Escaping from Bad Decisions: A Behavioral Decision-Theoretic Perspective (Perspectives in Behavioral Economics and the Economics of Behavior) [1 ed.] 0128160322, 9780128160329

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Escaping From Bad Decisions

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Perspectives in Behavioral Economics and the Economics of Behavior

Escaping From Bad Decisions A Behavioral Decision-Theoretic Perspective

Kazuhisa Takemura Department of Psychology & Center for Decision Research, Waseda University

Series Editor

Morris Altman

Academic Press is an imprint of Elsevier 125 London Wall, London EC2Y 5AS, United Kingdom 525 B Street, Suite 1650, San Diego, CA 92101, United States 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom Copyright © 2021 Elsevier Inc. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-12-816032-9 For Information on all Academic Press publications visit our website at https://www.elsevier.com/books-and-journals

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Contents

About the author Preface 1

2

Introduction: Escaping from bad decisions 1.1 The classical problem of bad decision-making and akrasia 1.2 Second-order desires and bad decisions 1.3 The perspective proposed in this book: avoiding bad decision-making through prescriptive heuristics based on scientific findings 1.3.1 The prescriptive approach of decision-making 1.3.2 Comparison of the approach adopted in this book with nudging and boosting 1.4 An overview of the contents of this book and suggestion to avoid bad decisions 1.4.1 The idea of worst and best decisions 1.4.2 Pluralism in decision-making 1.4.3 Prescriptive pluralistic decision-making 1.5 Conclusion and future perspectives References Formal definitions of the worst decisions, best decisions, and bad decisions 2.1 Framework to describe decision-making 2.1.1 What is the best and bad decision? 2.1.2 Preference relation and set theory 2.1.3 Ordering and comparative judgment 2.1.4 Various forms of comparative judgments 2.1.5 Various types of preference relation 2.2 Worst option, best option, and bad decision 2.2.1 Definition of worst and best options 2.2.2 Relationship between worst and best options 2.3 Conditions for guaranteeing preference relations of the worst and best options 2.3.1 Existence condition of worst option 2.3.2 Existence condition of best option 2.3.3 Relation of the worst and best options

xvii xix 1 1 3

5 5 7 9 9 11 12 13 14

17 17 17 18 19 19 21 21 21 22 24 24 25 25

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2.4

Necessary and sufficient conditions for the existence of worst and best options 2.4.1 Necessary and sufficient conditions for the existence of worst option 2.4.2 Necessary and sufficient conditions for the existence of best option 2.4.3 Necessary and sufficient conditions for the existence of worst and best options 2.5 Conclusion References

27 28 29

3

Rational choice, irrational choice, and bad decisions 3.1 Economic man and rational decision-making 3.2 Greatest element rationalizability 3.2.1 Greatest element rationalizability and the best option 3.2.2 Criteria of rationality and weak order 3.2.3 Criteria of irrationality and weak order 3.2.4 Criteria of rationality and irrationality 3.3 Maximal-element rationalizability 3.3.1 Maximal-element rational choice 3.3.2 Maximal-element irrationality and bad decision 3.3.3 Maximal-element irrationality and rationality 3.4 Conclusion References

31 31 33 33 33 35 37 40 40 42 44 45 46

4

Preference ordering and measurement 4.1 Understanding preference relationships through ordering decisions and behavioral observations 4.2 Aspects of ordering decisions 4.2.1 Properties of preference relations 4.2.2 Equivalence relation 4.2.3 Relationship system 4.2.4 Total order and representation theorem 4.2.5 Weak order and representation theorem 4.3 What is the measurement of preference relations? 4.3.1 Correspondence and measurement 4.3.2 On the measurement and representation of preference relation 4.3.3 Uniqueness and measurement scale level 4.4 Quantitative representation of possible psychophysical laws and preference relations in terms of scale levels 4.4.1 Psychophysical laws 4.4.2 Representational measurement approach 4.5 Conclusion References

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26 26 27

49 50 50 51 51 52 54 56 56 57 58 62 62 64 66 67

Contents

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69 69 70 71 71 72 74 75 75 77 77 77 78 79

6

Rational preference, irrational preference, and revealed preference 5.1 Rationality criteria and revealed preference 5.2 The concept of revealed preference 5.3 Utility functions and indifference curves 5.3.1 Indifference curve 5.3.2 Perfect substitute goods 5.3.3 Complete complementary goods 5.3.4 Indifference curve groups for noneconomic goods 5.3.5 Indifference curve group of neutral goods 5.4 Revealed preference 5.4.1 What is revealed preference? 5.4.2 Principle of revealed preference 5.4.3 Weak axiom of revealed preference 5.4.4 Strong axiom of revealed preference 5.4.5 A more general definition of rationality and revealed preference 5.5 Irrational choice and revealed preference 5.6 Revealed attention 5.7 Empirical testing of acyclic preference relations 5.7.1 Empirical investigation of acyclicity 5.7.2 Nontransitivity and thresholds 5.7.3 A decision-making model to explain nontransitivity 5.8 Conclusion References Multiattribute decision-making, multiobjective optimization, and the additive conjoint system 6.1 Plurality of values and multiattribute decision-making 6.2 Difficulties of multiattribute decision-making 6.2.1 Multiattribute decision-making and information search 6.2.2 Multiattribute decision-making, best decision, and worst decision 6.2.3 Multiattribute decision-making and intransitivity of preference 6.2.4 Difficulty of multiattribute decision-making and its psychological cause 6.3 Theoretical examination when multiattribute decision-making does not satisfy weak order property of preference 6.3.1 Preference based on the dominance principle 6.3.2 Preference based on the principle of the maximum number of dominant attributes 6.3.3 Impossibility theorem of multiattribute decision-making 6.4 Multiattribute decision-making and multioptimization 6.4.1 Multioptimization 6.4.2 Concept of multiobjective optimization

80 82 82 84 84 86 87 88 89

91 92 92 92 93 94 94 96 97 97 98 101 101 102

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6.5

Additive conjoint structure and quasi best decision 6.5.1 Making the best decision with a single attribute and utility function 6.5.2 Multiattribute decision-making and additive conjoint structure 6.5.3 Axiomatic properties of additive conjoint structure 6.6 Conclusion References

7

8

A computer simulation of cognitive effort and the accuracy of two-stage decision strategies in a multiattribute decision-making process 7.1 Introduction 7.2 Findings and problems of previous research on decision strategies 7.2.1 Decision strategies identified 7.2.2 Computer simulation studies of multiattribute decision-making process and problems 7.3 Purpose and methods of computer simulation 1 7.3.1 Purpose of computer simulation 1 7.3.2 Method of computer simulation 1 7.4 Results and discussion of computer simulation 1 7.4.1 Strategies and cognitive effort in the first-stage 7.4.2 First-stage strategies and relative accuracy 7.4.3 Relationship between relative accuracy and cognitive effort 7.4.4 Relationship between the number of options, cognitive effort, and relative accuracy 7.4.5 Relationship between the number of attributes and cognitive effort and relative accuracy 7.5 Purpose and method of computer simulation 2 7.5.1 Purpose of computer simulation 2 7.5.2 Method of computer simulation 2 7.6 Results and discussion of computer simulation 2 7.6.1 Relationship between the number of options left in the second-stage and cognitive effort 7.6.2 Relationship between the number of alternatives left in the second-stage and relative accuracy 7.7 General discussion 7.8 Conclusions and problems of this study References A computer simulation of bad decisions and good decisions: an extended analysis of two-stage decision strategies 8.1 A comparison between additive strategy (WAD) and lexicographic strategy (LEX) in multiattribute decision-making

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113 113 114 114 117 119 119 120 122 122 122 122 125 129 133 133 133 134 134 135 135 137 139

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8.2

9

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Methodology of this study 8.2.1 Target decision strategy 8.2.2 Indicators of decision-making 8.2.3 Method of computer simulation 8.3 Results and discussion of computer simulation 8.3.1 Cognitive effort (elementary information processes) 8.3.2 Choice rate of the worst option 8.3.3 Relative accuracy defined by the difference from the minimum value and by Payne et al 8.3.4 Relative accuracy divided by cognitive effort (an index of efficiency) 8.3.5 Best choice rate 8.4 General discussions 8.5 Conclusion References

143 143 143 144 145 145 150

A process tracing study of decision strategies and bad decisions 9.1 Implementation of the additive decision strategy and bad decision: a pilot study 9.1.1 Previous research on the choice accuracy and its problem 9.1.2 Purpose of the experiment 9.1.3 Method 9.1.4 Result and discussion 9.2 How to examine the effect of a second-stage decision-making strategy using process tracking on the bad decisions 9.2.1 Issues to be examined and the purpose of this study 9.2.2 Method of monitoring information acquisition as a process tracking technique 9.2.3 Overview of the experiment 9.2.4 Methods of the experiment 9.3 Results and discussion of the experiment 9.3.1 Indicators used in the analysis 9.3.2 Relationship between decision time and worst choice adoption rate 9.3.3 Worst choice rate 9.3.4 Correlation between decision time, worst choice adoption rate, and questionnaire 9.3.5 Crisis rate by strategy 9.3.6 Best choice rate for each strategy 9.3.7 Correlation between decision time, best option choice rate, and questionnaire 9.4 Conclusion References

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179 179 180 180 180 181 181 182 182 184 189 189 189 192 195 196 198 200 203 205

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Contents

A process tracing study of bad decisions: using eye tracking in food decision-making 10.1 The problem of risky food decision-making and the assumptions of this study 10.2 Method of the eye-tracking experiment 10.2.1 Participants 10.2.2 Experimental setup 10.2.3 Decision-making issues 10.2.4 Experimental procedures 10.2.5 Content of instruction 10.3 Results and discussion 10.3.1 Choice results and decision time in the food decision-making task 10.3.2 Results of the number of times a region was viewed for each food 10.3.3 Relationship between questionnaire food choice scores and eye-tracking data (average number of gazes per area) 10.3.4 Comparison of gazed behavior between worse decision and better decision 10.3.5 Relationship between the eye-tracker experiment and the questionnaire experiment 10.4 Questionnaire survey 10.4.1 Survey participants 10.4.2 Methodology of the questionnaire survey 10.4.3 Results and discussion of the questionnaire survey 10.5 Conclusion References Decision strategies and bad group decision-making: a group meeting experiment 11.1 Group decision and groupthink 11.2 Method of the experiment 11.2.1 Overview of the experiment 11.2.2 Participants in the experiment 11.2.3 Procedures before conducting the experiment 11.2.4 Experimental stimuli 11.2.5 Questionnaire 11.2.6 Experimental procedures 11.2.7 Instruction 11.3 Results and discussion 11.3.1 Outline of analyzing the experimental results 11.3.2 Agreement rate between the two bad choices 11.3.3 Tabulations of bad decisions 11.3.4 An examination of the ease of choosing the bad option in a majority-based choice

207 207 209 209 209 209 212 213 214 214 216 217 218 219 219 220 220 221 223 223

225 225 227 227 228 228 229 231 231 232 234 234 235 235 237

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11.3.5 Logistic regression analysis on irrational decision-making 237 11.4 Conclusion 243 References 245 12

13

An observational experiment in group decision-making: Can people detect bad group decisions? 12.1 Cognitive processes and groupthink in group decision-making 12.2 Pilot Study 1 12.2.1 Purpose of Pilot Study 1 12.2.2 Overview of the experiment 12.2.3 Making videos of a meeting scene (making experimental stimuli) 12.2.4 Method 12.2.5 Results 12.2.6 Discussion 12.3 Pilot Study 2 12.3.1 Purpose 12.3.2 Overview of Pilot Study 2 12.3.3 Method of Pilot Study 2 12.3.4 Results 12.3.5 Discussion 12.4 Method of the experiment 12.4.1 Creation of experimental stimuli for the experiment 12.4.2 Implementation of the experiment 12.5 Result of experiment 12.5.1 Experiment 1 12.5.2 Experiment 2 12.6 Discussion 12.6.1 Experiment 1 12.6.2 Experiment 2 12.6.3 Interaction between control and experimental groups 12.7 Conclusion References Revisiting the group decision-making experiment 13.1 Irrationality and bad decision-making in group decision-making 13.2 Preliminary survey 13.2.1 Purpose of the preliminary survey 13.2.2 Questionnaire 13.2.3 Implementation of the preliminary survey 13.2.4 Results and discussion of the preliminary survey 13.3 Method for group decision-making experiment 13.3.1 Experimental design 13.3.2 Stimulus creation 13.3.3 Questionnaire

247 247 249 249 249 249 250 251 252 252 252 253 253 254 256 258 258 259 262 262 264 266 266 267 267 267 268 269 269 271 271 271 272 272 273 273 273 274

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13.3.4 Implementation of the experiment 13.3.6 Outline of the analysis 13.4 Results 13.4.1 Analysis of the desirability of a meeting decision 13.4.2 Analysis of the desirability of the meeting process 13.4.3 Correlation analysis 13.5 Discussion 13.5.1 Desirability of the meeting decision 13.5.2 Desirability of the meeting process 13.5.3 Correlation coefficient between desirability of decision and desirability of process in meetings 13.6 Conclusion and future prospects References 14

The detection of bad decisions and a voting experiment 14.1 Detection of bad group decision-making and groupthink 14.2 Method of Experiment 1 14.2.1 Outline of Experiment 1 14.2.2 Experimental design 14.2.3 Experimental stimuli 14.2.4 Questionnaire 14.2.5 Implementation of the experiment 14.2.6 Instruction 14.3 Results and discussion of Experiment 1 14.3.1 Correlation analysis 14.3.2 Analysis of the desirability of decisions in meetings 14.3.3 Analysis of the desirability of the meeting process 14.3.4 Analysis of the sensitivity of the consumption deadline 14.3.5 Analysis of voting 14.4 Method of Experiment 2 14.4.1 Overview of the experiment 14.4.2 Experimental design 14.4.3 Stimuli 14.4.4 Questionnaire 14.4.5 Implementation of the experiment 14.4.6 Instruction 14.5 Results and discussion of Experiment 2 14.5.1 Correlation analysis 14.5.2 Analysis of the desirability of decisions 14.5.3 Analysis of the desirability of the meeting process 14.5.4 Analysis of consummation sensitivity 14.5.5 Analysis of voting 14.6 Conclusion and future prospects References

275 278 278 278 280 281 281 281 282 283 283 284 285 285 287 287 288 288 289 290 290 292 292 293 294 296 298 299 299 299 300 300 300 302 304 304 304 305 305 306 307 309

Contents

15

Situation dependence of group and individual decision making and bad decisions 15.1 Decision-making strategies for individual decision-making and group decision-making by majority rule 15.2 Consequences from Condorcet’s Jury Theorem 15.3 Group decision-making in the situations where independence among group members is not ensured 15.4 Experimenton situation dependence of decision-making and bad decisions 15.4.1 Outline of the experiment 15.4.2 Decision task 15.4.3 Preliminary study 15.4.4 Experiment 15.5 Conclusion References

16

The contingent focus model and bad decisions 16.1 Situation dependence of decision-making and bad decisions 16.2 Framing effect as situation-dependent preference reversal 16.3 Inadequacy of utility theory for explaining the framing effect 16.4 Prospect theory explains the framing effect and its problem 16.5 Concept of the contingent focus model 16.6 Formulation of contingent focus model 16.7 Representation theorem of contingent focus model 16.8 Conclusion and future perspective References

