modal order equals the theoretical optimal has been estimated in one study14 to be 30%, the proportion of those whose modal order equals the mean demand has been estimated to be 25%, and the proportion of participants who order randomly has been estimated to be 10%. Finally, research has also investigated people’s behavior at the extreme (q ∗ = 0 or 1) and middle (q ∗ = 0.5) points of the range of possible orders.15 The Appendix discusses how well various optimization and heuristic models describe these findings.

5.2

Optimization

Sometimes in science, a major idea does not develop in the way its originator had in mind.16 In the behavioral sciences, this is the case for the concept of bounded rationality. Herbert Simon said that he did not himself construe bounded rationality as a type of optimization, especially one which might include a negative connotation, such as optimization under cognitive limitations.17 Nevertheless, this is the predominant interpretation of bounded rationality in behavioral economics and also in behavioral operations management. It is also a standard way of describing human behavior in the newsvendor problem as illustrated by the following models. Quantal choice model. Are you always rational? Erm…, you answer, not always, but often. A way of capturing behaviors in which ‘better decisions are made more often, but not always’ is to say that the probability of choosing an option increases with the option’s worth. As we saw in Chapter 3, the probability of choosing option O over O ' , with worths ( ) ek·w(O) w(O) and w O ' , may be computed as k·w(O) ' . The parameter e +ek·w( O ) k > 0 controls the sensitivity of choice probability on differences in option worth. For example, if k is very large then it is basically certain that the gamble with the higher worth is chosen, whereas if k is very small then the

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choice is almost random. Option worth could be measured by expected utility or, in the newsvendor problem, by expected profit. This approach is called quantal choice modeling, and it enjoys multiple interrelated mathematical foundations.18 Xuanming Su has applied it to a number of inventory settings, including the newsvendor problem.19 According to the quantal choice model, the probability that a retailer places an order q is given by the following equation. Pr (q) =

ek·E D [π (q)] ∫10 ek·E D [π (q)] dq

(5.3)

Su interprets the parameter k in Eq. 5.3 as the ‘extent of cognitive and computational limitations suffered by the decision maker’ (emphasis added).20 He then postulates various demand distributions and goes on to analytically derive the distribution of q and its expected value. For instance, Su shows that for uniform demand the distribution of q is normal, truncated over the range of demand and that the pull-to-center effect is always predicted assuming non-extreme values of k. On the other hand, because the normal distribution is symmetric, the quantal choice model cannot capture the asymmetry of the effect for high and low profit products. Finally, the free parameter k allows the model to accommodate individual differences, but only partially because some experimental participants do not exhibit the pull-to-center effect which the model always predicts. Similar to other optimization models of decision under risk, the quantal choice model is silent about how people could actually be computing choice probabilities. The same holds for the next optimization model, which, as optimization models of strategic interaction, assumes that people can compute equilibria. Impulse balance equilibrium model. Axel Ockenfels and Reinhard Selten zoom in the learning that may occur in newsvendor problems.21 Since the Schweitzer and Cachon study, it is known that experimental participants can exhibit patterns of demand chasing, where the demand realized in the previous period has a disproportionate effect on the current order. Such behavior resonates with the concept of impulse balance, wherein a previous order that ended up being over, or under, q ∗ creates an impulse to balance the experience and order respectively less or more in the current period.22 The core assumption of this approach is that people are able to identify the equilibrium order quantity which is the order that

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is such that the two impulses of ordering less or more than before are equal. The theory holds that people order this quantity. Like Su, Ockenfels and Selten dub their model as following ‘a limited cognition approach’.23 Unlike Su, they arrive at a parameter-free equation that specifies q as a function of q ∗ . The equation is given below and graphed in Fig. 5.2. One can see that a pull-to-center effect,24 which is asymmetrical, is predicted. Because the model is parameter-free, however, individual differences cannot be accommodated. q=

1+

√

1

(5.4)

(1−q ∗ )(2−q ∗ ) q∗

The decision objective in the newsvendor problem is to maximize expected profit. This objective expresses a neutral attitude towards risk. But as we saw in Chapters 2 and 3, people often make risk averse or risk seeking choices. It is thus reasonable to ask whether a descriptive model should assume that retailers transform values or probabilities. The quantal

q

1

0 0

1

q*

Fig. 5.2 The equation of Ockenfels and Selten’s impulse balance equilibrium model, q = √ 1 1−q ∗ )(2−q ∗ ) 1+ ( q∗

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choice and impulse balance equilibrium approaches do not make such assumptions. Prospect theory can choose to make them or not. Does this choice make a difference in being able to describe newsvendor behavior? Prospect theory. In the newsvendor literature, the original thinking about prospect theory was that it cannot capture the pull-to-center effect.25 For example, Schweitzer and Cachon point out that, for a newsvendor scenario where financial losses cannot occur, and if the reference point r = 0, the risk aversion assumed in prospect theory always leads to under-ordering. In two ingenuous efforts, however, it has been shown that extensions of prospect theory can in fact predict a pull-to-center effect which is asymmetrical.26 Both extensions relax the assumption of a zero reference point. Xiaoyang Long and Javad Nasiry suggest that the reference point is a convex combination27 of the maximum and minimum possible profit, whereas B. Vipin and R. K. Amit propose a more complex relationship. Notably, Long and Nasiry prove analytically that human behavior can be captured with a piece-wise linear utility function and without probability weighting. This result is reminiscent of the analyses of prospect theory and the priority heuristic in Chapter 3, where such functions can predict people’s choices between gambles. It should be noted that the pull-tocenter effect is predicted always (for all parameter values) as it was also the case for the quantal choice and impulse balance equilibrium models. This fact again limits the extent to which individual differences can be accommodated. The results on the optimization models presented in this section suggest that it is not necessary to transform values and probabilities in order to describe newsvendor behavior. Can one do the same with even simpler approaches to modeling bounded rationality? Can one assume that people do not optimize and still be able to build models that describe newsvendor behavior? The answer is yes. How to do it? There are hints in Ford Harris’ quote. When he said that ‘the chances are many mistakes costing money will be made’, Harris focused on the difficulty of estimating the characteristics (e.g., item demand, cost, and price) of the newsvendor problem and the effects this difficulty would have. He went on to suggest practical remedies (emphases added): ‘a matter that calls, in each case, for a trained judgment, for which there is no substitute.… using the formula as a check, is at least warranted… it is easy to apply such correction factors as deemed necessary’. In other words, Harris suggested that analytical theory and

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practical intuition be blended. There are many ways of doing so, and here I propose two, both of which focus on how practitioners adjust or correct theory. The core idea is that if theory suggests that q ∗ = 0.75, it might be appropriate for the retailer to order, say, q = 0.7 or q = 0.8, or another value ‘close’ to 0.75. The research question is to understand how participants in experiments and practitioners make their adjustment/ correction factors. The next two sections explore some ways.

5.3

Anchoring and Adjustment Heuristic

Harris’ ideas converge with evidence from the literature on behavioral forecasting28 and behavioral inventory control.29 For instance, a survey of forecasting organizations by Robert Fildes and Fotis Petropoulos30 found that 71% of the organizations adjust software forecasts by combining them with their own judgments or even rely exclusively on these judgments. This literature has suggested that practitioners might be using anchoring and adjustment heuristics .31 Interestingly, Schweitzer and Cachon made the same suggestion. What is an anchoring and adjustment heuristic? Theory. Enter again Amos Tversky and Daniel Kahneman. They found that people, when asked to estimate a target variable, can be overly affected by available information on another variable that is in fact irrelevant to the value of the target variable.32 This phenomenon is called anchoring. For example, when in one experiment people were asked to estimate the proportion of African countries in the United Nations (in 1974; this is the target variable), they appeared to use as a starting point the result of a random spin of a wheel of fortune ranging from 0 to 100, which was shown to them: If the median result of the wheel of fortune was 10, the median estimate was 25%; and if the result was 45, the estimate was 65%. In both cases, the adjustment of the anchor towards the correct solution33 of 82% was not sufficient.34 Which variables serve as anchors in a newsvendor setting? And how can we model the adjustment? Schweitzer and Cachon proposed two possibilities, (i) anchoring at the mean demand and (ii) anchoring at previously made orders. In (i), adjustment is towards the theoretically optimal order and in (ii) towards previously experienced demands. In both cases, the adjustment is assumed to be linear. Both possibilities have strengths and weaknesses.35 Here I focus on (i) because it is more readily comparable to the heuristic presented in the next section.

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q

1

w = 0.33 w = 0.5 w = 0.67

0 0

1

q*

Fig. 5.3 Illustration of the anchoring and adjustment heuristic for w = 0.33, which means q = 0.67q ∗ + 0.17; w = 0.5, which leads to q = 0.5q ∗ + 0.25; and w = 0.67, which means q = 0.33q ∗ + 0.33

Based on the above, the anchoring and adjustment heuristic can be written as follows where w is a free parameter that ranges from 0 to 1. q = w(0.5) + (1 − w)q ∗

(5.5)

Note that, whereas this equation does not explicitly specify a process of thinking, the heuristic does do so. The retailer is assumed to first anchor on the mean demand 0.5, and then to adjust this anchor towards the theoretically optimal order q ∗ . ∗ −q . Contrasting Predictions. Solving for w in Eq. 5.5, we get w = qq∗ −0.5 this identity with Eq. 5.2 shows that w = s, or that the anchor weight equals the size of the pull-to-center effect. Furthermore, the identity together with the condition w > 0 imply the pull-to-center effect: If q ∗ > 0.5 then q < q ∗ , and if q ∗ < 0.5 then q > q ∗ .36 Thus, the anchoring and adjustment heuristic of Eq. 5.5 predicts the effect for all values of its parameter w (except of course for w = 0 or 1).37 For example, if w = 0.5, then q = 0.5q ∗ + 0.25, which implies q = 0.625 for q ∗ = 0.75 and q = 0.375 for q ∗ = 0.25. This property

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constrains the ability of the heuristic to capture individual differences as it was also the case for the quantal choice model. For further illustrations of the heuristic’s predictions, see the curves in Fig. 5.3. With regard to the asymmetry of the pull-to-center effect, the anchoring and adjustment heuristic makes a very strong prediction. The difference of the effect between a high (H ) and a low (L) profit case q ∗ −q q ∗ −q H equals q H∗ −0.5 − q ∗L −0.5L = w − w = 0. Note that this fact holds for any two H L ∗ + q ∗ = 1 as in the statement of the finding cases, and not only for q H L (Sect. 5.1). The meta-analysis of Zhang and Siemsen,38 however, has found this difference to be statistically significant across 54 comparisons, even if in 15 of these comparisons the effect size was indeed close to zero. In order for Eq. 5.2 to produce a nonzero asymmetry, w should have a different value for high and low profit products, that is, the heuristic should have two free parameters.

5.4

Correction Heuristic

The anchoring and adjustment heuristic does not assume that people optimize. The heuristic of the present section is also non-optimizing. Furthermore, both heuristics fit with Harris’ notion of changing the theoretical optimal. But the two heuristics model the change in different ways. The anchoring and adjustment heuristic starts from the mean demand and implements a typically insufficient, often also called biased, adjustment towards the theoretically optimal order. On the other hand, the correction heuristic starts from the theoretically optimal order and employs a corrective process to change this order with the aim of making it more appropriate for practice. Theory. It was said previously that, if q ∗ = 0.75, a retailer might think that it is appropriate to order q = 0.7 or q = 0.8. Let us go one step further and say that she thinks that any order between 0.7 and 0.8 is appropriate. Why might this be? Plausible reasons are provided in the behavioral forecasting literature, as reviewed by Paul Goodwin and his colleagues.39 The retailer could distrust the output of an opaque piece of software and decide to tinker with the output. She might go for a small deviation from the software thinking that it would not make a real difference in the real world, whereas it would at least give her a sense of ownership of the ordering process, or even help justify her role in the company. Or she might have some privileged knowledge of the market,

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on the basis of which she might decide to make a larger correction to the output of the software. Political and social pressures might also play a role,40 and also affect the size of the correction. Or a manager could just look around, notice that others tinker with software output and decide that he might as well do the same. More precisely, the correction heuristic assumes that the retailer thinks that the theoretically optimal order q ∗ can be corrected by any order q such that |q ∗ − q| ≤ t, with 0 ≤ q ≤ 1, where t is a parameter denoting how much could the retailer deviate from q ∗ . This formulation rings a bell—it is similar to Step 2 of the priority heuristic (Sect. 3.3). And in the same vein as the priority heuristic, the assumption of the correction heuristic is that the retailer’s order q is ‘weighted’ to be the arithmetic mean41 of all possible corrections q, or to put it more simply, the midpoint of the interval of q. The heuristic can be written as the following sequence of steps. Correction heuristic: Step 1. The retailer determines her parameter t, which expresses how much she could deviate from the theoretically optimal order q ∗ . She thinks that an order q is admissible when |q ∗ − q| ≤ t, with 0 ≤ q ≤ 1. Step 2. Using the inequality in Step 1, the retailer finds the interval of her possible orders. Step 3. The retailer calculates the midpoint of the interval she found in Step 2. This is the order q she places. The correction heuristic might lead the retailer’s order q to deviate from q ∗ or not. For example, if q ∗ = 0.75 and t = 0.05, then the interval of q is [0.7, 0.8], thus q = 0.75, and there is no deviation from q ∗ . But if q ∗ = 0.75 and t = 0.5, the interval of q is [0.25, 1], and thus q = 0.625, which denotes (one part of) a pull-to-center effect. More generally, the formulas in the following Eq. 5.6 summarize the heuristic mathematically.42 l(q ∗ , t) + u(q ∗ , t) , where q= 2{ ( ∗ ) } ( ) { } l q , t = max 0, q ∗ − t and u q ∗ , t = min 1, q ∗ + t

(5.6)

Predictions. By analyzing the four possible combinations of the values of l(q ∗ ) and u(q ∗ ) in Eq. 5.6, I derived conditions under which the correction heuristic implies, and does not imply, the pull-to-center effect. The Appendix provides detail on the derivations. The conditions are

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provided in Eq. 5.7. Even though equalities hold in all conditions, I do not include them in this chapter since they are also not included in the usual statement of the effect. q ∗ + (1 − t) < q∗ 2 q∗ + t > q∗ If q ∗ < t < 1 − q ∗ , then q = 2 } { If t > max q ∗ , 1 − q ∗ , then q = 0.5 { } If t < min q ∗ , 1 − q ∗ , then q = q ∗

If 1 − q ∗ < t < q ∗ , then q =

(5.7)

Let us look at some numerical examples. For any value of t between 0.25 and 0.75, the correction heuristic can capture the pull-to-center effect found by Schweitzer and Cachon. For the high profit case q ∗ = 0.75, the top condition in Eq. 5.7 applies for t = 0.5, and captures one part of the effect since q = 0.625. For the low profit case q ∗ = 0.25, the second top condition in the equation applies again for t = 0.5 and captures the other part of the pull-to-center effect since q = 0.375. On the other hand, for retailers with more extreme values of t, outside the (0.25, 0.75) range, the correction heuristic implies different behaviors than those found by Schweitzer and Cachon. For instance, assuming q ∗ = 0.75, retailers with t = 0.9 are expected to order the mean demand 0.5 (the penultimate condition of Eq. 5.7 applies), and retailers with t = 0.1 are expected to order the theoretical optimal 0.75 (bottom condition). It is worth emphasizing that, unlike all other models discussed in this chapter, the correction heuristic does not imply the pull-to-center effect for all values of its parameter t and of the theoretically optimal order q ∗ . Thus, this prediction is strong (Chapter 4) and makes the correction heuristic falsifiable in a unique, among the models discussed in the present chapter, sense: Based on a retailer’s estimated t, the heuristic might predict no effect for a particular value of order q ∗ (as in the examples just above), but empirically this retailer might exhibit the pull-to-center effect. The prediction also suggests that the heuristic could accommodate individual differences, although the degree to which this is the case is an empirical question tackled in the next section. The correction heuristic, as the priority heuristic, exhibits piece-wise linear patterns. Figure 5.4 provides illustrations. The pull-to-center effect is not predicted when 0.33 ≤ q ∗ ≤ 0.67 for t = 0.33 or 0.67 (in the former case q = q ∗ and in the latter one q = 0.5).

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q

1

t = 0.33 t = 0.5 t = 0.67

0 0

1

q*

Fig. 5.4 Illustration of the correction heuristic for t = 0.33, which means q = 0.5q ∗ + 0.17 for q ∗ < 0.33, q ∗ for 0.33 ≤ q ∗ ≤ 0.67, and 0.5q ∗ + 0.33 for q ∗ > 0.67; for t = 0.5 which leads to q = 0.5q ∗ + 0.25; and for t = 0.67, which means that q = 0.5q ∗ + 0.33 for q ∗ < 0.33, 0.5 for 0.33 ≤ q ∗ ≤ 0.67, and 0.5q ∗ + 0.17 for q ∗ > 0.67

What about the asymmetry of the pull-to-center effect? To analyze the predictions of the correction heuristic for this effect, it is useful to first compute the heuristic’s predictions for the size of the effect. Combining Eqs. 5.2 and 5.6 and rearranging terms, one finds that the following holds. q ∗ − (1 − t) 2q ∗ − 1 ∗ q −t If q ∗ < t < 1 − q ∗ , then s = ∗ 2q − 1 { } If t > max q ∗ , 1 − q ∗ , then s = 1 { } If t < min q ∗ , 1 − q ∗ , then s = 0

If 1 − q ∗ < t < q ∗ , then s =

(5.8)

As can be seen in the Appendix, Eq. 5.8 implies that the difference between the size of the effect for a high and for a low profit condition, ∗ +q ∗ = 1, always equals zero for the correction heuristic. For such that q H L

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Table 5.1 Summary of the theoretical results on how the models presented in the chapter can describe the empirical data Pull-to-center effect

Asymmetry of pull-tocenter effect

Individual differences

Quantal choice model

Predicted for (non-extreme) parameter values

Not predicted

Impulse balance equilibrium model Prospect theory

Always predicted (there are no parameters)

Always predicted (there are no parameters) Predicted for all parameter values

Can accommodate partially because some retailers do not exhibit the pull-to-center effect Cannot accommodate because there are no parameters

Anchoring and adjustment heuristic Correction heuristic

Predicted for all parameter values

Cannot be predicted with one parameter; can with two

Predicted for some, but not all, parameter values. This strong prediction makes the heuristic falsifiable

Cannot be predicted with one parameter; can with two

Predicted for all parameter values

Can accommodate partially because some retailers do not exhibit the pull-to-center effect Can accommodate partially because some retailers do not exhibit the pull-to-center effect Can accommodate

∗ = 0.75, q ∗ = 0.25, and t = 0.6. From the top condition example, let q H L in Eq. 5.8, the size of the effect for the high profit case equals 0.75−0.4 1.5−1 = 0.7. Furthermore, from the second top condition in Eq. 5.8, the size of the effect for the low profit case also equals 0.7 = 0.25−0.6 0.5−1 . As for the anchoring and adjustment heuristic, for the correction heuristic to be able to produce an asymmetry, two free parameters, t H and t L , are needed. Interim summary I: Theoretical results. The theoretical results on how the models presented in this chapter can qualitatively describe the

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empirical data are summarized in Table 5.1. As in all general types of decisions studied in this book, the various models, optimization and heuristic, have their strengths and weaknesses. It is an empirical question of what the quantitative performance of the models would be in a prediction exercise. I am not aware of such exercises in the newsvendor literature. The next section presents one.

5.5

Predictive Power

The bulk of newsvendor empirical evidence refers to uniformly distributed ∗ = 0.75 and a low profit case q ∗ = 0.25. In demand, a high profit case q H L the meta-analysis of Zhang and Siemsen, I identified 13 such studies, and copied their data in Table 5.2. In each study, the dependent variable is the mean size of the pull-to-center effect for each profit case. Thus there is a total of 13 data points where each data point is a pair of numbers. I focused on a comparison between the two heuristics because they both have one parameter and similar functional forms. It will be clear how the method employed to assess the predictive power of the heuristics could also be used for the quantal choice model and prospect theory Table 5.2 Mean size of the pull-to-center effect s from empirical studies where demand is uniformly distributed, high profit case ∗ = 0.75 and low qH profit case q L∗ = 0.25 (from Zhang and Siemsen, 2018, Table 2)

Study43

Schweitzer and Cachon Bolton and Katok Bostian et al. Lurie and Swaminathan de Vèricourt et al. Schiffels et al. Kocakbiyikoglu et al. Käki et al. Fügener et al. Zhao and Zhao Feng and Zhang Chen and Li Lee et al.

Mean effect size s (high profit case)

Mean effect size s (low profit case)

0.53

0.77

0.57 0.57 0.88

0.51 0.59 0.30

0.75 0.37 0.99

0.64 0.70 0.65

0.49 0.44 0.63 0.98 0.71 0.66

0.67 1.00 0.39 0.32 0.62 0.65

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(for the additional information needed to do so, see the Appendix). As benchmarks, I used two models that require no parameter estimation; the impulse balance equilibrium model, and a random model that is equally likely to produce an effect size s from 0 to 1.44 Cross-validation. Previously in this book, a model’s predictive power was assessed by fitting the model in one study and evaluating the thus fixed model in another study (Chapter 3), or by fitting a model to one dependent variable and evaluating the fixed model on another dependent variable (Chapter 4). These methods are popular in the behavioral sciences. In this chapter, I employ a method that has its roots in statistics45 and is heavily utilized in machine learning.46 It is called cross-validation. In standard cross-validation, the available set of data is split into two subsets. Each model’s parameters are estimated in one subset. This subset is called the training set. The model, as fixed in the training set, is evaluated in the other subset. This other subset is called the test set. The process of splitting the dataset and fitting and evaluating the models is repeated a large number of times so that variation—due to the split of the dataset—is averaged out. Two common ways of splitting a dataset are 50% and leave-one-out cross-validation. In 50% cross-validation, the test and training sets are each (approximately) half of the whole dataset. In leave-one-out cross-validation, each data point is used as a test set. In this study, we considered all training set sizes from 1 to 12. Because these training sets are small, we were able to enumerate all possible training (and test) sets. The predictive power of a model is its mean power across all test sets used. Predictive power may be measured in a number of ways, such as by quantitative accuracy (Chapter 3) or through qualitative patterns (Chapter 4). Here power is measured by the mean squared error between model predictions and actual observations in the test set. What is this sum? Let us say that the test set consists of one data point, the pair of numbers in the first row of Table 5.2, s H = 0.53 and s L = 0.77. Consider the correction heuristic, and assume that its parameter value has been estimated to be t = 0.6. From Eq. 5.8, this fixed model makes the predictions q H = 0.7 and q L = 0.7. Thus, its mean squared error equals (0.53−0.7)2 +(0.77−0.7)2 = 0.02. 2 How were the parameters of models estimated in the training set? Parameter values were chosen so as to minimize the mean squared error

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between model predictions and observations in this set. For example, say again that the training set consists of the numbers in the first row of Table 5.2, s H = 0.53 and s L = 0.77. The parameter value t = 0.6 would be chosen over t = 0.3. This is so because for t = 0.3, it follows that q H = 0.1 and q L = 0.1, and the mean squared error is 2 2 = (0.53−0.1) +(0.77−0.1) = 0.63, which is larger than 0.02 for t = 0.6. 2 Results. Figure 5.5 shows the performance of the four models as learning curves . A learning curve is a model’s performance, here mean squared error, as a function of the training set size. Some results in the figure are not surprising, whereas others are. As expected, both heuristics perform much better than the two benchmarks. The impulse balance equilibrium benchmark performs (0.22) more similarly to the random benchmark (0.27) than the heuristics (below 0.1); it appears to be too simple to predict people’s orders observed across a number of studies. The learning curves for both benchmarks are flat because their predictions are independent of the training set.47 There is

Mean squared error

0.28

0.18

Random model Impulse balance equilibrium model Anchoring and adjustment heuristic Correction heuristic

0.08

0 1

2

3

4

5

6

7

8

9

10

11

12

Training set size

Fig. 5.5 The performance of the two heuristics and the two benchmarks as a function of the training set size. The curves for the heuristics are identical

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a small learning effect for the two heuristics (a 0.02 difference between a training set size of 12 versus 1). The surprise is that the performance of the two heuristics is identical. After the fact, one can explain this result as follows. For both cases here, ∗ = 0.75 and q ∗ = 0.25, the effect size predicted by the correction qH L heuristic, when 0.25 < t < 0.75, equals 2t − 0.5 (from the top two conditions of Eq. 5.8).48 The anchoring and adjustment heuristic predicts w for 0 < w < 1, and this is the same prediction with the correction heuristic’s prediction of 2t − 0.5 for 0.25 < t < 0.75. For example, when the training set has six data points, the mean value of the best-fitting estimate of t = 0.57 and correspondingly the mean value of the bestfitting estimate of w = 0.64 = 2(0.57) − 0.5, which leads to the same prediction (0.64). As was the case for non-compensatory linear models and fast-and-frugal trees for making strategic or risky decisions, the two heuristics for placing orders implement different processes but produce the same outcomes. The only possibility for the correction heuristic to make a different prediction from the anchoring and adjustment heuristic is if the best-fitting estimate of t in the training set is above 0.75 or below 0.25 (the predictions are then respectively 1 and 0, from the bottom two conditions of Eq. 5.8), but I checked and such estimates were never obtained. Figure 5.6 provides histograms of parameter estimates for the two heuristics when the training set has six data points (and thus there are 1716 estimates). Interim summary II: Empirical results. The results of the crossvalidation prediction exercise are consistent with the theoretical analyses (Table 5.1). Interestingly, the predictive power of the two non-optimizing heuristics was found empirically to be identical. This result might seem surprising because the predictions of the heuristics can be different (Figs. 5.3 and 5.4), but after the fact we could explain the result. To the extent that the empirical results appear satisfactory, the common idea of the two heuristics, that people change the theoretical optimal, thus receives support. The modeling challenge in the future is how to connect this idea with other explanations of newsvendor behavior, such as minimizing ex-post inventory errors, learning from demand realizations, making random mistakes, or exhibiting overconfidence.49

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Fig. 5.6 Histograms of best-fitting parameter estimates for the two heuristics when the training set has six data points; each bin has a width of 0.02

5.6

Assessment and Integration of Models

As before, we assess optimization and heuristic models on the criteria of cognitive processes, predictive power, transparency and usefulness of output. As said in the introduction, there is some bad news regarding the cognitive process. Cognitive processes: Bad news. The conceptual analysis of this chapter produced the same result as previous chapters—there is a gap between heuristics and optimization. Whereas heuristics explicate the cognitive processes underlying behavioral outcomes,50 optimization models of inventory control do not attempt to describe these processes. We do not know how exactly people in the lab or on the job are optimizing utilities, or computing probabilities and equilibria.

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The news is actually worse. In previous chapters, there were remedies for the gap: In decision under risk, cognitive psychometrics (Sect. 3.7) can be used to enhance the explainability of prospect theory or relate it to the priority heuristic, and in strategic interaction an inequity-aversion model can be cast in the form of a process (Sect. 4.5) or related to a fast-andfrugal tree at the level of outcomes (Sect. 4.6). But in inventory control such gap-bridging work has not been done, and it is not clear how to do it. Unlike inequity-aversion models, quantal choice, prospect theory, and impulse balance equilibrium do not have a form that readily suggests a process interpretation. Furthermore, quantal choice and impulse balance equilibrium models are non-linear and thus it is not immediately obvious how to relate them to linear (anchoring and adjustment) or piece-wise linear (correction) heuristics. For the moment, theoretical integration of optimization and heuristics appears elusive. There is nevertheless a reason for optimism. Based on the work of Long and Nashiry, prospect theory can, for the purposes of describing newsvendor behavior, be implemented as a piece-wise linear model (Sect. 5.2). It might be fruitful to perform a cognitive psychometrics exercise featuring this version of prospect theory and the two heuristics. Transparency, usefulness, and predictive power: Good news. Take first the criterion of predictive power. I am not aware of studies of predictive power of models in the newsvendor problem. This chapter presented such a study of the anchoring and adjustment and correction heuristics, and also of the impulse balance equilibrium optimization model. In predicting the size of the pull-to-center effect, the average difference in cross-validated power among these three methods is smaller than their average difference from the random-ordering benchmark, even though the impulse balance model lags behind the heuristics. More studies of predictive power are needed, also testing optimization models such as quantal choice and prospect theory, as well as more sophisticated benchmarks that could include adjustable parameters. Other promising directions include employing extra dependent variables such as the placed order and response times (see Chapters 3 and 4), or utilizing qualitative data from observations, surveys, or interviews. Finally, consider model transparency and output usefulness. First, let us relate again to the previous chapters. The typical result was that optimization was less transparent than heuristics, although in some cases—as for the inequity aversion models in Chapter 4—there were remedies for

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this. Additionally, optimization typically provided more, and more quantitative, output than heuristics, although again in some cases—as for the priority heuristic in Chapter 3—there were remedies for that, and also it was not obvious that more output was always more valid and useful. In the present chapter differences in model transparency and output usefulness are smaller, and in some cases, there are no differences or they appear to be negligible. To see this, recall that model transparency and output usefulness refer to how the target users perceive the models. One can expect that, in inventory control, most users might well be equipped to understand and apply the models presented here. This can be so because the users have had an education in operations research or management science, say in the course of a university or college degree, or through workshops and seminars in a job context. Many of the optimization and heuristic models presented in this chapter are often discussed in operations curricula or training. Furthermore, the output of the models, which is the actually placed order q in the backdrop of the theoretically optimal order q ∗ , is easy to understand. And interestingly, this output is the same for all models.51 Now, a range or distribution of order quantities can also be provided. A shift from point to distributional output is widely considered to be a good idea.52 Although it is not always clear how to do this in a principled manner,53 some of the models presented here can quite readily output such distributions. First, the quantal choice model outputs a probability distribution by construction, given in Eq. 5.3. And second, the parameters of prospect theory as well as of the two heuristics can be utilized to calculate distributions of offers across retailers, by using knowledge about how these model parameters are empirically distributed in experimental populations (see Fig. 5.6 for the case of the two heuristics, and in a new exercise the same could be done for prospect theory). The good news on transparency and usefulness suggests that, for inventory control, integration of models can occur at the level of practice. Below are some thoughts on how. Model-based integration of inventory practice. I posit that presenting practitioners with multiple models that each output an order quantity can help improve the practice of inventory control. My proposal is that this suite of models include prescriptive and descriptive decision models, such as those sampled in the present chapter. There are at least two arguments supporting this position.

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To begin with, the more general idea of enhancing inventory practice by infusing forecasting with decision-making elements and models is not new. Aris Syntetos and his group at Cardiff University Business School have forcefully advocated for it. For instance, they propose research on how inventory managers process the output of inventory software and why they might decide to change it.54 They frame this work as a theoretical contribution and I agree. But of course, such theoretical understanding could also enable fruitful practical intervention. Say that research has shown that, before placing an order, a manager first anchors at the previous mean demand. An open discussion can ensue about why the manager does so, what he more generally sees as the advantages of anchoring, and so on. If the manager also employs an adjustment towards the software output, the discussion can include the reasons for performing the adjustment and the particular way it is done. Second, consider the more specific part of the proposal—to include descriptive models of inventory decision making, such as those analyzed in this chapter. Inventory control is an area of operational work where theory and practice are actually integrated, with practitioners receiving suggestions from theory-based software. But currently the only theory used is prescriptive expected profit maximization (Sect. 5.1). Why can software not also make suggestions based on descriptive theories? Making multiple suggestions and articulating the rationales underlying them can enhance the engagement and buy-in of practitioners, especially if some of these suggestions represent the practitioners’ point of view. A retailer presented with a heuristic suggestion might think: I often do something like that! How about it?—This software takes my approach seriously.55 Other retailers might be moved by descriptive optimization models such as prospect theory. Simple and transparent behavioral interventions, such as presenting and explaining multiple models, have not been exhausted in the practice of inventory control.56 To the best of my knowledge, such interventions have not been implemented and assessed in the lab or on the job.

5.7

Bounded Rationality and AI in Operations

Starting from the 1940s and 1950s, Herbert Simon dared to forcefully point out that the information and computations required by standard ‘rational’ economics and decision theory are beyond the reach of unaided human cognition. Friedman and Savage’s contemporary thesis

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(see Chapter 2) is that experts somehow have all relevant information and are able to process it optimally, and that it is not important to know how exactly they do so, would not work for Simon.57 He asked58 (emphasis and parenthesis added): How do humans reason when the conditions for rationality postulated by the model of neoclassical economics [infinite, or at least ample, resources of information and computation] are not met?

In other words, Simon framed behavioral science as the study of the cognitive processes underlying human reasoning, when optimization is out of reach. This kind of reasoning is what Simon meant by bounded rationality. He postulated that people satisfice 59 : Whereas economic man maximises, selects the best alternative from among all those available to him, his cousin, administrative man, satisfices, looks for a course of action that is satisfactory or ‘good enough’.

Even though the contrast between optimizing and satisficing behavior is evident in the quote above, most researchers have interpreted bounded rationality in the backdrop of optimization.60 Peter Todd and Gerd Gigerenzer point out61 that two of the three main interpretations of bounded rationality do just that: Optimization under constraints , which is prominent in economics, models the bounds of the world and finds optimal solutions to such models62 ; and cognitive illusions , as in the heuristics-and-biases research program of Amos Tversky and Daniel Kahneman, focuses on the bounds of the human mind and demonstrates the alleged resulting sub-optimality.63 The lion’s share of research in behavioral operations does the same, with modeling work following the optimization-under-constraints approach (e.g., prospect theory), and experimental work following the cognitive-illusions approach (e.g., demonstrating deviations from expected utility maximization). The third interpretation of Simon’s bounded rationality is simple heuristics (e.g., priority and correction heuristics) wherein the focus is on how bounded cognitive processes interact with the bounded world, with the objective of making satisfactory decisions. I have called the simpleheuristics approach pragmatic because it breaks away from comparisons with ideals of optimization.64 As such, this approach might hold promise for understanding operational decision making on the job.

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Now, recall that Simon’s concern with the infeasibility of standard ‘rationality’ referred to unaided human cognition. In operations, it is definitely possible that human cognition is supported—in fact, providing such support is one of the pronounced goals of research in operations. Does that change the interpretation of bounded rationality in operational contexts? Yes. Did Simon comment? He did. As a pioneer of decision support systems and of AI, in the late 1950s he engaged in a heated exchange, in the pages of Operations Research, with one of the field’s early giants, Richard Bellman.65 In the exchange, after Simon makes the case that operations research has been proven useful in ‘well-structured’ problems that can be formulated explicitly and quantitatively, he goes on to argue that operations research would soon be able to help with ‘ill-structured’ problems; for example, where ‘an executive… is searching for words, not numbers’.66 How? By using computer algorithms that search for, recognize, and choose satisfactory solutions to problems—in short, by using artificial algorithms that exhibit human bounded rationality. Herbert Simon was a visionary. He predicted that, within ten years (i.e., by 1968), a digital computer will67 : Be the world’s chess champion, unless the rules bar it from competition; discover and prove an important new mathematical theorem; write music that will be accepted as possessing considerable aesthetic value.

More than 60 years later, the only point in this list that unequivocally has been vindicated is the top one.68 And interestingly this success refers to well-structured problems, with explicit, logically stated rules, such as Chess and Go.69 These kinds of games are difficult problems, to be sure, but they still are well-structured. Despite some hyperbole that machine learning algorithms now know us better than we know ourselves and can predict our decisions, such claims are not supported by evidence.70 The most challenging of operational decisions continue to be ill-structured, full of implicit, sometimes illogical, and often changing rules. Richard Bellman, in his usual candor,71 brought this kind of challenge to the forefront,72 in a passage that was and remains relevant:

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Anyone who has examined the formidable difficulties in the formulation and recognition of problems, the construction of criteria, and the prescription of policies, much less the programming of machines to accomplish some of these tasks, will deplore statements of this type [Simon’s predictions].

One cannot overestimate Simon’s contributions to the twentieth century’s behavioral and management sciences. But Bellman proved to be right in not being convinced that Simon’s genius brand of bounded rationality and AI, or the subsequent enormous advances in complex statistical and machine learning modeling, had then cracked, or would until today be able to crack, ill-structured decision problems.73 A case of ill-structured decision problems are decisions under uncertainty. In the next chapter, we will take a look at work that extends Simon’s vision in employing simple heuristics to make operational decisions under uncertainty.

5.8

Summary

Table 5.3 summarizes the results of the conceptual analyses of optimization and heuristic models aimed at describing newsvendor behavior (Sects. 5.6 and 5.7; also drawing from Table 5.1), as well as the first empirical exercise evaluating the predictive power of models. This summary is more complicated than those in previous chapters, but again one sees that all models have something to offer. A distinguishing feature of the analyses here is that they revealed the potential for the practical integration of descriptive models.

Can predict the pull-to-center effect. Not yet assessed empirically

Can predict the pull-to-center effect and its asymmetry. Found to not predict well the size of the effect

Can predict the pull-to-center effect and its asymmetry. Not yet assessed empirically

Impulse balance equilibrium model

Prospect theory

Predictive power

Not specified. Unlike in decision under risk, unclear how to leverage heuristics to explain it

Not specified. Bounded rationality seen as inferior

Not specified. Bounded rationality seen as inferior

Cognitive processes

Usefulness of output

Outputs what practitioners want to know: order quantity. By construction outputs a distribution of orders Might well be transparent to Outputs what practitioners practitioners with some want to know: order operations training. Could quantity. Not clear how it support integration in practice, could output a distribution although mathematically it of orders might be the most challenging model Might well be transparent to Outputs what practitioners practitioners with some want to know: order operations training. Can quantity. Could output a support integration in practice distribution across retailers

Might well be transparent to practitioners with some operations training. Can support integration in practice

Transparency

Summary of the analyses of optimization and heuristic models for describing people’s newsvendor behavior

Quantal choice model

Table 5.3

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Correction heuristic

Anchoring and adjustment heuristic

Can predict the pull-to-center effect and its asymmetry. Found to predict best the size of the effect Can predict the pull-to-center effect and its asymmetry. Found to predict best the size of the effect

Predictive power

Specified: First correct the ‘optimal’ taking a range around it, and then order this range’s midpoint, aiming at ‘satisficing’

Specified: First anchor at mean demand, and then insufficiently adjust towards the ‘optimal’

Cognitive processes

Should be transparent to practitioners with, or even without, any operations training. Can support integration in practice

Should be transparent to practitioners with, or even without, any operations training. Can support integration in practice

Transparency

Outputs what practitioners want to know: order quantity. Can output a distribution across retailers

Outputs what practitioners want to know: order quantity. Can output a distribution across retailers

Usefulness of output

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Notes 1. Ford W. Harris, “How Much Stock to Keep on Hand,” Factory: The Magazine of Management 10 (1913): 240. 2. For an exception, see Tobias Stangl and Ulrich W. Thonemann, “Equivalent Inventory Metrics: A Behavioral Perspective,” Manufacturing and Service Operations Management 19, no. 3 (2017): 472–488. 3. The newsvendor problem has been studied prescriptively in operations research by Philip M. Morse and George E. Kimball, Methods of Operations Research (Cambridge, MA: MIT Press, 1951) and descriptively in operations management as reviewed by Michael Becker-Peth and Ulrich W. Thonemann, “Behavioral Inventory Decisions,” in The Handbook of Behavioral Operations, eds., Karen Donohue, Elena Katok, and Stephen Leider (New York, NY: Wiley, 2018): 393–432. An economist is credited with the first presentation of the problem, see Francis Y. Edgeworth, “The Mathematical Theory of Banking,” Journal of the Royal Statistical Society 51, no. 1 (1888): 113–127, and three others formulated the standard context for it in Kenneth J. Arrow, Theodore Harris and Jacob Marschak, “Optimal Inventory Policy,” Econometrica (1951): 250–272. According to Evan L. Porteus, Foundations of Stochastic Inventory Theory (Palo Alto, CA: Stanford University Press, 2002), virtually all stochastic inventory theory relies on the newsvendor problem. 4. Becker-Peth and Thonemann, “Behavioral inventory decisions” reviews other paradigms for behavioral inventory control, including multiple newsvendors and multiple products. For other drosophilas of behavioral operations management, such as the beer distribution game and its associated bullwhip effect, see the various chapters in Donohue et al., The Handbook of Behavioral Operations. 5. Arrow et al., “Optimal Inventory Policy”. 6. Maurice E. Schweitzer and Gérard P. Cachon, “Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence,” Management Science 46, no. 3 (2000): 404–420. An earlier study by Robert E. Hoskin, “Opportunity Cost and Behavior,” Journal of Accounting Research (1983): 78–95, has received relatively little attention. 7. For collections of studies, see Yinghao Zhang and Enno Siemsen, “A Meta-Analysis of Newsvendor Experiments: Revisiting the Pull-to-Center Asymmetry,” Production and Operations Management 28, no. 1 (2019): 140–156, and Becker-Peth and Thonemann, “Behavioral Inventory Decisions”. Some studies feature learning and training modules; for example, the newsvendor problem might be explained to participants in detail, or participants might be provided with statistical information on past demand, feedback on the profit that has been achieved in previous rounds of the experiment, and so on.

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8. This uniform distribution, and all others in experiments discussed in this chapter, are discrete-valued. That is, here only the integer numbers in the interval [1, 300] are admissible. 9. Gary E. Bolton and Elena Katok, “Learning by Doing in the Newsvendor Problem: A Laboratory Investigation of the Role of Experience and Feedback,” Manufacturing and Service Operations Management 10, no. 3 (2008): 519–538. See also Becker-Peth and Thonemann, “Behavioral Inventory Decisions”, 410–411, for a discussion of other experimental manipulations the pull-to-center effects is resilient to, including some debiasing techniques. 10. Gary E. Bolton, Axel Ockenfels and Ulrich W. Thonemann, “Managers and Students as Newsvendors,” Management Science 58, no. 12 (2012): 2225–2233. 11. The orders of all three groups were statistically significantly lower than q ∗ and not statistically significantly different from each other, and both results held for both kinds of information. 12. Zhang and Siemsen, “A Meta-Analysis of Newsvendor Experiments”. 13. Ibid. 14. Bolton and Katok, “Learning by Doing in the Newsvendor Problem”. 15. Axel Ockenfels and Reinhard Selten, “Impulse Balance in the Newsvendor Game,” Games and Economic Behavior 86 (2014): 237–247; B. Vipin and R. K. Amit, “Describing Decision Bias in the Newsvendor Problem: A Prospect Theory Model,” Omega 82 (2019): 132–141. 16. For example, Charles Darwin’s ideas of biological evolution changed dramatically after they were merged with genetics; see Theodosius Dobzhansky, Genetics of the Evolutionary Process (New York, NY: Columbia University Press, 1971). 17. Gerd Gigerenzer, Peter M. Todd and the ABC Research Group, Simple Heuristics That Make Us Smart (New York, NY: Oxford University Press, 1999), 12. Historian of economics and cognitive science Enrico Petracca has analyzed deeply the various interpretations of bounded rationality in the behavioral sciences in the backdrop of Simon’s own multitude of writings; see for example Enrico Petracca, “A Cognition Paradigm Clash: Simon, Situated Cognition and the Interpretation of Bounded Rationality,” Journal of Economic Methodology 24, no. 1 (2017): 20–40, and Enrico Petracca, “On the Origins and Consequences of Simon’s Modular Approach to Bounded Rationality in Economics,” The European Journal of the History of Economic Thought (2021): 1–24. 18. These models have been developed in psychology; see Louis L. Thurstone, “A Law of Comparative Judgment,” Psychological Review 34, no. 4 (1927): 273–286, and R. Duncan Luce, “On the Possible Psychophysical Laws,” Psychological Review 66, no. 2 (1959): 81–95; as well as economics as in Daniel L. McFadden, “Quantal Choice Analysis: A Survey,” Annals

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19. 20. 21. 22.

23. 24. 25.

26.

27. 28.

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of Economic and Social Measurement 5, no. 4 (1976): 363–390, and are also related to random utility models; see Charles F. Manski, “The Structure of Random Utility Models,” Theory and Decision 8, no. 3 (1977): 229–254. Xuanming Su, “Bounded Rationality in Newsvendor Models,” Manufacturing and Service Operations Management 10, no. 4 (2008): 566–589. Ibid., 571. Ockenfels and Selten, “Impulse Balance in the Newsvendor Game”. Ockenfells and Selten also add a ‘loss impulse’ which leads to losses counting twice as much as gains, as per the common estimate of the loss-aversion parameter λ = 2 in prospect theory (see also Chapter 3). Ockenfels and Selten, “Impulse Balance in the Newsvendor Game,” 238 (emphasis in the original). The point where the curve meets the ‘optimal’ diagonal line is located at q ∗ = 0.38. Louis Eeckhoudt, Christian Gollier and Harris Schlesinger, “The RiskAverse (and Prudent) Newsboy,” Management Science 41, no. 5 (1995): 786–794; Schweitzer and Cachon, “Decision Bias in the Newsvendor Problem with a Known Demand Distribution”; Mahesh Nagarajan and Steven Shechter, “Prospect Theory and the Newsvendor Problem,” Management Science 60, no. 4 (2014): 1057–1062. As in the impulse balance equilibrium model, this pull-to-center effect is not, strictly speaking, the same with the effect stated in (PtC), because over-ordering does not switch to under-ordering at q ∗ = 0.5. For details see Xiaoyang Long and Javad Nasiry, “Prospect Theory Explains Newsvendor Behavior: The Role of Reference Points,” Management Science 61, no. 12 (2015): 3009–3012, and Vipin and Amit, “Describing Decision Bias in the Newsvendor Problem”. A convex combination of two numbers a and b is the weighted sum w a + (1 − w)b, where 0 ≤ w ≤ 1. A common term for this literature is ‘judgmental’ forecasting. For a review, see Paul Goodwin, Brent Moritz and Enno Siemsen, “Forecast Decisions,” in Donohue et al., The Handbook of Behavioral Operations, 433–458. There is more research on behavioral forecasting than on behavioral inventory control (except for the newsvendor problem) or on the interaction of the two. For reviews of the latter two areas see Aris A. Syntetos, Nicholas C. Georgantzas, John E. Boylan and Brian Dangerfield, “Judgement and Supply Chain Dynamics,” Journal of the Operational Research Society 62 (2011): 1138–1158; Aris A. Syntetos, Inna Kholidasari and Mohamed M. Naim, “The Effects of Integrating Management Judgement Into OUT Levels: In or Out of Context?,” European Journal of Operational Research 249, no. 3 (2016): 853–863; and Thanos E. Goltsos, Aris

5

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31. 32. 33. 34.

35. 36.

37. 38. 39.

40. 41.

42.

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A. Syntetos, Christoph H. Glock and George Ioannou, “Inventory–Forecasting: Mind the Gap,” European Journal of Operational Research 299 no. 2 (2022): 397–419. Robert Fildes and Fotios Petropoulos, “Improving Forecast Quality in Practice,” Foresight: The International Journal of Applied Forecasting 36 (2015): 5–12. Goodwin et al., “Forecast Decisions”, 438–439. Amos Tversky and Daniel Kahneman, “Judgment Under Uncertainty: Heuristics and Biases,” Science 185, no. 4157 (1974): 1124–1131. https://www.un.org/en/library/unms. See also Nicholas Epley and Thomas Gilovich, “The Anchoring-andAdjustment Heuristic: Why the Adjustments Are Insufficient,” Psychological Science 17, no. 4 (2006): 311–318. For a discussion, see Becker-Peth et al., “Behavioral Inventory Decisions”. The condition w < 1 implies q > 0.5. This prediction does not always hold empirically; see Zhang and Siemsen, “A Meta-Analysis of Newsvendor Experiments”. For w = 0 the heuristic reduces to expected value maximization; and for w = 1 the heuristic predicts q = 0.5. Zhang and Siemsen, “A Meta-Analysis of Newsvendor Experiments”, 7, Fig. 1. See for example Paul Goodwin, “Integrating Management Judgment and Statistical Methods to Improve Short-Term Forecasts,” Omega: The International Journal of Management Science 30 no. 2 (2002): 127–135; Dilek Önkal and M. Sinan Gönül, “Judgmental Adjustment: A Challenge for Providers and Users of Forecasts,” Foresight: The International Journal of Applied Forecasting 1 (2005): 13–17; Goodwin et al., “Forecast Decisions”. For instance, if performance is measured by service levels, inventory managers might inflate forecasts and orders. This assumption might be especially appropriate if one is trying to predict the mean quantity ordered by a group of newsvendors on a single problem, or the mean quantity ordered by a single newsvendor across multiple problems. Similarly to the anchoring and adjustment heuristic, for the extreme value t = 0 the correction heuristic reduces to expected profit maximization, and for t = 1 the correction heuristic always predicts q = 0.5. Here are the references to the 13 studies, from top to bottom row in Table 5.2: Schweitzer and Cachon, “Decision Bias in the Newsvendor Problem With a Known Demand Distribution”; Bolton and Katok, “Learning by Doing in the Newsvendor Problem”; A. J. A. Bostian, Charles A. Holt and Angela M. Smith, “Newsvendor ‘Pull-to-Center’ Effect: Adaptive Learning in a Laboratory Experiment,” Manufacturing and Service

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Operations Management 10, no. 4 (2008): 590–608; Nicholas H. Lurie and Jayashankar M. Swaminathan, “Is Timely Information Always Better? The Effect of Feedback Frequency on Decision Making,” Organizational Behavior and Human Decision Processes 108, no. 2 (2009): 315–329; Francis De Vericourt et al., “Sex, Risk and the Newsvendor,” Journal of Operations Management 31, no. 1–2 (2013): 86–92; Sebastian Schiffels et al., “On the Assessment of Costs in a Newsvendor Environment: Insights from an Experimental Study,” Omega 43 (2014): 1–8; Ayse Kocabiyikoglu, Celile Itir Gogus and M. Sinan Gönül, “Revenue Management vs. Newsvendor Decisions: Does Behavioral Response Mirror Normative Equivalence?,” Production and Operations Management 24, no. 5 (2015): 750–761; Anssi Käki et al., “Newsvendor Decisions Under Supply Uncertainty,” International Journal of Production Research 53, no. 5 (2015): 1544–1560; Andreas Fügener, Sebastian Schiffels and Rainer Kolisch, “Overutilization and Underutilization of Operating RoomsInsights from Behavioral Health Care Operations Management,” Health Care Management Science 20, no. 1 (2017): 115–128; Yingshuai Zhao and Xiaobo Zhao, “How a Competing Environment Influences Newsvendor Ordering Decisions,” International Journal of Production Research 54, no. 1 (2016): 204–214; Tianjun Feng and Yinghao Zhang, “Modeling Strategic Behavior in the Competitive Newsvendor Problem: An Experimental Investigation,” Production and Operations Management 26, no. 7 (2017): 1383–1398; Kay-Yut Chen and Shan Li, “The Behavioral Traps in Making Multiple, Simultaneous, Newsvendor Decisions,” Working Paper (Arlington, TX: University of Texas, 2018); Yun Shin Lee, Yong Won Seo and Enno Siemsen, “Running Behavioral Operations Experiments Using Amazon’s Mechanical Turk,” Production and Operations Management 27, no. 5 (2018): 973–989. 44. For the high profit case q ∗ = 0.75 this model would pick randomly an order q from the interval [0.5, 0.75] because only then is the effect size ∗ −q s = qq∗ −0.5 = 3 − 4q in the interval [0, 1]; and for the low profit case q ∗ = 0.25 the model picks randomly an order q from the interval [0.25, ∗ −q = 4q − 1 in the 0.5] because only then is the effect size s = qq∗ −0.5 interval [0, 1]. I also tested a model where a new random number was generated for each of the 26 effect sizes in Table 5.2, and the difference in performance was negligible. 45. Mervyn Stone, “Cross-Validatory Choice and Assessment of Statistical Predictions,” Journal of the Royal Statistical Society: Series B (Methodological) 36, no. 2 (1974): 111–133. 46. Payam Refaeilzadeh, Lei Tang and Huan Liu, “Cross-Validation,” Encyclopaedia of Database Systems 5 (2009): 532–538.

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47. For the random model, the reported performance is the average over 5000 repetitions. ∗ −(1−t) 48. For example, if q ∗ = 0.75, then the top formula s = q 2q implies ∗ −1 49.

50.

51.

52.

53.

54.

55.

s = 0.75−(1−t) 2(0.75)−1 = 2t − 0.5. For definitions and evidence for these four explanations see, respectively, Schweitzer and Cachon, “Decision Bias in the Newsvendor Problem with Known Demand Distribution”; Bostian et al., “Newsvendor ‘Pull-toCenter’ Effect”; Mirko Kremer, Stefan Minner, and Luk N. Van Wassenhove, “Do Random Errors Explain Newsvendor Behavior?,” Manufacturing and Service Operations Management 12, no. 4 (2010): 673–681; Yufei Ren and Rachel Croson, “Overconfidence in Newsvendor Orders: An Experimental Study,” Management Science 59, no. 11 (2013): 2502– 2517. In Chapters 2 and 3 this outcome was a choice between risky option or the time it took to make that choice, and in Chapter 4 the outcome was the decision of accepting or rejecting an offer in a bargaining game or the time it took to make this decision. An exception might be the utilities computed by prospect theory, but these are typically not used in newsvendor experiments, and they certainly need not be presented to practitioners. See Goltsos et al., “Forecasting-Inventory”, 410, for a discussion in the realm of forecasting for inventory decision making. More generally, see the ‘Taleb-Ioannidis debate’ in the International Journal of Forecasting: Nassim Nicholas Taleb, Yaneer Bar-Yam and Pasquale Cirillo, “On Single Point Forecasts for Fat-Tailed Variables,” International Journal of Forecasting 38, no. 2 (2022): 413–422; John P. A. Ioannidis, Sally Cripps and Martin A. Tanner, “Forecasting for COVID-19 Has Failed,” International Journal of Forecasting 38, no. 2 (2022): 423–438; and Pierre Pinson and Spyros Makridakis, “Pandemics and Forecasting: The Way Forward Through the Taleb-Ioannidis Debate,” International Journal of Forecasting 38, no. 2 (2022): 410–412. For a discussion of this issue, see Konstantinos V. Katsikopoulos, Özgür Sim¸ ¸ sek, Marcus Buckmann and Gerd Gigerenzer, “Reply to commentaries on ‘Transparent Modelling of Influenza Incidence’: Recency Heuristics and Psychological AI,” International Journal of Forecasting 38, no. 2 (2022): 630–634. See for instance Syntetos et al., “The Effects of Integrating Management Judgement into OUT Levels,” 861, 862; Goltsos et al., “ForecastingInventory”. As Paul Goodwin remarked (November 2, 2022; personal communication), “this might reduce egocentric discounting of the software’s advice”.

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56. This point is made by Goltsos et al., “Forecasting-Inventory”, 407–408, for all interventions—not just behavioral ones—in inventory control. 57. See for example Herbert A. Simon, “Rational Decision-Making in Business Organizations”, Nobel Prize Lecture (8 December 1978), available at https://www.nobelprize.org/prizes/economic-sciences/1978/simon/ lecture. 58. Herbert A. Simon, “The Scientist as Problem Solver,” in Complex Information Processing: The Impact of Herbert A. Simon, eds., D. Klahr and K. Kotovsky (Hillsdale, NJ: Lawrence Erlbaum, 1989): 377. 59. Herbert A. Simon, Administrative Behavior: A Study of Decision-Making Processes in Administrative Organizations (New York, NY: Macmillan, 1957): xxv. 60. For historical analyses of how this happened see Petracca, “A Cognition Paradigm Clash”, and Petracca, “On the Origins and Consequences of Simon’s Modular Approach to Bounded Rationality in Economics”, as well as references therein. 61. Peter M. Todd and Gerd Gigerenzer, “Bounding Rationality to the World,” Journal of Economic Psychology 24, no. 2 (2003): 143–165. 62. See for example George J. Stigler, “The Economics of Information,” Journal of Political Economy 69, no. 3 (1961): 213–225; and Thomas J. Sargent, Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures (New York, NY: Oxford University Press, 1993). 63. Daniel Kahneman, “Maps of Bounded Rationality: Psychology for Behavioral Economics,” American Economic Review 93, no. 5 (2003): 1449– 1475. 64. Konstantinos V. Katsikopoulos, “Bounded Rationality: The Two Cultures,” Journal of Economic Methodology 21, no. 4 (2014): 361–374. 65. Herbert A. Simon and Allen Newell, “Heuristic Problem Solving: The Next Advance in Operations Research,” Operations Research 6, no. 1 (1958): 1–10; Richard Bellman, “On ‘Heuristic Problem Solving’ by Simon and Newell”, Operations Research 6, no. 3 (1958): 448–449; and Herbert A. Simon and Allen Newell, “Reply: Heuristic Problem Solving,” Operations Research 6, no. 3 (1958): 449–450. 66. Simon and Newell, “Heuristic Problem Solving,” 5. 67. Simon and Newell, “Heuristic Problem Solving,” 7. 68. AlphaGo, AlphaGo Zero, and AlphaZero are machine learning algorithms, which since the late 2010s, have been beating the human world champions in games such as chess, Go and shogi. See David Silver et al., “Mastering the Game of Go Without Human Knowledge,” Nature 550, no. 7676 (2017): 354–359; and David Silver et al., “A General Reinforcement Learning Algorithm That Masters Chess, Shogi and Go Through Self-Play,” Science 362, no. 6419 (2018): 1140–1144.

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69. For a critical perspective on these, and other, successes of machine learning, see Konstantinos V. Katsikopoulos et al., Classification in the Wild: The Science and Art of Transparent Decision Making (Cambridge, MA: MIT Press, 2020): 81–85; and Gerd Gigerenzer, How to Stay Smart in a Smart World (London, UK: Penguin, 2022). 70. Ibid. It seems that such claims are more prevalent in areas other than AI itself. When Marc Canellas and I submitted a critical piece to AI Magazine, pointing out the limits to predicting human behavior with ‘big data analytics’, the reception was considerably more positive than what we have experienced in our respective fields of business and law; see Konstantinos V. Katsikopoulos and Marc C. Canellas, “Decoding Human Behavior with Big Data? Critical, Constructive Input from the Decision Sciences,” AI Magazine 43, no. 1 (2022): 1–13. On the other hand, AI capabilities are indeed improving fast, and as this book is being written, one might be impressed by the accomplishments of the Generative PreTrained Transformer (GPT) 3.5 (https://beta.openai.com/docs/modelindex-for-researchers), even if they do not refer to making decisions under uncertainty (and as this book is being proofed, we have gotten the even more impressive ChatGPT, although it also does not deal with uncertainty) For an interesting investigation of the judgment and decision performance of GPT-3 in classic lab tasks from cognitive psychology, see Marcel Binz and Eric Schulz, “Using Cognitive Psychology to Understand GPT-3,” Proceedings of the National Academy of Sciences, in press. 71. For an entertaining taste of that, see Richard Bellman, Eye of the Hurricane (Singapore: World Scientific, 1984). 72. Bellman, “On ‘Heuristic Problem Solving’ by Simon and Newell,” 450 (emphasis added). 73. Until his untimely death, Bellman remained unconvinced of AI— see Richard Bellman, An Introduction to Artificial Intelligence: Can Computers Think? (Stamford, CT: Thomson, 1978); and Bellman, Eye of the Hurricane. For a positive assessment of the successes and potential of a synthesis of Simon’s AI and heuristics, see Jochen Reb, Shenghua Luan and Gerd Gigerenzer, Smart Management: How Heuristics Help Leaders Make Good Decisions in an Uncertain World (Cambridge, MA: MIT Press, in press), who call this synthesis psychological AI .

CHAPTER 6

Decision Under Uncertainty

Mary Anne Evans was a poet, novelist, and writer known by her pen name George Eliot. In Felix Holt, she explores the intricacies of social and political life in nineteenth-century England. Even in situations where the rules are supposed to be well-defined, as in chess, Eliot sees the complications that can be brought about by human nature1 : Fancy what a game of chess would be if… you were not only uncertain about your adversary’s men, but a little uncertain also about your own… if your pawns, hating you because they are pawns, could make away from their appointed posts that you might get checkmate on a sudden. You might be the longest headed of deductive reasoners, and yet you might be beaten by your own pawns. You would be especially likely to be beaten if you depended arrogantly on your mathematical imagination… Yet this imaginary chess is easy compared with the game a man has to play against his fellowmen with other fellowmen for his instruments.

Trying to work, interact, or simply co-exist with other people generates uncertainty. This kind of uncertainty cannot be meaningfully reduced to probability. For example, can you pin down probabilities for the following events?—A client backs away from a handshake agreement a company was sure they had in the bag; a middle-level manager picks up the phone to call the client without consulting with the boss; the boss is upset at the

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manager until it is revealed that the client signed the agreement, at which point all are happy. If an academic leaves the lab to work with other people and institutions in the wild,2 she has to face the challenge of making decisions under non-probabilistic—often called radical3 —uncertainty. Approaches based on stochastic modeling may be on shaky grounds. After decades of distinguished modeling work, Richard Bellman asserted that the function of mathematics in the real world is to avoid responsibility and that in most situations we might as well toss a coin.4 Exaggeration? Perhaps, to a degree. But Bellman was not alone in having such ideas. Foundational thinkers of operations research, including Russell Ackoff, Jonathan Rosenhead, and John Mingers5 criticized what they saw as the over-mathematization of models for the analysis of operations, and emphasized soft skills and communication with decision makers in plain and precise language. The soft and behavioral operations research toolboxes do include formal tools, such as process flowcharts and causal loop diagrams,6 but not all tools have to come with opaque equations (e.g., fast-and-frugal trees can be employed in a mathematical way, but also as only a graphical tool). In this view, models might be useful, sometimes necessary, but they should be easy to understand and use, and transparent to decision makers. As in the quote from Felix Holt, over-reliance on mathematics, at the expense of using common sense about human behavior, can be a trap. The field of behavioral operations heeds these ideas. In the First Summer School on Behavioural Operational Research at Aalto University in 2016, Alberto Franco said: “In the beginning it is all about models, models, models… in the end it is all about talk, talk, talk…”.7 The taxonomy of behavioral operational research by Martin Kunc and his colleagues includes operational work beyond modeling, and Elliot Bendoly and his colleagues in their handbook of behavioral operations management emphasize experiential learning over pure model-based analysis. Cognitive Operations focuses on mathematical modeling. In Chapters 2–5 we saw models that cover a spectrum from simple sequential heuristics to more complex stochastic optimization. In the present chapter, we venture out of this mathematical comfort zone, and consider simple rules that have been developed by talking to practitioners rather than by relying on axioms or statistics. Some of these rules can be cast in

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mathematical form whereas others remain verbal, though still precise. In this chapter, Cognitive Operations has it both ways. More specifically, the first section analyzes a prototype of decision making in the wild, the case of a peace-keeping operation in Afghanistan. The research goal is to describe the behavior of soldiers guarding NATO checkpoints. A very simple rule is presented which as the minimax and maximax rules of Chapter 1 relies on a single attribute—is the vehicle approaching the checkpoint complying with the soldier’s instructions? I also explore the feasibility of some optimization models from decision and game theory (Chapters 3 and 4). The next section considers how successful organizations manage to make their supply chains flexible and robust in the face of serious and uncertain disruptions. Particular problems, such as supplier sourcing, can be addressed by simple heuristics such as fast-and-frugal trees (although the trees used here do not make a yes/ no classification decision but suggest a course of action that might not always be exact). General insights on managing supply chain uncertainty are summarized in a verbal four-step guide, which encompasses both optimization and heuristics. The chapter also serves as a prelude to the next chapter which takes a broader view of cognitive modeling, and more generally cognitive and behavioral science in operations. A theme running through the present chapter, which differentiates it from the previous ones, is considering together descriptive as well as prescriptive aspects of decision making. In this vein, I also review the theory of ecological rationality developed by Gerd Gigerenzer, Peter Todd, and their colleagues.