17

An experiment on, and psyschometric analysis of, the contingent focus model 17.1 Risk attitudes and the contingent focus model 17.1.1 Properties of risk attitudes under the assumption of a contingent focus model 17.1.2 Proof of the nature of the risk attitude 17.2 Experiment of contingent focus model and measurement 17.2.1 A simple parameter estimation method for contingent focus model 17.2.2 A simple estimation method in which the choice ratio and utility are considered to be ratio scale 17.2.3 Estimating the strength of preferences that can be rated 17.2.4 Estimation method assuming utility with error term 17.3 Experiment of contingent focus model 17.3.1 Experiment of the contingent focus model and the focusing hypothesis 1: experiment of the reflection effect

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311 311 320 328 330 331 331 333 334 339 340 343 343 344 347 348 349 351 354 357 359

363 363 366 367 368 368 369 371 372 374

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17.3.2

Experiment of the contingent focus model and the focasing hypothesis 2: Asian disease problem 17.3.3 Quantitative analysis of the experimental results 17.3.4 Testing the focusing hypothesis of the contingent focus model using the information monitoring acquisition method 17.3.5 Discussion of the experimental results 17.4 Conclusion and future perspectives References 18

19

The contingent focus model and its relation to other theories 18.1 Expected utility theory 18.2 A counterexample to expected utility theory: Allais paradox 18.3 Nonadditive probability and nonlinear utility theory 18.4 Why nonlinear utility theory cannot explain the framing effect 18.5 Framing effects and prospect theory 18.6 Relationship between the contingent focus model and nonlinear expected utility theory and prospect theory 18.7 Conclusion and future perspectives References The mental ruler model: Qualitative and mathematical representations of contingent judgment 19.1 Contingent judgment 19.2 Contingent judgment and the problems in its modeling 19.2.1 Contingent judgment 19.2.2 Why is it difficult to explain contingent judgment by utility theory? 19.2.3 Existing models explaining contingency of judgment 19.2.4 Problems of the previous contingent judgment models 19.3 Qualitative description of “mental ruler” 19.3.1 Basic hypothesis of the model and basic property of mental ruler 19.3.2 Basic function of mental ruler 19.3.3 Compatibility of stimulus
response structures as a mental ruler construction principle 19.4 Mental ruler explanation using set theory and its mathematical description 19.4.1 Definition of the situation 19.4.2 Definition of subjective situation 19.4.3 Structure of mental ruler 19.4.4 Subadditivity of the mental ruler and its mathematical description 19.4.5 Threshold as graduation of the mental ruler 19.4.6 Restructure of the subjective situation and the mental ruler

377 379

381 385 385 388 391 391 394 396 399 400 404 407 409

413 413 414 414 415 416 417 418 418 419 421 422 422 422 423 424 426 427

Contents

19.4.7 Mental ruler as a set function Explanation of experimental findings 19.5.1 Interpretation of experimental results by Tversky and Kahneman 19.5.2 Interpretation of the experiment by Hsee 19.5.3 Interpretation of the evaluation experiment on the value of saved lives 19.5.4 Interpretation of the perceptual judgment experiment 19.5.5 Interpretation of price judgment experiment 19.5.6 Interpretation of probability weighting function 19.6 Conclusion and future perspectives References 19.5

20

21

How attention arises in and influences decision-making 20.1 Function of attention 20.2 Psychological model of attention 20.3 Mathematical model of attention rate to social events 20.4 Propositions and considerations derived from the model 20.5 Application to the psychometric model for attention rate to Covid-19 problem 20.5.1 Purpose of the study 20.5.2 Analysis and results 20.5.3 Discussion 20.6 Control of attention by psychological experiment 20.6.1 Experiment in which the speed and acceleration of change of the target were controlled 20.6.2 Experiments on stimulus variability and attention 20.7 Model of category focusing and construction of mental ruler 20.7.1 Prospect theory and the mental box model 20.7.2 Category-focusing hypothesis and the mental box model 20.7.3 Empirical study of mental box model 20.8 Conclusion and future perspective References Escaping from bad decisions and future perspective 21.1 Epistemology of bad decision 21.2 Individual decision and group decision strategies 21.3 Situational dependence of individual decision-making and its psychological laws 21.4 Nudges, boosts, and metacognition 21.5 Metacognitive model of decision-making process 21.6 Conclusion References

Author index Subject index

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429 431 431 432 434 435 436 439 444 445 449 449 452 453 455 456 456 457 459 464 464 467 471 471 472 477 483 485 489 489 490 493 495 496 500 501 503 509

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About the author

Kazuhisa Takemura is a Japanese psychologist and educator. Besides serving as a professor at the Department of Psychology, Waseda University, he is also the director of the University’s Center for Decision Research, a professor at the Waseda MBA school, and a research fellow at the Waseda Research Institute for Science and Engineering. He received his BA and MA degrees from the Department of Psychology, Doshisha University, in 1983 and 1985, and received his PhD (System Science) from Tokyo Institute of Technology in 1994, and an additional PhD (Medical Science) from Kitasato University in 2013. He has also worked abroad as a visiting researcher at James Cook University, La Trobe University, and Australian National University (Australia); the Tinbergen Institute (the Netherlands); Gothenburg University and Stockholm University (Sweden); the University of Konstanz (Germany); and National Cheng Kung University (Taiwan). He was also a Fulbright Senior Researcher at the Department of Social and Decision Science, Carnegie Mellon University (USA) from 1999 to 2000, and a visiting professor at the Department of Psychology, St. Petersburg State University (Russia) in 2008, at Venice International University (Italy) in 2015. His main research area is human judgment and decision-making, especially the mathematical modeling of preferential judgment and choice. He received a Hayashi Award (Distinguished Scholar) from the Behaviormetric Society (in 2002), an Excellent Paper Award from Japan Society of Kansei Engineering in 2003, Book Awards from the Japanese Society of Social Psychology (in 2010) and the Behaviormetric Society (in 2016), a Fellow Award from the International Association of Applied Psychology (in 2018), and Kimura Award, Transdisciplinary Federation of Science and Technology (in 2021). In the course of his career, he has taught extensively on behavioral decision theory at many universities (Waseda University, Tokyo University, Osaka University, University of Tsukuba, Kobe University, Nagoya University, Tokyo Institute of Technology, Gakushuin University, Rikkyo University, Tokyo International University, Kitasato University, Venice International University, St. Petersburg State University, and National Cheng Kung University).

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Preface

Bad decisions are made even in serious situations such as selecting a personal career or selecting an important policy in management and politics. In this book, I will first introduce the conceptual and mathematical frameworks for decision theory and multi-attribute decision-making theory and give the formal definitions of the worst decision, the best decision, and bad decision. I will explain from a theoretical point of view why it is difficult for many people to escape from the bad decision. I will then give some examples of bad decisions that were determined as bad decisions in experimental studies in both individual and group settings. In experimental studies, people tended to make bad decisions even in fatal situations if they focused on the trivial aspects of a problem. Interestingly, bad decisions are not very related to educational background. In addition to providing a psychological model of bad decisions in multi-attribute situations, I offer some suggestions based on empirical research and computer simulation studies on how to avoid making bad decisions. This book also provides an overview of the idea of bad decisions from behavioral and mathematical perspectives and related theoretical and empirical findings. Behavioral decision theory is described briefly as the general term for descriptive theories to explain the psychological processes. As the studies of G. H. A. Simon who won the Nobel Prize for economics in 1978, D. Kahneman, and R. Thaler who won the prize in 2002 and 2017, respectively, suggest, the psychological methodology and knowledge of decision study have been applied widely in such fields as economics, business administration, and engineering, and are expected to become useful in the future. This book will explain various behavioral and mathematical models of bad decision phenomenon related to micro- and macro-economic phenomenon. Numerous models have been proposed to explain the psychological processes related to such phenomenon. This book will also introduce some new models that are useful to explain human bad decisions. It ends with some speculation about the future of modern economic psychology while referring to their relation with fields related to neuroscience, such as neuroeconomics, that have been developed in recent years. This book covers a range from classical to relatively recent major studies related to economic psychology. Reading this book requires no advanced expertise. Nonetheless, introductory knowledge of psychology, business administration, and economics and approximately high school graduate level mathematics should improve a reader’s comprehension of the content. In addition, each chapter includes a corresponding reference, which can be referred to when studying more details related to decision theory.

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Preface

The information provided in this book has been also used for lectures at Waseda University, Gakushuin University, Rikkyo University, The University of Tokyo, Tokyo Institute of Technology, Nagoya University, Kansai University, Osaka University of Human Sciences, Osaka University, Kobe University, University of Tsukuba, Saint Petersburg State University, Russia, National Cheng Kun University, Taiwan, and Venice International University, Italy. Questions and answers exchanged with students at all of those places have contributed greatly to the compilation of this book. Particularly I have received highly valuable opinions from graduate students taking the Takemura Seminar at Waseda University and from researchers in decision-making studies through usual discussions. Above all, Dr. Hajime Murakami, Mr. Keita Kawasugi, Ms. Kaori Kanaoka, and Nene Yamazaki of Waseda University helped with some of the proofreading, corrections, and editing files of figures and tables. Firstly, I would like to thank the series editor, Prof. Morris Altman, the Elsevier team, especially Ms. Rachel Pomrey, Person Devlin, Mr. Graham Nisbet, Mr. Surya Narayanan, and anonymous reviewers for this book for their helpful comments. The research discussions and workshops for the Experimental Social Science Project (headed by Prof. Tatsuyoshi Saijo at Kochi University of Technology) and Economic Behavior Project conducted under a Grant-in-Aid for Scientific Research on Priority Areas of The Ministry of Education, Culture, Sports, Science and Technology (No. 19046007), Grant-in-Aid for Scientific Research A (No. 24243061, No.16H02050, No.18H03641, and No. 19H00601), Grant-in-Aid for Scientific Research B (No. 16H03725, and No. 16H03676), Grant-in-Aid for Scientific Research C (No. 17K03637), Grant-in-Aid for Challenging Exploratory Research (No. 18K18570, and No. 18K18701), and Waseda University Grand-inAid for Research, which have allowed me to exchange opinions with researchers from various fields including experimental psychology, behavioral economics, social psychology, consumer psychology, and experimental economics. Prof. Satoshi Fujii at Kyoto University, who has been conducting joint research on economic decision-making for nearly two decades, also provided me with extremely informative advice and suggestions on a regular basis. A part of our joint research is introduced in this book. Prof. Hidehiko Takahashi at Tokyo Medical and Dental University, Prof. Yutaka Nakamura at University of Tsukuba, Prof. Yoichiro Fujii at Meiji University, Prof. Takayuki Sakagami, Prof. Toshiko Kikkawa, the late Mr. Shigetaka Ohkubo, Prof. Mitshuiro Okada at Keio University, Prof. Mayuko Nakamaru, Tokyo Institute of Technology, Prof. Kaori Karasawa at the University of Tokyo, Prof. Naoko Nishimura at Ritsumeikan University, Prof. Yutaka Matsushita at Kanazawa Institute of Technology, Prof. Mieko Fujisawa at Kanazawa University, Prof. Tsuyoshi Hatori at Ehime University Prof. Yumi Iwamitsu at Kitasato University, Prof. Mikiya Hayashi at Meisei University, Prof. Takashi Ideno at Tokuyama University, Prof. Yuki Tamari at University of Shizuoka, Prof. Henry Montgomery at Stockholm University, Prof. Marcus Selart at the Norwegian School of Economics and Business Administration, Prof. Michael Smithson at the Australian National University, Prof. Yuri Gatanov at Saint Petersburg State University, Prof. Baruch Fischhoff at Carnegie Mellon University,

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Prof. Colin Camerer at California Institute of Technology, and Prof. Cheng-Ta Yang at National Cheng Kung University have given me useful comments for our joint research on economic decision-making through daily practice, which also benefitted this book. I have been participating in the 30-year-old Cognitive and Statistical Decision Making Research SIG (headed by Prof. Kazuo Shigemasu at Keio University) from its inception. Moreover, I continue to learn much from researchers in economic psychology and decision studies such as Prof. Gerrit Antonides of Wageningen University, Prof. Tommy G¨arling of Gothenburg University, Prof. David Leiser at Ben-Gurion University of the Negev, Prof. Tomasz Zaleskiewicz of SWPS University of Social Sciences and Humanities, Prof. Ola Svenson of Stockholm University, Prof. Shuzo Abe, Prof. Hiroo Sasaki, Prof. Mamoru Kaneko, Prof. Yukihiko Funaki, Prof. Tsuyoshi Moriguchi, Prof. Naoto Onzo, Prof. Kazumi Shimizu, and Prof. Kenpei Shiina of Waseda University, Tetsuso Sugimoto of Sophia University, Prof. Mitsuro Nagano of Kyoto Tachibana University, Prof. Taizoh Motonishi, Prof. Yasuhiro Ukai of Kansai University, Prof. Manabu Akiyama of Kobegakuin University, Prof. Tatsuya Kameda, and Prof. Makoto Abe of University of Tokyo. I am most appreciative of the guidance and encouragement offered by predecessors such as the late Prof. Sotohiro Kojima (Doshisha University), Prof. Osamu Takagi (Kansai University), Prof. Kazuo Shigemasu (Keio University), Prof. Nozomu Mastubara (University of Tokyo), and Prof. Tomio Kinoshita (International Institute for Advances Studies). Finally, this book is the fruit of valuable advice from numerous people with whom I have become acquainted but whose names have not been put into print here. I am truly grateful for all of their support. Kazuhisa Takemura

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Introduction: Escaping from bad decisions

1

In this chapter, I will discuss the problem of bad decision-making from the perspective of Aristotle’s akrasia, and then from the perspective of pluralistic decisionmaking. It also gives an overview of the book and the perspective it stands for by comparing it to that of nudge and boost. The perspective described in this book can be interpreted as a part of so-called prescriptive decision-making, but it is neither nudge nor boost, which are popular in recent years, but heuristics to avoid irrational decision-making based on problem transparency and mathematical scientific thinking. The way to avoid bad decisions, as described in this book, is not to think about the best decision but to first narrow down the options only from the decision maker’s own fundamentally most important values. This idea is cognitively unburdensome, and it avoids bad decisions while maintaining transparency in decisionmaking. The basic idea of this book is explained in this chapter in terms of historical background.

1.1

The classical problem of bad decision-making and akrasia

While people often want to make the best decisions for themselves, they may also make decisions that are not so desirable from their perspective. For example, a person may make an impulsive purchase when shopping that he or she did not originally want to make, or make a medical decision that may be dangerous to health or life. On the other hand, in a group, it is also possible to adopt a risky option that was not originally desired by all members and that is inferior in terms of the preference relationship of the entire group. This is called groupthink in social psychology, but from the overall perspective of decision-making at the individual and group levels, it can be called irrational or bad decision-making. In this book, I will use the terms “irrational decision-making” and “bad decision-making” without distinction, but since many researchers have different definitions and usages of what irrational means, I will use the term “bad decision-making” here. A bad decision is not a decision made by a researcher or an expert such as myself, but a decision made by a decision maker who thinks that he or she should not make such a decision. For example, the decision of an alcoholic to drink alcohol even though he thought that he would stop drinking because it would ruin his life. This also corresponds to the decision-making that Aristotle called akrasia (Ancient Greek: ἀκρασ
ια, English: akrasia, acrasia). It is also referred to as an Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00008-9 © 2021 Elsevier Inc. All rights reserved.