6.1

A Peace-Keeping Operation: Compliance Heuristic

As this book is being written, multiple wars and other conflicts are going on in the world. A common mitigating response in such situations, even in areas of relatively little tension, is the use of checkpoints. Checkpoints are physical entities designed to control the flow of vehicular or pedestrian traffic. Such control is crucial for ensuring some peace. Typically, checkpoints are guarded by military personnel. The job of the soldiers is to classify oncoming traffic as civilian or hostile. Making such classifications correctly is a matter of life and death for everyone involved. If soldiers correctly infer that the occupants of an oncoming vehicle or approaching pedestrians are civilians posing no

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threat, then soldiers would make sure that the civilians are searched and then continue their travel unharmed. On the other hand, if the vehicle occupants or pedestrians are deemed to potentially be suicide attackers, or posing another type of serious threat, soldiers would escalate the use of force and this can include injuring, or even killing, the approaching people even if they are innocent. And conversely if suicide attackers or other dangerous individuals are not spotted, then the soldiers may be injured or killed. The above decision process includes substantial uncertainty. Civilians may approach checkpoints too fast and make themselves appear as threats because they are nervous or do not understand the soldiers’ commands, and think they can go straight through.8 Civilians may also try to speed through a checkpoint if they doubt that it is a genuine one.9 Analogously, soldiers can never be sure if a vehicle or a person behaving erratically is dangerous or confused, or if it is indeed harmless when it behaves friendly. Can the probabilities of such events be computed or estimated? If not, how can a decision be made? A few years back, my then doctoral student Niklas Keller and I attempted to provide some answers.10 The literature on peace-keeping operations does not present probabilities, at least not any that practitioners use.11 Rather, the guidance provided to checkpoint guards is qualitative, avoids the discussion of outcomes and probabilities, and emphasizes decisions, for which it shifts the burden to those on the ground. For example, the card disseminated to NATO personnel in the 1999 Operation Kosovo Force reads12 (emphasis added): “When the situation permits, use a graduated escalation of force…” The soldiers are the ones who decide when and how to escalate force, and they have to do so without a probability calculus. So, what do they do? Data. Keller was able to secure data from real checkpoints in Afghanistan that had recorded critical (non-routine) encounters between soldiers and oncoming vehicles from 2004 to 2009. The data could be extracted from official reports made publicly available in 2010 by Wikileaks.13 Can this data be used to estimate probabilities at checkpoints? Before answering, let us first look at a relevant excerpt of a report (redacted): At XXXX TF (task force) Kandahar reports XXXXXXXXXXXXXXX section injured 2xLN’s (local nationals) at XXXXXXX in XXXXXX district of XXXXX province. A white Toyota corolla [sic] with 2xLN’s in it was

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approaching too fast, FF (friendly forces) told vehicle to stop a number of times, vehicle failed to stop. FF engaged vehicle wounding 1x LN in car and 2nd LN (child) ran into mosque wounded.

This excerpt tells us the attributes of the encounter, the soldier’s decision, and the ensuing outcome. There are two attributes, namely that (i) the car has two occupants, and (ii) the car did not comply with soldier’s instructions. The decision of the soldier was to shoot at the car, after presumably classifying it as possibly hostile. The outcome was two injured people, which represents an incorrect decision because a subsequent search of the car—not discussed in the excerpt above—showed that there was no explosive device in the vehicle. Originally, 1087 reports were available. Two independent raters coded the reports and inferred the attributes, decisions, and outcomes in each report. Because the raters could not agree in 27 cases, the number of reports eventually analyzed was 1060. Table 6.1 shows the decisions, which together with the truth, determine the outcome.14 As in all binary classification tasks, there are four possible outcomes: a hit (the soldier correctly identifies a hostile vehicle as hostile); a miss (the soldier incorrectly identifies a hostile vehicle as civilian); a false alarm (the soldier incorrectly identifies a civilian vehicle as hostile, denoted as FA); and a correct rejection (the soldier correctly identifies a civilian vehicle as civilian, denoted as CR). Table 6.1 shows that unaided decision making was overall accurate (in 923 out of 1060 encounters) but also had some obvious shortcomings. First, there were zero hits and seven misses, that is, none of the seven suicide attackers were identified. This resulted to all checkpoint personnel dying in these encounters. Second, there was a considerable number of false alarms (130 FA). These resulted to 204 civilians being injured or Table 6.1 Analysis of the soldier classifications in non-routine encounters at Afghanistan checkpoints between 2004 and 2009 (from Keller and Katsikopoulos 2016)

Hostile Civilian

Hostile

Civilian

0 hits 7 misses

130 FA 923 CR

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killed. Why did these errors happen? Could an aid be designed to avoid them in the future? A descriptive model can answer the first question and a prescriptive model the second one. Exploring optimization. The descriptive and prescriptive analyses of the checkpoint data exhibit challenges for the optimization approach. Building optimization models for a decision under uncertainty typically involves reducing this decision, in one way or another, to a decision under risk or to a strategic interaction. Let us try to do the former for the soldier’s task. The logic of expected utility theory (Chapter 2) suggests that the soldier should classify an approaching vehicle as hostile if and only if the following condition holds, where p(·) and p(·) denote the probabilities and utilities of the four possible outcomes. p(hit)u(hit) + p(F A)u(F A) ≥ p(miss)u(miss) + p(C R)u(C R). (6.1) How to fill in the values of the parameters in condition 6.1? One possibility is to use the data from Table 6.1. Of course, this data refers only to non-routine encounters in Afghanistan checkpoints, so it must be taken with a grain of salt. For example, the estimates p(hit) = 0 and p(miss) = 1 can seem suspect. Assuming one wishes to proceed, the 923 130 and p(C R) = 1,053 . Plugging these Table 1 data also imply p(F A) = 1,053 four estimates in condition (6.1) and performing the algebra, the condition can be rewritten as below, where we assumed that u(C R) = 0 since neither soldiers nor civilians are harmed in this case, and that u(miss) and u(F A) < 0 because soldiers and civilians will respectively be harmed in these cases. u(miss) ≥ 0.12. u(F A)

(6.2)

Condition 6.2 seems close to providing an answer, but it is actually very far from doing so. The condition says that for the soldier to classify a vehicle as hostile, she must value her life, which would be lost in the case of a miss, minus the value of the suicide attacker which would also be gained in this case,15 at least 0.12 times more than she values the life of a civilian which would be lost in the case of a false alarm. Does she? Should she? These are absurd questions. Trying to answer them shows the limits of the expected utility approach. There are two common responses to the above criticism. First, one might say that of course nobody wants to explicitly weigh the value of

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one life against that of another life, but implicitly the choices that soldiers make correspond to exactly such relative evaluations. Leaving aside the fact that this is an unfalsifiable thesis, it still fails to advise the soldier what to do before the encounter. The second response is to note that not all classifications of an oncoming vehicle as hostile must result to civilians losing their live(s); soldiers are sometimes able to make civilians comply by incurring some injuries, often by shooting at the car. In this case, u(F A) would arguably be clearly smaller in absolute value than u(miss), and (6.2) would lead to a decision strategy—the soldier should classify all vehicles as hostile. But this strategy is too extreme. And importantly the response itself reveals that the space of decision options if one insists on modeling the checkpoint problem as a decision under risk as above is not sufficiently rich: If the soldier would classify all vehicles as hostile, how will she know in which cases to shoot at drivers and in which cases to shoot at cars ? Two optimization approaches for modeling the checkpoint problem more richly are game theory (Chapter 4), and sequential decision making under risk, which have not been covered in this book. Both approaches might face the same issues with a decision under risk—it is not clear how to estimate the values of the parameters,16,17 or the resulting decision strategies are too extreme, descriptively or prescriptively (see Appendix). Simple heuristics: Compliance. Unlike optimization, the simple heuristics approach can scale to decisions under uncertainty. As in decisions under risk, one can first consider the attributes available to the decision maker and then combine them in simple ways, such as ordering or adding them. Recall from the report excerpt that two attributes relevant for the soldier are whether the vehicle is complying, and how many occupants are in the vehicle. The compliance attribute is very informative for descriptive purposes and the occupancy attribute is very effective for prescription. More specifically, in a fitting exercise, the compliance attribute was the only attribute Keller and I identified that was mentioned in all 1053 reports involving civilians. Furthermore, in 1020 of these cases, the soldier escalated force when the vehicle failed to comply, that is, did not slow down or stop. And similarly, as long as a vehicle complied, force was never increased. In sum, the following heuristic can largely summarize soldier behavior.

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Compliance heuristic: Increase the level of force only if the oncoming vehicle is not complying.

As the minimax and maximax heuristics (Chapter 2), the compliance heuristic can be represented as an extremely simple fast-and-frugal tree; see Fig. 6.1. Unlike the optimization models considered above and in the Appendix, the compliance heuristic does not classify all vehicles as belonging to the same category. But still, this attempt at adaptive decision making did not prevent the 204 observed civilian casualties. One might suspect that the heuristic is too simple in that, when it is applied repeatedly, it can lead the soldier to over-escalate force. Semi-structured interviews with experienced practitioners, such as armed forces instructors and combat-experienced personnel, corroborated this hypothesis.18 These experts suggested the use of the occupancy attribute so as to identify civilians before the compliance attribute is activated. The idea is that it is highly unlikely that multiple suicide attackers occupy the same vehicle as this would be a waste of resources for the insurgent side; indeed, after the fact we found that all 7 recorded suicide attacks involved one person in the car. Keller and I operationalized this idea19 in the fastand-frugal tree in Fig. 6.2: The tree asks first if there is more than one occupant in the vehicle, and if so, the vehicle is immediately classified as civilian. If there is only one occupant in the vehicle, the compliance attribute is used next, and it is now applied to a smaller and potentially more dangerous subset of vehicles. A catch-all attribute, which includes any other indications of a possible threat (e.g., intelligence suggests that a particular approaching vehicle might be dangerous), is used last. How well does this tree perform? Applied after the fact to the 1053 encounters involving civilians, it leads to 78 classifications as hostile. Note that, by construction, all of these vehicles include just one occupant, the

Fig. 6.1 The compliance heuristic represented as a fast-and-frugal tree

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Fig. 6.2 A fast-and-frugal tree for classifying vehicles approaching a checkpoint as civilian or hostile (Adapted from Keller and Katsikopoulos 2016)

driver. Thus, in the worst-case scenario that the soldier could not make the driver comply without injuring or killing him, there would have been 78 civilian casualties, had the fast-and-frugal tree been used in Afghanistan checkpoints. In this section, despite the lack of some information (no hits have been recorded in the available non-routine incidents), a formal aid for decision makers could be induced by consulting with practitioners. But expert wisdom cannot always be captured formally. The next section presents more informal models.

6.2

Making Supply Chains Flexible and Robust

On the 11th of March in 2011, Japan recorded a powerful earthquake. The T¯ohoku earthquake spawned a tsunami that reached heights of 40 meters and traveled at 700 kilometers an hour. Besides the human toll, the infrastructure damage caused disruptions in supply chains that were felt throughout the commercial world. For example, Kureha, a company meeting 70% of the demand for a polymer needed for manufacturing batteries for mobile devices prior to the tsunami, had to curtail its delivery

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capacity. As a consequence, tech giants such as Apple and Samsung could not deliver on schedule. With the benefit of hindsight, it seems clear that original equipment manufacturers should not rely on a single supplier. Well then, how many suppliers should a manufacturer have—two, three, the more the better? And how should these suppliers be chosen? Finally, how much work should each supplier be asked to do? Ça˘grı Haksöz has investigated such questions by looking into successful practices in his native Turkey,20 and elsewhere.21 The following three simple rules allow supply chains to become more flexible (which here means able to respond adaptively to adverse events such as the Japanese tsunami) as well as more robust (that is, to be little affected by adverse events to begin with), while using few resources. Dual (or multiple) sourcing. Kordsa Global is a leader is producing industrial fabrics and reinforcement materials in nine countries. Haksöz cites Kordsa’s head of procurement, as employing dual sourcing (two suppliers): We prefer to have suppliers at different geographic areas such as one in Europe and one in the US or Asia. There are tax and customs benefits for such an arrangement, as well as proximity considerations. We can mitigate natural disaster risks better in such a portfolio, that is, when a hurricane hits the US shores, Europe is safe; likewise, when the Rhine River has water shortage issues in Europe, the American supplier will stay unaffected.

Dual sourcing can be determined by using supplier attributes in more involved ways than only relying on the location attribute as in the quote above. For instance, a ten-billion-dollars US manufacturer of wireless transmission components had an assembly plant in China and a second one in Mexico because the Chinese plant had lower costs and the Mexican plant had shorter delivery times.22 Theoretical analyses suggest that such combinations of a low-cost/low-speed supplier and a high-cost/highspeed supplier can generate essentially all of the value of a full supplier portfolio.23 More generally, Christopher Tang and Brian Tomlin have provided analytical arguments for why dual sourcing might just hit the sweet spot that avoids the cost and complexity of coordinating with too many suppliers while obtaining most of the benefits of multiple sourcing.24

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1/N . If two suppliers (or more) have been identified, how should we allocate work to each one of them? Recall from Chapter 3 the 1/ N heuristic for investment in a portfolio of N assets, wherein wealth is allocated equally across the assets. The analog here is to allocate work equally to the suppliers. Of course, in practice one cannot expect that supply work is allocated perfectly according to 1/N . Here’s what the Turkish tire manufacturer Brisa does25 : We have long term relationships with raw material suppliers. We do not purchase in the spot market. We need approved suppliers to work with. Once we have a number of suppliers, we use a dual sourcing strategy. That is, we procure 60% from supplier A and 40% from supplier B in order to manage supplier related risks. Our main goal is to establish fruitful long term strategic alliances with suppliers, not just procure for only a few years.

The reason for Brisa diverging from the 50-50 allocation is not carelessness or computational error. Rather it is a concern about the supplier’s situation, so that the relationship can thrive. If a supplier is big or needs work, give them more than 50%; if a supplier is small or over-extended, give them less than 50%, and how much more or less than 50% to give would depend on the context. Haksöz points out that Li and Fung, a worldwide matchmaker of manufacturers and suppliers, in fact suggest numbers.26 The 30–70% rule. Li and Fung propose that the work allocated to each supplier should range from 30 to 70% of their capacity. The lower bound aims at sustaining the commitment of both suppliers and manufacturers, and the upper bound aims at leaving some supplier capacity free so that they can engage with other manufacturers, and potential mutual dependency be better controlled. The two numbers are of course indicative and Li and Fung are clear that they are the outcome of trained intuition, not labored analysis. Can one put the three simple rules discussed in this section (dual or multiple sourcing, 1/N , 30–70%) together in a simple model for describing and prescribing successful practice in supplier sourcing? Ça˘grı Haksöz, Gerd Gigerenzer, and I suggested the fast-and-frugal tree below. Unlike the trees presented elsewhere in the book, the tree of Fig. 6.3 is not making yes/no classification decisions, but suggests courses of action,

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Fig. 6.3 A fast-and-frugal tree that puts together the three simple rules discussed in this section, for describing and prescribing successful practice in supplier sourcing (Adapted from Haksöz et al.). It is assumed that supply chain managers go through the tree repeatedly until the bottom-left exit is reached

which might not always be exact but purposefully leave room for any discretion that supply chain decision makers might wish to exercise. Sourcing suppliers is one element of uncertainty in supply chains that necessitates effective decision making. A host of additional decisions need to be made—for example the inventory decisions in Chapter 5—and the general question is when that should be done by optimization and when by heuristics. The theory of ecological rationality provides quantitative answers and qualitative insights that are discussed in the next section. This section also integrates the insights into the management of supply chain uncertainty, via a verbal four-step process.

6.3

Ecological Rationality

A basic principle of operations modeling is that an optimization model necessarily achieves the best possible performance only if the assumptions on which it is based are valid in the real world. But this principle is often forgotten and optimization models are pronounced optimal without empirical assessment, as illustrated in one of Russell Ackoff’ oft-repeated ‘fables’27 : A very large intersystem distribution problem was modeled as a linear programming (LP) problem, and its optimal solution was derived; the argument offered for implementing this solution was that its performance was superior, according to the LP model, to that of any other solution.

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It is crucial to empirically compare the performance of optimization models and alternatives. This is standard practice in model-based research areas which overlap with operations such as forecasting and machine learning. Some work in operations which relies on these areas, such as credit scoring, has developed a tradition of comparing the performance of optimization and heuristic models on real—also called natural—datasets.28 But generally decision making research in operations assumes that optimization is automatically superior to simple heuristics. This is curious because for decades forecasting and machine learning, and earlier psychometrics, have found that simple models can sometimes make more accurate decisions than optimization.29 The present section surveys such evidence. The research question is not if a simple approach can beat a more complex one, but rather: Under which conditions does simple beat more complex, and vice versa? This is the core question of the theory of ecological rationality. In a major but still somewhat neglected contribution, Gerd Gigerenzer and Peter Todd contrast the idea of ecological rationality to the standard logical rationality of decision theory, as in expected utility theory and game theory. Ecological rationality does not aim to satisfy all types of internal logical consistency but rather champions the match of the decision method with the environment in which the decision is taken. This does not mean that ecological rationality accepts illogical reasoning such as holding that a statement and its negation can both be true, or that it espouses elementary mistakes such as 1 + 1 = 3. But a heuristic can occasionally violate axioms of decision theory, such as transitivity, and still make accurate decisions—lexicographic heuristics are a case in point. Matching the decision environment is key to making right decisions. For example, in environments where an attribute exists that is much more informative than all other attributes, deciding based on this single attribute may be correct most of the time, as in checkpoint decisions made based on the occupancy attribute. And conversely in environments where no such attribute exists, single attribute or lexicographic heuristics might have poor accuracy. Ecological rationality can be used to both describe and prescribe human decision making. In this book, we have seen that different optimization models and simple heuristics are descriptively superior in different environments—for example, the priority heuristic predicts human choices under risk more accurately than prospect theory (Chapter 3), and prospect theory can predict the asymmetry of the

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pull-to-center effect in inventory ordering whereas the anchoring and adjustment and correction heuristics cannot (Chapter 5). Psychologists have dedicated decades in uncovering conditions under which people use simple heuristics or more complex models such as linear regression; see for example a special issue in the journal Judgment and Decision Making edited by Ben Newell and Arndt Bröder.30 It has been found that most people use heuristics most of the time if a decision must be made quickly, information is expensive (financially or cognitively) to gather, or a single/ few attributes of the problem strongly point towards an option. Most of this work has been done in the lab, but there is also converging evidence in the wild.31 This section focuses on applying ecological rationality to prescriptive decision making. That is, the section presents evidence on the relative performance of simple heuristics and more complex optimization models, and theoretically explains this evidence.32 Evidence: Relative model performance. A number of studies have looked at specific decisions and single datasets, as in the checkpoint situation. An issue with such work is that it is not clear whether the results represent isolated incidents or even cherry picking. More comprehensive answers have been given in collections and reviews of studies.33 Here I outline four studies that included multiple datasets.34 First, Jean Czerlinski and her colleagues studied 20 datasets from the fields of biology, economics, environmental science, demography, health, psychology, and transportation.35 The average number of options in a dataset was 67, and the authors considered all choices between two options. The task was to identify the option with the higher criterion value (e.g., in an economics dataset, where the two options were professorships in Universities, the objective was to choose the professorship with the higher salary). Czerlinski and colleagues used 50% cross-validation to compare the predictive accuracy of linear regression, a lexicographic heuristic called take-the-best , and tallying 36 a heuristic that compares two options by comparing the sum of each option’s attribute values (after these values are scaled appropriately). On average, the accuracy of take-the-best was 72%, of tallying 69%, and of linear regression 68%.37 Next, Laura Martignon and her colleagues38 compared the predictive accuracy of two versions of fast-and-frugal trees with logistic regression and Breiman’s decision trees (Chapters 2 and 3). The authors used 30 classification datasets from the UC Irvine Machine Learning Repository. For example, in one dataset the task was to use a patient’s symptoms to classify the patients as having high or low risk of heart disease. The

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size of the training set was small (15% of whole dataset), medium (50%), or large (85% of the dataset), and it had an effect: The best-performing optimization model outperformed the best-performing heuristic for the large training set by 82% vs. 78%, but the difference shrank to 76% vs. 75% for the small training set. Third, Özgür Sim¸ ¸ sek employed the 20 datasets of Czerlinski and added 31 more.39 She used a state-of-the-art variant of linear regression (elastic net regularization). For those datasets with fewer than 1000 data points, all training sets equalling the whole dataset minus one datapoint were used, whereas larger datasets were split into 1000 folds and models were trained in all possible sets of 999 folds. The regularized regression outperformed the most accurate lexicographic heuristic just by 79 to 78%. And finally, Jan Malte Lichtenberg and Sim¸ ¸ sek used a similar database to her study, with 60 datasets, and compared the performance of tallying and variants, comparing them with optimizing models such as regularized regressions and random forests.40 The task was to estimate the criterion value of options, and model performance was measured by the root mean squared error (difference) between the true criterion value and modelestimated criterion value. The best optimizing model had an average error of 0.71, whereas tallying scored 0.79. The results varied considerably across datasets, with no single heuristic performing well across all datasets, but a heuristic that performed well existing in every dataset. In sum, one can conclude that the performance of simple heuristics and optimization models is not very different on the average, but this result can change considerably across datasets. It is thus important to develop a theory of when to use one approach and when the other. Theory: The bias-variance decomposition. Three decades ago, applied mathematician Stuart Geman and his colleagues derived a decomposition of the error of a model in prediction.41 About two decades later, initially Gerd Gigerenzer and Henry Brighton, and afterward Özgür Sim¸ ¸ sek, showed that the equation of Geman and colleagues could be used to organize the theoretical results of ecological rationality.42 To see how, let us first present the equation. Consider a task of estimation, sometimes also called regression. The goal is to use a training set T —consisting of known pairs (ai , vi ) where ai are the attributes of option i and vi is the criterion value of the option— to derive a model f (a, T ) for predicting the criterion value v of any new option in a test set, based on its attribute values a. It is reasonable to

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  measure prediction error by E T (v − f (a, T ))2 . It turns out that this error is given by the following equation43 :   E T [(v − f (a, T ))2 ] = E T [ f (a, T ) − E T [v|a]]2 + E T { f (a, T ) − E T [ f (a, T )]}2 + E T [(v − E T [v|a])2 ]

(6.3)

Equation (6.3) decomposes the prediction error into three terms. The term in the bottom line of (6.3) is the irreducible error E T [(v − E T [v|a])2 ] that no modeler can do anything about since it is independent of the model f (a, T ); it is the variance of v given a. The two top terms in the right-hand side of the equation are determined by 2 the model; more precisely they are the bias  E T [ f (a, T ) −44E T [v|a]] , and 2 the variance E T { f (a, T ) − E T ( f (a, T )} of the model. How does the bias-variance decomposition of the prediction error help in comparing simple heuristics and optimization models? To garner the insight, note first the following: Typically bias and variance are negatively correlated. For example, a model with no parameters (i.e., always predicting the same constant), would have zero variance but typically high bias, whereas a mathematically flexible polynomial with many parameters can have essentially zero bias but would also tend to have high variance. Now, recall that the heuristics of this book have zero or one parameters that are used in a simple way, whereas the optimization models have multiple parameters that enter quite flexible forms. Thus, one might expect that typically simple heuristics have low variance and optimization models have low bias. The unknowns are the bias of simple heuristics and the variance of the optimization models. That is, we can state the following two organizing principles of ecological rationality45 : When simple heuristics have low enough bias, they outperform optimization models. When optimization models have low enough variance, they outperform simple heuristics .

A number of conditions emanate from these two principles. Consider the first conditions for the bias of heuristics. When simple heuristics have low enough bias. In a line of analytical results that can be couched in the language of multi-attribute choice, researchers such as Robin Hogarth and Manel Baucells have assumed that

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an option’s criterion value v is a linear function of its attribute values ai ,  46 There are two v = w a i i , where wi , ai ≥ 0 and w1 ≥ w2 ≥ . . .. i conditions that guarantee that, if attributes are binary, the lexicographic heuristic which order attributes in decreasing order of their weights wi correctly compares any number of options according to their criterion ¸ sek concluded,48 that under value.47 Such results suggest, as Özgür Sim¸ these conditions, lexicographic heuristics may not introduce too much bias. The first condition, non-compensatoriness, has been presented in  w for all i, as in the example w1 = 4, w2 = 2 Chapter 4: wi ≥ k k>i and w3 = 1. This condition expresses that the first attribute a1 dominates the other two attributes a2 and a3 put together. More generally, each attribute dominates all attributes that would be inspected after it. Why is non-compensatoriness useful for lexicographic heuristics? Say that there are two options A and B, each with three attributes, and respective value vectors (1, 1, 0) and (0, 1, 1); and the attribute weights are w1 = 4, w2 = 2 and w3 = 1. Our lexicographic heuristic chooses option A (because 1 > 0 for a1 , the attribute inspected first). This is the correct choice because the criterion value of A is 6 and it is 3 for B. More generally, it can be proven49 that non-compensatoriness guarantees that there exists a dominant attribute that makes the correct choice, where our lexicographic heuristic always chooses based on this dominant attribute. The second condition that guarantees zero bias for our lexicographic heuristic that order attributes in decreasing order of their weights wi is the following: There is an option that achieves the maximum, over all options, values of  ak for all i. (6.4) k≤i

Condition (6.4) also expresses dominance, in the sense that one option has higher sums of attribute values than all other options. Because this holds for all cumulative profiles (a1 , a1 + a2 , a1 + a2 + a3 , . . .), the condition is called cumulative dominance.50 Note that unlike noncompensatoriness, cumulative dominance operates in the space of options, not in the space of attributes.

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Why is cumulative dominance useful for lexicographic heuristics? For similar reasons with why non-compensatoriness is. Consider the same example as before—there are two options A and B with respective value vectors (1, 1, 0) and (0, 1, 1) and the attribute weights are w1 = 4, w2 = 2 and w3 = 1. Condition (6.4) holds because 1 > 0 (for i = 1), 1 + 1 > 0 + 1 (for i = 2) and 1 + 1 + 0 = 0 + 1 + 1 (for i = 3); option A is called a cumulative dominant option. As said above, our lexicographic heuristic chooses A, which is right. More generally, it can be proven that cumulative dominance guarantees that a cumulative dominant option has the highest value, and that our lexicographic heuristic always chooses a cumulatively dominant option.51 Do dominant attributes and options occur in the wild? An analysis of 51 natural datasets found that they do.52 For example, across binary or binarized datasets, a dominant attribute occurred 93% of the time and a dominant option 87%. In a sense, the cases of dominant attributes and options represent easy decision tasks: In both cases, there exists, respectively, a perfectly informative attribute and a clearly superior option—the decision maker has to identify those and apply the right simple heuristic. Conversely, if dominant attributes and options do not exist or cannot be identified, then more involved analyses are needed, and this is the province of optimization models. Furthermore, as announced above, there is another class of conditions that favors optimization. When optimization models have low enough variance. Optimization models are typically information-greedy and perform very well when given high quality information. Using the bias-variance decomposition lens, such information leads to less variance in the estimation of the parameters of optimization models. One scenario of high quality information requires (i) high volume of data, sometimes referred to as abundant information,53 and (ii) a stable process that generates the data.54 Note that both conditions have to obtain; in other words, big data is not necessarily of high quality.55 Conversely, when information is scant 56 or the data-generating process changes and this is not detected,57 optimization models tend to have higher variance, and it makes more sense to use simple heuristics. Such decision tasks can be dubbed difficult. Table 6.2 summarizes the above results about the best-performing family of methods for each type of task.

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Table 6.2 Best-performing family of methods for each type of task Type of task

Best-performing family of methods

Easy (e.g., there is a dominant option or attribute) Difficult (e.g., scant information or undetectable change in data-generating process) Other (e.g., there are no dominant options or attributes; abundant information and stable data-generating processes)

Simple heuristics

6.4

Simple heuristics

Optimization models

Summary and a Guide

In this chapter, we saw some modeling challenges in decision making under uncertainty. In the checkpoint example, meaningful optimization models could not be built, and a simple heuristic had to be built based on non-statistical, qualitative interview information. In supplier sourcing, successful practice could be summarized by a fast-and-frugal tree, but this tree does not make clear classifications, rather it makes non-exact suggestions for action. A flurry of further examples, from management and leadership, has been gathered by Jochen Reb and his colleagues.58 Models for decisions under uncertainty cannot always count on the clarity present in other kinds of decision making, and thus models here had to be more verbal than models in other chapters. Still, as said, verbal modeling does not have to mean vague or sloppy, and it can be effective. The insights of this chapter can be put together in the following four-step guide for managing supply chain uncertainty.59 1. Ensure that your company does not behave defensively (e.g., ‘we have always used this software, for which we pay expensive technical support’ or ‘we have always trusted our gut feelings, and that works fine’), but remains open to adopting simple heuristics or optimization models, depending on the task at hand. 2. Identify the type of the task: Is it easy, difficult or other (see Table 6.2)? 3. Consult Table 6.2 to decide whether to use heuristics or optimization for the task.

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4. Record the performance of the approach you chose and use it to possibly update Table 6.2 for the domain in which you work. In conclusion, recall the quotes by Mervyn King and John Kay (Chapter 2), and John Maynard Keynes (Chapter 3). King and Kay talk of narratives as a description of successful decision making in the wild, and Keynes points out the amalgam of perspectives needed for good decision theory. These impactful economists invite modelers to accept that sometimes they have to go beyond models. In this chapter, this challenge was taken on to some extent, by building verbal cognitive models. The next chapter goes further by pondering more generally the kinds of interventions that cognitive and behavioral science can offer to operations.

Notes 1. George Eliot, Felix Holt, The Radical (Edinburgh, UK: William Blackwood and Sons, 1866): Ch. 29. 2. The “in the wild” metaphor, that means “not in the lab,” is often used in cognitive science, see Edwin Hutchins, Cognition in the Wild (Cambridge, MA: MIT Press, 1995). It is very close to “in the field”, emphasizing more vividly the challenges of working outside the lab. 3. Andrew W. Lo and Mark T. Mueller, “Warning: Physics Envy May Be Hazardous to your Wealth!” (https://papers.ssrn.com/sol3/papers.cfm? abstract_id=1563882); Mervyn King and John Kay, Radical Uncertainty: Decision-Making for an Unknowable Future (London: Hachette, 2020). 4. Richard Bellman, An Introduction to Artificial Intelligence: Can Computers Think? (Stamford, CT: Thomson, 1978): 50. 5. Russell L. Ackoff, “Optimization + Objectivity = Optout,” European Journal of Operational Research 1, no. 1 (1977): 1–7; Jonathan Rosenhead and John Mingers, Rational Analysis for a Problematic World Revisited (Hoboken, NJ: John Wiley and Sons, 2001). 6. Jay W. Forrester, “System Dynamics, Systems Thinking, and Soft OR,” System Dynamics Review 10, no. 2–3 (1994): 245–256. 7. See also the editorial to a special journal issue on behavioral operational research by L. Alberto Franco and Raimo P. Hämäläinen, “Behavioural Operational Research: Returning to the Roots of the OR Profession,” European Journal of Operational Research 249, no. 3 (2015): 791–195. In psychology too, decision making has been viewed as a process of sense

6

8.

9. 10.

11.

12. 13. 14.

15. 16.

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making based on language; see for instance Jerome S. Bruner, “DecisionMaking as a Discourse,” in Uncertain Outcomes, ed. Clifford R. Bell (Lancaster, England: MTP Press, 1979): 93–113, and references therein. Sarah Holewinski, “Escalation of Force: The Civilian Perspective,” in Escalation of Force Handbook (Fort Leavenworth, KS: Center for Army Lessons Learned, 2017): 81–82. For example, people working for the government are sometimes arrested or killed at bogus checkpoints. Niklas Keller and Konstantinos V. Katsikopoulos, “On the Role of Psychological Heuristics in Operational Research; and a Demonstration in Military Stability Operations,” European Journal of Operational Research 249, no. 3 (2016): 1063–1073. Ibid; Konstantinos V. Katsikopoulos et al., Classification in the Wild: The Science and Art of Transparent Decision Making (Cambridge, MA: MIT Press, 2020), Sec. 6.1. Ibid., Fig. 6.2. Accessed July 29, 2010 from http://wikileaks.org/wiki/Afghan_War_Dia ry,_2004-2010. Keller and Katsikopoulos, “On the Role of Psychological Heuristics in Operational Research; and a Demonstration in Military Stability Operations”. The suicide attacker would lose his life in the case of a miss, but this loss is a gain from the perspective of NATO. Models of sequential decision making under risk can capture dynamic aspects of decisions. In the checkpoint problem, such models may include different states that encapsulate the information available to the soldier and can change during the encounter, for example at which point, if any, the driver of the approaching vehicle complies to the soldier’s instructions. The decision strategy may depend on the state, and thus may be richer than the one-size-fits-all strategy outputted by static decision under risk models such as expected utility theory. A well-known sequential decisions under risk model is Markov decision processes, see Martin L. Puterman, Markov Decision Processes: Discrete Stochastic Dynamic Programming, John Wiley and Sons (Hoboken, NJ, 2014); in the checkpoint problem one should also consider delays in the observation of states, the collection of consequences, and so on, as in Konstantinos V. Katsikopoulos and Sascha E. Engelbrecht, “Markov Decision Processes with Delays and Asynchronous Cost Collection,” IEEE Transactions on Automatic Control 48, no. 4 (2003): 568–574. Models of sequential decision making under risk, such as Markov decision processes, have multiple parameters, including the probabilities of transitioning from one state to another, that are challenging to estimate.

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17. Some game theory models can capture information asymmetries in strategic interaction. In the checkpoint problem, inspection games appear suitable, see Rudolf Avenhaus, Bernhard von Stengel, and Shmuel Zamir, “Inspection Games,” Handbook of Game Theory With Economic Applications, no. 3 (2002): 1947–1987. In an inspection game, there are two players: the inspector (here the soldier) and the inspectee (here the driver of the approaching vehicle), where the identity of the inspector is known to the inspectee but not vice versa. The inspector’s objective is to classify the inspectee as acting lawfully or not. There is only one lawful action which is unequivocally unlawful (here a suicide attack), whereas there is a choice of unlawful actions which are all inconclusive, to varying degrees (e.g., various types of failure to comply). The inspector observes the action of the inspectee and maps it to a classification of the inspectee as acting lawfully or not. But, as for Markov decision processes, intention games come with multiple parameters, such as the probabilities of unlawful actions, that are challenging to estimate. Interestingly, Avenhaus and his colleagues acknowledge issues of applicability: “practical questions abound, and the allocation of inspection effort to various sites, for example, is usually based on rules of thumb” (http://www.maths.lse.ac. uk/personal/stengel/TEXTE/insp.pdf, 35). 18. Katsikopoulos et al., Classification in the Wild, 134. 19. See Keller and Katsikopoulos, “On the Role of Psychological Heuristics in Operational Research”. For a discussion of how the tree was received by practitioners and the public, see Katsikopoulos et al., Classification in the Wild, 137–138. 20. Ça˘grı Haksöz, Risk Intelligent Supply Chains: How Leading Turkish Companies Thrive In the Age of Fragility (Boca Raton, FL: CRC Press, 2013). 21. See Ça˘grı Haksöz, Konstantinos V. Katsikopoulos, and Gerd Gigerenzer, “Less Can Be More: How to Make Operations More Flexible and Robust with Fewer Resources,” Chaos: An Interdisciplinary Journal of Nonlinear Science 28, no. 6 (2018): 063102, and references therein. 22. Gad Allon and Jan A. Van Mieghem, “Global Dual Sourcing: Tailored Base-Surge Allocation to Near-and Offshore Production,” Management Science 56, no. 1 (2010): 110–124. 23. Qi Fu, Chung-Yee Lee and Chung-Piaw Teo, “Procurement Management Using Option Contracts: Random Spot Price and the Portfolio Effect,” IIE transactions 42, no. 11 (2010): 793–811. 24. Christopher Tang and Brian Tomlin, “The Power of Flexibility for Mitigating Supply Chain Risks,” International Journal of Production Economics 116, no. 1 (2008): 12–27. 25. Haksöz, Risk Intelligent Supply Chains.

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26. Victor K. Fung, William K. Fung, and Yoram Jerry R. Wind, Competing in a Flat World: Building Enterprises for a Borderless World (Hoboken, NJ: Pearson Prentice Hall, 2007). 27. Russell L. Ackoff, “The Future of Operational Research is Past,” Journal of the Operational Research Society 30, no. 2 (1979): 97; and elsewhere as Russell L. Ackoff, “Optimization + Objectivity = Optout,” European Journal of Operational Research 1, no. 1 (1977): 1–2. 28. Notice here the move from searching for an optimal model in the wild, which may not be knowable, to comparing models, as in Stefan Lessmann, Bart Baesens, Hsin-Vonn Seow, and Lyn C. Thomas, “Benchmarking State-of-the-Art Classification Algorithms for Credit Scoring: An Update of Research,” European Journal of Operational Research 247, no. 1 (2015): 124–136. This idea is not new. In an early piece taking stock of operations research, the celebrated quantum chemist and operations researcher George Kimball wrote: “In my experience when a moderately good solution to a problem has been found, it is seldom worthwhile to spend much time trying to convert this into the ‘best’ solution.”—see George. E. Kimball, “A Critique of Operations Research,” Journal of the Washington Academy of Sciences 48, no. 2 (1958): 35. 29. Such early articles in forecasting, machine learning, and psychometrics are, correspondingly: Spyros Makridakis and Michele Hibon, “Accuracy of Forecasting: An Empirical Investigation,” Journal of the Royal Statistical Society: Series A (General) 142, no. 2 (1979): 97–125; Robert C. Holte, “Very Simple Classification Rules Perform Well on Most Commonly Used Datasets,” Machine Learning 11, no. 1 (1993): 63–90; and Robyn M. Dawes and Bernard Corrigan, “Linear Models in Decision Making,” Psychological Bulletin 81, no. 2 (1974): 95–106 (notably, a related article dates back to almost a century ago; Samuel S. Wilks, “Weighting Systems for Linear Functions of Correlated Variables when There Is No Dependent Variable,” Psychometrika 3, no. 1 (1938): 23–40). An explanation for the neglect of finding that simple decision models can outperform more complex ones in operational/operations research and management is provided in our article with Ian Durbach and Theodor Stewart—we pointed out that work in multi-attribute choice and multicriteria decision analysis, unlike work in forecasting, machine learning and psychometrics, compares optimization and heuristics in fitting not prediction; see Konstantinos V. Katsikopoulos, Ian N. Durbach, and Theodor J. Stewart, “When Should We Use Simple Decision Models? A Synthesis of Various Research Strands,” Omega 81 (2018): 17–25. 30. Ben Newell and Arndt Bröder, “Cognitive Processes, Models and Metaphors in Decision Research,” Judgment and Decision making 3, no. 3 (2008): 195–204. 31. Katsikopoulos et al., Classification in the Wild.

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32. A related literature on the comparison as well as the synthesis of simple heuristics and more complex models, which is not covered here, is the work on the recognition heuristic (i.e., choose recognized over unrecognized options), or other expressions of human intuition—see Daniel G. Goldstein and Gerd Gigerenzer, “Models of Ecological Rationality: The Recognition Heuristic,” Psychological Review 109, no. 1 (2002): 75–90; and Konstantinos V. Katsikopoulos, Martin Egozcue, and Luis Fuentes Garcia, “A Simple Model for Mixing Intuition and Analysis,” European Journal of Operational Research 303, no. 2 (2022): 779–789. 33. Gerd Gigerenzer, Peter M. Todd, and the ABC Research Group, Simple Heuristics That Make Us Smart (New York: Oxford University Press, 1999); Laura Martignon and Ulrich Hoffrage, “Fast, Frugal, and Fit: Simple Heuristics for Paired Comparison,” Theory and Decision 52, no. 1 (2002): 29–71; Peter M. Todd, “How Much Information Do We Need?,” European Journal of Operational Research 177, no. 3 (2007): 1317–1332; Gerd Gigerenzer, Ralph Hertwig, and Thorsten Pachur, Heuristics: The Foundations of Adaptive Behavior (New York: Oxford University Press, 2011); Konstantinos V. Katsikopoulos, “Psychological Heuristics for Making Inferences: Definition, Performance, and the Emerging theory and Practice,” Decision Analysis 8, no. 1 (2011): 10– 29; Peter M. Todd, Gerd Gigerenzer, and the ABC Research Group, Ecological Rationality: Intelligence in the World (New York: Oxford University Press, 2012); Henry Brighton and Gerd Gigerenzer, “The Bias Bias,” Journal of Business Research 68, no. 8 (2015): 1772–1784; Katsikopoulos et al., “When Should We Use Simple Decision Models?”; Katsikopoulos et al., Classification in the Wild. 34. Some technical issues, such as whether the attributes values were binary or continuous, are brushed over. 35. Jean Czerlinski, Gerd Gigerenzer, and Daniel G. Goldstein, “How Good Are Simple Heuristics?” in Simple Heuristics that Make Us Smart, eds. G. Gigerenzer, P. M. Todd and the ABC Research Group (New York: Oxford University Press, 1999): 97–118. 36. Tallying, also called equal/unit-weights linear model, is a psychometrics favorite; see Philip Bobko, Philip L. Roth and Maury A. Buster, “The Usefulness of Unit Weights in Creating Composite Scores: A Literature Review, Application to Content Validity, and Meta-Analysis,” Organizational Research Methods 10, no. 4 (2007): 689–709. It has also been used successfully in bioinformatics; see for example Sihai Dave Zhao, Giovanni Parmigiani, Curtis Huttenhower and Levi Waldron, “Más-OMenos: A Simple Sign Averaging Method for Discrimination in Genomic Data Analysis,” Bioinformatics 30, no. 21 (2014): 3062–3069.

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37. For a larger study of the same task with 56 datasets and more heuristics and optimization models, see Marcus Buckmann and Özgür Sim¸ ¸ sek, “Decision Heuristics for Comparison: How Good Are they?.” In Imperfect Decision Makers: Admitting Real-World Rationality 2017: 1–11. 38. Laura Martignon, Konstantinos V. Katsikopoulos and Jan K. Woike, “Categorization with Limited Resources: A Family of Simple Heuristics,” Journal of Mathematical Psychology 52, no. 6 (2008): 352–361. 39. Özgür Sim¸ ¸ sek, “Linear Decision Rule as Aspiration for Simple Decision Heuristics,” Advances in Neural Information Processing Systems 26 (2013): 2904–2912. 40. Jan Malte Lichtenberg and Özgür Sim¸ ¸ sek, “Simple Regression Models,” Proceedings of the Neural Information Processing Systems 2016 Workshop on Imperfect Decision Makers 58 (2017): 13–25. 41. Stuart Geman, Elie Bienenstock and René Doursat, “Neural Networks and the Bias/Variance Dilemma,” Neural Computation 4, no. 1 (1992): 1–58. 42. Gerd Gigerenzer and Henry Brighton, “Homo Heuristicus: Why Biased Minds Make Better Inferences,” Topics in Cognitive Science 1, no. 1 (2009): 107–143; Sim¸ ¸ sek, “Linear Decision Rule as Aspiration for Simple Decision Heuristics”. 43. For simplicity, the notation I use does not explicate that all terms are conditioned on a and T ; for the full version see Geman et al., “Neural Networks and the Bias/Variance Dilemma,” 9. 44. One can expect that a model’s bias contributes to its error, but this might be less clear to see for variance. An intuition is that when a model makes different predictions for v based on the same a (for different T ), this increases the discrepancy between the model’s predictions and the true observations (assuming no association between the variance of f (a, T ) given a and the true variance of v given a). 45. I am not aware of these principles stated as such elsewhere. They are inspired by the thinking of Henry Brighton and Özgür Sim¸ ¸ sek. Brighton noticed that, to analyze a model’s performance, it is useful to think separately in terms of its bias and its variance and hypothesized that when simple heuristics perform well it is because of their low variance; and Sim¸ ¸ sek discovered and highlighted that simple heuristics can have low bias in the wild. 46. See for example Robin M. Hogarth and Natalia Karelaia, “Simple Models for Multiattribute Choice with Many Alternatives: When it Does and Does not Pay to Face Trade-Offs with Binary Attributes,” Management Science 51, no. 12 (2005): 1860–1872; and Manel Baucells, Juan A. Carrasco and Robin M. Hogarth, “Cumulative Dominance and Heuristic Performance in Binary Multiattribute Choice,” Operations Research 56,

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51. 52. 53. 54.

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no. 5 (2008): 1289–1304. Linear functions are standard in multi-attribute utility theory, as in Ralph L. Keeney and Howard Raiffa, Decision with Multiple Objectives: Preferences and Value Tradeoffs (New York: John Wiley and Sons, 1993). Another common formulation additionally includes multiplicate attribute interactions, and some of the ecological rationality results described here hold for this formulation as well; see Konstantinos V. Katsikopoulos, Martin Egozcue, and Luis Fuentes Garcia, “Cumulative Dominance in Multi-Attribute Choice: Benefits and Limits,” EURO Journal on Decision Processes 2, no. 1 (2014): 153–163. There are also analogous conditions for classification tasks; see Martignon et al., “Categorization with Limited Resources”. Sim¸ ¸ sek, “Linear Decision Rule as Aspiration for Simple Decision Heuristics,” 2911. Martignon and Hoffrage, “Fast, Frugal, and Fit,” Th. 3. Manel Baucells, Juan A. Carrasco and Robin M. Hogarth, “Cumulative Dominance and Heuristic Performance in Binary Multiattribute Choice,” Operations Research 56, no. 5 (2008): 1289–1304. Ibid., Th. 3 and 4. Sim¸ ¸ sek, “Linear Decision Rule as Aspiration for Simple Decision Heuristics,” 2908. Martignon and Hoffrage, “Fast, Frugal, and Fit,” Sec. 4.4 and 4.5. Katsikopoulos et al., Classification in the Wild provide a number of demonstrations in empirical work in the wild. Jennifer Castle sketches an analytical proof showing that the standard optimization model in a forecasting task with a linear data-generating process (plus errors) achieves zero bias if this process is stable, but has higher bias than a very simple heuristic if the data-generating process changes and this change is not detected; see Jennifer Castle, “Commentary on ‘Transparent Modelling of Influenza Incidence’: Is the Answer Simplicity or Adaptability?,” International Journal of Forecasting 38, no. 2 (2022): 623. The heuristic is to forecast the most recent observation, commonly referred to as (often derogatorily) naïve forecasting but empirically found to outperform big data (Google Flu Trends ); see Konstantinos V. Katsikopoulos, Özgür Sim¸ ¸ sek, Marcus Buckmann, and Gerd Gigerenzer, “Transparent Modeling of Influenza Incidence: Big Data or a Single Data Point from Psychological Theory?,” International Journal of Forecasting 38, no. 2 (2022): 613–619. A convincing and influential article on this point is David Lazer, Ryan Kennedy, Gary King and Alessandro Vespignani, “The Parable of Google Flu: Traps in Big Data Analysis,” Science 343, no. 6176 (2014): 1203– 1205; see also Gerd Gigerenzer, How to Stay Smart in a Smart World (London, UK: Penguin, 2022).

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56. Terry Williams, Knut Samset, and Kjell Sunnevåg, Eds, Making Essential Choices with Scant Information: Front-End Decision Making in Major Projects (London, UK: Palgrave Macmillan, 2009). 57. Castle, “‘Commentary on ‘Transparent Modelling of Influenza Incidence’”. 58. Jochen Reb, Shenghua Luan, and Gerd Gigerenzer, Smart Management: How Heuristics Help Leaders Make Good Decisions in an Uncertain World (Cambridge, MA: MIT Press, in press). 59. Haksöz et al., “Less Can Be More,” Sec. IV.

CHAPTER 7

Behavioral and Cognitive Interventions

In a 1979 European Journal of Operational Research article Ackoff vehemently complained that the field is not interdisciplinary1 : For example, a doctor may see the incapacity of an elderly woman as a result of her weak heart; an architect as deriving from the fact that she must walk up three flights of steep stairs to the meager room she rents; an economist as due to her lack of income; a social worker as a consequence of her children’s failure to “take her in”, and so on. Planning such an old lady’s future ought to involve all these points of view and many others… OR provides no such treatment. Its interdisciplinarity is a pretention, not a reality.

In this chapter, I will not attempt to settle the question of how interdisciplinary work on operations is. It is true by construction, of course, that the field of behavioral operations is interdisciplinary, and Cognitive Operations demonstrates this fact. The main point of this book is to assess various optimization and heuristic decision models on the criteria of predictive power, specification of cognitive processes, transparency, and usefulness of output. Chapters 2–6 provide empirical and analytical assessments that can support readers to choose a model that describes well human behavior in the task at hand. Whereas in the same article Ackoff also bleakly pronounced that ‘the future of operational research is past’ for prescribing human decision making—a position that is beyond the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6_7

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scope of this book to discuss—this is not the case for describing human decision making. Cognitive operations have a future. Ackoff insists that modeling is useful only if it goes beyond formal points of view. How can we put more flesh on this statement? In their 20-year retrospective, Karen Donohue, Özalp Özer and Yanchong Zheng provide a framework for the research goals of behavioral operations, organizing goals into four categories: describe, predict, utilize, and improve.2 The categories of describing and predicting behavior relate to mathematical modeling, and have been analyzed in previous chapters. The present chapter touches on research on how to utilize and improve human decisions. This research is conceptual and empirical and studies behavioral and cognitive interventions in the wild.3 In the first section I discuss a study of behavior with AI , and in the next section I look into two main approaches to improving behavior from behavioral and cognitive science, nudge and boost 4 and also discuss a study that compares these approaches. The final section provides a summary and eases into the book’s concluding chapter.

7.1

Behavior with AI

The fourth industrial revolution, or Industry 4.0,5 aims at rapid change in industry and business, creating high hopes for more environmentally and socially responsible production and consumption. A central tool of Industry 4.0 is the use of AI for connecting more closely to the physical and digital worlds. In a 2021 McKinsey global survey capturing a full range of regions, industries, company sizes, and specialties, 1013 out of 1843 participants said that their organization had adopted at least one AI capability.6 One such capability is augmented reality, which is used in manufacturing. For example, smart glasses that superimpose digital information on physical objects support activities such as assembling and sorting. What happens when smart glasses are utilized in a manufacturing setting? Are workers able to use the AI to do their job more accurately and faster than before? If yes, does this learning persist and possibly generalize to other jobs? More broadly, how do workers behave with AI? I am not aware of many studies that provide such answers. In one exception, David Wuttke and his colleagues tested workers in a factory in southern Germany.7 A strength of this study is that it employed a controlled framed field experiment 8 In this type of experiment, participants perform their actual job in the way they would normally do; the

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only differences from an experiment in the wild are that the conditions are arranged by the experimenter and that the participants know that they are in an experiment. In Wuttke and colleagues’ study, 25 workers were randomly assigned to the AI condition9 and another 25 to the paper condition. In the AI condition participants received their instructions via smart glasses that recorded what the participant saw, reacted based on this information, displayed the appropriate instructions, and provided haptic feedback after the participant completed their task. Participants in the paper condition received instructions in a printout that had graphical illustrations and text explanations. The content and detail provided were similar in the two conditions, by using the same graphics and words to the extent possible. Each participant had to perform a simple and a difficult task, randomly ordered. To ease the exposition, let us focus on the difficult task. This task required a series of production steps, such as assembling, soldering,10 and assuring quality. A critical manipulation of the Wuttke and colleagues’ study is that participants were tested twice—first when they were learning and performing the task with the instructions available to them (guided learning ), and later on when the instructions were removed and they had to perform the task based on their memory and understanding of it ( free recall ). In both tests, participants were asked to work on the task until the product had zero defects. The dependent variable was response time. What might one expect to find? The authors hypothesized that, under guided learning, completion time would be shorter in the AI condition because the steps are presented readily to the workers; whereas in the paper condition workers have to go back and forth between the two-dimensional illustrations and the 3D reality. The extra cognitive work needed in the paper condition should, however, activate deeper processing and better learning; thus Wuttke and colleagues also hypothesized that, under free recall, completion time would be shorter in the paper condition.11 As Fig. 7.1 shows, the two hypotheses are supported by the data. Whereas under guided learning the average completion time of a production task was much shorter in the AI condition (60 versus 33 min), the pattern was reversed in free recall with the time to complete a task being shorter in the paper condition (47 versus 57 min).12 It is noteworthy

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60

Paper AI

57

Completion time (min)

47

33

Guided learning

Free recall

Fig. 7.1 Mean completion times of a manufacturing production task, when instructions were readily available (guided learning) and when instructions were not available (free recall); in both cases instructions were provided by an AI system or on paper (Adapted from Wuttke et al.)

that performance in the challenging free recall test improved in the paper condition13 but clearly deteriorated in the AI condition.

7.2

Nudge and Boost

Psychologists have been long concerned with how to change human behavior for the ‘better’, focusing on people’s motivations, emotions, and beliefs.14 Richard Thaler and Cass Sunstein drew from research on people’s decision making to build a very popular theory of behavioral change.15 The main idea in Thaler and Sunstein’s book Nudge is to employ interventions that steer people towards a behavior while preserving their freedom of choice. The interventions are not regulatory (e.g., no bans) or monetary (e.g., no incentives), and aim to steer towards the person’s ‘interest’. The behavioral science of decision making is crucial in creating the intervention—the method is to harness a bias in behavior: For example, given that people tend to stick with a default option, the choice environment (often called choice architecture) can be changed so

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that the default option becomes a beneficial one such as donating one’s organs or using green energy.16,17 Nudge aims at changing behavior directly without changing the underlying cognitive processing. A person nudged towards organ donation retains their underlying preference for taking the default option; in fact, retaining and harvesting this preference is necessary for the nudge intervention to work.18 This is why we said above that nudge is steering people. As an alternative, one might attempt to change behavior by changing the underlying cognitive processing, and thus by empowering people. The approach to behavioral change that aims at empowering people by improving their cognitive processing has been called boost by Ralph Hertwig and Till Grüne-Yanoff.19 For example, one can try to improve the take-up of organ donation and green electricity consumption by boosting people’s understanding of the societal benefits of these actions. The focus of boost on processes, unlike their neglect in nudge, suggests that boost is more aligned with the simple heuristics modeling approach, unlike nudge that is more aligned with optimization.20 In this sense, boosts can be seen as cognitive interventions . Are boosts really that different from nudges? And, if yes, is getting one’s cognition boosted just another name for getting an education at school? Distinctions between these concepts have been clearly discussed by an interdisciplinary team of healthcare researchers and philosophers.21 Consider for instance the issue of how to reduce smoking. A nudge would consist of making tobacco products less visible in stores. Education could consist of transmitting information about the harmful effects of smoking on health. A boost would be to introduce smokers to meditation techniques that provide the relaxation sought in smoking and over the long term enhance self-control over nicotine cravings. More generally, I subscribe to the view that nudges and boosts differ in their theoretical basis—nudge assumes that people’s cognitive biases cannot be changed whereas boost holds that people can learn new skills or tools that allow them to overcome such biases.22 Boosts improve understanding and thinking, as education aims to do as well, but the difference is that the usual targets of boosts, such as making better financial and health decisions or accurately assessing real-world risks, are typically not addressed in school. In a refreshing turn, behavioral scientist Riccardo Viale coined the neologisms nudgood and nudgevil that can help further elucidate differences between nudge, boost and other approaches to behavioral change.23 Boosts are developed and tested in

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various institutions, including the Winton Centre for Risk and Evidence Communication of the University of Cambridge; see https://wintoncen tre.maths.cam.ac.uk, and the Harding Center for Risk Literacy of the University of Potsdam; see https://www.hardingcenter.de/en.24,25 It has been emphasized throughout this book that models should be compared to each other, and the same principle holds for interventions. Even though there are theoretical analyses of the conditions under which one might expect nudge to outperform boost and vice versa,26 there are virtually no studies that compare empirically nudge and boost. One exception is a controlled field experiment (for this term see Sect. 7.1) by Henrico van Roekel and his colleagues27 on how to improve hand hygiene in hospitals.28 Van Roekel and his colleagues developed and tested a nudge and a boost in three non-intensive wards, similar in personnel structure, number of beds, and types of incidents handled, in a regional hospital in a large Dutch city. Initially, 11 semi-structured interviews with heads of wards and nurses were used to identify barriers to the compliance of nurses with hand hygiene protocols. Subsequently, the research team developed a nudge and a boost to help overcome these barriers, and each intervention was randomly allocated to one of the wards (the third ward served as a control group where no intervention was made). The nudge focused on reframing the perception of the protocol from a burden for the nurse to that of care for the patient. The poster and flyers used to present the nudge featured an image of hands being cleaned and the tagline ‘in good hands’. The boost focused on enhancing the understanding of the frequency of hospital infections and the role of hand hygiene in these infections. The poster and flyers used to provide the boost included facts such as ‘one in every twenty patients received a hospital-induced infection’ and ‘research shows that in two American hospitals, the number of MRSA29 infections decreased by half after healthcare employees improved their hand hygiene’. The authors point out that each intervention has elements of the other; for example, nudge provided information about ‘hand hygiene moments’ that goes beyond just reframing. As with models, interventions may be integrated. The dependent variable used to evaluate the effectiveness of the interventions was compliance rate, measured by the number of moments where a hand hygiene action was actually performed divided by all potential hand hygiene moments (the latter moments are called observations). An example of an observation is when a nurse finishes contact with a patient,

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and an example of a hand hygiene action is when the nurse uses water and soap to clean hands. Figure 7.2 shows compliance rates for nudge and boost. Similarly to the behavior-with-AI experiment, participants were tested twice—first immediately after the intervention (76 observations) and then a second time with a delay of one week (67 observations). The pattern of results in Fig. 7.2 is similar to the pattern in Fig. 7.1: One intervention, nudge, produced better results in the short term (89% versus 77%), whereas the other intervention, boost, produced better results in the longer term (80% versus 75%).30 Note that in the delayed test boost essentially retained its performance, whereas nudge deteriorated. In sum, it is crucial to develop a theory of ecological rationality for interventions, as it has been done for models (Sect. 6.3): In some cases, nudge might outperform boost and in other cases the other way around, and one needs a guide for a-priori identifying these types of cases. Furthermore, an ecological rationality theory might also be needed when comparing nudges among themselves. A Bayesian meta-analysis of 440 statistical effect sizes of nudge interventions concluded that on the

Nudge Boost

89

80 75

Compliance rate (%)

77

Immediate test

Delayed test

Fig. 7.2 Mean rates of compliance with a hand hygiene hospital protocol, when a nudge was presented and when a boost was provided; in both cases participants were tested immediately after the intervention and then a second time with a delay of one week (Adapted from Roekel et al.)

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average there is no evidence for nudge effectiveness, but there is evidence for heterogeneity in effectiveness across nudges.31

7.3

Summary

Cognitive Operations is not only about modeling work for describing and predicting human behavior. This chapter presented conceptual and empirical work for utilizing and improving people’s operational behavior, and its underlying cognition. The next, concluding chapter summarizes some of the book’s lessons from analyzing models and interventions, with an eye to the future.

Notes 1. Russell L. Ackoff, “The Future of Operational Research Is Past,” Journal of the Operational Research Society 30, no. 2 (1979): 101–102. 2. Karen Donohue, Özalp Özer, and Yanchong Zheng, “Behavioral Operations: Past, Present, and Future,” Manufacturing and Service Operations Management 22, no. 1 (2020), Fig. 1. 3. See also L. Alberto Franco, Raimo P. Hämäläinen, Etienne A. Rouwette, and Ilkka Leppänen, “Taking Stock of Behavioural OR: A Review of Behavioural Studies with an Intervention Focus,” European Journal of Operational Research 293, no. 2 (2021): 401–418. 4. Richard H. Thaler and Cass R. Sunstein, Nudge: Improving Decisions and Health, Wealth and Happiness (New Haven, CT: Yale University Press, 2008); Ralph Hertwig and Till Grüne-Yanoff, “Nudging and Boosting: Steering or Empowering Good Decisions,” Perspectives on Psychological Science 12, no. 6 (2017): 973–986. 5. For a general article see Heiner Lasi, Peter Fettke, Hans-Georg Kemper, Thomas Feld, and Michael Hoffmann, “Industry 4.0,” Business and Information Systems Engineering 6, no. 4 (2014): 239–242; and for an operations management perspective see Tava Lennon Olsen and Brian Tomlin, “Industry 4.0: Opportunities and Challenges for Operations Management,” Manufacturing and Service Operations Management 22, no. 1 (2020): 113–122. 6. https://www.mckinsey.com/capabilities/quantumblack/our-insights/glo bal-survey-the-state-of-ai-in-2021. On the other hand, company executives are much more skeptical about the returns of AI in practice; for evidence and discussion see Jochen Reb, Shenghua Luan, and Gerd Gigerenzer, Smart Management: How Heuristics Help Leaders Make Good Decisions in an Uncertain World (Cambridge, MA: MIT Press, in press).

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7. David Wuttke, Ankit Upadhyay, Enno Siemsen, and Alexandra WuttkeLinnemann, “Seeing the Bigger Picture? Ramping Up Production with the Use of Augmented Reality,” Manufacturing and Service Operations Management 24, no. 4 (2022): 2349–2366. 8. Glenn W. Harrison and John A. List, “Field Experiments,” Journal of Economic literature 42, no. 4 (2004): 1009–1055. 9. The authors call this the ‘AR’ (augmented reality) condition. 10. A process used to create a permanent bond between metal workpieces. 11. Wuttke et al. invoke the idea that deeper processing leads to better verbal memory and learning, as presented by Fergus I. M. Craik and Robert S. Lockhart, “Levels of Processing: A Framework for Memory Research,” Journal of Verbal Learning and Verbal Behavior 11, no. 6 (1972): 671–684. This has also been found in the motor domain; see Richard A. Schmidt and Robert A. Bjork, “New Conceptualizations of Practice: Common Principles in Three Paradigms Suggest New Concepts for Training,” Psychological Science 3, no. 4 (1992): 207–218. 12. For statistical significance tests, see Wuttke et al., “Seeing the Bigger Picture”: 2358–2359. 13. Schmidt and Bjork in “New Conceptualization of Practice,” convincingly argue that experimental manipulations that slow down the speed of skill acquisition might enhance long(er)-term retention and generalization. 14. For a very popular instance see Albert Bandura, “Self-Efficacy: Toward a Unifying theory of Behavioral Change,” Psychological Review 84, no. 2 (1977): 191–215. 15. Thaler and Sunstein, Nudge. 16. Eric J. Johnson and Daniel G. Goldstein, “Do Defaults Save Lives?,” Science 302, no. 5649 (2003): 1338–1339; Daniel Pichert and Konstantinos V. Katsikopoulos, “Green Defaults: Information Presentation and Pro-Environmental Behaviour,” Journal of Environmental Psychology 28, no. 1 (2008): 63–73. The power of defaults is stunning: For example, in 2002, more than 99% of the citizens of Austria, Belgium, France, Hungary, Poland and Portugal stayed with their country’s organ donation default whereas in countries such as Denmark, Netherlands, United Kingdom and Germany where the default was no organ donation, the corresponding percentage ranged between 4 and 28%. And in 2006 more than 99% of the households in Schönau, Germany retained the green electricity service assigned to them years before, whereas across Germany the corresponding percentage was 1%. 17. The alternative options of not donating organs or using grey electricity were available in the above natural experiments, and in this sense freedom of choice was preserved. On the other hand, at least some of this freedom must have been taken away, otherwise the effect of the defaults could not have been that strong; for further analysis see Riccardo Rebonato, Taking

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19. 20.