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Escaping from Bad Decisions

ancient Greek word meaning “lack of self-control,” “weakness of will,” or “the tendency of the mind to indulge in what it knows to be bad behavior” and is primarily a term in ancient Greek philosophy, modern philosophy, and ethics, also known as the akrasia problem. Akrasia is a matter discussed in detail in Aristotle’s Nicomachean Ethics. The background to this is the following theory of Socrates, a philosopher of the generation before him. In Plato’s dialogs, Protagoras, Socrates discussed the causes of human beings engaging in bad behavior. After examining the issue using the Socratic method of question and answer and the idea of “metrics,” Socrates finally concluded that “we commit bad acts because we do not know that they are bad acts,” in other words, “evil is born of ignorance.” In other words, Socrates said, “If a man knows that a bad act is a bad act, he will not voluntarily engage in a bad act.” Such an interpretation is also consistent with the interpretation of the revealed preference principle in economics (Richter, 1971; Suzumura, 2009). If a person takes an action in spite of other alternatives, it is because he or she has a preference for that action; otherwise, it is because of force majeure or ignorance. Therefore Becker’s (1962) economic interpretation that what is generally considered to be a bad act is also a rational act for the individual may be considered along this line of interpretation. However, this is not the case in reality, and there are countless cases of akrasia, that is, cases in which people commit acts that they know are wrong. Based on this reasoning, Aristotle discussed akrasia in his Nicomachean Ethics and discussed the punishment of drunkenness as an example. In the Middle Ages, Thomas Aquinas discussed incontinence (incontinentia), which is a synonym for akrasia, and Buddhist thought had a similar awareness of the problem of akrasia. Acrasia has often been discussed in contemporary philosophy and ethics since the end of the 20th century and the 21st century, often within the context of issues such as irrationality, free will, and action theory (Yamamoto, 2008). As Socrates argued, we can assume that a person would never willingly choose what he knows to be evil for him. It may be that a person who knows what is good for him must always choose the good. We can also think that people who choose actions that are bad for them simply do not know what is truly good for them and what is bad for them. For example, when you see a pedestrian in a crosswalk and you have two choices: step on the brake or step on the gas pedal; if you know that stepping on the brake is good for you, you will step on the brake, and if you know that stepping on the gas pedal is bad for you, you will step on the brake. However, it is possible to make a decision to step on the gas pedal even though we know it is a good decision. In this case, it could be an illusion that you thought you were stepping on the brake, but you were actually stepping on the gas pedal. However, if a person is trying to lose weight and decides to eat a lot of hamburgers or ramen noodles, it cannot be called an error. According to Yamamoto (2008), there are three conditions for akrasia as follows: first, akrasia must be an act that goes against the actor’s judgment. For example, if I eat a hamburger because I decide that I should eat a hamburger, that is not akrasia. This is because the act does not violate the judgment of the actor.

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Second, the act of akrasia requires the element of “contrary” to be an act of akrasia. The akratic actor (akrates) must have ordinary logical ability and must be aware that his action is contrary to his judgment. If a person eats a hamburger knowing that he should not eat it, but he does not know that it is a hamburger, or he does not realize that he should not eat it because of an error in reasoning, then his action is not akrasia. Akrasia is not an act based on such misperceptions or errors in reasoning. Third, akrasia must be an intentional act. If a person judges that he should not touch a person in an elevator, even for a moment, but is pushed by a person and touches the person, this movement is against the judgment of the actor, and the actor is aware of it. But this is not an act of akrasia, because it is not an intentional act to be pushed by someone and to touch someone. In order for an action to be akrasia, it must be an intentional action. To clarify the problem of akrasia, it is necessary to explain how an action that satisfies all three of these conditions can be formed (Yamamoto, 2008). The problem of akrasia is often dealt with in relation to the problems of selfcontrol, time discounting, and impulsivity in conventional behavioral economics and psychology, but this book addresses the problem of bad decision-making from a slightly different perspective. However, in this book, we will focus on this problem from a different perspective, because the perspectives of self-control, time discounting, and impulsivity view akrasia from the perspective of lack of self-control and losing to desires and temptations, rather than from the aspect of intentional acts as mentioned earlier. In this book, I take the perspective that bad decisions can deliberately be chosen, rather than such interpretations as lack of self-control or being defeated by desire or temptation. Also, as in the Akrasia example mentioned earlier, if we think of the problem in terms of two choices, not choosing the good option implies choosing the bad option, but when there are three or more options, and in multiattribute decision-making where there are multiple attributes to be considered, focusing on the bad or irrational aspects is not as important as in previous research.

1.2

Second-order desires and bad decisions

In this book, bad decisions are interpreted as being due to the intentions of the person, but how should we think about such a problem? As mentioned earlier, according to the idea of revealed preferences in economics, human preferences can be inferred from acts of choice. As will be explained in later chapters, the internal consistency of human decision-making is assumed behind the theory on revealed preferences. From this point of view, as long as a decision has internal consistency, it can be considered to be rational. And bad decision-making cannot happen if there is internal consistency. However, it is also conceivable that people do not always make the choices they prefer. In most theories of psychology, motives and internal tendencies

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are inferred from the preferences chosen, similar to the theory of revealed preferences in economics. This is also true in modern personality, social, and clinical psychology, and there seems to be an implicit assumption in psychoanalysis as well. However, it is also possible that we make decisions that are completely undesirable even if our preference relations are consistent. For example, can we say that a person who constantly commits self-harming acts wants to do so? For example, selfinjurious behavior such as wrist cutting, which is seen in borderline personality disorder, would be inconsistent if the person did it regardless of whether he or she wanted to be injured. A more extreme example would be the act of choosing death on one’s own despite a strong desire to live. There are many testimonies from people who have experienced suicide that many suicide victims do not really want to die, and it is difficult to understand them in terms of revealed preference. There are also examples where the opposite is true. There can be a situation where the person thinks that he should die for the organization to which he belongs, but he does not want to die for the book. An example of such a contradictory decision-making situation is the case of the Kamikaze Special Attack Team, or “kamikaze,” as it was commonly called, formed by the former Japanese military during World War II, October 20, 1944; the Kamikaze Special Attack Team is also known as the “body attack” as well as the “Kamikaze Suicide Attack.” Aircraft suicide attacks are sometimes called “air suicide attacks,” while naval suicide attacks such as the Kaiten and Shinyo are called “underwater suicide attacks” or “water suicide attacks.” According to the Association for the Commemoration of Victims of Suicide Attacks, a total of 6418 people died in suicide attacks, of which 3903 were killed by aircraft, most of them around the age of 20. Formally, suicide attacks were treated as voluntary acts, but there are accounts that they were half forced. It is difficult to consider such acts as the result of the decision maker’s own rational preferences, and there appear to be many examples of discrepancies between actual decision-making and actual preferences. Whether the example of the suicide mission was a bad decision for the individual or not is also difficult to say, as there are individual differences according to the testimonies of the suicide mission members. Even if such examples involve the issue of individual rights and national goals, the way to capture the perspectives in the decision-making is complex. Judging and interpreting such ultimate decision problems is difficult, but it is always difficult to think of many decisions in terms of revealed preferences and consider them to have been rational for the person if they were consistent. No matter what the situation, there always seems to be room for irrational decisions that the person does not want to make. In this sense the author, like Aristide’s discussion of akrasia, takes the point of view that there can be decisions that are both intentional and irrational and bad for the person. We can not only think of human beings as having a desire to do something but can also think of this desire as having a hierarchy. For example, when we are thirsty, we want to drink water, and this desire is a first-order one. For example, consider an actor who has a desire to smoke a drug. This desire is of first order for this actor. It is possible that the actor wants to continue the desire to a drug and wants to have this desire to smoke drugs. This desire to smoke drugs is the second-level desire. It is

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possible that the actor has the same first-order desire to smoke drugs but really wants to stop. In this case the actor has a second-order desire not to have smoke drugs. This is a case where the first-order desire is not recognized by the second-order desire. According to the philosopher Frankfurt (1971), humans are not the only ones who have desires and motives and make choices. Not only do we have them, but so also do members of other species, some of which seem to deliberate or even make decisions based on prior thought. However, what seems to be particularly characteristic of humans is that we are able to form what we call “second-order desires” or “desires of the second order.” As suggested by Stanovich (2010), the concept of second-order desires can be used to further consider rationality in decision-making. In other words, irrational decisions are those that are considered bad from the perspective of second-order needs but can be considered rational from the perspective of first-order needs. This is what we call irrational decision-making, and it can also be called bad decision-making (Takemura, 2018, 2020). From a psychological point of view, a bad decision would be an example of a decision that, from a metacognitive point of view, is a bad decision, but we would deliberately choose it in an actual decision-making situation. In this book, bad decisions are viewed from the perspective of second-order desires, or second-order preferences, and from the perspective of metacognition. A decision may be judged as good from the perspective of second-order preferences at the time of decision-making but may be judged as bad after the fact. However, a posteriori judgment is subject to hindsight interpretation and unconscious rationalization due to cognitive dissonance. For example, in the Aesop’s Tale, the fox who could not get the grapes interpreted that he did not need to get the grapes because they were too sour. Even if we think at the time of the decision that it is a good decision to somehow devise a way to take the grapes, when the action fails, we may reinterpret it as a good decision not to intentionally take the grapes. In this sense, thinking about posteriori decision-making involves ambiguity of interpretation. Therefore in this book, I would like to consider irrational decision-making and bad decision-making in terms of whether the person was making a decision that he or she wanted to make or a decision that he or she did not want to make at the time of decision-making. In this book, we will discuss the empirical findings by reporting not only the theoretical considerations and the results of computer simulations, but also the results of our experiments and surveys on human judgment and decision-making.

1.3

The perspective proposed in this book: avoiding bad decision-making through prescriptive heuristics based on scientific findings

1.3.1 The prescriptive approach of decision-making While many previous studies in behavioral economics and behavioral decision theory have emphasized the perspective of seeking better or optimal decisions, this

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book focuses its examination on irrational or bad decisions that are undesirable to decision makers. Although many phenomena related to irrational decision-making have been reported in the fields of cognitive psychology, social psychology, clinical psychology, behavior analysis, and behavioral economics, they have nevertheless not been sufficiently clarified by empirical and theoretical studies of the microscopic decision-making process. Although the findings of previous studies are important, there is a need for methodologies and findings of basic research on the micro-decision-making process that are backed by empirical and theoretical studies. The position proposed in this book will be a prescriptive approach in behavioral decision theory. An approach called a prescriptive approach exists as the third one after normative theory and descriptive theory (Bell, Raiffa, & Tversky, 1988). The term “prescriptive” is derived from prescriptions issued by physicians. The prescriptive approach aims to support good decision-making according to the actual conditions of problems. In actual decision-making problems such as social consensus building and management decision-making, strict normative theory cannot be established in some cases because of uncertainty, including ambiguity and ignorance, rendering the approach using normative theory unfeasible. Sole dependence on description, as the descriptive theory espouses, might not engender problem-solving. Accordingly, this approach is extremely important considering the support for decision-making in solving real problems. The knowledge of behavioral decision theory that describes how people make decisions in reality is expected to facilitate the adoption of this approach considerably. While the traditional prescriptive approach takes the perspective of seeking the best optimal decision as much as possible, this book takes the prescriptive approach of avoiding the worst decisions, which is slightly different from the traditional prescriptive approach. While people often want to make the best decisions, they may also make decisions that are undesirable from their point of view. Especially in clinical situations, such problems can be more serious. For example, it has been reported that mentally ill patients, cancer patients, and others may make unwanted choices in various critical decision-making situations in their social lives; take actions that are dangerous to their health, life, and property; and become highly stressed and depressed. On the other hand, in collegial decision-making, not only with individuals but also with families, couples, and friends, interactions can lead to the adoption of dangerous and most inferior choices that the individuals did not want at all. A tentative operational definition of the worst choice is to consider the least desirable option (in simplified form, the lowest value of additive multiattribute utility) in terms of the decision maker’s multidimensional values, and to choose an option that is not Pareto superior to it. In other words, it means that we choose the worst case or the option that is not the worst but is clearly not better than it. While most research in decision science has examined human irrationality based on the criterion of the best decision, this study focuses on the worst decision, which is undesirable for the decision maker in clinical situations, and examines how it can be avoided. In contrast to the decision-making research of Nobel laureates such as Thaler and Kahneman, who examined the phenomenon from the perspective of deviations from normative

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models such as expected utility theory, we will examine the worst decisions from the perspective of what exactly they are understood to be and how they can be avoided. The theories and methodologies related to this are mainly those that have been developed by the author’s research group. The problematic points at the bottom of this book are present in contemporary clinical psychology and are also dealt with in a broad sense by social psychologists. In recent years, decision scientists have been conducting clinical research on medical and clinical psychological situations, and this type of research has been increasing. However, research by decision scientists to date has not taken the prescriptive perspective that the underlying theory prevents the worst from happening.

1.3.2 Comparison of the approach adopted in this book with nudging and boosting The prescriptive perspective of this book also has some similarities with nudges and boosts in behavioral economics, which have become popular in recent years, but I would like to clarify the differences between the concepts in this book and those in particular. Kahneman describes two different systems for information processing as to why people may have conflicting interests—System 1 is fast, automatic, and highly susceptible to environmental influences. System 2 processing is slow, reflective, and takes into account explicit goals and intentions. System 1 processing takes over decision-making when the situation is overly complex or overwhelming for the individual’s cognitive abilities, or when the individual is faced with time constraints or other pressures. System 1 processing relies on a variety of judgmental heuristics to make decisions, so that decisions are more rapid. Saylor and Sustain track maladaptive behavior to the point where System 1 processing overcomes the explicit values and goals of the individual. It is well documented that habitual behavior resists change without the disruption of the environmental cues that trigger the behavior. Nudging methods are intended to use judgmental heuristics for the benefit of the parties creating the set of choices. In other words, nudging alters the environment so that the resulting choice is the most positive or desirable outcome when heuristic or System 1 decision-making is used. An example of such a tweak would be to switch the placement of junk food in the store, placing fruit and other healthy options next to the cash register and moving the junk food to another part of the store. With the advancement of economics, it has become clear that the context in which decisions are made has a powerful bias on human decision-making and behavior. While this bias can cause unwanted consequences in our daily choices, it can also be used as a tool to guide us to make better choices. Thaler and Sunstein (2008) proposed that the influence of the context of a decision can be used to influence decisions and behavior. They named the use of the influence of decision contexts to influence decisions and actions as “nudge” and argued that it is useful to design decision contexts so that they benefit individuals and society. While nudges