21. 22.

23. 24. 25.

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Liberties: A Critical Examination of Libertarian Paternalism (Berlin, Germany: Springer, 2012). “Work” here means that the rate of organ donation increases as a result of the intervention. Note, however, that this does not necessarily imply that the rate of transplantation increases as well, as there might be other barriers to overcome (e.g., organizational ones); for evidence on this point from 35 OECD countries see Adam Arshad, Benjamin Anderson, and Adnan Sharif, “Comparison of Organ Donation and Transplantation Rates Between Opt-Out and Opt-In Systems,” Kidney International 95, no. 6 (2019): 1453–1460. See for example Hertwig and Grüne-Yanoff, “Nudging and Boosting”. For arguments on this point, see Konstantinos V. Katsikopoulos, “Bounded Rationality: The Two Cultures,” Journal of Economic Methodology 21, no. 4 (2014): 361–374; for further discussion see Riccardo Viale, Nudging (Cambridge, MA: MIT Press, 2022): 141. Thomas Rouyard, Bart Engelen, Andrew Papanikitas, and Ryota Nakamura, “Boosting Healthier Choices,” British Medical Journal 376 (2022). For a balanced and practical exposition of this view, see a piece by journalist Michael Bond, “Risk School: Can the General Public Learn to Evaluate Risks Accurately, or Do Authorities Need to Steer it Towards Correct Decisions? Michael Bond Talks to the Two Opposing Camps,” Nature 461, no. 7268 (2009): 1189–1193. For a different analysis, see Viale, Nudging: 138–142. Viale, Nudging: 157–164. Interestingly, the same individual, ex hedge-fund manager David Harding, has financed both initiatives. A particularly useful technique for boosting the accurate assessment of health risks and supporting health decisions is fact boxes; see https://www.hardingcenter.de/en/transfer-and-impact/factboxes. Healthcare fact boxes summarize statistical information on benefits and harms of medical treatments in formats that are realtively easy to people to process. Developing and testing fact boxes for assessing operational risks and supporting operational decisions beyond healthcare is a great research challenge for behavioral operations. See Samuli Poyhonen, Jaakko Kuorikoski, Timo Ehrig, Konstantinos V. Katsikopoulos, and Shyam Sunder, “Nudge, Boost or Design? Limitations of Behaviorally Informed Policy Under Social Interaction,” Journal of Behavioral Economics for Policy 2, no. 1 (2018): Table 1. An example of a condition where boost might outperform nudge is when people are motivated to improve their decision competency; conversely, nudge might outperform boost when people do not have such motivation.

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27. Henrico van Roekel, Joanne Reinhard and Stephan Grimmelikhuijsen, “Improving Hand Hygiene in Hospitals: Comparing the Effect of a Nudge and a Boost on Protocol Compliance,” Behavioural Public Policy 6, no. 1 (2022): 52–74. 28. In 1847 Hungarian physician Ignaz Semmelweis observed that hand washing in his department at the Vienna General Hospital made a big difference in infections and deaths. The importance of hand hygiene was not recognized for a while, but after the germ theory of disease was accepted it started to rapidly gain ground, and later to be considered obvious. Today hospitals have standardized protocols for ensuring hand hygiene. Nevertheless, many studies report compliance rates of less than 50% that have been claimed to result, at least partially, in 20% of all deaths in hospitals; see van Roekel et al., “Improving Hand Hygiene in Hospitals” and references therein. 29. Methicillin-resistant Staphylococcus aureus are a group of bacteria responsible for difficult-to-treat infections. 30. For statistical significance tests see van Roekel et al., “Improving Hand Hygiene in Hospitals”: 66–68. Compliance rates for the control condition were 56% in the immediate test and 61% in the delayed test. 31. Maximilian Maier, František Bartoš, T. D. Stanley, David R. Shanks, Adam J. L. Harris, and Eric-Jan Wagenmakers, “No Evidence for Nudging After Adjusting for Publication Bias,” Proceedings of the National Academy of Sciences 119, no. 31 (2022): e2200300119.

CHAPTER 8

Lessons Learned and a Positive Look Ahead

‘Poet laureate of punk’ Patti Smith has been producing wonderful art for decades. In the Year of the Monkey, Smith shares the advice of writer William Burroughs that kept her going through tough times1 : William Burroughs: “Build a good name. Keep your name clean. Don’t make compromises, don’t worry about making a bunch of money or being successful—be concerned with doing good work and make the right choices and protect your work. And if you build a good name, eventually, that name will be its own currency.” Patti Smith: “Yeah, William, but my name’s Smith.”

I agree with the conclusion of Karen Donohue, Özalp Özer, and Yanchong Zheng, and of others, that behavioral operations has a good name, being an established and fundamental research field.2 Cognitive Operations is a contribution to the field’s effort to keep its good name and ensure that it has staying power, by showing in action some principles of descriptive science. These principles span all stages of scientific work, including making strong theoretical predictions, building and testing multiple models or interventions, and analyzing the data by appropriate statistical methods. The principles should eclipse individual researchers’ skills or tastes for particular types of theories, models, interventions, and statistics. Doing so has led to a number of discoveries, a sample of which © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6_8

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Table 8.1 Lessons from research on models of and interventions for human decision making Research question

Lessons learned

How to model people’s switch from risk aversion for gains to risk seekingness for losses?

Optimization (expected utility theory) and heuristics (minimax/maximax) may fit data equally well, but can differ in process specification, model transparency, and usefulness of output A zero-parameter heuristic (priority) can predict data better than a multi-parameter optimization model (prospect theory) Not-commonly used dependent variables (e.g., response time) can be used to compare the performance of models (inequity aversion; mirror tree) Two heuristics (anchoring and adjustment; correction) can assume very different processes, and still make essentially identical predictions When only qualitative information is available, it can be challenging to develop optimization models (from decision and game theory), but it may be possible to develop heuristics (compliance) There is more than one approach to behavioral change (nudge; boost). Nudge and boost have essentially not been compared empirically, although there is one study, and a meta-analysis of nudge

How to model people’s violations of expected utility theory? How to study people’s strategic interactions in bargaining games?

How to model the boundedly rational orders placed by inventory controllers?

How to model human decision making in a highly uncertain situation, such as a security checkpoint?

How to design an intervention for changing people’s behavior, for example for improving their health?

are showcased in Table 8.1. In its left column the table presents a research question from each one of Chapters 2–7. The right column of the table presents corresponding answers, framed as general lessons. This book has three goals. The first goal is, as suggested by Stephanie Eckerd and Elliot Bendoly3 to ensure the openness of the field to multiple points of view. Most models and interventions to date come from the optimization approach, and the book introduces the alternative of simple heuristics as well. The second goal of the book is to support readers in selecting a modeling approach that suits the decision problem at hand. The third goal is to point out cases where the approaches have been successfully integrated. Cognitive Operations will have achieved its purpose if it can support academics and practitioners in understanding

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existing models and creating new ones that open the black box and predict people’s decisions in transparent and useful ways.

Notes 1. Patti Smith, Year of the Monkey (London, UK: Bloomsbury Publishing, 2012). 2. Karen Donohue, Özalp Özer and Yanchong Zheng, “Behavioral Operations: Past, Present, and Future,” Manufacturing and Service Operations Management 22, no. 1 (2020): 1526; Behnam Fahimnia, Mehrdokht Pournader, Enno Siemsen, Elliot Bendoly and Charles Wang, “Behavioral Operations and Supply Chain Management–A Review and Literature Mapping,” Decision Sciences 50, no. 6 (2019): 1128; and Rachel Croson, Kenneth Schulz, Enno Siemsen and M. Lisa Yeo, “Behavioral Operations: The State of the Field,” Journal of Operations Management 31, no. 1–2 (2013): 1. 3. Stephanie Eckerd and Elliot Bendoly, “The Study of Behavioral Operations”, in Social and Psychological Dynamics in Production and Service Settings, eds., Elliot Bendoly, Wout van Wezel and Daniel G. Bachrach (New York: Oxford University Press, 2015): 3–23.

Appendix

This appendix includes technical explanations and supplements to points made in the main text, as well as additional results. The material is arranged by chapter. Chapter 3: Decision Under Risk Common ratio effects. Consider the following pair of choices, again posed by Daniel Kahneman and Amos Tversky.1 Case A: (6000, 0.45; 0, 0.55) or (3000, 0.90; 0, 0.10)? Case B: (6000, 0.001; 0, 0.999) or (3000, 0.002; 0, 0.998) In a lab experiment, 86% of participants chose (3000, 0.90; 0, 0.10) in case A and 73% chose (6000, 0.001; 0, 0.999) in case B. This finding is called the possibility effect as the majority choice changes when the gains go from being ‘probable’ in case A to being merely ‘possible’ in case B. The possibility effect is an instance of a family of findings called common ratio effects , wherein the ratio of the gain probabilities in the two left gambles in the two cases is equal to the same ratio in the two right 0.45 0.90 1 = 0.002 = 450 in this example. Generally, common ratio gambles; 0.001 effects, for gambles with equal expected values, can be written as below. (x, p; 0, 1 − p) is chosen to(y, kp; 0, 1 − kp) © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6

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and (y, ckp; 0, 1 − ckp) is chosen to(x, cp; 0, 1 − cp); where y > x > 0, k =

x , c > 0, y

(CR)

In the possibility effect discussed here, x = 3000, p = 0.90, y = 1 . Common ratio effects are important for 6000, k = 0.5, and c = 450 decisions under risk because they contradict the independence axiom of expected utility theory (Chapter 3). Predicting different empirical phenomena simultaneously. As mentioned in Chapter 3, the known parameterizations of prospect theory do not allow it to capture the whole array of observed empirical phenomena. In fact, the estimates provided by Tversky and Kahneman (Table 3.1, first row), α = 0.88, β = 0.88, λ = 2.25, γ = 0.61 and δ = 0.69, cannot capture the possibility effect—in case A, contrary to the observed choice, the theory says that w(0.45)u(6000) = 845.0 > 816.1 = w(0.90)u(3000). On the other hand, it has been shown analytically that the priority heuristic can capture common ratio and common consequence effects as well as the four-fold pattern of risk attitude.2 More precisely, using the same notation as in the above statement (CR), and the statements (CC) and (RA) in Chapter 3, the priority heuristic logically implies the following. Common ratio effects whenever (1 − k) p > 0.1 > (1 − k)cp Common consequence effects whenever xy > 0.1 > p(1 − q) Four-fold pattern of risk attitude if ‘large’ p is interpreted as p > 0.1 The statements above depend only on the characteristics of the decision task, x, y, p, q, c, k. The fixed thresholds of the heuristic, 0.1, also play a role in the statements. Exactly because its parameters are fixed, the priority heuristic predicts these different empirical phenomena simultaneously.3 The next two behavioral phenomena refer to evaluating gambles. To be able to apply the heuristic, one can utilize the linear function for the certainty equivalent of the heuristic in Eq. 3.4. Then the priority heuristic can provide explanations for and predict these phenomena. Interestingly both of these explanations can be related to the concept of risk aversion employed in the utility optimization approach.

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Saint Petersburg paradox. This phenomenon played a key role in the launching of modern descriptive decision theory.4 In 1713, Nicolas Bernoulli posed a puzzle to Pierre Remond de Montmort, which in 1738 his cousin Daniel Bernoulli5 made widely known in an article in the Papers of the Imperial Academy of Sciences in Petersburg. Here is a modern version of the puzzle6 : Consider the following gamble: You may flip a coin. If it comes up heads, you receive 1 dollar. If it comes up tails, you will flip it again. If it comes up heads, you receive 2 dollars. If it comes up tails, you will flip it again. If it comes up heads, you receive 4 dollars. This process repeats until the coin comes up heads, with the payoff for heads doubling each time it comes up tails. If the opportunity to play this gamble was on sale, what is the maximum amount of money that you would pay for it?

The paradox is that, whereas the expected-value of the gamble can be argued to be infinite,7 most reasonable people would pay only a relatively small amount to play. There is more theoretical speculation than empirical evidence on how much money people actually offer in order to play the Saint Petersburg game. Benjamin Hayden and Michael Platt ran a survey experiment with 220 participants, where 200 were taken from a list of readers of The New York Times and 20 were Duke University students.8 The researchers found that the median valuation of the gamble was 1.5 dollars, which coincides with its true median outcome. The modal offer, made by 68 participants, was 1 dollar and only 28 participants valued the gamble at 8 dollars or more. Daniel Bernoulli’s explanation for the Saint Petersburg paradox is that people have a utility function that exhibits diminishing sensitivity (Chapter 2). This idea spawned the revision of linear expected value theory into non-linear expected utility theory. Another explanation is that realistic players might doubt that very large sums could or would be paid out by the house. Nevertheless, when quantified, both of these explanations overestimate the observed valuations, implying offers in the vicinity of 20 dollars.9 Another idea, put forth eighteenth-century mathematicians such as D’Alembert, Buffon, and Condorcet, is that ‘small’ probabilities are essentially set to zero and their respective outcomes are ignored.10 The sticking point here is that it is not clear when a probability is ‘small’. The theory of the priority heuristic can help address this criticism by

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suggesting that a probability p is ‘small’ whenever p ≤ 0.1. This auxiliary assumption implies that the gamble is truncated to the following outcomes: x = 1 with probability 0.5, x = 2 with probability 0.25, and x = 4 with probability 0.125. Thus, the minimum outcome is xmin = 1 and the maximum outcome is xmax = 4. Using Eq. 3.4, the value of the gamble is predicted to equal xmin + 0.1xmax = 1.4. The certainty equivalent of the priority heuristic weights the minimum outcome of the gamble much more than all other outcomes, and embodies the degree of risk aversion required to predict the Saint Petersburg paradox. What about prospect theory? Pavlo Blavatskyy11 analytically showed that prospect theory implies that the expected utility of the gamble is finite only if the parameter α of its utility function (Eq. 3.1) is smaller than the parameter γ of its probability-weighting function (Eq. 3.2). Intuitively, the degree of risk aversion required must be large enough to offset the weighting of probability. Blavatskyy also points out that none of the conventional parameterizations of prospect theory with these functions satisfy the condition α < γ . Thus, prospect theory, with the functions in Eqs. 3.1 and 3.2, cannot predict the Saint Petersburg paradox. On the other hand, if prospect theory uses the so-called Prelec probabilityγ weighting function,12 w( p) = e−[− ln( p)] , it can generate the paradox if γ is estimated to lie between 0 and 1 (e.g., George Wu and Richard Conzalez13 found that γ = 0.44). Equity premium puzzle. What with all the buzz around the stock market, people do not invest in it that much. The difference between return on stocks and risk-free assets is too large for the observed choice of risk-free assets to be consistent with expected utility theory, in the 1−a following sense.14 Consider the utility function u(x) = x 1−a−1 where a > 

(x) 0, which has a measure of relative risk aversion −xu u  (x) = a. To account for the predominance of investment in assets, a should be between 30 and 40, when theory and empirical estimation suggest15 that it should be around 1. This puzzling, from the point of view of expected utility theory, finding is a cornerstone of the behavioral finance field. To argue that a = 30 is implausible, Jeremy Siegel and Richard Thaler calculated that it implies that the certainty equivalent (according to expected utility theory) of a gamble G that pays x or −0.5x, each with probability 0.5, equals −0.49x, meaning that one would pay almost as much as the worst outcome to avoid playing, which they found ‘absurd’.16

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Thaler and Benartzi provided an explanation that does not require risk aversion.17 They put forth the idea of myopic loss aversion, which is a combination of the concepts of loss aversion and reference points that feature in optimization models such as prospect theory (Chapter 3). Myopic loss aversion means that there is loss aversion and that investors evaluate their portfolios frequently (and thus reset their reference point). Prospect theory with the piece-wise linear utility function u(x) = x for x ≥ 0 and 2.25x for x < 0, and without weighting probabilities can fit the empirical data. Interestingly, the priority heuristic is consistent with the degree of risk aversion suggested by the equity premium puzzle. Using Eq. 3.4, the certainty equivalent of G in the Siegel-Thaler example, according to the priority heuristic, equals −0.5x + 0.1x = −0.4x. This indicates that the degree of risk aversion required to explain the equity premium puzzle might be the result of applying a simple heuristic. Chapter 4: Strategic Interaction The equilibria predicted by inequity-aversion theory. Using the same notation as in Eq. 4.1, here is the mutually optimal behavior of the two players in an ultimatum game.18 As said in the text, this optimal behavior underconstraints the model’s parameters—for example, the responder’s behavior does not contain information about their α and the proposer’s behavior does not contain information about their β. Responder (R): If the offer is larger or equal to 0.5, accept it. Otherwise, αR . If t R < 0.5, accept all offers larger calculate the threshold t R = 1+2α R than t and reject all offers smaller than t. Proposer (P ): If β P > 0.5, offer 0.5. Otherwise, calculate the responder’s αR . If β P < 0.5, offer t R . If β P = 0.5, make any offer threshold t R = 1+2α R between t R and 0.5 (including these two values).

Chapter 5: Inventory Control Correction heuristic and pull-to-center effect. Consider Eq. 5.6, which l q ∗ ,t +u q ∗ ,t reads q = ( ) ( ) , where l(q ∗ , t) = max{0, q ∗ − t} and u(q ∗ , t) = 2

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min{1, q ∗ + t}. In principle, there are four possible combinations of the values of l(q ∗ , t) and u(q ∗ , t). All of these combinations are feasible. For example, l(q ∗ , t) = q ∗ −t and u(q ∗ , t) = 1 obtain whenever q ∗ −t > 0 and 1 < q ∗ + t respectively, or after tidying up, whenever 1 − q ∗ < t < ∗ q ∗ . In this case, q = q +(1−t) . Also l(q ∗ , t) = 0 and u(q ∗ , t) = q ∗ + t 2 ∗ obtain whenever q − t < 0 and q ∗ + t < 1 respectively, or whenever ∗ q ∗ < t < 1 − q ∗ . And in this case q = q 2+t . These are the top two cases of Eq. 5.7. The two bottom cases of the equation can be handled similarly. In terms of the pull-to-center effect (PtC), note that if 1 − q ∗ < t < ∗ q (which implies that q ∗ > 0.5), then the case of under-ordering is predicted: q=

q ∗ + (1 − t) q∗ + q∗ < = q∗ 2 2

q=

0+1 (q ∗ − t) + 1 > = 0.5. 2 2

and

And if q ∗ < t < 1 − q ∗ (which implies that q ∗ < 0.5), then the case of over-ordering is predicted: q=

q∗ + q∗ q∗ + t > = q∗ 2 2

and q=

0+1 0 + (q ∗ + t) < = 0.5. 2 2

Correction heuristic and asymmetry of pull-to-center effect. I use ∗ and q ∗ such that q ∗ > 0.5, Eq. 5.8 to show that, for two orders q H L H ∗ ∗ ∗ q L < 0.5 and q H + q L = 1, the difference between the respective effect sizes equals zero, and this holds for all values of t. ∗ > 0.5, it is not possible that the condition q ∗ < t < Because q H H ∗ 1 − q H holds. I will consider the other three conditions in Eq. 5.8. ∗ < t < q ∗ . Then, because of q ∗ + q ∗ = Assume first that 1 − q H H H L ∗ 1, it also holds that q L < t < 1 − q L∗ , and the difference equals ∗ −1+t ∗ −t ∗ −(1−t) qH q ∗ −t q ∗ −(1−t) qH 1−q H (1−q ∗ )−t − 2qL∗ −1 = H2q ∗ −1 − 2 1−qH∗ −1 = 2q = 0. ∗ −1 ∗ −1 + 2q ∗ −1 2q H ( ) L H  H  H  H ∗ ∗ ∗ ∗ Second assume that t > max q H , 1 − q H or t < min q H , 1 − q H . Then

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    also t > max 1 − q L∗ , q L∗ or t < min 1 − q L∗ , q L∗ respectively, and the difference between effect sizes again equals 0 (respectively 1 – 1 or 0 – 0). Human behavior and model predictions at extreme and middle points. Axel Ockenfells and Reinhard Selten asked participants at the Cologne Laboratory for Economic Research to place an order19 q for q ∗ = 0, 0.1, . . . , 0.9, 1. They found20 that q = 0.05 for q ∗ = 0, q = 0.5 for q ∗ = 0.5, and q = 0.995 for q ∗ = 1. Ockenfells and Selten’s impulse balance equilibrium model predicts respectively q = 0, 0.5, and 1. Note that these are the predictions of expected profit maximization since in all cases q = q ∗ . Thus, prospect theory, as well as the anchoring and adjustment and correction heuristics can also make the same predictions as long as their parameters are chosen so that the models reduce to expected profit maximization.21 The quantal choice model can capture q = 0.5 for q ∗ = 0.5, but for q ∗ = 0 or 1 predicts a substantially higher, respectively, lower q.22 Cross-validation resources for quantal choice model and prospect theory. In order to follow the cross-validation procedure described in Sect. 5.5 for another model, it suffices to know the model’s predicted order q as a function of the theoretically optimal order q ∗ .23 In what follows, assume that the distribution of demand is uniform. Xuanming Su derived the following equation for the quantal choice model (using the notation of Sect. 5.2; see also Ockenfells and Selten24 ):    1 g k 1 − q ∗ − g(−kq ∗ ) ∗ (A.1) q=q − k G(k[1 − q ∗ ]) − G(−kq ∗ ) where g is the probability density function of the standard normal distribution and G is the cumulative probability function of the same distribution. And Xiaoyang Long and Javad Nasiry25 derived the following equation for prospect theory: q=

p − w + η(1 − β) p p + η(λ − 1)β 2 p + ηp

(A.2)

where the utility function of this version of prospect theory equals ηx for x ≥ 0 and ληx for x < 0, and its reference point, assuming that the placed order is q, equals β( p − w)q + (1 − β)( pxmin − wq).

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Chapter 6: Decision Under Uncertainty The game tree approach. The game tree in Fig. A.1 models the uncertainty about the identity of the driver of the approaching vehicle, as well as the granularity of the soldier’s decision to shoot, which could mean shooting at the driver or shooting at the car (assuming, for purposes of illustration, that decisions are taken with a probability of one). The rectangle on the left denotes the uncertainty about the driver, ovals represent the driver’s and soldier’s choices, and long rectangles on the right contain the payoffs to the soldier and driver. Short rectangles in the middle are used to denote that, by default, the soldier does not shoot when the driver complies. All numbers are for illustration, and correspond to model parameters that need to be estimated. We will (i) derive the decision strategy equilibrium, and (ii) note that the resulting ‘optimal’ strategies are too extreme, both descriptively and prescriptively. As in the decision under risk model, the probability that the driver 7 ; to simplify is an attacker can be estimated from Table 6.1 as 1060 computations, we have rounded this number to 0.001. The other model parameters are the payoffs to the soldier and driver. For example, if the

Fig. A.1

A game tree model of the checkpoint problem

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driver is an attacker who complies, and the soldier does not shoot at, let us say that the payoff (to NATO) from the death of the soldier is –1000. Throughout Fig. A.1, –1000 is used as the value of death for the ‘side’ which the life was lost to. It is a value much bigger, in absolute terms, to all other values, as for instance +100 which is assumed to be the value of a dead soldier to the insurgents. Table A.1 provides the payoff matrix of the checkpoint problem, where the numbers are expected payoffs to the soldier and driver based on the information in Fig. A.1. For example, when the driver complies, the expected payoff for the soldier equals 0.001(−1000) + 0.999(0) = −1. These payoffs are the same for the two soldier decisions—shoot at driver or shoot at car—which are augmented here to include the default decision of not shooting if the driver complies and also has the same payoffs. Based on Table A.1, the ‘optimal’ strategy of the driver is to comply because it maximizes her payoff of the soldier’s decision. Given that the driver complies, the soldier is indifferent between his two options because they deliver the same payoff. In both cases, since the driver complies, the ‘optimal’ strategy for the soldier is to not shoot. These game-theoretic prescriptions are descriptively inadequate. In all 1060 incidents, the drivers, attackers as well as civilians, at some point failed to comply.26 And soldiers shot at civilians in 130 out of their 1053 encounters, and also must have shot at the 7 attackers at some point. Prescriptively, this game-theoretic solution has a mixed record. For both civilians and attackers, it is a good idea to comply, albeit for different reasons—the civilian does not want to get hurt, and the attacker wants to fool the soldier—and this is captured by game theory as modeled here. From the soldier’s side, however, it would be unthinkable to never shoot, as the above analysis suggests. There might be scope to extend the analysis, for example by including probabilities of taking decisions. Table A.1 The payoff matrix of the checkpoint problem, where the numbers are expected payoffs based on the information in the game tree of Fig. A.1

Soldier shoots at driver (does not shoot at compliant drivers) Soldier shoots at car (does not shoot at compliant drivers)

Driver complies

Driver does not comply

Soldier receives −1 Driver receives +0.1 Soldier receives −1 Driver receives +0.1

Soldier receives −149.1 Driver receives −1000 Soldier receives −51.0 Driver receives −4.9

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Notes 1. Daniel Kahneman and Amos Tversky, “Prospect Theory: An Analysis of Decision Under Risk,” Econometrica 47, no. 2 (1979): 263–291. 2. Konstantinos V. Katsikopoulos and Gerd Gigerenzer, “One-Reason Decision-Making: Modeling Violations of Expected Utility Theory,” Journal of Risk and Uncertainty 37, no. 1 (2008), res. 1, 2, 4 and 5. 3. The heuristic also always predicts reflection effects; Ibid., res. 3. 4. Gerárd Jorland, “The Saint Petersburg Paradox 1713–1937,” in The Probabilistic Revolution: Ideas in History Vol 1, eds., Lorenz Krüger, Lorraine J. Daston, and Michael Heidelberger (Cambridge, MA: MIT Press, 1987), 157–190. 5. Daniel Bernoulli, “Specimen Theoriae Novae de Mensura Sortis,” Commentarii Academiae Scientiarum Imperialis Petropolitanae, 1738; English translation by Louise Sommer with notes by Karl Menger, “Exposition of a New Theory on the Measurement of Risk,” Papers of the Imperial Academy of Sciences in Petersburg, reprinted in Econometrica (1954): 23–26. 6. Benjamin Y. Hayden and Michael L. Platt, “The Mean, the Median, and the St. Petersburg Paradox,” Judgment and Decision Making 4, no. 4 (2009): 260. ∞ 1 i−1 ∞ 1 7. This expected value equals i=1 2 = i=1 2 , which is a divergent 2i series. 8. No significant differences were found between these two groups. For details, see Hayden and Platt, “The Mean, the Median, and the St. Petersburg Paradox”. 9. Ibid. 10. Paul A. Samuelson, “St. Petersburg Paradoxes: Defanged, Dissected, and Historically Described,” Journal of Economic Literature 15, no. 1 (1977): 24–55. 11. Pavlo R. Blavatskyy, “Back to the St. Petersburg Paradox?,” Management Science 51, no. 4 (2005): 677–678. 12. Drazen Prelec, “The Probability Weighting Function,” Econometrica (1998): 497–527. 13. George Wu and Richard Gonzalez, “Curvature of the Probability Weighting Function,” Management Science 42, no. 12 (1996): 1676– 1690. 14. Rajnish Mehra and Edward C. Prescott, “The Equity Premium: A Puzzle,” Journal of Monetary Economics 15, no. 2 (1985): 145–161. 15. Ibid. 16. Jeremy J. Siegel and Richard H. Thaler, “Anomalies: The Equity Premium Puzzle,” Journal of Economic Perspectives 11, no. 1 (1997): 192.

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17. Shlomo Benartzi and Richard H. Thaler, “Myopic Loss Aversion and the Equity Premium Puzzle,” The Quarterly Journal of Economics 110, no. 1 (1995): 73–92. 18 Ernst Fehr and Klaus M. Schmidt, “A Theory of Fairness, Competition, and Cooperation,” Quarterly Journal of Economics 114, no. 3 (1999): 826. The result for the proposer applies only if she does not know the preferences of the responder. 19 There were about 30 participants for each value of q ∗ . Each participant placed 200 orders. The results provided in the text are averages across these 200 orders. 20. Axel Ockenfels and Reinhard Selten, “Impulse Balance in the Newsvendor Game,” Games and Economic Behavior 86 (2014), 240, Fig. 1. 21. For prospect theory this is accomplished by setting α = β = γ = δ = λ = 1; for the anchoring and adjustment heuristic by w = 0; and for the correction heuristic by setting t = 0. For the two heuristics, the prediction q = 0.5 for q ∗ = 0.5 holds for all values of w and t. 22. Ockenfells and Selten, “Impulse Balance in the Newsvendor Game,” 243, Fig. 2. 23. More precisely, this is the expected order, where the expectation is taken with regards to the demand distribution. 24. Ibid., 242, Eq. 10. 25. Xiaoyang Long and Javad Nasiry, “Prospect Theory Explains Newsvendor Behavior: The Role of Reference Points,” Management Science 61, no. 12 (2015): 3010, prop. 1. 26. Niklas Keller and Konstantinos V. Katsikopoulos, “On the Role of Psychological Heuristics in Operational Research; and a Demonstration in Military Stability Operations,” European Journal of Operational Research 249, no. 3 (2016): 1063–1073.

Bibliography

Ackoff, Russell L. “Optimization + Objectivity = Optout.” European Journal of Operational Research 1, no. 1 (1977): 1–7. Ackoff, Russell L. “The Future of Operational Research Is Past.” Journal of the Operational Research Society 30, no. 2 (1979): 101–102. Albers, Walter. “Prominence Theory as a Tool to Model Boundedly Rational Decisions.” In Bounded Rationality: The Adaptive Toolbox, eds., Gerd Gigerenzer and Reinhard Selten, 297–317. Cambridge, MA: MIT Press, 2001. Allon, Gad, and Jan A. Van Mieghem. “Global Dual Sourcing: Tailored BaseSurge Allocation to Near-and Offshore Production.” Management Science 56, no. 1 (2010): 110–124. Allon, Gad, and Mirko Kremer. “Behavioral Foundations of Queueing Systems.” In The Handbook of Behavioral Operations, eds. Karen Donohue, Elena Katok, and Stephen Leider, 325–366. Hoboken, NJ: Wiley, 2018. Analytis, Pantelis Pipergias, Daniel Barkoczi, and Stefan M. Herzog. “Social Learning Strategies for Matters of Taste.” Nature Human Behaviour 2, no. 6 (2018): 415–424. Arkes, Hal R., Gerd Gigerenzer, and Ralph Hertwig. “How Bad Is Incoherence?” Decision 3, no. 1 (2016): 20–39. Arnauld, Antoine, Pierre Nicole, and John Ozell. Logic or the Art of Thinking. Cambridge, UK: Cambridge University Press, 1996 (original work published in 1662). Arrow, Kenneth J., Theodore Harris, and Jacob Marschak. “Optimal Inventory Policy.” Econometrica (1951): 250–272.