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Escaping from Bad Decisions

are welcomed for the benefits they bring to individuals and society, doubts have been raised about whether they sufficiently respect the freedom of choice and autonomy of individuals (Bovens, 2008). It is true that nudges do not involve coercion. However, many nudges are manipulative in that they work against the automatic systems of decision makers (Mackay & Robinson, 2016). Even if the freedom to disobey nudges is granted, decision makers cannot resist nudges if they are not aware of them. In response to these criticisms, Thaler and Sunstein suggest that disclosing nudges ensures freedom of choice and autonomy. The choice architect discloses the effects and intentions of the nudge, and the decision maker is expected to be able to place his or her decision more under control by referring to the disclosed information. However, it is not obvious that the disclosure of nudges provides decision makers with freedom from manipulation by nudges. Bias modification studies have shown that not only are decision makers less likely to be aware of their biases, but they are also less likely to correct their biases when they are pointed out (Wilson & Brekke, 1994). The claim that disclosure of nudges can ensure freedom of choice needs to be empirically verified. This study examines the extent to which decision makers are aware of the influence of nudges, and whether the disclosure of nudges leads to the freedom of choice. The subject of this study is the decision to donate organs. Prior research has shown that opt out decisionmaking is more likely to increase the consent rate for organ donation than opt in decision-making (Johnson & Goldstein, 2003). Nudging is a small change in the environment that is simple and inexpensive to implement. There are several different approaches to nudging, including defaults, social proof heuristics, and increasing the salience of the desired option. Thus nudges are thought to increase the likelihood that individuals will make certain choices or behave in certain ways by modifying their environment so that automatic cognitive processes are triggered to prioritize desired outcomes. An individual’s behavior does not necessarily coincide with their intentions. For example, an individual may want to lose weight in normal times, but if they are very hungry, they may underestimate their diet by craving ramen noodles. Nudge methods may use simplified decision-making strategies (heuristics) for the benefit of the party making the set of choices. In other words, nudges are intended to modify the environment so that the resulting choices are the most desirable outcomes, even when heuristics are used. The concept of nudging, however, is paternalistic, as its proponents admit, and contains judgments for authorities who are more knowledgeable and capable of rational reasoning, rather than in terms of rationality for the individual. They responded to various criticisms of nudge through several arguments, defending nudge theory and arguing that some form of paternalism is inevitable. On the other hand, boosts began in the fast-and-frugal heuristics tradition (Gigerenzer, Todd, & the ABC Research Group, 1999; Gigerenzer, Gaissmaier, Kurz-Milcke, Schwartz, & Woloshin, 2007; Gigerenzer, Hertwig, & Pachur, 2011). Boosts do not focus on the immediate individual behaviors as, not same as the nudge, they aim at building new decision competences or fostering existing ones (Hertwig & Grune-Yanoff, 2017). Boosts take their interventions using the

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cognitive heuristics. Boosts try to improve decision skills or decision tools with the purpose of extending the decision maker’s ability. An example of a boost is training people to use simple rules of thumb for their decision-making. Boosts do not adopt a paternalistic approach. The approach of this book is closer to the boost approach. The paternalistic or nudge approach, which was used in many parts of the world for the COVID-19 problem, may have been effective, but it seems to have had problems in understanding the decision makers and in ensuring transparency of the problem. There seemed to be problems in ensuring the transparency of the issue. In this sense, my position is closer to boost’s approach. However, the position of this book is to take a more multidimensional perspective than the traditional boosting research, and to use heuristics that can achieve the avoidance of irrationality based on the findings of mathematical analysis and computer simulation of multiattribute decision-making. Although the underlying purpose of the boosting approach can be interpreted as the search for rationality, the position of this book is centered on the avoidance of bad decisions and irrational decisions. Hence, I dare to call it “a prescriptive heuristics approach based on mathematical scientific findings.”

1.4

An overview of the contents of this book and suggestion to avoid bad decisions

1.4.1 The idea of worst and best decisions In our daily lives, we make a variety of decisions. From deciding what to have for lunch, to deciding on a personal course of action, to making policy decisions and other decisions of a more serious nature, there is no such thing as a decision that we do not make. When we think of practical activities and choices in life, we can think of “decision-making” as being multidimensional. In the Nicomachean Ethics, Aristotle states that in the act of human choice, we are in search of the highest good (agaton). This is easier to understand if we think of it this way. Why do people want to get a good education? Because it will help them get a good job. Then why do they want to get a good job? Because they want to live a good life. Why do they want to live a good life? It can be traced back to the fact that we want to be good (Takemura, 2014, 2020). The question is whether that goodness is not the highest good. If there is an Aristotelian supreme good, then there may be a “supreme evil” as well. To say that we avoid the worst has a broader meaning than to say that we achieve the best. As a familiar example, let us consider the issue of COVID-19, which has been a global epidemic since 2020. Many countries, both in the socialist and capitalist spheres, intervened with lockdown policies and emergency declarations that considerably limited the sovereignty of individuals. For example, when considering whether or not to take a lockdown policy, many governments have taken a lockdown policy or a policy with similar restrictions on sovereignty, considering first

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and foremost the health hazards and life-threatening effects of COVID-19. In the case of Japan, there was no lockdown policy, but two emergency policies were implemented for more than 2 months with equivalent sovereignty restrictions. Many Japanese people welcomed or tolerated these restrictions on sovereignty. Such a policy might be considered a decision that avoided the worst. In fact, the mass media sent out the message that if it is a question of human life or economy, life is more important, and both the government and local governments campaigned to accept the restriction of sovereignty to protect human life. However, as will be discussed in later chapters, it is open to question whether this prevention of COVID-19 infection was based on the greatest emphasis on human life. This is because human life does not depend only on COVID-19, but also on other things. In fact, in Japan, the policy of refraining from going out has led to an increase in economic deprivation, which, in turn, has led to an increase in suicides, so it is not easy to conclude whether the policy of refraining from going out has saved lives. What can be said, however, is that many people seemed to have the goal of avoiding the worst case scenario of emergency situations, the worst case scenario in which many people die from COVID-19 and the worst case scenario in which many more people die from medical collapse. The avoidance of bad decisions is not very conscious in normal situations, but in such potentially life-threatening situations, it is shared by many people. On the other hand, let us look at the positive side of decision-making. Let us consider a person who buys a TV(television). Let us say that person decides to buy a TV from company A with the brand name X. Why did he buy the TV from Company A with the brand name X? One person considers that Company A’s TVs are durable and have beautiful images. Another person liked the design, energy efficiency, cost-effectiveness, and environmental friendliness of the X brand. Another said that the price was comparatively cheaper than similar products from other companies and that they offered a lot of discounts. Another said that the price was relatively low compared to similar products from other companies, and that they were able to get a lot of discounts, and that the atmosphere of the salesperson was good. Looking at all this, the reasons for people’s decision-making are complex and diverse, even within a single individual. So, when we think about why it is good to have a low price and good design, and what it means to be environmentally friendly, we can see that ultimately it is because people are thinking about their personal happiness and the happiness of others, such as the satisfaction of their personal consumer life and the improvement of the environment. This is because they are thinking about individual happiness and the happiness of others. In addition, the highest good may be considered when we search for a higher level of value. Similarly, to consider the bad side (the highest evil), let us consider how people can prevent infection against COVID-19. For an individual, refraining from going out not only prevents infection by COVID-19 but also helps prevent infection from infectious viruses such as the flu and also avoids the risk of infecting others. On the other hand, going out without refraining from going out can lead to social criticism and increased risk of infection, but there are also other factors to consider, such as freedom of movement, interaction with others, and the health-promoting effects of

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going out. When an individual refrains from going out, it means that he or she has taken his or her own health and the lives of others into consideration and has avoided the worst case scenario of death or illness for himself or others.

1.4.2 Pluralism in decision-making With regard to good decision-making, Aristotle’s argument is based on the assumption that there is a supreme good, but is there really a unitary value? In Aristotle’s argument, happiness is the highest good, but he seems to suggest that happiness is not only pleasure or virtue but is also pluralistic. However, according to Berlin, Machiavelli was the first to argue for the plurality of values in Western thought, and even more explicitly, it was Berlin who stated these things. The plurality of values means, for example, that respect for human life is very important, but so is freedom, and that both of these values are important in an absolute sense, and that in some situations they are incompatible. The very ultimate situation can be clearly understood by considering the dilemma of life in literature. In fact, at the time of the Great East Japan Earthquake, there was a debate about whether to issue a large amount of government bonds to fund reconstruction to respect human life and welfare, or whether to prevent the issuance of a large amount of government bonds to ensure the economic stability of the people, which also shows that it was difficult to reconcile at least two values (Takemura, 2014). At the time of the COVID-19 issue, on the contrary, many people placed more weight on the goal or value of avoiding deaths from COVID-19 infections as much as possible, over the goal or value of allowing massive international issuance and maintaining economic activity. In this case, it was understandable that the two values were both important in an absolute sense, and that they were both important, but it suggested that the multiple values were incompatible, and those who thought they were compatible also argued that the trade-off between the multiple values was difficult. The same is true if we consider the negative aspects of decision-making and consider the worst decision. It is easy to think of the worst in one dimension, but it is much harder to think of the worst by considering values and attributes across multiple dimensions. Currently, there are three levels of assertions of value pluralism (Crowder, 1994). The first is one that sees value pluralism as a fact. The second is a normative demand for value pluralism. The third is a metaethical argument. Of these the most powerful argument for value pluralism is the third one. The strongest position on value pluralism at the metaethical level comes in the form of a continuation or interpretation of the intellectual legacy of Berlin (Isaiah Berlin, 1969
90). Berlin describes the plurality of values, the incompatibility and conflict of values, and the impossibility of commensurability of values. These three elements are also the pillars of today’s value pluralism. Those who argue for value pluralism generally agree with these three points, but their positions diverge especially over the concept of the incommensurability of value. George Crowder has also organized the three positions on the incommutability of value (Crowder, 2002). The first is to interpret incommutability as the incomparability of value, which is the strongest interpretation of incommutability. The second is to interpret incommutability as immeasurability of value, which is the weakest interpretation of incommutability. In

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this interpretation, only the reduction of values to “utility” and their quantitative comparison, as in utilitarianism, is rejected. However, it does allow for an ordinal ordering of values. The third position, so to speak, is somewhere in between these two, namely, the impossibility of ranking values. This is the position of Crowder himself. Crowder explains value pluralism in the following four points: 1. Existence of universal values: certain values are universal and objective. 2. Plurality: many values are significant to human flourishing. 3. Impossibility of commensurability: values cannot be ranked in a way that is unrelated to context or in an abstract way. 4. Value conflicts: value conflicts are not accidental, but inevitable in the human world (Crowder, 2002).

In this chapter, I will also consider value pluralism as described by Crowder. In this book, I would like to consider what good and bad decision-making looks like when we take this perspective. That is, I consider that both “good decisions” and “bad decisions” are pluralistic, or at least satisfy pluralistic criteria such as formal rationality, happiness, justice, beauty, and virtue (Takemura, 2011, 2018).

1.4.3 Prescriptive pluralistic decision-making Decision-making from a pluralistic perspective is psychologically difficult, as we will see later, and moreover, it is difficult from a formal perspective. In my previous works, I argued that decision-making from a pluralistic perspective is nevertheless important (Takemura, 2011, 2014). In an extreme case, decision-making with unidimensional attributes may satisfy formal rationality and facilitate the best decision-making. Although unidimensional decision-making is easy for many people to make, it is not always desirable when we focus on the plurality of values. How to consider such contradictions is the perspective given in this book. Considering the modern society, with serious situations coming up in various aspects, a lot of information to be processed, and a large mental load on decision makers, people seem to have a strong preference for decisions that are psychologically easy and formally rational. For example, it seems that people tend to prefer decisions that are overly formalistic, with excessive application of compliance and accountability, and excessive demands for procedural rationality. Or, for example, it seems that people often make decisions by comparing only those attributes that are easily noticeable or numerically comparable. To take a familiar example, when choosing a gas station, stores that are even a yen cheaper per liter are extremely crowded, causing traffic jams on the surrounding roads. However, considering the issue of time and other services, it is open to question whether going to a cheaper store is really the best choice. When I was in the United States, I saw a similar phenomenon happening in stores that were only a cent or two cheaper per gallon. People tend to be sensitive to price, which is the most noticeable and salient attribute characteristic, and do not take into account the less comparable and less focused quality of service. In terms of value standards, it seems that many people try to decide things only from the perspective of formal procedural justice. Takahashi, Takemura, Ideno,

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Ohkubo, and Tamari (2010) conducted a questionnaire survey and suggested that this psychological tendency to pursue formalism is not done out of a sense of justice but out of a psychological avoidance of responsibility, and that individuals with this tendency are rather less altruistic. Furthermore, previous social psychological research on decision-making has shown that individuals who pursue rationality tend to have higher levels of depression and lower levels of subjective well-being (Schwartz et al., 2002). In this light, I believe that "good decision making" can be achieved by recognizing rationality as an important criterion, but also by daring to put oneself in a multidimensional quandary and thinking about decision making in a multidimensional way. Multidimensional thinking can lead to information overload and confusion. For this reason, people tend to make decisions that place more weight on less important attributes that are easy to see, but how can we prevent this from happening? It is possible that this way of deciding can lead to bad decisions. For example, when you think diet is important but you are hungry, you may see an advertisement (POP) for a fatty food that is easily visible and decide based on that impression. In such a case, there is room for the decision maker to make a bad decision. The results of the experiments shown in the following chapters also show that when we try to integrate a lot of information to make a decision, we end up choosing the worst option. The method I propose is to consider as many options as possible, extract one value that is most important to the decision maker, choose the best option based on that value, keep two candidates if there is room, and decide on the last candidate after examining as much information as possible across multiple dimensions. Such a method is a two-stage decision-making process that combines lexicographic and additive methods described in the later chapters, and our previous computer simulation results show that the results are not much different from those of the additive method, which considers all the information added together, and the cognitive costs associated with decision-making are low (Takemura, 2014, 2020). The results are not much different from those of the additive type. It has also been found to be relatively efficient in terms of avoiding bad decisions (Takemura, 2018). In terms of considering the most important attributes in decision-making, it is necessary to abstract the most multiple important attributes appropriately. For example, when considering countermeasures against infectious diseases against COVID-19, human life may be the most important thing, but here, considering countermeasures only for deaths caused by COVID-19 is not considered to be a good countermeasure. If human life is important, it seems to me that we should consider human life from a comprehensive perspective, including other infectious diseases, accidents, and suicides.

1.5

Conclusion and future perspectives

In this chapter, I related bad decision-making to the classical akrasia problem as well and conveyed the core of this book, which is how to avoid bad decision-making by focusing on the pluralism of decision-making. The approach of this book is to preach transparent prescriptive decision-making through heuristics of bad decision-making based on mathematical scientific thinking. In this chapter, we will discuss nudge’s ideas and he

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Escaping from Bad Decisions

explained the similarities and differences with boost’s idea. In particular, nudging has received a lot of attention due to Saylor’s Nobel Prize in Economics in 2017, but the transparency of the decision problem and the subjectivity of the decision maker are not guaranteed, and there seems to be a limit to the extent to which it can be ethically justified (Rizzo & Whitman, 2019). In particular, the paternalistic policy in this global epidemic of COVID-19 seems to have often been questionable in terms of conveying objective information to decision makers and allowing them to make impartial decisions. For example, the Japanese media and government public relations agencies reported only the number of deaths and infections caused by COVID-19 on a daily basis and did not disclose the deaths of other influenza strains for comparison. The number of deaths and infections caused by COVID-19 was shown in real numbers, but the infection and mortality rates were not presented in the news. This was a nudge approach to prevent the risk of COVID-19 infection and encourage people to refrain from going out, but it did not ensure transparency in decision-making in terms of boosting. Also, internationally, YouTube, Twitter, and other SNS were operated under the rule that the contents that are contrary to the WHO’s view should not be communicated, but I was not sure to what extent this was appropriate in terms of the transparency of decision-making. In this chapter, I pointed out the necessity of thinking about decision-making and social policy from the perspective of avoiding practically irrational decisions and particularly emphasized the differences with nudges. Behind the basic position of this chapter is the value judgment that it is important to protect more passive freedom, unlike the libertarian paternalism in nudge’s thinking. This corresponds to the philosopher Berlin’s discussion of the problem of positive and negative liberty when explaining the concept of freedom. Nudge’s position corresponds to the concept of positive freedom, while the author’s position corresponds to negative freedom. Which position is more desirable is a normative debate and should be left to the reader’s judgment, but one should be aware that paternalism can often lead to totalitarian tendencies in times of emergency, such as the selfrestraint police in the corona disaster or the easy suppression of basic human rights. It seems to me that we need to be careful. The problem of bad decision-making is inversely related to the problem of good decision-making when there are only two options and one attribute, but not necessarily exactly the opposite of good decision-making when there are three or more options and two or more attributes. As such, the approach in this book is more focused on the problem of bad decision-making, although it also pays attention to aspects of good decision-making, which means that the goal it aims to achieve is slightly different from both nudging and boosting.

References Becker, G. S. (1962). Irrational behavior and economic theory. Journal of Political Economy, 70, 1
13. Bell, D. E., Raiffa, H., & Tversky, A. (1988). Descriptive, normative, and prescriptive interactions in decision making. In D. E. Bell, H. Raiffa, & A. Tversky (Eds.), Decision making: Descriptive, normative, and prescriptive interactions (pp. 9
30). Cambridge: Cambridge University Press.

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Bovens, L. (2008). The ethics of nudge. In T. Gru¨ne-Yanoff, & S. O. Hansson (Eds.), Preference change: Approaches from philosophy, economics and psychology (pp. 207
219). Berlin: Springer. Crowder, G. (1994). Pluralism and liberalism. Political Studies, 42, 293
305. Crowder, G. (2002). Liberalism and value pluralism. London: Continuum. Frankfurt, H. (1971). Freedom of the will and the concept of a person. Journal of Philosophy, 68, 5
20. Gigerenzer, G., Gaissmaier, W., Kurz-Milcke, E., Schwartz, L. M., & Woloshin, S. (2007). Helping doctors and patients to make sense of health statistics. Psychological Science in the Public Interest, 8, 53
96. Available from https://doi.org/10.1111/j.1539-6053.2008.00033.x. Gigerenzer, G., Hertwig, R., & Pachur, T. (Eds.), (2011). Heuristics: The foundations of adaptive behavior. Oxford: Oxford University Press. Gigerenzer, G., Todd, P. M., & the ABC Research Group. (1999). Simple heuristics that make us smart. Oxford: Oxford University Press. Hertwig, R., & Grune-Yanoff, T. (2017). Nudging and boosting: Steering or empowering good decisions. Perspectives on Psychological Science, 12, 973
986. Johnson, E. J., & Goldstein, D. (2003). Do defaults save lives? Science (New York, NY), 302, 1338
1339. Mackay, D., & Robinson, A. (2016). The ethics of organ donor registration policies: Nudges and respect for autonomy. The American Journal of Bioethics, 16, 3
12. Richter, M. K. (1971). Rational choice. In J. S. Chipman, L. Hurwicz, M. K. Richter, & H. F. Sonnenschein (Eds.), Preference, utility and demand (pp. 29
58). New York: Harcourt Brace Jovanovich. Rizzo, M. J., & Whitman, G. (2019). Escaping paternalism: Rationality, behavioral economics, and public policy. Cambridge: Cambridge University Press. Schwartz, B., Ward, A., Monterosso, J., Lyubomirsky, S., White, K., & Lehman, D. R. (2002). Maximizing vs satisficing: Happiness is a matter of choice. Journal of Personality and Social Psychology (83, pp. 1178
1197). Stanovich, K. E. (2010). Decision making and rationality in the modern world. Oxford: Oxford University Press. Suzumura, K. (2009). Kousei Keizaigaku no Kiso [Foundations of welfare economics]. Tokyo: Iwanami Shoten. (in Japanese). Takahashi, N., Takemura, K., Ideno, T., Ohkubo, S., & Tamari, Y. (2010). Aimai Jitai Ni Okeru Keishikisei Tsuikyuu Keikou Ga Soshikinai Deno Ihan Ni Taisuru Ishiki To Shakai Handan Ni Ataeru Eukyou [Effect of tendency to seek formality in ambiguous situations on the awareness of violation in an organization and social judgment]. In: Paper presented at the 51st conference of the Japanese Society of Social Psychology (pp. 762
763) (in Japanese). Takemura, K. (2011). Tazokusei Ishikettei no Moderu to Yoi Ishikettei [Model of multi attribute decision making and good decision]. Operations Research, 56(10), 583
590. (in Japanese). Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical descriptions of human choice behavior. Tokyo: Springer. Takemura, K. (2018). Avoiding bad decisions: From the perspective of behavioral economics. In: Keynote paper presented at the international congress of applied psychology. Montreal. Takemura, K. (2020). Behavioral decision theory. Oxford research encyclopedia of politics. Oxford: Oxford University Press. Available from http://doi.org/10.1093/acrefore/ 9780190228637.013.958.

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Thaler, R. H., & Sunstein, C. R. (2008). Nudge: Improving decisions about health, wealth, and happiness. New Haven, CT: Yale University Press. Wilson, T. D., & Brekke, N. (1994). Mental contamination and mental correction: Unwanted influences on judgments and evaluations. Psychological Bulletin, 116, 117
142. Yamamoto, M. (2008). Arisutoteresu no Akurasia ron [Aristotle on akrasia]. Kagaku tetsugaku, 41(1), 45
57. (in Japanese).

Formal definitions of the worst decisions, best decisions, and bad decisions

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This chapter considers formal aspect of bad decision and gives formal definitions of the worst and the best decision introducing set theoretic representation of preference. This chapter first presents the conceptual framework of the decision-making phenomenon and utilizes set theory to conduct a more rigorous discussion. The concept of decision-making is based on the premise that at least the best and worst options can be chosen and the options can be ordered in descending order of preference. The chapter explores the logical conditions of preference relations for the existence of the worst and best options.

2.1

Framework to describe decision-making

2.1.1 What is the best and bad decision? What is bad decision? Bad decision cannot be defined by other persons but can be defined by decision makers themselves. Bad decision can be considered irrational decision-making. To consider bad decision-making from a theoretical point of view, I will introduce a conceptual frame work of decision theory in the following section. First, I will consider bad decision as choosing a worst or a quasiworst option from a perspective of decision-making. A perspective could be retrospective reflection of decision-making or foresight perspective or metaperspective consideration. Bad decision may be rational from the present perspective. However, bad decision may be irrational from the metaperspective. For example, suppose that a person makes decision of sucking drug. For the metaperspective of the decision maker, if the sucking drug is considered a worst decision, taking drug is bad decision even if she or he makes decision of taking drug by complete and rational preference order. Although decision-making broadly refers to the function of the consciousness to make a decision, it can also be technically defined as the act of selecting an alternative from a group of alternatives, that is, the choice of action (Takemura, 2014). Selecting a preferred means of transportation, deciding which product to purchase, and determining which proposal to adopt are examples of decision-making. We make decisions as consumers about purchasing various goods. At times, we must make decisions related to corporate activities and political issues. Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00005-3 © 2021 Elsevier Inc. All rights reserved.

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Escaping from Bad Decisions

At this point, we review the decision-making phenomenon using the concept of aggregation (Takemura, 2014, 2020). Let A denote a finite set of alternatives. Its elements are organized into mutually exclusive alternatives a1 , . . ., ai , . . ., al (l is the number of alternatives), which can be described as set A 5 fa1 , . . ., ai , . . ., al g (although set A can be assumed as an infinite set, it is considered finite in this case for simplification. The following is also treated as a finite set to simplify the expressions). The method of defining a set by enumerating its components in this way is called extensional definition. For instance, the elements of A can be interpreted as the alternatives consisting of stocks invested, which are a1 , . . ., ai , . . ., al . From the formal perspectives of decision-making, the best decision is defined to be adopting the most preferred alternative. The worst decision is defined as adopting the most inferior alternative. A bad decision can be defined as adopting an alternative that is indifferent to the worst alternative. Bad decision is the worst one and is easily found in single attribute case. However, it would be difficult to identify a bad decision in multiattribute decision problem. Tracing back to social psychological literature, the classical founders of social psychology investigated bad decisions (e.g., Asch’s conformity study, Milgram’s obedience study, Zimbardo’s prison study, and Janis’s groupthink study). Classical and seminal behavioral economic studies by Simon, Tversky, Kahneman, Allais, Ellsberg, and Thaler also examined bad decisions to some extent, although they focused more on the departure from the best decision (optimality) rather than the aspects of bad decisions.

2.1.2 Preference relation and set theory People in ancient India, ancient China, and ancient Greece considered human preference judgment. Basically, judgment begins with the recognition of relations (Takemura, 2014, 2019, 2020). Consider a situation. An apple and an orange are placed on a plate. Two boys, Taro and Jiro, appear; Taro eats the apple and Jiro eats the orange. A set {apple, orange} of fruits is placed on the plate and a set {Taro, Jiro} of persons exist. The possibilities of who eats what are sets of combinations between the sets of the plate and the person {(apple, Taro), (apple, Jiro), (orange, Taro), (orange, Jiro)}. This implies that possibilities exist where Taro eats the apple, Jiro eats the apple, Taro eats the orange, and Jiro eats the orange. In set theory, these combinations of two sets are called a direct product, which indicates the possibilities that can occur. Let a part (called a subset) of this direct product be denoted by R 5 {(apple, Taro), (orange, Jiro)}. This set represent the relationship that Taro eats the apple and Jiro eats oranges. In this manner, we can express the relationship between Taro and Jiro and the apple and orange on the plate using subset R of the direct product showing possibilities. Set theory is used in mathematics. However, with the use of abstract theory, the relation that forms the basis of judgment can be expressed. When describing the relationship somewhat more abstractly from another perspective, consider that an ordered pair (x, y) belongs to R such that x and y are in the

Formal definitions of the worst decisions, best decisions, and bad decisions

19

relationship with R. Accordingly, we can express it by writing as xRy and state that “x is related to y with relation R.” In the aforementioned example the relationship between two sets of people and fruits can be called a binary relation. Furthermore, for example, considering a plate with different fruits, we can express the fruits Taro and Jiro are among those on the second plate using the subset of the direct product. In this case the relationship can be represented using the three-term relation. In general, relationships can be represented by the n-term relation.

2.1.3 Ordering and comparative judgment Accordingly, we have shown that relationships can be represented using set theory. However, how can we describe the ordering of subjects? Ordering judgment is a situation of binary judgment wherein when two subjects are compared, you judge which is higher or lower, larger or smaller, or whether subjects are different or the same. For example, when comparing the length of two lines segments, you judge which segment is longer or shorter. Although such binary judgment may not look like ordering, comparative judgment is actually being performed in this case. This is the basis of judgment of ordering. A slightly different example is a case where you compare two subjects and choose one as per your preference. From the word “ordering,” you may imagine a situation where you order many subjects, but from a basic point of view, ordering can be considered to occur from the comparison of two subjects. We regard such comparative judgment between two simple subjects as judgment of ordering. Such judgment of ordering can be thought of as a result of comparative judgment among elements of a collection (set) of a subject. We can represents the result of comparative judgment with the subset by considering the direct product of the subject set. In the abovementioned example, if you consider a set X with two elements X 5 {apple, orange} and make the direct product, then you have X 3 X 5 {(apple, apple), (apple, orange), (orange, apple), (orange, orange)}. Then, for example, if R 5 {(apple, orange)}, then the result of comparative judgment—namely, that the apple is preferred to the orange—may be expressed. If the apple is represented by symbol x, and the orange is represented by symbol y, then the preference relation can be described as xRy. Sometimes xRy is represented by another representation xhy. Here the symbol h indicates the preference relation as the same as R. In this chapter the symbol h is also so used as the same meaning of R. However, h is commonly used to indicate special preference relation such as weak order that holds completeness and transitivity as defined in the next section.

2.1.4 Various forms of comparative judgments Comparative judgments have various forms. In ordinary psychology, cases for judgment exist where on being shown two options, you are asked to “choose either one.” This approach is called a forced choice method, and you may choose neither option in some cases. Even if you make a comparative judgment, ordering the

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subjects appropriately is not always possible. We list the standards that divide the judgment properties as follows: 1. Completeness (comparability or connectivity): ’ x; yAX; xhy3yhx. This is such a relation in which y ð ’ x; yAXÞ; xhy, or yhx of set X of alternatives exists. “xAX” means that x is an element of X, ’ x; yAX; xhy indicates that for all x, y in X, xhy holds. The symbol “ ’ ” indicates “for all”. Moreover, the symbol “3’’ is a logical symbol for “or,” which means that at least one of them holds true. In decision-making, either xRy or yRx is true. For example, if a set of fruits is X and xRy is defined as the relation such that y is preferred to x or they are indifferent, then we can deduce that banana is preferred to strawberry or they are indifferent and that strawberry is preferred to banana or they are indifferent. It is not comparable and does not satisfy completeness in case “you do not know which one you prefer or whether they are indifferent.” Completeness is, in some cases, defined as follows: ’ x; yAX; x 6¼ y!xhy3yhx. However, the former definition of completeness leads reflectivity property. In this chapter, I use the former definition of completeness: ’ x; yAX; xhy3yhx. 2. Reflectivity: in a comparative judgment of the same subject, a relation such as xRx may exist. For example, when a set of fruits is X and R makes the relation of the same preference, given that the strawberry and strawberry are preferred equally, they satisfy reflectivity. Reflectivity can be derived from completeness property if ’ x; yAX; xhy3yhx. Irreflexivity is also defined as a relation that does not hold reflectivity. 3. Symmetry: when making a comparative judgment, when the order relation of the subjects is reversed, if xRz, then the same relation as zRx can be obtained. For example, when a set of fruits is X and R makes the relation of the same preference, if banana is preferred as much as strawberry, then strawberry is also preferred as much as banana, thereby satisfying the symmetry. 4. Antisymmetry: when making a comparative judgment, if the order relation of the subjects is reversed, the same relationship is obtained. If xRz, it is zRx and x 5 z is always obtained; thus the antisymmetry is satisfied. For example, when the set of real numbers is X and the relation of equal magnitude is R, this relationship is satisfied. However, when the set of fruits is X and R makes the relation of the same preference, even if banana is preferred as much as strawberry, it does not make the strawberry and banana equal. Thus they do not satisfy antisymmetry. 5. Transitivity: a transitive relationship states that for elements x, y, z, if xRy and yRz, then xRz holds true. For example, if a set of fruits is X and xRy is defined as a relation such that y is preferred to x or they are indifferent, then transitivity is satisfied. This means that if a relation exists where banana is preferred to orange or they are indifferent, banana is preferred to strawberry or they are indifferent, and strawberry is preferred to orange or they are indifferent, then transitivity is satisfied. Alternatively, considering the relation xRy such that the weight of object x is heavier than that of y, if x is heavier than y and y is heavier than z, then x is heavier than z. This idea holds true as long as the balance is functioning. In addition, when the transitivity does not hold true, the relation is a three-way standoff. For example, if the relation of paper
rock
scissors is shown by ., then the relation among paper, rock, and scissors is such that rock . scissors and scissors . paper, but because rock . paper does not hold true, . does not satisfy transitivity. 6. Acyclicity: acyclicity can be defined as a relation in which the asymmetric part of relation has no cycles. For any options, if x1, x2,. . . xk, if x1Px2, x2Px3,. . ., xk21Pxk hold true, then xkPx1 does not hold true. That is, ’ x1 ; x2 ; . . .; xk AX; x1 Px2 ; x2 Px3 ; :::; xk-1 Pxk . : ðxk Px1 Þ.