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6

199

200

BIBLIOGRAPHY

Arshad, Adam, Benjamin Anderson, and Adnan Sharif. “Comparison of Organ Donation and Transplantation Rates Between Opt-Out and Opt-In Systems.” Kidney International 95, no. 6 (2019): 1453–1460. Artigner, Florian M., and Gerd Gigerenzer. “Adaptive Heuristic Pricing.” Academy of Management Proceedings 2016, no. 1: 13915. Aumann, Robert J. “A Synthesis of Behavioural and Mainstream Economics.” Nature Human Behaviour 3, no. 7 (2019): 668–669. Avenhaus, Rudolf, Bernhard von Stengel, and Shmuel Zamir. “Inspection Games.” In Handbook of Game Theory with Economic Applications. Vol. 3. 2002: 1947–1987. Bandura, Albert. “Self-Efficacy: Toward a Unifying Theory of Behavioral Change.” Psychological Review 84, no. 2 (1977): 191–215. Baucells, Manel, Juan A. Carrasco, and Robin M. Hogarth. “Cumulative Dominance and Heuristic Performance in Binary Multiattribute Choice.” Operations Research 56, no. 5 (2008): 1289–1304. Baucells, Manel, and Konstantinos V. Katsikopoulos. “Descriptive Models of Decision Making.” In Wiley Encyclopaedia of Operations Research and Management Science, ed. James J. Cochran. Hoboken, NJ: Wiley, 2010. Bearden, Neil J., and Amnon Rapoport. “Operations Research in Experimental Psychology.” Tutorials in Operations Research (2005): 213–236. Becker-Peth, Michael, and Ulrich W. Thonemann. “Behavioral Inventory Decisions.” In The Handbook of Behavioral Operations, eds., Karen Donohue, Elena Katok, and Stephen Leider, 393–432. New York, NY: Wiley, 2018. Benartzi, Shlomo, and Richard H. Thaler. “Myopic Loss Aversion and the Equity Premium Puzzle.” The Quarterly Journal of Economics 110, no. 1 (1995): 73–92. Bertel, Sven, and Alex Kirlik. “Fast and Frugal Heuristics.” In Wiley Encyclopaedia of Operations Research and Management Science, ed. James J. Cochran. Hoboken, NJ: Wiley, 2010. Bell, David E., Howard Raiffa, and Amos Tversky, eds. Decision Making: Descriptive, Normative, and Prescriptive Interactions. Cambridge, UK: Cambridge University Press, 1988. Bellman, Richard. An Introduction to Artificial Intelligence: Can Computers Think? Stamford, CT: Thomson, 1978. Bellman, Richard. Eye of the Hurricane. Singapore: World Scientific, 1984. Bellman, Richard. “On ‘Heuristic Problem Solving’ by Simon and Newell.” Operations Research 6, no. 3 (1958): 448–449. Bendoly, Elliot, and Daniel G. Bachrach. “Behavioral Operations in Practice and Future Work”. In The Handbook of Behavioral Operations Management: Social and Psychological Dynamics in Production and Service Settings, eds., Elliot Bendoly, Wout van Wezel, and Daniel G. Bachrach, 398–411. New York: Oxford University Press, 2015.

BIBLIOGRAPHY

201

Bendoly, Elliot, Wout van Wezel, and Daniel G. Bachrach, eds. The Handbook of Behavioral Operations Management: Social and Psychological Dynamics in Production and Service Settings. New York: Oxford University Press, 2015. Bertsimas, Dimitris, and Jack Dunn. “Optimal Classification Trees.” Machine Learning 106, no. 7 (2017): 1039–1082. Bernoulli, Daniel. “Specimen Theoriae Novae de Mensura Sortis.” Commentarii Academiae Scientiarum Imperialis Petropolitanae, 1738 (English translation: Sommer, Louise. “Exposition of a New Theory on the Measurement of Risk.” Papers of the Imperial Academy of Sciences in Petersburg, reprinted in Econometrica (1954): 23–26). Bingham, Christopher M., and Kathleen M. Eisenhardt. “Rational Heuristics: The ‘Simple Rules’ That Strategists Learn from Process Experience.” Strategic Management Journal 32, no. 13 (2011): 1437–1464. Binmore, Kenneth G. Fun and Games: A Text on Game Theory. Lexington, MA: D. C. Heath, 1992. Binmore, Ken, and Avner Shaked. “Experimental Economics: Where Next?” Journal of Economic Behavior and Organization 73, no. 1 (2010): 87–100. Binz, Marcel, and Eric Schulz. “Using Cognitive Psychology to Understand GPT-3.” Proceedings of the National Academy of Sciences 120, no. 6 (2023): e2218523120. Birnbaum, Michael H. “New Paradoxes of Risky Decision Making.” Psychological Review 115, no. 2 (2008): 463–501. Birnbaum, Michael H., and Alfredo Chavez. “Tests of Theories of Decision Making: Violations of Branch Independence and Distribution Independence.” Organizational Behavior and Human Decision Processes 71, no. 2 (1997): 161–194. Blake, Thomas, Chris Nosko, and Steven Tadelis. “Consumer Heterogeneity and Paid Search Effectiveness: A Large-Scale Field Experiment.” Econometrica 83, no. 1 (2015): 155–174. Blanco, Mariana, Dirk Engelmann, and Hans T. Normann. “A Within-Subject Analysis of Other-Regarding Preferences.” Games and Economic Behavior 72, no. 2 (2011): 321–338. Blavatskyy, Pavlo R. “Back to the St. Petersburg Paradox?” Management Science 51, no. 4 (2005): 677–678. Bobko, Philip, Philip L. Roth, and Maury A. Buster. “The Usefulness of Unit Weights in Creating Composite Scores: A Literature Review, Application to Content Validity, and Meta-Analysis.” Organizational Research Methods 10, no. 4 (2007): 689–709. Bolton, Gary E., and Axel Ockenfels. “ERC: A Theory of Equity, Reciprocity, and Competition.” American Economic Review 90, no. 1 (2000): 166–193.

202

BIBLIOGRAPHY

Bolton, Gary E., Axel Ockenfels, and Ulrich W. Thonemann. “Managers and Students as Newsvendors.” Management Science 58, no. 12 (2012): 2225– 2233. Bolton, Gary E., and Elena Katok. “Learning by Doing in the Newsvendor Problem: A Laboratory Investigation of the Role of Experience and Feedback.” Manufacturing and Service Operations Management 10, no. 3 (2008): 519–538. Bolton, Gary E., and Yefen Chen. “Other-Regarding Behavior: Fairness, Reciprocity, and Trust.” In The Handbook of Behavioral Operations, eds. Karen Donohue, Elena Katok, and Stephen Leider, 325–366. Hoboken, NJ: Wiley, 2018. Bond, Michael. “Risk School: Can the General Public Learn to Evaluate Risks Accurately, or Do Authorities Need to Steer It Towards Correct Decisions? Michael Bond Talks to the Two Opposing Camps.” Nature 461, no. 7268 (2009): 1189–1193. Bostian, A. J. A., Charles A. Holt, and Angela M. Smith. “Newsvendor ‘Pull-to-Center’ Effect: Adaptive Learning in a Laboratory Experiment.” Manufacturing and Service Operations Management 10, no. 4 (2008): 590–608. Bourgin, David D., et al. “Cognitive Model Priors for Predicting Human Decisions.” In International Conference on Machine Learning (Long Beach, CA: 2019): 5133–5141. Boylan, John E., et al. “Reproducibility in Forecasting Research.” International Journal of Forecasting 31, no. 1 (2015): 79–90. Brandstätter, Edouard, Gerd Gigerenzer, and Ralph Hertwig. “The Priority Heuristic: Making Choices Without Trade-Offs.” Psychological Review 113, no. 2 (2006): 409–432. Brandstätter, Eduard, Gerd Gigerenzer, and Ralph Hertwig. “Risky Choice With Heuristics: Reply to Birnbaum (2008), Johnson, Schulte-Mecklenbeck, and Willemsen (2008), and Rieger and Wang (2008).” Psychological Review 115, no. 1 (2008): 281–289. Breiman, Leo, et al. Classification and Regression Trees. Boca Raton, Florida: CRC Press, 1984. Brighton, Henry, and Gerd Gigerenzer. “The Bias Bias.” Journal of Business Research 68, no. 8 (2015): 1772–1784. Bruner, Jerome S. “Decision-Making as a Discourse.” In Uncertain Outcomes, ed. Clifford R. Bell, 93–113. Lancaster, England: MTP Press, 1979. Buckmann, Marcus, and Özgür Sim¸ ¸ sek. “Decision Heuristics for Comparison: How Good Are They?” In Imperfect Decision Makers: Admitting Real-World Rationality, 1–11, 2017. Busemeyer, Jerome M., and Peter D. Bruza. Quantum Models of Cognition and Decision. Cambridge, MA: Cambridge University Press, 2012.

BIBLIOGRAPHY

203

Camerer, Colin F. Behavioral Game Theory: Experiments in Strategic Interaction. Princeton: Princeton University Press, 2003. Camerer, Colin F., George Loewenstein, and Matthew Rabin, eds. Advances in Behavioral Economics. Princeton: Princeton University Press, 2004. Camerer, Colin F., and Teck-Hua Ho. “Violations of the Betweenness Axiom and Nonlinearity in Probability.” Journal of Risk and Uncertainty 8, no. 2 (1994): 167–196. Carney, Dana R., Amy J. C. Cuddy, and Andy J. Yap. “Power Posing: Brief Nonverbal Displays Affect Neuroendocrine Levels and Risk Tolerance.” Psychological Science 21, no. 10 (2010): 1363–1368. Carter, Craig R., Lutz Kaufmann, and Alex Michel. “Behavioral Supply Management: A Taxonomy of Judgment and Decision-Making Biases.” International Journal of Physical Distribution and Logistics Management 37, no. 8 (2007): 631–669. Castle, Jennifer. “Commentary on ‘Transparent Modelling of Influenza Incidence’: Is the Answer Simplicity or Adaptability?” International Journal of Forecasting 38, no. 2 (2022): 622–624. Chater, Nick, and Mike Oaksford, eds. The Probabilistic Mind: Prospects for Bayesian Cognitive Science. New York: Oxford University Press, 2008. Chen, Kay-Yut, and Shan Li. “The Behavioral Traps in Making Multiple, Simultaneous, Newsvendor Decisions.” Working Paper (Arlington, TX: University of Texas, 2018). Clausing, Don P., and Konstantinos V. Katsikopoulos. “Rationality in Systems Engineering: Beyond Calculation or Political Action.” Systems Engineering 11, no. 4 (2008): 309–328. Copernicus, Nicolaus. On the Revolutions of the Heavenly Spheres (1543; New York: Prometheus, 1995, translated by Charles Glenn Wallis). Craik, Fergus I. M., and Robert S. Lockhart. “Levels of Processing: A Framework for Memory Research.” Journal of Verbal Learning and Verbal Behavior 11, no. 6 (1972): 671–684. Croson, Rachel, Kenneth Schulz, Enno Siemsen, and M. Lisa Yeo. “Behavioral Operations: The State of the Field.” Journal of Operations Management 31, no. 1–2 (2013): 1–5. Cui, Tony H., and Yaozhong Wu. “Incorporating Behavioral Factors into Operations Theory.” In The Handbook of Behavioral Operations, eds. Karen Donohue, Elena Katok, and Stephen Leider, 89–119. Hoboken, NJ: Wiley, 2018. Currie, Christine, S. M., et al. “How Simulation Modelling Can Help Reduce the Impact of COVID-19.” Journal of Simulation 14, no. 2 (2020): 83–97. Czerlinski, Jean, Gerd Gigerenzer, and Daniel G. Goldstein. “How Good Are Simple Heuristics?” In Simple Heuristics that Make Us Smart, eds. G.

204

BIBLIOGRAPHY

Gigerenzer, P. M. Todd, and the ABC Research Group, 97–118. New York: Oxford University Press, 1999. Daskalakis, Constantinos, Paul W. Goldberg, and Christos H. Papadimitriou. “The Complexity of Computing a Nash Equilibrium.” SIAM Journal on Computing 39, no. 1 (2009): 195–259. Davis, Andrew M. “Biases in Individual Decision-Making.” In The Handbook of Behavioral Operations, eds. Karen Donohue, Elena Katok, and Stephen Leider, 151–198. Hoboken, NJ: Wiley, 2018. Dawes, Robyn M., and Bernard Corrigan. “Linear Models in Decision Making.” Psychological Bulletin 81, no. 2 (1974): 95–106. Dawes, Robyn M., and Matthew Mulford. “The False Consensus Effect and Overconfidence: Flaws in Judgment or Flaws in how We Study Judgment?” Organizational Behavior and Human Decision Processes 65, no. 3 (1996): 201–211. Daston, Lorraine. Classical Probability in the Enlightenment. Princeton, NJ: Princeton University Press, 1988. De Miguel, Victor, Lorenzo Garlappi, and Raman Uppal. “Optimal versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?” The Review of Financial Studies 22, no. 5 (2007): 1915–1953. De Treville, Suzanne, Tyson R. Browning, Julian N. Marewski, and Jordi Weiss. “Toyota Production System Practices as Fast-and-Frugal Heuristics.” Journal of Operations Management 69 (2023): 522–535. De Vericourt, Francis, et al. “Sex, Risk and the Newsvendor.” Journal of Operations Management 31, no. 1–2 (2013): 86–92. Dobzhansky, Theodosius. Genetics of the Evolutionary Process. New York, NY: Columbia University Press, 1971. Domingos, Pedro. “A Few Useful Things to Know About Machine Learning.” Communications of the ACM 55, no. 10 (2012): 78–87. Donohue, Karen, Elena Katok, and Stephen Leider, eds. The Handbook of Behavioral Operations. Hoboken, NJ: Wiley, 2018. Donohue, Karen, and Kenneth Schulz. “The Future Is Bright: Recent Trends and Emerging Topics in Behavioral Operations.” In The Handbook of Behavioral Operations, eds. Karen Donohue, Elena Katok, and Stephen Leider, 619–651. Hoboken, NJ: Wiley, 2018. Donohue, Karen, Özer Özalp, and Yanchong Zheng. “Behavioral Operations: Past, Present, and Future.” Manufacturing and Service Operations Management 22, no. 1 (2020), 191–202. Drechsler, Mareile, Konstantinos V. Katsikopoulos, and Gerd Gigerenzer. “Axiomatizing Bounded Rationality: The Priority Heuristic.” Theory and Decision 77, no. 2 (2014): 183–196. Du, Ding-Zhu, Panos M. Pardalos, and Weili Wu. “History of Optimization.” In Encyclopaedia of Optimization, eds. Christodoulos A. Floudas and Panos

BIBLIOGRAPHY

205

M. Pardalos, 1538–1542. New York: Springer Science and Business Media, 2008. Durbach, Ian N., et al. “Fast and Frugal Heuristics for Portfolio Decisions with Positive Project Interactions.” Decision Support Systems 138 (2020): 113399. Durbach, Ian N., and Theodor J. Stewart. “Using Expected Values to Simplify Decision Making Under Uncertainty.” Omega 37, no. 2 (2009): 312–330. Eckerd, Stephanie, and Elliot Bendoly. “The Study of Behavioral Operations.” In The Handbook of Behavioral Operations, eds. Karen Donohue, Elena Katok, and Stephen Leider, 3–23. Hoboken, NJ: Wiley, 2018. Eckerd, Stephanie, Scott DuHadway, Elliot Bendoly, Craig R. Carter, and Lutz Kaufmann. “On Making Experimental Design Choices: Discussions on the Use and Challenges of Demand Effects, Incentives, Deception, Samples, and Vignettes.” Journal of Operations Management 67, no. 2 (2021): 261–275. Edgeworth, Francis Y. “The Mathematical Theory of Banking.” Journal of the Royal Statistical Society 51, no. 1 (1888): 113–127. Edwards, Ward. “The Theory of Decision Making.” Psychological Bulletin 51, no. 4 (1954): 380–417. Eeckhoudt, Louis, Christian Gollier, and Harris Schlesinger. “The Risk-Averse (and Prudent) Newsboy.” Management Science 41, no. 5 (1995): 786–794. Einhorn, Hillel J., and Robin M. Hogarth. “Unit Weighting Schemes for Decision Making.” Organizational Behavior and Human Performance 13, no. 2 (1975): 171–192. Eliot, George. Felix Holt, The Radical. Edinburgh, UK: William Blackwood and Sons, 1866. Epley, Nicholas, and Thomas Gilovich. “The Anchoring-and-Adjustment Heuristic: Why the Adjustments Are Insufficient.” Psychological Science 17, no. 4 (2006): 311–318. Erev, Ido, et al. “Combining a Theoretical Prediction With Experimental Evidence to Yield a New Prediction: An Experimental Design With a Random Sample of Tasks” (Columbia University and Technion: Unpublished Manuscript, 2002). Erev, Ido, et al. “From Anomalies to Forecasts: Toward a Descriptive Model of Decisions Under Risk, Under Ambiguity, and From Experience.” Psychological Review 124, no. 4 (2017): 369–400. Erickson, Paul, et al. How Reason Almost Lost Its Mind: The Strange Career of Cold War Rationality. Chicago, IL: University of Chicago Press, 2013. Fahimnia, Behnam, Mehrdokht Pournader, Enno Siemsen, Elliot Bendoly, and Charles Wang. “Behavioral Operations and Supply Chain Management—A Review and Literature Mapping.” Decision Sciences 50, no. 6 (2019): 1127– 1183.

206

BIBLIOGRAPHY

Fehr, Ernst, and Klaus M. Schmidt. “A Theory of Fairness, Competition, and Cooperation.” The Quarterly Journal of Economics 114, no. 3 (1999): 817– 868. Fehr, Ernst, and Klaus M. Schmidt. “On Inequity Aversion: A Reply to Binmore and Shaked.” Journal of Economic Behavior and Organization 73, no. 1 (2010): 101–108. Fehr, Ernst, and Klaus M. Schmidt. “The Economics of Fairness, Reciprocity and Altruism–Experimental Evidence and New Theories.” In Handbook of the Economics of Giving, Altruism and Reciprocity, eds. Serge-Christophe Kolm and Jean M. Ythier 1, 615–691. Amsterdam, The Netherlands: North Holland, 2006. Feng, Tianjun, and Yinghao Zhang. “Modeling Strategic Behavior in the Competitive Newsvendor Problem: An Experimental Investigation.” Production and Operations Management 26, no. 7 (2017): 1383–1398. Feynman, Richard P., Matthew Sands, and Robert B. Leighton. The Feynman Lectures on Physics: The New Millennium Edition. New York: Basic Books, 2015. Fildes, Robert, and Fotios Petropoulos. “Improving Forecast Quality in Practice.” Foresight: The International Journal of Applied Forecasting 36 (2015): 5–12. Fischbacher, Urs, Ralph Hertwig, and Adrian Bruhin. “How to Model Heterogeneity in Costly Punishment: Insights From Responders’ Response Times.” Journal of Behavioral Decision Making 26, no. 5 (2013): 466. Fishburn, Peter C. “Lexicographic Orders, Utilities and Decision Rules: A Survey.” Management Science 20, no. 11 (1974): 1442–1471. Fishburn, Peter C. “The Irrationality of Transitivity in Social Choice.” Behavioral Science 15, no. 2 (1970): 119–123. Fishburn, Peter C., and Gary A. Kochenberger. “Two-Piece von NeumannMorgenstern Utility Functions.” Decision Sciences 10, no. 4 (1979): 503–518. Flick, Uwe. “Triangulation in Qualitative Research.” In A Companion to Qualitative Research, eds. Uwe Flick, Ernst von Kardoff, and Ines Steinke, 178–183. Thousand Oaks, CA: Sage, 2004. Forrester, Jay W. “System Dynamics, Systems Thinking, and Soft OR.” System Dynamics Review 10, no. 2-3 (1994): 245–256. Franco, L. Alberto, and Raimo P. Hämäläinen. “Behavioural Operational Research: Returning to the Roots of the OR Profession.” European Journal of Operational Research 249, no. 3 (2015): 791–195. Franco, L. Alberto, Raimo P. Hämäläinen, Etienne A. Rouwette, and Ilkka Leppänen. “Taking Stock of Behavioural OR: A Review of Behavioural Studies with an Intervention Focus.” European Journal of Operational Research 293, no. 2 (2021): 401–418.

BIBLIOGRAPHY

207

Fränkel, Gottfried S., and Donald L. Gunn. The Orientation of Animals: Kineses, Taxes and Compass Reactions. Oxford: Oxford University Press, 1940. Frederik, Jesse, and Maurits Martijn. “The New Dot Com Bubble Is Here: It’s Called Online Advertising.” The Correspondent, November 6, 2019. Friedman, Daniel, R. Mark Isaac, Duncan James, and Shyam Sunder. Risky Curves: On the Empirical Failure of Expected Utility. Milton Park, UK: Routledge, 2014. Friedman, Milton. Essays in Positive Economics. Chicago: University of Chicago Press, 1953. Friedman, Milton, and Leonard J. Savage. “The Utility Analysis of Choices Involving Risk.” Journal of Political Economy 56, no. 4 (1948): 279–304. Fu, Qi, Chung-Yee Lee, and Chung-Piaw Teo. “Procurement Management Using Option Contracts: Random Spot Price and the Portfolio Effect.” IIE Transactions 42, no. 11 (2010): 793–811. Fügener, Andreas, Sebastian Schiffels, and Rainer Kolisch. “Overutilization and Underutilization of Operating Rooms-Insights from Behavioral Health Care Operations Management.” Health Care Management Science 20, no. 1 (2017): 115–128. Fung, Victor K., William K. Fung, and Yoram Jerry R. Wind. Competing in a Flat World: Building Enterprises for a Borderless World. Hoboken, NJ: Pearson Prentice Hall, 2007. Galeotti, Andrea, et al. “Network Games.” The Review of Economic Studies 77, no. 1 (2010): 218–244. Gao, Song, Emma Frejinger, and Moshe Ben-Akiva. “Adaptive Route Choices in Risky Traffic Networks: A Prospect Theory Approach.” Transportation Research Part C: Emerging Technologies 18, no. 5 (2010): 727–740. Geman, Stuart, Elie Bienenstock, and René Doursat. “Neural Networks and the Bias/Variance Dilemma.” Neural Computation 4, no. 1 (1992): 1–58. Gigerenzer, Gerd. “A Theory Integration Program.” Decision 4, no. 3 (2017): 133–145. Gigerenzer, Gerd. How to Stay Smart in a Smart World. London, UK: Penguin, 2022. Gigerenzer, Gerd. “On the Supposed Evidence for Libertarian Paternalism.” Review of Philosophy and Psychology 6, no. 3 (2015): 361–383. Gigerenzer, Gerd, and Henry Brighton. “Homo Heuristicus: Why Biased Minds Make Better Inferences.” Topics in Cognitive Science 1, no. 1 (2009): 107– 143. Gigerenzer, Gerd, Peter M. Todd, and the ABC Research Group. Simple Heuristics That Make Us Smart. New York, NY: Oxford University Press, 1999.

208

BIBLIOGRAPHY

Gigerenzer, Gerd, Ralph Hertwig, and Thorsten Pachur, eds. Heuristics: The Foundations of Adaptive Behavior. New York, NY: Oxford University Press, 2011. Gigerenzer, Gerd, and Reinhard Selten, eds. Bounded Rationality: The Adaptive Toolbox. Cambridge, MA: MIT Press, 2002. Gibreth, Frank B. Jr., and Ernestine Gilbreth Carey. Cheaper by the Dozen. New York: Thomas Y. Crowell, 1994. Giering, Götz. Process-Tracing Choice Quality in Riskless Multi-Attribute Decisions. PhD dissertation, Loughborough University, 2021. Gilovich, Thomas, Robert Vallone, and Amos Tversky. “The Hot Hand in Basketball: On the Misperception of Random Sequences.” Cognitive Psychology 17, no. 3 (1985): 295–314. Gladwin, Christina H. Ethnographic Decision Tree Modeling. Newbury Park, CA: Sage, 1989. Glöckner, Andreas, and Thorsten Pachur. “Cognitive Models of Risky Choice: Parameter Stability and Predictive Accuracy of Prospect Theory.” Cognition 123, no. 1 (2012): 21–32. Glymour, Clark. “Bayesian Ptolemaic Psychology.” In Probability and Inference: Essays in Honour of Henry E. Kyburg Jr. London: King’s College Publications, 2007. Glymour, Clark. “Osiander’s Psychology.” Behavioral and Brain Sciences 34, no. 4 (2011): 199–200. Goldstein, Daniel G., and Gerd Gigerenzer. “Models of Ecological Rationality: The Recognition Heuristic.” Psychological Review 109, no. 1 (2002): 75–90. Goltsos, Thanos E., Aris A. Syntetos, Christoph H. Glock, and George Ioannou. “Inventory–Forecasting: Mind the Gap.” European Journal of Operational Research 299, no. 2 (2022): 397–419. Goodwin, Paul. “Integrating Management Judgment and Statistical Methods to Improve Short-Term Forecasts.” Omega: The International Journal of Management Science 30 no. 2 (2002): 127–135. Goodwin, Paul, Brent Moritz, and Enno Siemsen. “Forecast Decisions.” In The Handbook of Behavioral Operations, eds. Karen Donohue, Elena Katok, and Stephen Leider, 433–458. Hoboken, NJ: Wiley, 2018. Griffiths, Thomas L. “Manifesto for a New (Computational) Cognitive Revolution.” Cognition, 135 (2015): 21–23. Güth, Werner. “On Ultimatum Bargaining Experiments—A Personal Review.” Journal of Economic Behavior and Organization 27, no. 3 (1995): 329–344. Güth, Werner, and Martin G. Kocher. “More Than Thirty Years of Ultimatum Bargaining Experiments: Motives, Variations, and a Survey of the Recent Literature.” Journal of Economic Behavior and Organization 108 (2014): 396–409.

BIBLIOGRAPHY

209

Güth, Werner, and Matthias Sutter. “Fairness in the Mail and Opportunism in the Internet: A Newspaper Experiment on Ultimatum Bargaining.” German Economic Review 4, no. 2 (2003): 243–265. Güth, Werner, Rolf Schmittberger, and Bernd Schwarze. “An Experimental Analysis of Ultimatum Bargaining.” Journal of Economic Behavior and Organization 3, no. 4 (1982): 367–388. Haksöz, Ça˘grı. Risk Intelligent Supply Chains: How Leading Turkish Companies Thrive In the Age of Fragility. Boca Raton, FL: CRC Press, 2013. Haksöz, Ça˘grı, Konstantinos V. Katsikopoulos, and Gerd Gigerenzer. “Less Can Be More: How to Make Operations More Flexible and Robust with Fewer Resources.” Chaos: An Interdisciplinary Journal of Nonlinear Science 28, no. 6 (2018): 063102. Hämäläinen, Raimo P., Jukka Luoma, and Esa Saarinen. “On the Importance of Behavioral Operational Research: The Case of Understanding and Communicating about Dynamic Systems.” European Journal of Operational Research 228, no. 3 (2013): 623–634. Hammond, Kenneth R. Human Judgment and Social Policy: Irreducible Uncertainty, Inevitable Error, Unavoidable Injustice. Oxford: Oxford University Press, 1996. Hariskos, Wasilios, and Konstantinos V. Katsikopoulos. “A Heuristic Theory of Other Regarding Preferences.” Working paper (Erfurt, Germany: 2017). Harris, Ford W. “How Much Stock to Keep on Hand.” Factory: The Magazine of Management, 10 (1913): 240–241. Harrison, Glenn W., and John A. List. “Field Experiments.” Journal of Economic literature 42, no. 4 (2004): 1009–1055. Haruvy, Ernan, Elena Katok, and Valery Pavlov. “Bargaining Process and Channel Efficiency.” Management Science 66, no. 7 (2020): 2845–2860. Hayden, Benjamin Y., and Michael L. Platt. “The Mean, the Median, and the St. Petersburg Paradox.” Judgment and Decision Making 4, no. 4 (2009), 260. Henrich, Joseph, et al. “In Search of Homo Economicus: Behavioral Experiments in 15 Small-Scale Societies.” American Economic Review 91, no. 2 (2001): 73–78. Hertwig, Ralph, and Thorsten Pachur. “Heuristics, History of.” In International Encyclopaedia of the Social and Behavioral Sciences, ed. James D. Wright, 829– 835. Amsterdam, Netherlands: Elsevier, 2015. Hertwig, Ralph, and Till Grüne-Yanoff. “Nudging and Boosting: Steering or Empowering Good Decisions?” Perspectives on Psychological Science 12, no. 6 (2017): 973–986. Hertwig, Ralph, Timothy J. Pleskac, Thorsten Pachur, and the ARC Research Group. Taming Uncertainty. Cambridge, MA: MIT Press, 2019. Hertwig, Ralph, Ulrich Hoffrage, and the ABC Research Group. Simple Heuristics in a Social World. New York: Oxford University Press, 2013.

210

BIBLIOGRAPHY

Hertwig, Ralph, Urs Fischbacher, and Adrian Bruhin. “Simple Heuristics in a Social Game.” In Ralph Hertwig, Ulrich Hoffrage and the ABC Research Group, Simple Heuristics in a Social World, 39–65. Oxford, UK: Oxford University Press, 2013. Heukelom, Floris. “A History of the Allais Paradox.” The British Journal for the History of Science (2015): 147–169. Hogarth, Robin M., and Natalia Karelaia. “Simple Models for Multiattribute Choice with Many Alternatives: When It Does and Does Not Pay to Face Trade-Offs with Binary Attributes.” Management Science 51, no. 12 (2005): 1860–1872. Holewinski, Sarah. “Escalation of Force: The Civilian Perspective.” In Escalation of Force Handbook, Center for Army Lessons Learned, 81–82. Fort Leavenworth, KS, 2017. Holte, Robert C. “Very Simple Classification Rules Perform Well on Most Commonly Used Datasets.” Machine Learning 11, no. 1 (1993): 63–90. Hoskin, Robert E. “Opportunity Cost and Behavior.” Journal of Accounting Research (1983): 78–95. Hutchins, Edwin. Cognition in the Wild. Cambridge, MA: MIT Press, 1995. Huysmans, Johan, et al. “An Empirical Evaluation of the Comprehensibility of Decision Table, Tree and Rule Based Predictive Models.” Decision Support Systems 51, no. 1 (2011): 141–154. Ioannidis, John P. A., Sally Cripps, and Martin A. Tanner. “Forecasting for COVID-19 Has Failed.” International Journal of Forecasting 38, no. 2 (2022): 423–438. Jarecki, Jana B., Jolene H. Tan, and Mirjam A. Jenny. “A Framework for Building Cognitive Process Models.” Psychonomic Bulletin and Review (2020): 1–12. Johnson, Eric J., and Daniel G. Goldstein. “Do Defaults Save Lives?” Science 302, no. 5649 (2003): 1338–1339. Johnson, Eric J., Michael Schulte-Mecklenbeck, and Martijn C. Willemsen. “Process Models Deserve Process Data: Comment on Brandstätter, Gigerenzer, and Hertwig (2006).” Psychological Review 115, no. 1 (2008): 263–272. Jorland, Gerárd. “The Saint Petersburg Paradox 1713–1937.” In The Probabilistic Revolution: Ideas in History Vol 1, eds. Lorenz Krüger, Lorraine J. Daston, and Michael Heidelberger, 157–190. Cambridge, MA: MIT Press, 1987. Kahneman, Daniel. “Maps of Bounded Rationality: Psychology for Behavioral Economics.” American Economic Review 93, no. 5 (2003): 1449–1475. Kahneman, Daniel, and Amos Tversky. “Prospect Theory: An Analysis of Decision Under Risk.” Econometrica, 47, no. 2 (1979): 263–291.

BIBLIOGRAPHY

211

Kaur, Harmanpreet, et al. “Interpreting Interpretability: Understanding Data Scientists’ Use of Interpretability Tools for Machine Learning.” In Proceedings of the 2020 CHI Conference on Human Factors in Computing Systems (Hawaii, 2020): 1–14. Karaliopoulos, Merkourios, Konstantinos V. Katsikopoulos, and Lambros Lambrinos. “Bounded Rationality Can Make Parking Search More Efficient: The Power of Lexicographic Heuristics.” Transportation Research Part B: Methodological 101 (2017): 28–50. Katsikopoulos, Konstantinos V. “Advanced Guide Signs and Behavioral Decision Theory.” In Handbook of Driving Simulation for Engineering, Medicine, and Psychology: An Overview, eds. Donald L. Fisher et al., 371–378. Boca Raton, FL: CRC Press, 2011. Katsikopoulos, Konstantinos V. “Bounded Rationality: The Two Cultures.” Journal of Economic Methodology 21, no. 4 (2014): 361–374. Katsikopoulos, Konstantinos V. “Psychological Heuristics for Making Inferences: Definition, Performance, and the Emerging Theory and Practice.” Decision Analysis 8, no. 1 (2011): 10–29. Katsikopoulos, Konstantinos V. “The Merits of Transparent Models.” In Behavioral Operational Research: A Capabilities Approach, eds. Leroy White, Jonathan Malpass, Martin Kunc, and Katharina Burger, 261–275. London: Palgrave Macmillan, 2020. Katsikopoulos, Konstantinos V., Yawa Duse-Anthony, Donald L., Fisher, and Susan A. Duffy. “Risk Attitude Reversals in Drivers’ Route Choice When Range of Travel Time Information Is Provided.” Human Factors 44, no. 3 (2002): 466–473. Katsikopoulos, Konstantinos V., and Ana Paula Bortoleto. “Congestion and Carbon Emissions.” In Handbook of Human Factors for Automated, Connected, and Intelligent Vehicles, eds. Donald L. Fisher et al., eds., 441–453. Boca Raton, FL: CRC Press, 2020. Katsikopoulos, Konstantinos V., and Barbara Fasolo. “New Tools for Decision Analysts.” IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 36, no. 5 (2006): 960–967. Katsikopoulos, Konstantinos V., and Gerd Gigerenzer. “Behavioral Operations Management: A Blind Spot and a Research Program.” Journal of Supply Chain Management 49, no. 1 (2013): 3–7. Katsikopoulos, Konstantinos V., and Gerd Gigerenzer. “One-Reason DecisionMaking: Modeling Violations of Expected Utility Theory.” Journal of Risk and Uncertainty 37, no. 1 (2008): 35–56. Katsikopoulos, Konstantinos V., Ian N. Durbach, and Theodor J. Stewart. “When Should We Use Simple Decision Models? A Synthesis of Various Research Strands.” Omega 81 (2018): 17–25.

212

BIBLIOGRAPHY

Katsikopoulos, Konstantinos V., and Laura Martignon. “Naïve Heuristics for Paired Comparisons: Some Results on their Relative Accuracy.” Journal of Mathematical Psychology 50, no. 3 (2006): 488–494. Katsikopoulos, Konstantinos V., and Marc C. Canellas. “Decoding Human Behavior with Big Data? Critical, Constructive Input From the Decision Sciences.” AI Magazine 43, no. 1 (2022): 1–13. Katsikopoulos, Konstantinos V., Martin Egozcue, and Luis Fuentes Garcia. “Cumulative Dominance in Multi-Attribute Choice: Benefits and Limits.” EURO Journal on Decision Processes 2, no. 1 (2014): 153–163. Katsikopoulos Konstantinos V., Martin Egozcue, and Luis Fuentes Garcia. “A Simple Model for Mixing Intuition and Analysis.” European Journal of Operational Research 303, no. 2 (2022): 779–789. Katsikopoulos, Konstantinos V., Özgür Sim¸ ¸ sek, Marcus Buckmann, and Gerd Gigerenzer. Classification in the Wild: The Science and Art of Transparent Decision Making. Cambridge, MA: MIT Press, 2020. Katsikopoulos, Konstantinos V., Özgür Sim¸ ¸ sek, Marcus Buckmann, and Gerd Gigerenzer. “Transparent Modeling of Influenza Incidence: Big Data or a Single Data Point from Psychological Theory.” International Journal of Forecasting 38, no. 2 (2022): 613–619. Katsikopoulos, Konstantinos V., and Sascha E. Engelbrecht. “Markov Decision Processes with Delays and Asynchronous Cost Collection.” IEEE Transactions on Automatic Control 48, no. 4 (2003): 568–574. Käki, Anssi, et al. “Newsvendor Decisions Under Supply Uncertainty.” International Journal of Production Research 53, no. 5 (2015): 1544–1560. Keeney, Ralph L., and Howard Raiffa. Decision with Multiple Objectives: Preferences and Value Tradeoffs. New York: Wiley, 1993. Kefalidou, Genovefa, and Thomas C. Ormerod. “The Fast and the not-SoFrugal: Human Heuristics for Optimization Problem Solving.” In Proceedings of the Annual Meeting of the Cognitive Science Society, vol. 36, no. 36 (Quebec City, 2014). Keller, Niklas, and Konstantinos V. Katsikopoulos. “On the Role of Psychological Heuristics in Operational Research; and a Demonstration in Military Stability Operations.” European Journal of Operational Research 249, no. 3 (2016): 1063–1073. Kendall, Graham, et al. “Good Laboratory Practice for Optimization Research.” Journal of the Operational Research Society 67, no. 4 (2016): 676–689. Keynes, John M. Essays in Biography. London: Palgrave Macmillan, 2010. Kimball, George E. “A Critique of Operations Research.” Journal of the Washington Academy of Sciences 48, no. 2 (1958). King, Mervyn, and John Kay. Radical Uncertainty: Decision-Making for an Unknowable Future. London: Hachette, 2020.

BIBLIOGRAPHY

213

Klein, Jonathan H., N. A. D. Connell, and Edgar Meyer. “Operational Research Practice as Storytelling.” Journal of the Operational Research Society 58, no. 12 (2007): 1535–1542. Knight, Frank. Risk, Uncertainty and Profit. Boston, MA: Houghton Mifflin, 1921. Kocabiyikoglu, Ayse, Celile Itir Gogus, and M. Sinan Gönül. “Revenue Management vs. Newsvendor Decisions: Does Behavioral Response Mirror Normative Equivalence?” Production and Operations Management 24, no. 5 (2015): 750–761. Korhonen, Pekka J., Herbert Moskowitz, and Jyrki Wallenius. “Choice Behavior in Interactive Multiple-Criteria Decision Making.” Annals of Operations Research 23, no. 1 (1990): 161–179. Kremer, Mirko, Brent Moritz, and Enno Siemsen. “Demand Forecasting Behavior: System Neglect and Change Detection.” Management Science 57, no. 10 (2011): 1827–1843. Kremer, Mirko, Stefan Minner, and Luk N. Van Wassenhove. “Do Random Errors Explain Newsvendor Behavior?” Manufacturing and Service Operations Management 12, no. 4 (2010): 673–681. Krüger, Paul M., et al. “Discovering Rational Heuristics for Risky Choice.” Working paper (Princeton, NJ: Princeton University, 2022). Kumar, Elizabeth I., et al. “Problems with Shapley-Value-Based Explanations as Feature Importance Measures.” In International Conference on Machine Learning (Vienna, 2020): 5491–5500. Kunc, Martin H., Jonathan Malpass, and Leroy White, eds. Behavioral Operational Research: Theory, Methodology and Practice. London: Palgrave Macmillan, 2016. Lasi, Heiner, Peter Fettke, Hans-Georg Kemper, Thomas Feld, and Michael Hoffmann. “Industry 4.0.” Business and Information Systems Engineering 6, no. 4 (2014): 239–242. Lazer, David, Ryan Kennedy, Gary King, and Alessandro Vespignani. “The Parable of Google Flu: Traps in Big Data Analysis.” Science 343, no. 6176 (2014): 1203–1205. Lee, Yun Shin, Yong Won Seo, and Enno Siemsen. “Running Behavioral Operations Experiments Using Amazon’s Mechanical Turk.” Production and Operations Management 27, no. 5 (2018): 973–989. Leider, Stephen. “Behavioral Analysis of Strategic Interactions: Game Theory, Bargaining, and Agency.” In The Handbook of Behavioral Operations, eds. Karen Donohue, Elena Katok, and Stephen Leider, 237–285. Hoboken, NJ: Wiley, 2018. Leland, Jonathan W. “Generalized Similarity Judgments: An Alternative Explanation for Choice Anomalies.” Journal of Risk and Uncertainty 9, no. 2 (1994): 151–172.

214

BIBLIOGRAPHY

Lessmann, Stefan, Bart Baesens, Hsin-Vonn Seow, and Lyn C. Thomas. “Benchmarking State-of-the-Art Classification Algorithms for Credit Scoring: An Update of Research.” European Journal of Operational Research 247, no. 1 (2015): 124–136. Lichtenberg, Jan Malte, and Özgür Sim¸ ¸ sek. “Simple Regression Models.” Proceedings of the Neural Information Processing Systems 2016 Workshop on Imperfect Decision Makers 58 (2017): 13–25. Lipton, Zachary C. “The Mythos of Model Interpretability: In Machine Learning, the Concept of Interpretability Is Both Important and Slippery.” ACM Queue 16, no. 3 (2018): 31–57. Lo, Andrew W., and Mark T. Mueller. “Warning: Physics Envy May Be Hazardous to Your Wealth!” https://papers.ssrn.com/sol3/papers.cfm?abs tract_id=1563882. Loch, Christoph H., and Yaozhong Wu. Behavioral Operations Management. Norwell, MA: Now Publishers, 2007. Long, Xiaoyang, and Javad Nasiry. “Prospect Theory Explains Newsvendor Behavior: The Role of Reference Points.” Management Science 61, no. 12 (2015), 3009–3012. Lopes, Lola L., and Gregg C. Oden. “The Role of Aspiration Level in Risky Choice: A Comparison of Cumulative Prospect Theory and SP/A Theory.” Journal of Mathematical Psychology 43, no. 2 (1999): 286–313. Lu, Yina, Andrés Musalem, Marcelo Olivares, and Ariel Schilkrut. “Measuring the Effect of Queues on Customer Purchases.” Management Science 59, no. 8 (2013): 1743–1763. Luan, Shenghua, and Jochen Reb. “Fast-and-Frugal Trees as Non-Compensatory Models of Performance-Based Personnel Decisions.” Organizational Behavior and Human Decision Processes 141 (2017): 29–42. Luan, Shenghua, Lael J. Schooler, and Gerd Gigerenzer. “A Signal-Detection Analysis of Fast-and-Frugal Trees.” Psychological Review 118, no. 2 (2011): 316–338. Luce, R. Duncan. “Four Tensions Concerning Mathematical Modeling in Psychology.” Annual Review of Psychology 46 (1995): 1–26. Luce, R. Duncan. “Semi-Orders and a Theory of Utility Discrimination.” Econometrica (1956): 178–191. Luce, R. Duncan. “On the Possible Psychophysical Laws.” Psychological Review 66, no. 2 (1959): 81–95. Lundberg, Scott M., and Su-In Lee. “A Unified Approach to Interpreting Model Predictions.” Advances in Neural Information Processing Systems (Long Beach, CA: 2017): 4765–4774. Lurie, Nicholas H., and Jayashankar M. Swaminathan. “Is Timely Information Always Better? The Effect of Feedback Frequency on Decision Making.”

BIBLIOGRAPHY

215

Organizational Behavior and Human Decision processes 108, no. 2 (2009): 315–329. Maccrimmon, Kenneth R. “Descriptive and Normative Implications of the Decision-Theory Postulates.” In Risk and Uncertainty, eds. K. Borch and J. Mossin (International Economic Association Conference, London: Palgrave Macmillan, 1968): 3–32. Maier, Maximilian, František Bartoš, T. D. Stanley, David R. Shanks, Adam J. L. Harris, and Eric-Jan Wagenmakers. “No Evidence for Nudging after Adjusting for Publication Bias.” Proceedings of the National Academy of Sciences 119, no. 31 (2022): e2200300119. Makridakis, Spyros, Rob J. Hyndman, and Fotios Petropoulos. “Forecasting in Social Settings: The State of the Art.” International Journal of Forecasting 36, no. 1 (2020): 15–28. Makridakis, Spyros, and Michele Hibon. “Accuracy of Forecasting: An Empirical Investigation.” Journal of the Royal Statistical Society: Series A (General) 142, no. 2 (1979): 97–125. Mallon, Eamonn B., and Nigel R. Franks. “Ants Estimate Area using Buffon’s Needle.” Proceedings of the Royal Society of London. Series B: Biological Sciences 267, no. 1445 (2000): 765–770. Manski, Charles F. “The Structure of Random Utility Models.” Theory and Decision 8, no. 3 (1977): 229–254. Manzini, Paola, and Marco Mariotti. “Sequentially Rationalizable Choice.” American Economic Review 97, no. 5 (2007): 1824–1839. Markowitz, Harry S. “Portfolio Selection.” The Journal of Finance 7, no. 1 (1952): 77–91. Marshall, Alfred. Principles of Economics. London: Macmillan, 1920. Martignon, Laura, Konstantinos V. Katsikopoulos, and Jan K. Woike. “Categorization with Limited Resources: A Family of Simple Heuristics.” Journal of Mathematical Psychology 52, no. 6 (2008): 352–361. Martignon, Laura, and Ulrich Hoffrage. “Fast, Frugal, and Fit: Simple Heuristics for Paired Comparison.” Theory and Decision 52, no. 1 (2002): 29–71. McFadden, Daniel L. “Quantal Choice Analysis: A Survey.” Annals of Economic and Social Measurement, 5, no. 4 (1976): 363–390. Mehra, Rajnish, and Edward C. Prescott. “The Equity Premium: A Puzzle.” Journal of Monetary Economics 15, no. 2 (1985): 145–161. Miller, Joshua B., and Adam Sanjurjo. “Momentum Isn’t Magic—Vindicating the Hot Hand with the Mathematics of Streaks.” The Conversation (March 28, 2018). Miller, Joshua B., and Adam Sanjurjo. “Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers.” Econometrica 86, no. 6 (2018): 2019–2047.

216

BIBLIOGRAPHY

Miller, Tim, Piers Howe, and Liz Sonenberg. “Explainable AI: Beware of Inmates Running the Asylum or: How I Learnt to Stop Worrying and Love the Social and Behavioural Sciences.” arXiv preprint arXiv:1712.00547 (2017). Mirowski, Philip. “Cyborg Agonistes: Economics Meets Operations Research in Mid-Century.” Social Studies of Science 29, no. 5 (1999): 685–718. Molnar, Christoph. Interpretable Machine Learning. Lulu.com, 2020. Monks, Thomas, et al. “Strengthening the Reporting of Empirical Simulation Studies: Introducing the STRESS Guidelines.” Journal of Simulation 13, no. 1 (2019): 55–67. Montibeller, Gilberto, and Detlof von Winterfeldt. “Cognitive and Motivational Biases in Decision and Risk Analysis.” Risk Analysis 35, no. 7 (2015): 1230– 1251. Morgan, Mary S. “Models, Stories and the Economic World.” Journal of Economic Methodology 8, no. 3 (2001): 361–384. Morgan, Mary S., and Till Grüne-Yanoff. “Modeling Practices in the Social and Human Sciences: An Interdisciplinary Exchange.” Perspectives on Science 21, no. 2 (2013): 143–156. Morse, Philip M., and George E. Kimball. Methods of Operations Research. Cambridge, MA: MIT Press, 1951. Nagarajan, Mahesh, and Steven Shechter. “Prospect Theory and the Newsvendor Problem.” Management Science 60, no. 4 (2014): 1057–1062. Neilson, William, and Jill Stowe. “A Further Examination of Cumulative Prospect Theory Parameterizations.” Journal of Risk and Uncertainty 24, no. 1 (2002): 31–46. Newell, Ben, and Arndt Bröder. “Cognitive Processes, Models and Metaphors in Decision Research.” Judgment and Decision Making 3, no. 3 (2008): 195– 204. Nilssom, Håkan, Jörg Rieskamp, and Eric-Jan Wagenmakers. “Hierarchical Bayesian Parameter Estimation for Cumulative Prospect Theory.” Journal of Mathematical Psychology 55, no. 1 (2011): 84–93. Ockenfels, Axel, and Reinhard Selten. “Impulse Balance in the Newsvendor Game.” Games and Economic Behavior 86 (2014): 237–247. Olsen, Tava Lennon, and Brian Tomlin. “Industry 4.0: Opportunities and Challenges for Operations Management.” Manufacturing and Service Operations Management 22, no. 1 (2020): 113–122. Önkal, Dilek, and M. Sinan Gönül. “Judgmental Adjustment: A Challenge for Providers and Users of Forecasts.” Foresight: The International Journal of Applied Forecasting 1 (2005): 13–17. Open Science Collaboration. “Estimating the Reproducibility of Psychological Science.” Science 349, no. 6251 (2015): aac4716.

BIBLIOGRAPHY

217

Pachur, Pachur, Ralph Hertwig, and Roland Wolkewitz. “The Affect Gap in Risky Choice: Affect-Rich Outcomes Attenuate Attention to Probability Information.” Decision 1, no. 1 (2014): 64–78. Pachur, Thorsten, et al. “Testing Process Predictions of Models of Risky Choice: A Quantitative Model Comparison Approach.” Frontiers in Psychology 4 (2013). Pachur, Thorsten, Renata S. Suter, and Ralph Hertwig. “How the Twain Can Meet: Prospect Theory and Models of Heuristics in Risky Choice.” Cognitive Psychology 93 (2017): 44–73. Pande, Shashwat M., Nadia Papamichail, and Peter Kawalek. “Compatibility Effects in the Prescriptive Application of Psychological Heuristics: Inhibition, Integration and Selection.” European Journal of Operational Research 295, no. 3 (2021): 982–995. Pareto, Vilfredo. Manual of Political Economy. Milan: Bocconi University, 1906. Passi, Samir, and Steven J. Jackson. “Trust in Data Science: Collaboration, Translation, and Accountability in Corporate Data Science Projects.” Proceedings of the ACM on Human-Computer Interaction 2, no. CSCW (2018): 1–28. Payne, John W., James R. Bettman, and Eric J. Johnson. The Adaptive Decision Maker. Cambridge, UK: Cambridge University Press, 1993. Petersen, Malte et al. “Business Education: Does a Focus on Pro-Social Values Increase Student’s Pro-Social Behavior?” Mind and Society, 18(2019): 181– 190. Petracca, Enrico. “A Cognition Paradigm Clash: Simon, Situated Cognition and the Interpretation of Bounded Rationality.” Journal of Economic Methodology 24, no. 1 (2017): 20–40. Petracca, Enrico. “On the Origins and Consequences of Simon’s Modular Approach to Bounded Rationality in Economics.” The European Journal of the History of Economic Thought (2021): 1–24. Phillips, Nathaniel D., Hansjörg Neth, Jan K. Woike, and Wolfgang Gaissmaier. “FFTrees: A Toolbox to Create, Visualize, and Evaluate Fast-and-Frugal Decision Trees.” Judgment and Decision Making 12, no. 4 (2017): 344–368. Pichert, Daniel, and Konstantinos V. Katsikopoulos. “Green Defaults: Information Presentation and Pro-Environmental Behaviour.” Journal of Environmental Psychology 28, no. 1 (2008): 63–73. Pinson, Pierre, and Spyros Makridakis. “Pandemics and Forecasting: The Way Forward Through the Taleb-Ioannidis Debate.” International Journal of Forecasting 38, no. 2 (2022): 410–412. Platt, John R. “Strong Inference.” Science 146 (1964): 347–353. Pleskac, Timothy J., et al. “The Ecology of Competition: A Theory of RiskReward Environments in Adaptive Decision Making.” Psychological Review 128, no. 2 (2020): 115–135.

218

BIBLIOGRAPHY

Porteus, Evan L. Foundations of Stochastic Inventory Theory. Palo Alto, CA: Stanford University Press, 2002. Poursabzi-Sangdeh, Forough, et al. “Manipulating and Measuring Model Interpretability.” In Proceedings of the 2021 CHI Conference on Human Factors in Computing Systems (2021): 1–52. Poyhonen, Samuli, Jaakko Kuorikoski, Timo Ehrig, Konstantinos V. Katsikopoulos, and Shyam Sunder. “Nudge, Boost or Design? Limitations of Behaviorally Informed Policy under Social Interaction.” Journal of Behavioral Economics for Policy 2, no. 1 (2018): 99–105. Prelec, Drazen. “The Probability Weighting Function.” Econometrica (1998): 497–527. Puterman, Martin L. Markov Decision Processes: Discrete Stochastic Dynamic Programming. Hoboken, NJ: Wiley, 2014. Rabin, Matthew. “Incorporating Fairness into Game Theory and Economics.” American Economic Review (1993): 1281–130. Ranehill, Eva, et al. “Assessing the Robustness of Power Posing: No Effect on Hormones and Risk Tolerance in a Large Sample of Men and Women.” Psychological Science 26, no. 5 (2015): 653–656. Rapoport, Amnon, and Vincent Mak. “Strategic Interactions in Transportation Networks.” In The Handbook of Behavioral Operations, eds. Karen Donohue, Elena Katok, and Stephen Leider, 557–586. Hoboken, NJ: Wiley, 2018. Reb, Jochen, Shenghua Luan, and Gerd Gigerenzer. Smart Management: How Heuristics Help Leaders Make Good Decisions in an Uncertain World. Cambridge, MA: MIT Press, in press. Rebonato, Riccardo. Taking Liberties: A Critical Examination of Libertarian Paternalism. Berlin, Germany: Springer, 2012. Refaeilzadeh, Payam, Lei Tang, and Huan Liu. “Cross-Validation.” Encyclopaedia of Database Systems 5 (2009): 532–538. Ren, Yufei, and Rachel Croson. “Overconfidence in Newsvendor Orders: An Experimental Study.” Management Science 59, no. 11 (2013): 2502–2517. Riefer, David M., et al. “Cognitive Psychometrics: Assessing Storage and Retrieval Deficits in Special Populations With Multinomial Processing Tree Models.” Psychological Assessment 14, no. 2 (2002): 184–201. Rieger, Marc O., and Mei Wang. “What Is Behind the Priority Heuristic? A Mathematical Analysis and Comment on Brandstätter, Gigerenzer, and Hertwig (2006).” Psychological Review 115 no. 1 (2008): 274–280. Rieskamp, Jörg. “The Probabilistic Nature of Preferential Choice.” Journal of Experimental Psychology: Learning, Memory, and Cognition 34, no. 6 (2008): 1446–1465. Robinson, Stewart, et al. “Facilitated Modelling With Discrete-Event Simulation: Reality or Myth?” European Journal of Operational Research 234, no. 1 (2014): 231–240.

BIBLIOGRAPHY

219

Rosenhead, Jonathan, and John Mingers. Rational Analysis for a Problematic World Revisited. Hoboken, NJ: Wiley, 2001. Roughgarden, Tim. Selfish Routing and the Price of Anarchy. Cambridge, MA: MIT Press, 2005. Rouyard, Thomas, Bart Engelen, Andrew Papanikitas, and Ryota Nakamura. “Boosting Healthier Choices.” British Medical Journal 376 (2022). Rubinstein, Ariel. “‘Economics and Psychology’? The Case of Hyperbolic Discounting.” International Economic Review 44, no. 4 (2003): 1207–1216. Rubinstein, Ariel. Modeling Bounded Rationality. Cambridge, MA: MIT Press, 1998. Rubinstein, Ariel. “Similarity and Decision-Making Under Risk (Is There a Utility Theory Resolution to the Allais Paradox?” Journal of Economic Theory 46, no. 1 (1988): 145–153. Rudin, Cynthia. “Stop Explaining Black Box Machine Learning Models for High Stakes Decisions and Use Interpretable Models Instead.” Nature Machine Intelligence 1, no. 5 (2019): 206–215. Ruggeri, Kai, et al. “Replicating Patterns of Prospect Theory for Decision Under Risk.” Nature Human Behaviour 4, no. 6 (2020): 622–633. Rumsfeld, Donald P. U.S. Department of Defense News Briefing. Washington, DC, February 12, 2002. Samuelson, Paul A. “A Note on the Pure Theory of Consumer’s Behaviour.” Economica 5, no. 17 (1938): 61–71. Samuelson, Paul A. “St. Petersburg Paradoxes: Defanged, Dissected, and Historically Described.” Journal of Economic Literature 15, no. 1 (1977): 24–55. Sanborn, Adam N., and Nick Chater. “Bayesian Brains Without Probabilities.” Trends in Cognitive Sciences 20, no 12 (2016): 883–893. Sargent, Thomas J. Bounded Rationality in Macroeconomics: The Arne Ryde Memorial Lectures. New York, NY: Oxford University Press, 1993. Savage, Leonard J. The Foundations of Statistics. Mineola, NY: Dover, 1954. Scheibehenne, Benjamin, Rainer Greifeneder, and Peter M. Todd. “Can There Ever Be Too many Options? A Meta-Analytic Review of Choice Overload.” Journal of Consumer Research 37, no. 3 (2010): 409–425. Schiffels, Sebastian, et al. “On the Assessment of Costs in a Newsvendor Environment: Insights from an Experimental Study.” Omega 43 (2014): 1–8. Schmidt, Richard A., and Robert A. Bjork. “New Conceptualizations of Practice: Common Principles in Three Paradigms Suggest New Concepts for Training.” Psychological Science 3, no. 4 (1992): 207–218. Schoemaker, Paul J. H. “Scenario Planning: A Tool for Strategic Thinking.” Sloan Management Review 36, no. 2 (1995): 25–50. Schweitzer, Maurice E., and Gérard P. Cachon. “Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence.” Management Science 46, no. 3 (2000): 404–420.

220

BIBLIOGRAPHY

Seeley, Thomas D. The Wisdom of the Hive: The Social Physiology of Honeybee Colonies. Cambridge, MA: Harvard University Press, 2009. Shapiro, Gary E. “Effect of Expectations of Future Interaction on Reward Allocations in Dyads: Equity or Equality.” Journal of Personality and Social Psychology 31, no. 5 (1975): 873–880. Shefrin, Hersh. Explainable AI as a Tool for Risk Manager. Northfield, MN: Professional Risk Managers’ International Association Institute, 2021. Siegel, Jeremy J., and Richard H. Thaler. “Anomalies: The Equity Premium Puzzle.” Journal of Economic Perspectives 11, no. 1 (1997), 192. Silver, David, et al. “A General Reinforcement Learning Algorithm that Masters Chess, Shogi, and Go through Self-Play.” Science 362, no. 6419 (2018): 1140–1144. Silver, David, et al. “Mastering the Game of Go without Human Knowledge.” Nature 550, no. 7676 (2017): 354–359. Simon, Herbert, A. “A Behavioral Model of Rational Choice.” The Quarterly Journal of Economics 69, no. 1 (1955): 99–118; Simon, Herbert A. Administrative Behavior: A Study of Decision-Making Processes in Administrative Organizations. New York, NY: Macmillan, 1957. Simon, Herbert A. “Rational Choice and the Structure of the Environment.” Psychological Review 63, no. 2 (1956): 129–138. Simon, Herbert A. The Sciences of the Artificial. Cambridge, MA: MIT Press, 1968. Simon, Herbert A. “The Scientist as Problem Solver.” In Complex Information Processing: The Impact of Herbert A. Simon, eds. D. Klahr and K. Kotovsky. Hillsdale, NJ: Lawrence Erlbaum, 1989. Simon, Herbert A. Models of Bounded Rationality: Empirically Grounded Economic Reason. Cambridge, MA, MIT press, 1997. Simon, Herbert A., and Allen Newell. “Heuristic Problem Solving: The Next Advance in Operations Research,” Operations Research 6, no. 1 (1958): 1–10. Simon, Herbert A., and Allen Newell. “Reply: Heuristic Problem Solving.” Operations Research 6, no. 3 (1958): 449–450. Sim¸ ¸ sek, Özgür. “Linear Decision Rule as Aspiration for Simple Decision Heuristics.” Advances in Neural Information Processing Systems (2013): 2904–2912. Slovic, Paul, et al. “The Affect Heuristic.” European Journal of Operational Research 177, no. 3 (2007): 1333–1352. Smith, Adam. An Inquiry into the Nature and Causes of the Wealth of Nations. London: W. Strahan and T. Cadell, 1776. Smith, Patti. Year of the Monkey. London, UK: Bloomsbury Publishing, 2012. Spiliopoulos, Leonidas, and Andreas Ortmann. “The BCD of Response Time Analysis in Experimental Economics.” Experimental Economics 21, no. 2 (2018): 383–433.

BIBLIOGRAPHY

221

Spiliopoulos, Leonidas, Andreas Ortmann, and Le Zhang. “Complexity, Attention, and Choice in Games Under Time Constraints: A Process Analysis.” Journal of Experimental Psychology: Learning, Memory, and Cognition 44, no. 10 (2018): 1609–1640. Spiliopoulos, Leonidas, and Ralph Hertwig. “A Map of Ecologically Rational Heuristics for Uncertain Strategic Worlds.” Psychological Review 127, no. 2 (2020): 245–280. Stangl, Tobias, and Ulrich W. Thonemann. “Equivalent Inventory Metrics: A Behavioral Perspective.” Manufacturing and Service Operations Management 19, no. 3 (2017): 472–488. Starmer, Chris. “Developments in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice Under Risk.” Journal of Economic Literature 38, no. 2 (2000): 332–382. Stewart, Ian. Do Dice Play God?: The Mathematics of Uncertainty. London: Hachette, 2019. Stigler, George J. “The Economics of Information.” Journal of Political Economy 69, no. 3 (1961): 213–225. Stocker, Alan A., and Eero P. Simoncelli. “Noise Characteristics and Prior Expectations in Human Visual Speed Perception.” Nature Neuroscience 9, no. 4 (2006): 578–585. Stone, Mervyn. “Cross-Validatory Choice and Assessment of Statistical Predictions.” Journal of the Royal Statistical Society: Series B (Methodological) 36, no. 2 (1974): 111–133. Su, Xuanming. “Bounded Rationality in Newsvendor Models.” Manufacturing and Service Operations Management 10, no. 4 (2008): 566–589. Sull, Donald N., and Kathleen M. Eisenhardt. Simple Rules: How to Thrive in a Complex World. Boston: Houghton Mifflin Harcourt, 2015. Syntetos, Aris A., Inna Kholidasari, and Mohamed M. Naim. “The Effects of Integrating Management Judgement Into OUT Levels: In or Out of Context?” European Journal of Operational Research 249, no. 3 (2016): 853–863. Syntetos, Aris A., Nicholas C. Georgantzas, John E. Boylan, and Brian Dangerfield. “Judgement and Supply Chain Dynamics.” Journal of the Operational Research Society 62 (2011): 1138–1158. Tako, Antuela, A., Naoum Tsioptsias, and Stewart Robinson. “Can We Learn From Simplified Simulation Models? An Experimental Study on User Learning.” Journal of Simulation 14, no. 2 (2020): 130–144. Taleb, Nassim Nicholas. Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets. New York: Random House, 2005. Taleb, Nassim Nicholas. Skin in the Game: Hidden Asymmetries in Daily Life. New York, NY: Allen Lane, 2018.