Formal definitions of the worst decisions, best decisions, and bad decisions

21

An example where acyclicity does not hold is the three-way standoff relation. For example, if the relation of paper
rock
scissors is shown by P, then the relation among paper, rock, and scissors is rockPscissors and scissorsPpaper; however, acyclicity is not satisfied because rockPpaper does not hold true.

2.1.5 Various types of preference relation A binary relation R on a set X can be grouped as described above properties. Based on the properties, various types of preference relation can be described. The various types of preference relations were summarized by Sen (1970) and Krantz, Luce, Suppes, and Tversky (1971): Quasiorder (preorder): reflexive and transitive relation. Partial order: reflexive, transitive, and antisymmetric relation. Strict partial order: irreflexive, and transitive relation. Weak order (complete quasiordering or total preorder): reflexive, transitive, and complete relation (this property is just a transitive and complete relation by the earlier definition). 5. Linear order (complete ordering): reflexive, transitive, complete, and antisymmetric (this property is just transitive, complete and antisymmetric relation by the abovementioned definition). 1. 2. 3. 4.

2.2

Worst option, best option, and bad decision

2.2.1 Definition of worst and best options Many people want to make best decision and avoid worst decision. Bad decisions are made even in serious situations such as selecting a personal career or selecting an important policy in management and politics (Takemura, 2011, 2018). Bad decisions cannot be defined by other persons but can be defined by decision makers themselves and can be considered irrational decision
making. To consider bad decision-making from theoretical point of view, I will introduce a conceptual frame work of decision theory in the following section. First, I will consider bad decision as choosing a worst or a quasiworst option from a perspective of decision-making. A perspective could be retrospective reflection of decision-making or foresight perspective or metaperspective consideration. Bad decision may be rational from the present perspective. However, bad decision may be irrational from the metaperspective. For example, suppose that a person makes decision of sucking drug. For the metaperspective of the decision maker, if the sucking drug is considered a worst decision, taking drug is bad decision even if she or he makes decision of taking drug by complete and rational preference order. Suppose, for example, a case where only two policy options exist in political decision. For example, decision-making is needed when choosing either policy A (e.g., increasing consumption tax) or policy B (e.g., maintaining status quo) for a politician. Actually, making policy is a complicated process and may differ among people, but for simplicity, the preference

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Escaping from Bad Decisions

relation will be considered for only a certain politician but not for every people. If the situation here would be too complicated, then a reader may think about consumer brand choice among a set of brands (e.g., smartphone products). Otherwise, the reader may consider election of a leader among political candidates. Which option is the best is unknown unless you examine the content of the options, but judging from the formal features is easy. For example, if you choose policy A, then you can say A is formally the best (better). If you chose policy B, then you can say B is formally the worst (or worse). In such a case, if policies A and B are comparable, then this result will be acceptable. However, when three or more options are available, the interpretation of the problem becomes somewhat complicated. For example, when policies A, B, and C (e.g., decreasing consumption tax) are presented, choosing the best policy among them becomes rather complicated. If policy A is preferred to B, policy B is preferred to C, and policy A is preferred to C, then policy A will be the best option, and policy C will be the worst option. However, if policy C is preferred to policy A, then the preference circles around A to B to C to A and the best option and the worst option cannot be decided. If the preference order is circling, then you will not be able to choose the worst option as well as the best option.

2.2.2 Relationship between worst and best options Here, let us define the worst and best options for decision makers using symbols from set theory by assuming completeness and transitivity. Let x be an element of X, where X denotes the set of options. For example, if X 5 {policy A, policy B, policy C}, then its elements are policy A, policy B, and policy C. If X 5 {x, y, z}, then its elements are options x, y, z. If you disprefer (dislike) x at least as much as the other elements in X, then x is called the worst option. The worst option can be a function of X, and R, and can be written as Cw (X,R). Cw (X,R) as the worst option is defined as “an element of X that satisfies the relationship R such that x is at least as bad as y for y in any X.” Formally, this can be expressed as follows: Cw (X,R) 5 {xAXj satisfies the relationship R such that x is at least as bad as y for y in any X}. Furthermore, if xRy is expressed as “the relationship R such that x is at least as bad as y,” then Cw (X,R) 5 {xAX| for any x, y of X, xRy} 5 {xAX| ’ x,yAX, xRy}. The abovementioned formula is called “Cw (X,R) is the set of elements of X that satisfies xRy for y in any X.” The fact that Cw (X,R) is not an empty set implies that the worst option exists. Next, let us define the best option. If you prefer x at least as much as the other elements in X, then x is called the best option. Cb (X,Q) as the best option is defined as “an element of X that satisfies the relationship Q such that x is at least as good as y for y in any X.” Formally, this can be expressed as follows: Cb (X,Q) 5 {xAXj satisfies the relationship Q such that x is at least as good as y for y in any X}. Furthermore, if xQy is expressed as “the relationship Q such that x is at least as good as y,” then Cb (X,Q) 5 {xAX| for any x, y of X, xQy} 5 {xAX| ’ x,yAX, xQy}

Formal definitions of the worst decisions, best decisions, and bad decisions

23

can be obtained. Similarly, if Cb (X,Q) is not an empty set, then the best option exists. The abovementioned preference relation Q and the dispreferring relation R might be totally different because “like” is not always opposite of “dislike.” However, it does not seem to be inadequate to assume dispreference has negative correctional relation to preference. It can be defined as: ’ x,yAX, xRy3yQx. By the abovementioned definitions, Cw (X,Q) 5 {xAX| ’ x,yAX, yQx}, and Cb (X,R) 5 {xAX| ’ x,yAX, yRx}. In other words the worst option can be defined as option x that is the least preferred to y for any y of X based on the preference relation Q. The best option can be defined as option x that is the least dispreferred to y for any y of X based on the preference relation R. Next, for simplicity, let us consider a relation defined from the relation R by assuming completeness and transitivity, that is, weak order. Relation xRy has been understood as “x is at least as bad as y,” and the following relations are defined: If it is not xRy or yRx, then it is xPy, that is, (xRy)^yRx!xPy. If it is xRy and yRx, then it is xIy, that is, xRy^yRx!xIy. If x is at least as bad as y and if it is not true that y is at least as bad as x, then xPy and x is dispreferred to y. If x is at least as bad as y and y is at least as good as x, then x is indifferent from y. Similarly, xQy has been understood as “x is at least as good as y,” and the following relations are defined: If it is not xQy and yQx, then it is xOy, that is, (xQy)^yQx!xOy. If it is xQy and yQx, then it is xJy, that is, xRy^yRx!xJy. If x is at least as good as y and if it is not true that y is at least as good as x, then xOy and x is preferred to y. If x is at least as good as y and y is at least as good as x, then x is indifferent from y. Therefore the worst and best options can be rewritten as follows: Cw (X,P) 5 {xAX| ’ x,yAX, xPy3xIy}, Cb (X,O) 5 {xAX| ’ x,yAX, xOy3xJy}. To avoid the worst option, decision maker should avoid the worst option Cw (X, R) or Cw (X,P) and should make choice among a set {xAX| ’ x,yAX, yPx} if there exist in the set X. Formally bad decision can be defined as {xAX| ’ x,yAX, xRy} 5 {xAX| ’ x, yAX, xPy3xIy}. It should be noted that we can see worst option as a mirror image of best option if we assume the abovementioned restricted properties. However, worst option is not always opposite relation of best option if we assume more complicated properties. In the abovementioned discussions, we assumed that preference relation is weak order. If we assume that the preference relation is not complete, bad decision is defined as the choice of the worst option or the option that is not comparable to the worst option. Even if the preference relation is acyclic and complete, similar consequence holds as discussed in the next section. It is self-evident that weak order holds acyclicity and completeness but does not always hold that acyclicity and completeness lead weak order preference. Therefore preference relation holds acyclicity and completeness is more relaxed preference than weak order preference.

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2.3

Escaping from Bad Decisions

Conditions for guaranteeing preference relations of the worst and best options

2.3.1 Existence condition of worst option In standard decision theory a decision maker is often assumed to be able to compare two options. This idea shows that completeness (connectivity) holds true. Thus when at least either xRy or yRx holds true, for example, if the set of policy is X and when xRy is defined as the relation such that y is dispreferred to x or they are indifferent, then we can deduce that policy x is dispreferred to y or they are indifferent and the policy y is preferred to z or they are indifferent. It is not comparable and does not satisfy completeness in case you do not know which one you prefer or whether they are indifferent. To consider the condition of worst option, let us introduce completeness and acyclicity properties. First as shown previously, completeness is expressed as follows: Completeness: ’ x; yAX; xRy3yRx. As described previously, this definition includes reflectivity. Accordingly, the relation ( ’ x; yAX), xRy, or yRx hold for any elements x and y in the option set X. Here, 3 is a logical symbol, indicating that at least either one holds true. The following reflective properties can be derived further from the completeness property. Reflectivity: ’ xAX; xRx. Second, acyclicity is that for any options x1, x2,. . ., xk, if x1Px2, x2Px3,. . ., xk21Pxk hold true, then xkPx1 does not hold true, that is, ’ x1 ; . . .; xk ; AX; x1Px2, x2Px3,. . ., xk21Pxk!: (xkPx1). A theorem suggests that in the selective set of finite elements, if the preference relation satisfies the properties of completeness and acyclicity, then the worst option exists. Next, we show the theorem on the worst option in the same manner of best option theorem proved by Sen (1970) and introduced by Feldman and Serrano (2005). Theorem 2.1: Theorem on existence of worst option. Let X be a finite set to be selected. If the relation R is complete and acyclic, then Cw (R,X) is not empty, that is, under this condition, the worst option exists. Proof: If you consider any element from X and it is judged as the worst, then this proof will end. Given that X has a finite number of elements and the relation R has completeness, either the existence of the worst option can be proved from the finite choices or the idea that the choice lasts forever holds true. Given that the elements of X are finite, if the choice lasts forever, because also for options x1, x2,. . ., xk, if x1Px2, x2Px3,. . ., xk21Pxk hold true, then circling such as xkPx1 occurs. This finding is contrary to the assumption. Therefore under this condition, the worst option will be available. Thus the proof is completed.

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2.3.2 Existence condition of best option In the same manner of worst option condition, a theorem of best option suggests that in the selective set of finite elements, if the preference relation satisfies the properties of completeness and acyclicity, then the best option exists. Next, we show the theorem on the best option according to Sen (1970) and introduced by Feldman and Serrano (2005). Theorem 2.2: Theorem on existence of best option (Sen, 1970) Let X be a finite set to be selected. If the relation Q is complete and acyclic, then Cb (Q,X) is not empty, that is, under this condition, the worst option exists. Proof: roof is the same as the worst options case. If you consider any element from X and it is judged as the worst, then this proof will end. Given that X has a finite number of elements and the relation Q has completeness, either the existence of the best option can be proved from the finite choices or the idea that the choice lasts forever holds true. Given that the elements of X are finite, if the choice lasts forever, because also for options x1, x2,. . ., xk, if x1Ox2, x2Ox3,. . ., xk21Oxk hold true, then circling such as xkOx1 occurs. This finding is contrary to the assumption. Therefore under this condition, the best option will be available. Thus the proof is completed.

2.3.3 Relation of the worst and best options As I described the theorem of the worst and the best options, the completeness and acyclic preference holds either the worst or best option. If the preference R and Q is acyclic, R is not always reverse order of Q because likeness is not always opposite to the dislikeness. Let us define xPy be not xRy and yRx [i.e., (xRy)^yRx], xOy be not xQy and yQx [i.e., (xQy)^yQx]. If the following relation, ’ x,yAX, xRy3 ’ x,yAX, yQx, holds, then the relation is equivalent to the following relation, ’ x,yAX, xPy3 ’ x,yAX, yOx, that is, ’ x, yAX, [xRy3yQx]3[xPy3yOx]. Theorem 2.3: Theorem of existence of worst and best options If we assume either ’ x,yAX, xRy3yQx or ’ x,yAX, xPy3yOx, then, the following relations hold concerning the worst and best options, and each relation is equivalent to each other. (1) Cw (X,R) 5 {xAX| ’ x,yAX, xRy} is nonempty ^Cb (X,R) 5 {xAX| ’ x,yAX, yRx} is nonempty if R is complete and acyclic preference. (2) Cw (X,Q) 5 {xAX| ’ x,yAX, yQx} is nonempty ^Cb (X,Q) 5 {xAX| ’ x,yAX, yQx} is nonempty if Q is complete and acyclic preference.

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(3) Cw (X,P or I) 5 {xAX| ’ x,yAX, xPy3x Iy} is nonempty ^Cb (X,P) 5 {xAX| ’ x,yAX, yPx3yJx} is nonempty if P is complete and acyclic preference. (4) Cw (X,O) 5 {xAX| ’ x,yAX, yOx} is nonempty ^Cb (X,O) 5 {xAX| ’ x,yAX, yOx or yJx} is nonempty if O is complete and acyclic preference.

Proof: Proof is the same as the worst options and the best option case. It is clear that ’ x,yAX, xRy3yQx, if and only if ’ x,yAX, xPy3yOx, because two statements are tautological. It is also clear that R is acyclic and complete if and only if Q is acyclic and complete and P is acyclic and complete if and only if O is acyclic and complete. Therefore either of the statements ’ x,yAX, xRy3yQx, or ’ x,yAX, xPy3yOx, holds, then the abovementioned theorem of the worst and best options holds because of the abovementioned theorems proved earlier. It is obvious that the best and worst options can be easily defined by either better preference or worse preference if the both preferences are a kind of inverse relationship. As I discussed previously, the bad decision is not opposite to the good decision. If this is the case, the situation might be complicated. There should be the situation that we should consider both sides. But, in many cases, we can consider the bad decision is the opposite to the good decision. This does not mean that avoiding bad decision equals to seeking good decision. Especially, avoiding the worst decision does not mean seeking the best decision. Avoiding the worst decision reveals seeking not worst options. The best option might be included in the not worst options, but we do not have to seek the best option by means of avoiding the worst option.

2.4

Necessary and sufficient conditions for the existence of worst and best options

2.4.1 Necessary and sufficient conditions for the existence of worst option The abovementioned discussion suggested the existence conditions of worst and best decision. There is necessary and sufficient condition for the existence of worst option under the assumption of completeness based on the theorem described by Sen (1970). The following theorem focuses on the existence of the worst option. Theorem 2.4: Theorem on necessary and sufficient conditions for the existence of worst option Let X be a finite set to be selected. Let R be complete. Only when R is acyclic, the selection subject X with finite elements has Cw (X,R) that is not empty, that is, under R satisfying completeness, the necessary and sufficient condition for the choice function to be the best option is that R is acyclic. Proof: In this proof the idea that when R is complete and acyclic, it has a nonempty Cw (X,R) that is the same as mentioned earlier. We now demonstrate that under R

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satisfying completeness, having nonempty Cw (X,R) that indicates that R is acyclic. Suppose R is not acyclic. Then, x1, x2, x3,. . ., xk exist, which become x1Px2, x2Px3,. . ., xk21Pxk, and xkPx1. If set X is {x1, x2, x3,. . ., xk}, then Cw (X,R) is empty. However, this contraposition result is that when R is complete, if it has a nonempty Cw (X,R), then R is acyclic. Thus the proof is completed.

2.4.2 Necessary and sufficient conditions for the existence of best option There is necessary and sufficient condition for the existence of best option under the assumption of completeness based on the theorem described by Sen (1970). The following theorem focuses on the existence of the best option. Theorem 2.5: Theorem on necessary and sufficient conditions for the existence of best option (Sen, 1970) Let X be a finite set to be selected. Let Q be complete. Only when Q is acyclic, the selection subject X with finite elements has Cb (X,Q) that is not empty, that is, under Q satisfying completeness, the necessary and sufficient condition for the choice function to be the best option is that Q is acyclic. Proof: This proof is the same as the abovementioned theorem on worst option. When Q is complete and acyclic, it has a nonempty Cb (X,Q) is the same as mentioned before. We now demonstrate that under Q satisfying completeness, having nonempty Cb (X,Q) indicates that Q is acyclic. Suppose Q is not acyclic. Then, x1, x2, x3,. . ., xk exist, which become x1Ox2, x2Ox3,. . ., xk21Oxk, and xkOx1. If set X is {x1, x2, x3,. . ., xk}, then Cb (X,Q) is empty. However, this contraposition result is that when Q is complete, if it has a nonempty Cb (X,R), then Q is acyclic. Thus the proof is completed.

2.4.3 Necessary and sufficient conditions for the existence of worst and best options There is necessary and sufficient condition for the existence of worst and best options under the assumption of completeness based on the theorem described by the former discussion of the existence of worst and best options. The following theorem focuses on the existence of the worst and the best options. Theorem 2.6: Theorem on necessary and sufficient conditions for the existence of worst and best options Let X be a finite set to be selected and define xPy be not xRy and yRx [i.e., (xRy)^yRx], and define xOy be not xQy and yQx [i.e., (xQy)^yQx]. If we assume

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either ’ x,yAX, xRy3yQx or ’ x,yAX, xPy3yOx, and either R or Q on X be complete, then the necessary and sufficient conditions for the following relations hold and each relation is equivalent to each other: (1) Cw (X,R) 5 {xAX| ’ x,yAX, xRy} is nonempty ^Cb (X,R) 5 {xAX| ’ x,yAX, yRx} is nonempty if and only if R is acyclic preference. (2) Cw (X,Q) 5 {xAX| ’ x,yAX, yQx} is nonempty ^Cb (X,Q) 5 {xAX| ’ x,yAX, yQx} is nonempty if and only if Q is acyclic preference. (3) Cw (X,P) 5 {xAX| ’ x,yAX, xPy3yIx} is nonempty ^Cb (X,P) 5 {xAX| ’ x,yAX, yOx or yJx} is nonempty if and only if P is acyclic preference. (4) Cw (X,O) 5 {xAX| ’ x,yAX, yOx} is nonempty ^Cb (X,O) 5 {xAX| ’ x,yAX, yOx or yJx} is nonempty if and only if O is acyclic preference.

Proof: Proof is the same as the worst options and the best option case. It is clear that ’ x,yAX, xRy3yQx, if and only if ’ x,yAX, xPy3yOx, and that ’ x,yAX, xRy is complete3xQy is complete if and only if ’ x,yAX, xPy is complete3yOx is complete. We can demonstrate that under either R, Q, P, or O satisfying completeness, having nonempty of each choice functions indicates the corresponding relation is acyclic. Suppose any of relation is not acyclic. Then, x1, x2, x3,. . ., xk exist, which indicates that each corresponding choice function is empty. However, this contraposition result is that when either of preference relation is complete. If each choice function has a nonempty, then each preference relation is acyclic. Moreover, it is clear that statement (1) is equivalent to statements (2), (3), and (4). The same relations hold for the statements (2), (3), and (4). Thus the proof is completed.

2.5

Conclusion

This chapter gave definitions of bad, worst, and best decisions by set theoretic perspective. It is obvious that the best and worst options can be easily defined by either better preference or worse preference if both preferences have a kind of inverse relationship. As I discussed before, the bad decision may not be the opposite to the good decision. If this is the case, the situation might be complicated. There should be the situation that we should consider both sides. But, in many cases, we can consider the bad decision is the opposite to the good decision. This does not mean that avoiding bad decision equals to seeking good decision. Especially, avoiding the worst decision does not mean seeking the best decision. Avoiding the worst decision reveals seeking not worst options. The best option might be included in the not worst options, but we do not have to seek the best option by means of avoiding the worst option. If we define the bad decision be choosing the worst decision, bad decision is choosing the worst decision if the preference relation is weak order or acyclic and complete. If we assume that the preference relation is not complete, bad decision is defined as the choice of the worst option or the option that is not comparable to the worst option. Definition of the bad decision of the worst option might be too strict.

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Not strict definition of bad decision might be not choosing the best option, which is line with traditional economic perspective. Even if adopting the strict definition of bad decision, bad decision is not uniquely defined in the multiattribute decision-making.

References Feldman, M. A., & Serrano, R. (2005). Welfare economics and social choice theory. New York: Springer. Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971). Foundations of measurement volume 1: Additive and polynomial representations. New York: Academic Press. Sen, A. K. (1970). Collective choice and social welfare. London: Oliver and Boyd. Takemura, K. (2011). Tazokusei ishikettei no shinri moderu to “yoi ishikettei” [Psychological model of multi-attribute decision making and good decision]. Oper¯eshonzu risachi, 56, ¯ 583
590. (in Japanese). Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical descriptions of human choice behavior. Tokyo: Springer. Takemura, K. (2018). Avoiding bad decisions: From the perspective of behavioral economics. In: Keynote paper presented at the international congress of applied psychology, Montreal, Canada. Takemura, K. (2019). Foundations of economic psychology: A behavioral and mathematical approach. New York: Springer. Takemura, K. (2020). Behavioral decision theory. Oxford research encyclopedia of politics. Oxford: Oxford University Press. Available from https://doi.org/10.1093/acrefore/ 9780190228637.013.958.

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Rational choice, irrational choice, and bad decisions

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This chapter considers rational choice and bad decisions. Traditional economics has relied on the assumption of “rational homo economics.” This chapter investigates the rationality of decision-making and focuses on the concept of the best and the worst choices. The concept of rational choice is based on the premise that at least the best and the worst options can be chosen and the options can be ordered in descending order of preference (Takemura, 2019). This chapter discusses on the concept of rationality and irrationality from the set-theoretic perspective. There are two types of rationality that are commonly used in the social choice literature (Bossert & Suzumura, 2010; Cato, 2016). The first type is so-called the greatest element rationalizability that requires the best option among alternatives. This type of rationality was considered in Chapter 2, Formal Definitions of the Worst Decisions, Best Decisions, and Bad Decisions, introduced by the best option. Another type of rationality is maximal-element rationalizability that requires no option in this set which is strictly preferred to any one of the chosen options. This type of rationality is related to Pareto optimality.

3.1

Economic man and rational decision-making

The term “economic man” (homo economicus) is used to describe a person who engages in economic behavior. According to Mikami (1987), the terms “economic man” and “economist” first appeared in a manuscript by W. Bagehot in 1880. However, according to Sasaki (2002), the term “economic man” has already appeared in the writings of Smith in the 18th century, where it is depicted as a person who acts on the basis of self-interest. In this chapter, rather than taking the traditional perspective of economics, I will use the term “economic man” in a broader sense of a person who makes decisions and takes actions in economic situations and consider the rationality of economic behavior. In this chapter, through the examination of the ideas of internal consistency of decision-making and revealed preference, I will show that one criterion of rationality, internal consistency of preference, which is assumed in utility theory, is only one of the formal rationality of economic behavior and may not be consistent with substantive rationality. Furthermore, I would like to point out that in psychology, internal consistency by manifest preference is included in the theoretical assumption of implicit human behavior. Finally, in this chapter, I will explain that even if we have formal rationality, we may come to a so-called irrational decision or bad decision. In addition to formal rationality, I point out the need to consider Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00002-8 © 2021 Elsevier Inc. All rights reserved.

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decision-making and social policy from the perspective of substantive rationality and avoiding irrational decisions. In addition, I will point out that there are cases where a decision is not rational from the viewpoint of procedural rationality as proposed by Simon but is rational in substance, and vice versa. There is a lot of debate about how to think about rationality. On the issue of rationality, Weber, a sociologist, tried to clarify that the fundamental principle that distinguishes modern European civilization from other civilizations is “rationality,” understanding the genealogy of its development as “liberation from the curse of this world.” He argued that the factors that led to the development of modern capitalism were primarily the intrasecular asceticism and rationalization of life produced by the religious ethics of Christian Calvinism. Weber’s discussion of rationality is multilayered, but I would like to briefly introduce it later because it is also instructive for decision theory. According to Weber’s (1922) description in “Types of Social Action”, social action can be classified into four types according to two axes. The first criterion is the presence or absence of reflective awareness of the meaning of the action, which classifies it into traditional or emotional actions and purposive or value-rational actions. The second criterion is whether the meaning of the act is oriented toward the act itself or toward the result of the act. Emotional and value-rational acts performed for value are the former, while purpose-rational acts aimed at the outcome of the act are the latter. The value-rational act is performed with the awareness of the significance and importance of the value of the act itself, and the decision is made and the act is performed as if the act itself has value, no matter what the result is. For example, “martyrdom” for religious reasons, which is done because of the value of doing the act, falls under this category. A purposive act is the one that is done as a means to an end, taking into account the compatibility of the end and the means. In the end, the outcome of the action becomes the issue, and the decision and the action become the means to achieve the end. In economics, it can be said that the economic man is concerned with purposive rational action in this sense. In addition to this classification of rationality, Weber (1972) proposes the concepts of formal and substantive rationalities to consider rationality in a more vivid manner. Weber states that “bureaucracy” is a typical organization of formal rationality, which emphasizes formal procedures. Substantive rationality, on the other hand, is the rationality about the results of decision-making and holds that the responsibility for substantive rationality is required beyond the scope of the formal rule when the rule does not necessarily fit the individual circumstances of applying the enacted statute. Thus Weber’s theory is about the bureaucratic organization, but if we apply it to the phenomenon of decision-making, we can get an interesting perspective. In other words, in decision theory, contradiction between formal and substantive rationalities may occur, and there are cases where decisions are value-rational and cases where decisions are goal-rational. Here, Simon, who has made significant contributions in the fields of psychology, economics, and management, considers the concept of limited rationality, which

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states that human rationality has limits, and he also proposes the concept of procedural rationality. Simon (1986) calls the rationality of the idea that behavior is substantively rational if it is appropriate for achieving a given goal under given conditions and constraints, and that given a goal, rational behavior is completely determined by the characteristics of the environment in which it is situated, substantive rationality. He, on the one hand, argued that rationality is assumed in traditional economics. On the other hand, he called the rationality about mental processes as well as outcomes, procedural rationality. This procedural rationality is psychological rationality that considers means and actions with full attention and deliberation and is assumed in traditional psychology (Simon, 1986). However, in a situation where there are many alternatives, there are cases where a decision satisfying procedural rationality that considers all alternatives does not satisfy substantive rationality, and conversely, there are cases where a decision satisfying rationality is made even in a situation that does not satisfy procedural rationality due to a simple method of decision-making. For example, the former example has been shown in empirical studies of decision-making, given many alternatives, and the latter example has been shown in empirical studies that say that simple decisionmaking strategies are relatively more rational (Takemura, 2018, 2020). In this chapter, this concept of rationality is formally explained later, and the relationship between rationality and irrationality and decision-making is also discussed.

3.2

Greatest element rationalizability

3.2.1 Greatest element rationalizability and the best option We illustrated two types of rationalizability. The first type of rationalizability is the greatest element rationalizability. Suppose a binary relation R on a set X and a nonempty subset SCX; it is defined that x is an R-greatest element of S if xAS and for every yAS, xRy. R-greatest element x indicates xRx because of the definition; therefore, R should be reflexive. A binary relation R on X rationalizes the choice function c on the budget space (X, S) if for every SAS, the choice set c(S) is the set of R-greatest elements of S. The set of the greatest elements in S is choice set as defined in Chapter 2, Formal Definitions of the Worst Decisions, Best Decisions, and Bad Decisions, and is denoted as C(S, R). To consider the rationalizability, every SCX should be discussed. However, for simplicity, the discussion of Chapter 2, Formal Definitions of the Worst Decisions, Best Decisions, and Bad Decisions, just focused on the set X and C(X, R).

3.2.2 Criteria of rationality and weak order 3.2.2.1 Two criteria of rationality We revealed that acyclicity and completeness are necessary to make the best decision. However, even if you have selected the best option, it is unclear as to whether

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it is rational. Next, let us consider the following two criteria for rationality according to Sen (1970): Property α: If an element x belonging to S1, which is a subset of the choice set S2, is the best element of S2, x is the best element in all X1. That is, ’ xAS1 CS2 ! ½xACbðS2 ; QÞ ! xACbðS1 ; QÞ: This property α is also called the condition of independence from unrelated options (Sen, 1970). Property β: If elements x, y belonging to S1, which is a subset of the selected set S2, are the best elements in S1 and x is the best in S2, y is also the best element in S2. That is, ’ x; y; ½x; yACbðS1 ; QÞ and S1 CS2  ! ½xACbðS2 ; QÞ ( ) yACbðS2 ; QÞ. Property β is such that if both x and y are the best options in X1, which is a subset of S2, if one x is the best option in S2, the other y is also a subset of S2; if y is the best option in S2, x is also the best option in S2. This property suggests that, for example, if option A, the best option in Japan, is the best in the world, option B, the best type of the same Japan, must also be the best in the world. Lemma 3.1: Lemma concerning α and β. The following proposition holds concerning property α and β (Sen, 1970). All the choice functions Cb(S, Q) generated by Q satisfy property α but do not necessarily satisfy property β (Sen, 1970). Proof: If x belongs to Cb(S, Q) for all y in X, it becomes xQy. Thus property α is satisfied in any subset of S. However, for example, considering the following binary relation with three options, property β is not satisfied. That is, when S 5 {x, y, z}, consider the preference relation of xJy, xQz, and zQy. Then, given that {x, y} 5 Cb ({x, y}, Q) and {x} 5 Cb ({x, y, z}, Q) are obtained, this relation obviously does not satisfy property β.