222

BIBLIOGRAPHY

Taleb, Nassim Nicholas, Yaneer Bar-Yam, and Pasquale Cirillo. “On Single Point Forecasts for Fat-Tailed Variables.” International Journal of Forecasting 38, no. 2 (2022): 413–422. Tang, Christopher, and Brian Tomlin. “The Power of Flexibility for Mitigating Supply Chain Risks.” International Journal of Production Economics 116, no. 1 (2008): 12–27. Thaler, Richard H., and Cass R. Sunstein. Nudge: Improving Decisions about Health, Wealth, and Happiness. New York: Penguin, 2009. Thurstone, Louis L. “A Law of Comparative Judgment.” Psychological Review 34, no. 4 (1927): 273–286. Tisdell, Clement A. Advanced Introduction to Bounded Rationality. Cheltenham, UK: Edward Elgar, 2022. Todd, Peter M. “How Much Information Do We Need?” European Journal of Operational Research 177, no. 3 (2007): 1317–1332 Todd, Peter M., and Gerd Gigerenzer. “Bounding Rationality to the World.” Journal of Economic Psychology 24, no. 2 (2003): 143–165. Todd, Peter M., Gerd Gigerenzer, and the ABC Research Group. Ecological Rationality: Intelligence in the World. New York, NY: Oxford University Press, 2012. Tversky, Amos. “Choice by Elimination.” Journal of Mathematical Psychology 9, no. 4 (1972): 341–367. Tversky, Amos. “Elimination by Aspects: A Theory of Choice.” Psychological Review 79, no. 4 (1972): 281–299. Tversky, Amos, and Craig R. Fox. “Weighing Risk and Uncertainty.” Psychological Review 102, no. 2 (1995): 269–283. Tversky, Amos, and Daniel Kahneman. “Judgment under Uncertainty: Heuristics and Biases.” Science 185, no. 4157 (1974): 1124–1131. Tversky, Amos, and Daniel Kahneman. “Advances in Prospect Theory: Cumulative Representation of Uncertainty.” Journal of Risk and Uncertainty 5, no. 4 (1992): 297–323. van Roekel, Henrico, Joanne Reinhard, and Stephan Grimmelikhuijsen. “Improving Hand Hygiene in Hospitals: Comparing the Effect of a Nudge and a Boost on Protocol Compliance.” Behavioural Public Policy 6, no. 1 (2022): 52–74. Viale, Riccardo. Nudging. Cambridge, MA: MIT Press, 2022. Viale, Riccardo, ed. Routledge Handbook of Bounded Rationality. Milton Park, UK: Routledge, 2020. Vipin, B., and R. K. Amit. “Describing Decision Bias in the Newsvendor Problem: A Prospect Theory Mode.” Omega 82 (2019): 132–141. von Neumann, John, and Oskar Morgenstern. Theory of Games and Economic Behavior. Princeton: Princeton University Press, 1944.

BIBLIOGRAPHY

223

von Winterfeldt, Detlof, and Ward Edwards. Decision Analysis and Behavioral Research. Cambridge, UK: Cambridge University Press, 1986. Wakker, Peter P. Prospect Theory for Risk and Ambiguity. Cambridge, UK: Cambridge University Press, 2010. Wertheimer, Max. “Studies on the Theory of Gestalt II.” Psychological Research 4 (1923): 301–350. White, Leroy, Martin H. Kunc, Katharina Burger, and Jon Malpass, eds. Behavioral Operational Research: A Capabilities Approach. London: Palgrave Macmillan, 2020. Williams, Terry, Knut Samset, and Kjell Sunnevåg eds. Making Essential Choices with Scant Information: Front-End Decision Making in Major Projects. London: Palgrave Macmillan, 2009. Wilks, Samuel S. “Weighting Systems for Linear Functions of Correlated Variables when There Is No Dependent Variable.” Psychometrika 3, no. 1 (1938): 23–40. Woodside, Arch G. “Moving Beyond Multiple Regression Analysis to Algorithms: Calling for Adoption of a Paradigm Shift from Symmetric to Asymmetric Thinking in Data Analysis and Crafting Theory.” Journal of Business Research 66, no. 4 (2013): 463–472. Woodside, Arch G. “Seating Gigerenzer, Gladwin, McClelland, Sheth and Simon at the Same Table: Constructing Workbench Theories of Decision Processes That Predict Outcomes Accurately.” In Handbook of Advances in Marketing in an Era of Disruptions: Essays in Honour of Jagdish N. Sheth, eds. Atul Parvatiyar, and Rajendra Sisodia, 445–480. New Delhi, India: Sage, 2019. Wu, George, and Richard Gonzalez. “Curvature of the Probability Weighting Function.” Management Science 42, no. 12 (1996): 1676–1690. Wuttke, David, Ankit Upadhyay, Enno Siemsen, and Alexandra WuttkeLinnemann. “Seeing the Bigger Picture? Ramping up Production with the Use of Augmented Reality.” Manufacturing and Service Operations Management 24, no. 4 (2022): 2349–2366. Yaari, Menahem E. “The Dual Theory of Choice Under Risk.” Econometrica (1987): 95–115. Yechiam, Eldad. “Acceptable Losses: The Debatable Origins of Loss Aversion.” Psychological Research 83, no. 7 (2019): 1327–1339. Zhang, Yinghao, and Enno Siemsen. “A Meta-Analysis of Newsvendor Experiments: Revisiting the Pull-to-Center Asymmetry.” Production and Operations Management 28, no. 1 (2019): 140–156. Zhao, Sihai Dave, Giovanni Parmigiani, Curtis Huttenhower, and Levi Waldron. “Más-O-Menos: A Simple Sign Averaging Method for Discrimination in Genomic Data Analysis.” Bioinformatics 30, no. 21 (2014): 3062–3069.

224

BIBLIOGRAPHY

Zhao, Yingshuai, and Xiaobo Zhao. “How a Competing Environment Influences Newsvendor Ordering Decisions.” International Journal of Production Research 54, no. 1 (2016): 204–214.

Author Index

A Ackoff, Russell L., 3, 144, 154, 162, 165, 171, 172, 178 Albers, Walter, 66 Allon, Gad, 8, 164 Analytis, Pantelis Pipergias, 72 Arkes, Hal R., 101 Arnauld, Antoine, 70 Arrow, Kenneth J., 134 Arshad, Adam, 180 Artinger, Florian M., 8 Aumann, Robert J., 75, 76, 79, 98 Avenhaus, Rudolf, 164

B Bachrach, Daniel G., 7, 29, 51, 69, 185 Baesens, Bart, 165 Bandura, Albert, 179 Barkoczi, Daniel, 72 Bearden, Neil J., 7 Becker-Peth, Michael, 134, 135, 137 Bell, David E., 7

Bellman, Richard, 130, 131, 140, 141, 144, 162 Benartzi, Shlomo, 64, 191, 197 Bendoly, Elliot, 3, 7, 8, 29, 32, 34, 51, 69, 144, 184, 185 Bernoulli, Daniel, 189, 196 Bertsimas, Dimitris, 71 Bettman, James R., 55, 71 Bingham, Christopher M., 31 Binmore, Kenneth G., 96 Birnbaum, Michael H., 67, 69, 70 Bjork, Robert A., 179 Blavatskyy, Pavlo R., 30, 190, 196 Bolton, Gary E., 26, 63, 96, 98, 108, 109, 121, 135, 137 Bond, Michael, 10, 180 Bostian, A.J.A., 121, 137, 139 Bourgin, David D., 69 Boylan, John E., 33, 136 Brandstätter, Edouard, 42, 47, 52, 53, 63, 65, 67, 70 Breiman, Leo, 9, 31, 71, 156 Brighton, Henry, 157, 166, 167 Bröder, Arndt, 156, 165

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6

225

226

AUTHOR INDEX

Bruner, Jerome S., 163 Buckmann, Marcus, 8, 29, 72, 139, 167, 168 Burger, Katharina, 7, 29 Busemeyer, Jerome M., 63

C Cachon, Gérard P., 107, 108, 111, 113, 114, 118, 121, 134, 136, 137, 139 Camerer, Colin F., 8, 68, 96–98 Canellas, Marc C., 71–73, 141 Carney, Dana R., 33 Carter, Craig R., 7, 34 Castle, Jennifer, 168, 169 Chater, Nick, 63, 100 Clausing, Don P., 101 Copernicus, Nicolaus, 69 Craik, Fergus, I.M., 179 Croson, Rachel, 7, 139, 185 Cui, Tony H., 29, 63 Currie, Christine, S.M., 8, 70

D Daskalakis, Constantinos, 100 Daston, Lorraine, 28 Davis, Andrew M., 29, 33, 63 Dawes, Robyn M., 34, 67, 165 De Miguel, Victor, 66 De Vericourt, Francis, 138 Domingos, Pedro, 68 Donohue, Karen, 2, 5, 7–9, 29, 32, 63, 66, 96, 97, 101, 134, 136, 172, 178, 183, 185 Drechsler, Mareile, 65 Durbach, Ian N., 9, 66–68, 165

E Eckerd, Stephanie, 3, 8, 28, 34, 184, 185

Edgeworth, Francis Y., 134 Edwards, Ward, 22, 28, 30–32 Eeckhoudt, Louis, 136 Ehrig, Timo, 180 Einhorn, Hillel J., 67 Eisenhardt, Kathleen M., 9, 19, 31 Eliot, George, 143, 162 Epley, Nicholas, 137 Erev, Ido, 50, 67, 69 Erickson, Paul, 96 F Fahimnia, Behnam, 7, 185 Fehr, Ernst, 81, 82, 86, 97–99, 197 Feng, Tianjun, 121, 138 Feynman, Richard P., 30 Fildes, Robert, 114, 137 Fischbacher, Urs, 70, 83, 84, 88, 97, 99 Fishburn, Peter C., 64, 65, 101 Flick, Uwe, 33 Forrester, Jay W., 162 Franco, L. Alberto, 144, 162, 178 Frederik, Jesse, 72 Friedman, Daniel, 69 Friedman, Milton, 8, 16, 21, 30, 38, 51 Fung, Victor K., 165 G Geman, Stuart, 157, 167 Giering, Götz, 70 Gigerenzer, Gerd, 8–10, 19, 29–31, 42, 63, 65–73, 101, 129, 135, 139–141, 145, 153, 155, 157, 164, 166–169, 178, 196 Gilbreth, Ernestine, 7 Gilbreth, Frank B. Jr., 7 Gilovich, Thomas, 33, 137 Glöckner, Andreas, 67, 68 Glymour, Clark, 51, 69

AUTHOR INDEX

Goldstein, Daniel G., 166, 179 Goltsos, Thanos E., 136, 139, 140 Gönül, M. Sinan, 137, 138 Gonzalez, Richard, 30, 65, 68, 72, 196 Goodwin, Paul, 29, 32, 33, 116, 136, 137, 139 Griffiths, Thomas L., 72 Grüne-Yanoff, Till, 10, 63, 175, 178, 180 Güth, Werner, 66, 77, 79, 80, 91, 97, 98, 100 H Haksöz, Ça˘grı, 152–154, 164, 169 Hämäläinen, Raimo P., 7, 162, 178 Hammond, Kenneth R., 63 Harris, Ford W., 105, 106, 113, 134 Harrison, Glenn W., 179 Haruvy, Ernan, 97 Henrich, Joseph, 79, 98 Hertwig, Ralph, 10, 29, 31, 42, 63, 65, 68, 70, 73, 83–92, 97–101, 166, 175, 178, 180 Herzog, Stefan M., 72 Heukelom, Floris, 64 Hibon, Michele, 67, 165 Hoffrage, Ulrich, 68, 97, 166, 168 Hogarth, Robin M., 67, 68, 100, 158, 167, 168 Holte, Robert C., 165 Hoskin, Robert E., 134 Hutchins, Edwin, 162 Huysmans, Johan, 31 Hyndman, Rob J., 67 I Ioannidis, John P. A., 139 J Jarecki, Jana B., 31, 70

227

Johnson, Eric J., 55, 70, 71, 179 Jorland, Gerárd, 64, 196 K Kahneman, Daniel, 8, 16, 18, 28–30, 37, 40, 41, 46, 47, 58, 63–67, 70, 114, 129, 137, 140, 187, 188, 196 Karelaia, Natalia, 67, 100, 167 Katok, Elena, 7, 26, 29, 63, 97, 121, 134, 135, 137 Katsikopoulos, Konstantinos V., 8, 9, 29–32, 63, 65, 67–74, 100, 101, 139–141, 147, 151, 163–168, 179, 180, 196, 197 Kaufmann, Lutz, 7, 34 Kay, John, 24, 32, 69, 72, 162 Keeney, Ralph L., 168 Kefalidou, Genovefa, 73 Keller, Niklas, 146, 147, 149–151, 163, 164, 197 Keynes, John M., 35, 63, 162 Kimball, George, E., 134, 165 King, Mervyn, 24, 32, 69, 72, 162 Kirlik, Alex, 9 Klein, Jonathan H., 9 Knight, Frank, 14, 29 Kocabiyikoglu, Ayse, 138 Korhonen, Pekka J., 7, 10 Kremer, Mirko, 8, 32, 139 Kunc, Martin H., 7, 10, 29, 32, 144 Kuorikoski, Jaako, 180 L Lasi, Heiner, 178 Lazer, David, 168 Lee, Yun Shin, 121, 138 Leider, Stephen, 7, 29, 63, 97, 134 Leland, Jonathan W., 74 Leppänen, Ilkka, 178 Lessmann, Stefan, 165

228

AUTHOR INDEX

Lichtenberg, Jan Malte, 157, 167 Lipton, Zachary, C., 9 List, John A., 179 Lo, Andrew W., 162 Loch, Christoph H., 7, 29, 32, 63, 96 Loewenstein, George, 8 Long, Xiaoyang, 113, 136, 193, 197 Lopes, Lola L., 67 Luan, Shenghua, 65, 66, 141, 169, 178 Luce, R. Duncan, 63, 73, 135 M Maier, Maximilian, 181 Makridakis, Spyros, 67, 139, 165 Mallon, Eamonn B., 30 Malpass, Jonathan, 7, 29 Manski, Charles F., 136 Manzini, Paola, 101 Mariotti, Marco, 101 Markowitz, Harry S., 16, 29, 30, 37, 46, 64 Marshall, Alfred, 14, 28, 32 Martignon, Laura, 65, 68, 100, 156, 166–168 McFadden, Daniel L., 135 Mehra, Rajnish, 196 Miller, Joshua B., 26, 33 Miller, Tim, 27, 33, 72 Mingers, John, 144, 162 Mirowski, Philip, 101 Molnar, Christoph, 71 Monks, Thomas, 33 Montibeller, Gilberto, 31 Morgan, Mary S., 35, 63 Morgenstern, Oskar, 30, 31, 78, 96 Moritz, Brent, 29, 32, 136 Morse, Philip M., 134 N Nagarajan, Mahesh, 136

Nasiry, Javad, 113, 136, 193, 197 Neilson, William, 30, 68 Newell, Allen, 140 Newell, Ben, 156, 165 Nilssom, Håkan, 30 O Ockenfels, Alex, 98, 108, 111, 112, 135, 136, 197 Olsen, Tava Lennon, 178 Önkal, Dilek, 137 Ortmann, Andreas, 71, 97 Özer, Özalp, 5, 8, 66, 96, 97, 172, 178, 183, 185 P Pachur, Thorsten, 29, 31, 57–59, 67, 68, 70, 73, 166 Pande, Shashwat M., 70 Papamichail, Nadia, 70 Pareto, Vilfredo, 32 Passi, Samir, 72 Payne, John W., 55, 71 Petersen, Malte, 98 Petracca, Enrico, 135, 140 Petropoulos, Fotios, 67, 114, 137 Phillips, Nathaniel D., 74 Pichert, Daniel, 179 Pinson, Pierre, 139 Platt, John R., 98 Pleskac, Timothy J., 29, 64 Porteus, Evan L., 134 Poursabzi-Sangdeh, Forough, 32 Poyhonen, Samuli, 180 Prelec, Drazen, 190, 196 Puterman, Martin L., 163 R Rabin, Matthew, 8, 98, 99 Raiffa, Howard, 7, 168 Ranehill, Eva, 33

AUTHOR INDEX

Rapoport, Amnon, 7, 32, 61, 73, 94, 101 Reb, Jochen, 66, 141, 161, 169, 178 Rebonato, Riccardo, 179 Refaeilzadeh, Payam, 138 Ren, Yufei, 139 Riefer, David M., 73 Rieger, Marc O., 65, 70, 73 Robinson, Stewart, 9, 70 Rosenhead, Jonathan, 144, 162 Rouwette, Etienne A., 178 Rouyard, Thomas, 180 Rubinstein, Ariel, 62, 73, 74, 98 Rudin, Cynthia, 71 Rumsfeld, Donald P., 29

S Samuelson, Paul A., 101, 196 Sanborn, Adam N., 100 Sanjurjo, Adam, 26, 27, 33 Sargent, Thomas J., 140 Savage, Leonard J., 21, 22, 30, 31, 38, 51, 64, 128 Scheibehenne, Benjamin, 33 Schiffels, Sebastian, 121, 138 Schmidt, Klaus M., 81, 97–99, 197 Schmidt, Richard A., 179 Schoemaker, Paul J.H., 32 Schooler, Lael J., 65 Schulz, Eric, 141 Schulz, Kenneth, 7, 8, 185 Schweitzer, Maurice E., 107, 108, 111, 113, 114, 118, 121, 134, 136, 137, 139 Seeley, Thomas D., 30 Selten, Reinhard, 66, 111, 112, 135, 136, 193, 197 Shaked, Avner, 99 Shapiro, Gary E., 97 Shefrin, Hersh, 56, 72 Siegel, Jeremy J., 190, 196

229

Siemsen, Enno, 7, 29, 32, 109, 116, 121, 134–138, 179, 185 Silver, David, 140 Simon, Herbert, A., 3, 4, 8, 9, 62, 65, 106, 110, 128–131, 135, 140, 141 Sim¸ ¸ sek, Özgür, 8, 29, 68, 72, 139, 157, 159, 167, 168 Slovic, Paul, 32 Smith, Adam, 18, 30 Smith, Patti, 183, 185 Spiliopoulos, Leonidas, 68, 71, 97 Stangl, Tobias, 134 Starmer, Chris, 64 Stewart, Ian, 28 Stewart, Theodor J., 67, 68, 165 Stigler, George J., 140 Stocker, Alan A., 63 Stone, Mervyn, 138 Sull, Donald N., 9 Sunder, Shyam, 69, 180 Sunstein, Cass R., 10, 174, 178, 179 Sutter, Matthias, 79, 80, 98 Su, Xuanming, 111, 136, 193 Syntetos, Aris A., 128, 136, 137, 139

T Tako, Antuela, A., 9, 70 Taleb, Nassim Nicholas, 24, 32, 72, 139 Tang, Christopher, 152, 164 Thaler, Richard H., 10, 64, 174, 178, 179, 190, 191, 196, 197 Thomas, Lyn C., 165 Thonemann, Ulrich W., 108, 134, 135 Thurstone, Louis L., 135 Tisdell, Clement A., 62, 74 Todd, Peter M., 8, 31, 33, 67, 68, 129, 135, 140, 145, 155, 166 Tomlin, Brian, 152, 164, 178

230

AUTHOR INDEX

Tsioptsias, Naoum, 9, 70 Tversky, Amos, 7, 8, 16, 18, 28–30, 33, 37, 40–42, 46, 47, 58, 63–67, 70, 73, 100, 129, 137, 187, 188, 196 V Van Roekel, Henrico, 176, 181 Van Wezel, Wout, 7, 29, 69, 185 Viale, Riccardo, 74, 175, 180 Vipin, B., 113, 135, 136 Von Neumann, John, 19, 20, 28, 30, 31, 44, 78, 96 Von Winterfeldt, Detlof, 31 W Wagenmakers, Eric-Jan, 30, 67, 181 Wakker, Peter P., 40, 65 Wallenius, Jyrki, 7, 10 Wang, Mei, 65

Wertheimer, Max, 31 White, Leroy, 7, 29, 70 Williams, Terry, 169 Woike, Jan K., 65, 100, 167 Woodside, Arch G., 9, 44, 65, 66 Wu, George, 30, 65, 68, 190, 196 Wuttke, David, 172–174, 179 Wu, Yaozhong, 7, 29, 63, 96

Y Yaari, Menahem E., 65 Yechiam, Eldad, 69

Z Zhang, Yinghao, 109, 116, 121, 134, 135, 137, 138 Zhao, Sihai Dave, 166 Zheng, Yanchong, 5, 8, 66, 96, 97, 172, 178, 183, 185

Subject Index

A ABC Research Group, 8, 31, 67, 68, 97, 135, 166 Adaptive decision maker, 55, 71 Adaptive toolbox, 55, 66 Adjustment, 114, 116, 126, 128 Algorithm, 53, 54, 71, 130, 140 Allais paradox, 38, 46, 49 Analytics, 5, 73 Anchoring, 114, 128 Anchoring and adjustment heuristic, 114–116, 120, 124, 133, 137, 197 Artificial intelligence (AI), 106, 130, 131, 141, 172–174, 178 As if approach, 51 As if model, 51 Asymmetry of pull-to-center effect, 120, 192

B Bargaining games, 76, 79, 84, 94, 98, 99, 108, 139, 184

Behavioral economics, 3, 6, 77, 81, 95, 96, 110 Behavioral game theory, 76, 98 Behavioral intervention, 2, 128 Behavioral operational research, 162 Behavioral operations management, 2, 7, 15, 26, 32, 63, 96, 106, 110, 134, 144 Behavioral operations research, 144 Behavioral science, 2, 3, 25, 28, 56, 77, 96, 110, 122, 129, 135, 145, 162, 174 Bias-variance decomposition, 157, 158, 160 Big data, 73, 141, 160, 168 Boost, 6, 172, 175–177, 180, 184 Bounded rationality, 61, 62, 106, 110, 129–131, 135 C Choice probability, 60, 110, 111 Classification, 92, 93, 145, 147, 149, 150, 156, 161, 164, 168 Cognitive illusions, 129

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 K. V. Katsikopoulos, Cognitive Operations, https://doi.org/10.1007/978-3-031-31997-6

231

232

SUBJECT INDEX

Cognitive intervention, 172, 175 Cognitive limitations, 110 Cognitive modeling, 6, 44, 145 Cognitive operations, 4, 5, 50, 144, 145, 171, 172, 178, 183, 184 Cognitive processes, 5, 21, 24, 25, 36, 62, 76, 91, 95, 106, 125, 129, 132, 133, 171 Cognitive psychology, 3, 6, 72, 77, 96, 141 Cognitive psychometrics, 57–59, 62, 73, 126 Cognitive science, 92, 135, 162, 172 Common consequence effects, 38, 39 Common ratio effects, 46, 187 Compliance heuristic, 150 Correction factor, 105, 113, 114 Correction heuristic, 116–120, 122, 124, 126, 129, 133, 137, 156, 191–193, 197 Correct rejection, 147 Cross-validation, 122, 124, 193 Cumulative dominance, 159, 160 D Decision analysis, 23 Decision support system, 110, 130 Decision tree, 19, 44, 55, 62, 156 Decision under risk, 2, 3, 6, 14–16, 18, 25, 36, 37, 39, 40, 49, 57, 60, 61, 76, 83, 107, 111, 126, 132, 148, 149, 163, 188, 194 Decision under uncertainty, 6, 15, 143, 148, 194 Descriptive model, 2, 3, 25, 80, 95, 112, 128, 131, 148 Dictator game, 77, 78, 84 Difficult decision task, 160 Diminishing sensitivity, 17, 18, 20, 40, 44, 49, 189 Dominant attribute, 159, 160 Dominant option, 160

Drosophila, 13, 106, 134 Dual sourcing, 152, 153

E Easy decision task, 160 Ecological rationality, 49, 145, 154–158, 168, 177 Equilibrium, 77, 78, 94, 101, 111, 113, 194 Equity premium puzzle, 36, 49, 57, 191 Expected utility theory, 16–25, 28, 32, 38, 39, 41, 51, 64, 78, 91, 148, 155, 163, 184, 188–190 Experiential learning, 144 Explainability, 5, 9, 53, 56, 126

F False alarm, 147, 148 Fast-and-frugal trees, 44, 45, 55, 62, 65, 66, 76, 84–86, 89, 93–95, 100, 124, 126, 144, 145, 150, 151, 153, 154, 156, 161 Field experiment, 172, 176 Fitting, 5, 47–49, 62, 66, 82, 87, 100, 122, 124, 149, 165 Fixed model, 47, 122 Fixed parameter, 46 Forecast, 114, 137, 168 Four-fold pattern of risk attitude, 37, 41, 49, 188 Free parameter, 18, 40, 41, 46, 48, 62, 111, 115, 116, 120

G Game theory, 76–78, 81, 91, 95, 145, 149, 164, 184, 195

SUBJECT INDEX

H Heuristics, 4, 19–21, 23, 25, 44–46, 49, 52, 55, 58, 59, 61, 62, 66, 71, 72, 83, 92, 99, 100, 106, 110, 114–119, 121, 123–128, 131, 132, 137, 141, 145, 149, 150, 153–158, 161, 165, 167, 168, 171, 184, 188, 196 Heuristics-and-biases, 4, 129 Hit, 21, 26, 27, 147, 152 Hot hand fallacy, 26, 27 Human factor, 105 I Idealized, 96 Ill-structured, 130, 131 Impulse balance equilibrium model, 111–113, 122, 126, 132, 136, 193 Individual differences, 36, 56, 57, 62, 84, 111–113, 116, 118, 120 Inequity aversion, 76, 81, 126, 184 Interviews, 19, 26, 75, 126, 161 In the wild, 144, 145, 156, 160, 162, 165, 167, 168, 172, 173 Intuition, 35, 71, 79, 114, 153, 166, 167 Inventory control, 6, 15, 106, 107, 114, 125–128, 134, 136, 140 Inventory cost, 105 L Learning curve, 123 Lexicographic heuristic, 44, 55, 57, 94, 100, 101, 155–157, 159, 160 Linear model, 44, 76, 93, 95, 124, 126, 166 Linear regression, 156, 157 Logistic regression, 156 Loss aversion, 3, 18, 20, 40, 44, 49, 69, 191

233

M Machine learning, 3, 5, 6, 36, 44, 47, 50, 55, 57, 62, 68, 122, 130, 131, 140, 141, 155, 165 Majority choice, 37, 47, 48, 62, 187 Maximax, 19–25, 31, 44, 45, 47, 51, 52, 145, 150, 184 Mean squared error, 50, 122, 123, 157 Minimax, 19–25, 28, 31, 44, 45, 47, 51, 52, 145, 150, 184 Mirror tree, 86, 87, 184 Miss, 26, 27, 147, 148, 163 Multi-attribute choice, 48, 55, 67, 68, 158, 165 Multi-criteria decision analysis, 165 Multiple-parameter model, 158

N Network games, 94 Neural networks, 50, 56, 57 Newsvendor problem, 106–108, 110–113, 126, 134, 136 Non-compensatory, 44, 93, 95, 99 Non-optimizing, 4, 106, 116, 124

O 1/N, 46, 66, 153 Open Science Collaboration, 26, 33 Optimal solution, 106, 107, 129, 154 Optimization, 3, 4, 8, 16, 21, 22, 25, 33, 40, 46, 47, 51–53, 55, 57, 58, 60, 61, 64, 69, 71, 76, 78, 84, 91–93, 96, 106, 110, 111, 113, 125–127, 129, 132, 145, 148–150, 154, 155, 157, 158, 160, 161, 165, 167, 168, 175, 184, 191 Optimization under constraints, 129 Option valuation, 57

234

SUBJECT INDEX

Order quantity, 107, 111, 127, 132, 133

P Parameter estimation, 81 Peace-keeping operation, 15, 145, 146 Piece-wise linear functions, 58, 81, 95 Pragmatic, 96, 129 Prediction error, 158 Predictive accuracy, 49, 99, 156 Predictive power, 5, 24, 36, 50, 62, 76, 87, 94, 95, 106, 121, 122, 124–126, 131–133, 171 Prescriptive model, 2, 3, 148 Principles of descriptive science, 183 Priority heuristic, 36, 37, 39, 42–53, 55, 57–59, 61, 62, 65, 76, 83, 117, 118, 127, 188, 189, 191 Priority tree, 86–91, 93, 95, 100 Probability weighting function, 40, 41, 46, 49, 51, 56, 57, 59, 65 Process, 5, 22, 23, 51, 52, 61, 88, 97, 115, 116, 122, 126, 128, 129, 144, 146, 154, 160, 162, 168, 179, 189 Process change, 160, 168 Process prediction, 52, 91 Process specification, 184 Profit, 46, 107–109, 111, 113, 116, 118, 120, 121, 128, 134, 137, 138, 193 Prospect theory, 3, 5, 30, 36, 37, 39–42, 46–52, 54, 56–59, 61, 62, 64, 66, 68, 83, 106, 113, 120, 126, 127, 129, 155, 184, 188, 190, 191, 193, 197 Psychometrics, 155, 165, 166 Pull-to-center effect (PtC), 107, 109, 111–113, 115–121, 126, 132, 135, 136, 156, 192

Q Quantal choice model, 111, 116, 121, 127, 193

R Random forest, 55, 157 Random model, 122, 139 Reference point, 40, 61, 113, 191, 193 Reflection effects, 37, 49, 196 Regularized regression, 157 Replication crisis, 25 Response time, 52, 62, 76, 89, 90, 92, 95, 126, 173, 184 Risk, 13, 14, 16, 17, 21, 24, 28, 37, 44, 49, 56, 65, 149, 152, 153, 155, 156, 163, 175, 190 Risk averse, 24, 37, 112 Risk seeking, 37, 112 Robustness, 49, 56

S Saint Petersburg paradox, 36, 49, 189, 190 Satisfice, 3, 129 Selfish tree, 85, 88, 90, 100 Semi-structured interview, 150, 176 Simple heuristics, 4, 6, 9, 19, 21, 31, 40, 42, 47, 53, 57, 64, 65, 67, 68, 71, 76, 80, 91, 93, 100, 106, 129, 131, 145, 149, 155, 156, 158, 160, 161, 166, 167, 175, 184 Simple rules, 4, 18–20, 25, 36, 144, 145, 152–154 Simplicity, 23, 46, 53, 55, 61, 85, 167, 168 Social motives, 76, 81, 84, 92, 99 Social preferences, 81, 84, 92, 98 Soft operations research, 4

SUBJECT INDEX

Software, 15, 114, 116, 117, 128, 139, 161 Statistics, 5, 26, 47, 122, 144, 183 Strategic interaction, 6, 19, 25, 48, 52, 57, 68, 71, 75, 76, 81, 83, 95, 107, 111, 126, 148, 164, 184, 191 Strong prediction, 78, 116, 120 Supplier sourcing, 145, 153, 154, 161 Supply chain, 15, 46, 76, 94, 97, 145, 151, 152, 154, 161

T Take-the-best, 156 Tallying, 156, 157, 166 Test set, 71, 122, 157 Theoretical integration, 106, 126 Threshold, 43, 46, 54, 57, 60–62, 66, 93, 188, 191 Training set, 50, 71, 122–125, 157 Transitivity, 96, 155

235

Transparency, 5, 9, 23, 24, 36, 53, 55, 56, 62, 76, 91, 95, 125–127, 132, 133, 171, 184 Transparent model, 5, 20, 44, 56 U Ultimatum game, 77–79, 81, 84, 94, 95, 97, 99, 191 Uncertainty, 15, 94, 107, 143–146, 154, 161, 194 Utility function, 3, 16–18, 20, 32, 40, 59, 76, 82, 84, 86, 92, 95, 113, 189–191 W Well-defined, 78, 143 Well-structured, 130 Z Zero-parameter model, 184