3.2.2.2 Rational choice and weak order An important theorem about rational choice has been presented (Sen, 1970). Theorem 3.1: Weak-order theorem on rational choice. A necessary and sufficient condition for the choice function Cb(S, Q) derived from the binary relation Q to satisfy the property β is that Q is weak order. Proof: We prove this theorem using the proof by contradiction. First, assuming that it is not in weak order, we need to prove that the choice function Cb(S, Q) derived

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from the binary relation R does not satisfy property β. Second, assuming that Q does not satisfy property β, we need to prove it is not in weak order. First, Q is assumed not to be in weak order. In this case, either completeness is not satisfied or transitivity does not hold true. When completeness is not satisfied, given that the choice function cannot be generated, property β is not satisfied. Next, transitivity is assumed not to be satisfied. Then, options x, y, z that become xOy, yJz, and zQx exist. Even though {y, z} 5 Cb({y, z}, Q) and {y} 5 Cb({x, y, z}, Q) result, {x} 5 Cb({x, y, z}, Q) does not hold true. Thus property β is not satisfied. Next, Q is assumed not to satisfy property β. Then, x; yA C(S1, Q) results when S1 CS2 and x, y, which result in xACbðS2 ; QÞ and :½yACbðS2 ; QÞ (: means negation in parentheses). Obviously, z can be present in X2 to be zOy and xQz. Given that x; yACbðS1 ; QÞ hold true, it becomes xJy; from the assumption of transitivity, zOy and yJx! zOx result. However, this finding is inconsistent with the assumed xQz. Therefore Q does not satisfy transitivity and is not in weak order. Thus the proof is completed. The weak order is a relation that satisfies completeness and transitivity. Completeness has been explained, and transitivity is the relation as described next, that is, transitivity: ’ x; y; zAA; xQy and yQz ! xQy. That is, if xQy and yQz hold true for any elements x, y, z ( ’ x; y; zAS) of A, xQz holds true. For example, when S is the set of options of policies in the same way as mentioned earlier, if you interpret xQy and if a relation exists such that brand x is preferred to brand y or they are indifferent, brand y is preferred to z or they are indifferent, and policy x is preferred to z or they are indifferent, transitivity is satisfied. If transitivity does not hold true, a three-way standoff relation exists. Acyclicity and transitivity are slightly different concepts. If transitivity holds true, the relation is acyclic, but the converse does not necessarily hold true. For instance, when S 5 {x, y, z}, let us consider the preference relation of xJy, yJz, and xOz. This idea obviously satisfies acyclicity, but it does not satisfy transitivity. In this manner, we found that the preference relation that satisfies the rationality criteria β can only be in weak order. Therefore weak order is considered to be a formal criterion that must be satisfied in rational choice, especially in traditional economics wherein we assume weak order for the decision-making of an economic entity. The fact that transitivity and completeness hold true indicates that the best decision-making that satisfies properties α and β can be made in daily living. If transitivity does not hold true, preference circles similar to the way paper
rock
scissors do, thereby preventing you from making the best decision. In addition, comparing things is impossible, and you cannot select the best decision in the first place.

3.2.3 Criteria of irrationality and weak order 3.2.3.1 Two criteria of irrationality We can infer irrationality through the earlier discussion of rationality. We can conclude that the most irrational decision is by choosing the worst option. At least, a

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bad decision includes irrational choice, and irrational choice includes choosing the worst option. On the basis of these inferences, we can define the most extreme case of irrationality from the worst option. Suppose a binary relation R on a set X and a nonempty subset SCX. Next, let us consider the following two criteria for irrationality on every subset S: Property γ: If an element x belonging to S1, which is a subset of the selected set S2, is the worst element of S2, x is the worst element in all S1. That is, ’ xAS1 CS2 ! ½xACwðS2 ; RÞ ! xACwðS1 ; RÞ: This property γ is also called the condition of independence from unrelated options (Sen, 1970). Property δ: If elements x, y belonging to X1, which is a subset of the selected set X2, are the worst elements in S1 and x is the worst in S2, y is also the worst element in S2. That is, ’ x; y; ½x; yACwðS1 ; RÞ and S1 CS2  ! ½xACwðS2 ; RÞ ( ) yACwðS2 ; RÞ Property δ is such that if both x and y are the worst options in S1, which is a subset of S2, if one x is the worst option in S2, the other y is also a subset of S2; if y is the worst option in X2, x is also the worst option in X2. This property suggests that, for example, if policy A, the worst in Japan, is the worst in the world, policy B, the worst type of the same Japanese policies, must also be the worst in the world. Lemma 3.2: Lemma concerning γ and δ. The following lemma holds concerning property γ and δ (Sen, 1970). All the choice functions Cw(S, R) generated by R satisfy property γ but do not necessarily satisfy property δ (Sen, 1970). Proof: If x belongs to Cw(S, R) for all y in S, it becomes xRy. Thus property γ is satisfied in any subset of S. However, for example, considering the following binary relation with three options, property δ is not satisfied. That is, when S 5 {x, y, z}, consider the preference relation of xIy, xPz, and zPy. Then, given that {x, y} 5 C({x, y}, R) and {x} 5 C({x, y, z}, R) are obtained, this relation obviously does not satisfy property γ.

3.2.3.2 Irrational choice and weak order A theorem about irrational choice has been presented in the same manner as the rational choice theorem by Sen (1970). Theorem 3.2: Weak-order theorem on irrational choice.

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A necessary and sufficient condition for the choice function Cb(S, R) derived from the binary relation R to satisfy the property δ is that R is weak order. Proof: We prove this theorem using the proof by contradiction as the same as the case of rational choice by Sen (1970). First, assuming that it is not in weak order, we need to prove that the choice function Cw(S, R) derived from the binary relation R does not satisfy property δ. Second, assuming that R does not satisfy property δ, we need to prove that it is not in weak order. First, R is assumed not to be in weak order. In this case, either completeness is not satisfied or transitivity does not hold true. When completeness is not satisfied, given that the choice function cannot be generated, property δ is not satisfied. Next, transitivity is assumed not to be satisfied. Then, options x, y, z that become xPy, yIz, and zRx exist. Even though {y, z} 5 Cw({y, z}, R) and {y} 5 Cw({x, y, z}, R) result, {x} 5 Cw({x, y, z}, R) does not hold true. Thus property δ is not satisfied. Next, R is assumed not to satisfy property δ. Then, x; yA Cw(X1, R) results when S1 CS2 and x, y, which result in xACwðS2 ; RÞ and :½yACwðS2 ; RÞ (: means negation in parentheses). Obviously, z can be present in X2 to be zPy and xRz. Given that x; yACwðS1 ; RÞ hold true, it becomes xIy; from the assumption of transitivity, zPy and yIx!zPx result. However, this finding is inconsistent with the assumed xRz. Therefore R does not satisfy transitivity and is not in weak order. Thus the proof is completed. Because of the properties of weak order of transitivity and completeness, if xRy and yRz hold true for any elements x, y, z of S ( ’ x; y; zAS), xRz holds true. For example, when X is the set of options of policies in the same way as mentioned earlier, if you interpret xRy and if a relation exists such that policy x is dispreferred to policy y or they are indifferent, policy y is dispreferred to z or they are indifferent, and policy x is dispreferred to z or they are indifferent, transitivity is satisfied. Moreover, if transitivity holds true, the relation is acyclic, but the converse does not necessarily hold true. For instance, when X 5 {x, y, z}, let us consider the dispreference relation of xIy, yIz, and xPz. This idea obviously satisfies acyclicity, but it does not satisfy transitivity in the same manner in the irrational choice.

3.2.4 Criteria of rationality and irrationality 3.2.4.1 Two criteria of rationality and irrationality We can infer relationship between rationality and irrationality though the discussion of Chapter 2, Formal Definitions of the Worst Decisions, Best Decisions, and Bad Decisions. Lemma 3.3: Lemma concerning property α and γ Let X be a finite set to be selected and define xPy be not xRy and yRx [i.e., : xRy4 yRx], and define xOy be not xQy and yQx [i.e., (: xQy4 yQx].

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If we assume either ’ x, yAS, xRy3yQx, or ’ x, yAS, xPy3yOx, property α holds if and only if property γ holds. That is, let us assume either ’ x, yAS, xRy3yQx, or ’ x, yAS, xPy3yOx, then the choice functions Cb(X, Q) generated by Q satisfy property α if and only if the choice functions Cw(X, R) generated by R satisfy property γ. Proof: It is clear that ’ x, yAS, xRy3yQx, if and only if ’ x, yAS, xPy3yOx. By the relation of R, Q, P, and O the statement that property α holds if and only if property γ holds can be obtained. Lemma 3.4: Lemma concerning property β and δ. Let X be a finite set to be selected and define xPy be not xRy and yRx [i.e., : xRy4 yRx], and define xOy be not xQy and yQx [i.e., (: xQy4 yQx]. If we assume either ’ x, yAS, xRy3yQx, or ’ x, yAS, xPy3yOx, property β holds if and only if property δ holds. That is, let assume either ’ x, yAS, xRy3yQx, or ’ x, yAS, xPy3yOx, the choice functions Cb(S, Q) generated by Q satisfy property β if and only if the choice functions Cw(S, R) generated by R satisfy property δ. Proof: It is clear that ’ x, yAS, xRy3yQx, if and only if ’ x, yAS, xPy3yOx. By the relation of R, Q, P, and O the statement that property β holds if and only if property δ holds can be obtained. Lemma 3.5: Lemma concerning property α, β, γ, and δ. Let S be a finite set to be selected and define xPy be not xRy and yRx [i.e.,:: xRy4 yRx], and define xOy be not xQy and yQx [i.e., (: xQy4 yQx]. If we assume either ’ x, yAS, xRy3yQx, or ’ x, yAS, xPy3yOx, property α holds if and only if property γ holds. That is, let us assume either ’ x, yAS, xRy3yQx, or ’ x, yAS, xPy3yOx, then the following statements hold and the statement (a) holds if and only if the statement (b) holds. (a) All the choice functions Cw(S, R) generated by R satisfy property γ and all the choice functions Cw(S, R) generated by R do not necessary satisfy property δ. (b) All the choice functions Cb(S, Q) generated by Q satisfy property α and all the choice functions Cb(S, Q) generated by Q do not necessary satisfy property β.

Proof: Each statement of (a) and (b) holds by the earlier discussion of Lemmas 3.1 and 3.2. The statements (a) and (b) are equivalent under the condition of the relation of R and Q by Lemmas 3.3 and 3.4. Lemma 3.6: Lemma concerning minimum and maximum element. Suppose a binary relation R and Q on a set X and a nonempty subset SCX; it is defined that x is an R-greatest element and Q-greatest element of S if xAS and for

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every yAS, xRy, and xQy, respectively. In the same manner, we can define R-minimum element x such that xAS and for every yAS, yRx, that is, Dw(S, R), and e Q-minimum element x such that xAS and for every yAS, yQx, Db(S, R), respectively. According to previously mentioned definitions, Cb(S, Q) 5 Dw(S, R) and Cw(S, R) 5 Db(S, Q). Proof: Cb(S, Q) is Q-greatest element of S if xAS and for every yAS, xQy. By the definition, Cb(S, Q) is Q-greatest element of S if xAS and for every yAS,yRx. This definition is the same as Dw(S, R), that is, R-minimal element of S. Similarly Cw(S, R) 5 Db(S, Q) by the definition. The previous lemma indicates that Q-greatest element of S is equal to R-minimum element of S, and that R-greatest element of S is equal to Q-minimum element of S by the assumption of the reverse relation of R and Q. This suggests that the minimum element can be irrational and the greatest element can be rational choice concerning the greatest element rationalization by Q if the worse and the better relative judgments have a reverse relation to each other. That is, it is shown that the best option is the greatest element and the worst option is the minimum one if the worse relative judgment of R has a reverse relationship with the better relative judgment of Q. Theorem 3.3: Theorem on necessary and sufficient conditions for rational and irrational choice concerning weak order. Let S be a finite set to be selected and define xPy be not xRy and yRx [i.e.,:: xRy4 yRx], and define xOy be not xQy and yQx [i.e., (: xQy4 yQx]. If we assume either ’ x, yAS, xRy3yQx, or ’ x, yAS, xPy3yOx, the necessary and sufficient conditions for the following relations hold and each relation is equivalent to each other. That is, assuming either ’ x, yAS, xRy3yQx, or ’ x, yAS, xPy3yOx, then the following relations hold and each relation holds if and only if any of the other relation holds. (a) A necessary and sufficient condition for the choice function Cw(S, R) binary relation R to satisfy the property δ is that R is weak order. (b) A necessary and sufficient condition for the choice function Cb(S, Q) binary relation Q to satisfy the property β is that Q is weak order. (c) A necessary and sufficient condition for the choice function Dw(S, R) binary relation R to satisfy the property δ is that R is weak order. (d) A necessary and sufficient condition for the choice function Db(S, Q) binary relation Q to satisfy the property β is that Q is weak order.

derived from the derived from the derived from the derived from the

Proof: Each statement of (a), (b), (c), and (d) holds by the earlier discussion of Theorems 3.1 and 3.2. The statements (a) and (d), and (b) and (c) are equivalent under the conditions of the relation of R and Q by Lemma 3.6. The statement (a) holds if and only if the statement (b) holds by Lemmas 3.3 and 3.4. The statement (c) holds if and only if the statement (d) holds. Therefore the earlier relations hold and each relation holds if and only if any of the other relation holds.

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Theorem 3.4: Theorem on necessary and sufficient conditions for the existence of maximum-element irrational and rational choice. As shown in Chapter 2, Formal Definitions of the Worst Decisions, Best Decisions, and Bad Decisions, the following relations can be obtained directly: Let X be a finite set to be selected and define xPy be not xRy and yRx [i.e., : xRy4 yRx], and define xOy be not xQy and yQx [i.e., (: xQy4 yQx]. If we assume either ’ x, yASCX, xRy3yQx, or ’ x, yASCX, xPy3yOx, the necessary and sufficient conditions for the following relations hold and each relation is equivalent to each other. That is, assuming either ’ x, yASCX, xRy3yQx, or ’ x, yASCX, xPy3yOx, then the following relations hold and each relation holds if and only if one of the other relation holds. (a) A necessary and sufficient condition for the greatest element choice function Cb(S, Q) derived from the binary preference relation Q is acyclic and complete. (b) A necessary and sufficient condition for the greatest element choice function Cw(S, R) derived from the binary dispreference relation R is acyclic and complete. (c) A necessary and sufficient condition for the minimum-element choice function Db(S, Q) derived from the binary preference relation Q is acyclic and complete. (d) A necessary and sufficient condition for the minimum-element choice function Dw(S, R) derived from the binary dispreference relation R is acyclic and complete.

Proof: Each statement of (a), (b), (c), and (d) holds by the earlier discussion of Theorems 2.5 and 3.3. The statements (a) and (d), and (b) and (c) are equivalent under the conditions of the relation of R and Q by Lemma 3.6. The statement (a) holds if and only if the statement (b) holds by Lemmas 3.3 and 3.4. The statement (c) holds if and only if the statement (d) holds. Therefore the earlier relations hold and each relation holds if and only if any of the other relation holds. Theorem 3.4 is eventually the same as Theorem 2.5. The interpretation of Theorem 3.4 is that the greatest element rationalization of the worst option can be obtained from the minimum-element rationalization of the best option if there is a reverse relationship between the better and the worse relative judgments. The theorem suggests that the worst decision and the best option can be obtained when the preference relation or dispreference relation holds acyclic and complete.

3.3

Maximal-element rationalizability

3.3.1 Maximal-element rational choice 3.3.1.1 Maximal-element rationalizability and not inferior option We illustrated the first type of rationalizability defined as the greatest element rationalizability. Next, we explain the second type of rationalizability defined as the maximal-element rationalizability that requires no option in this set which is strictly preferred to any one of the chosen options. This type of rationality is related to Pareto optimality.

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Suppose a binary relation Q on a set X and a nonempty subset SCX; it is defined that x is an R-maximal element of S if xAS and for every yAS,:(yOx), that is, every yAS,:(yQx :(xQy)). The maximal element is not inferior to any other element in S and is denoted as Mb(X, Q). This notion is in line with Pareto optimality. To consider the rationalizability, every SCX should be discussed. Let X 5 {x, y}. Suppose the following preference relation holds xQx, xQy, and yQy. In such case, we will have Mb(X, Q) 5 {x, y} 5 X. Assuming weak-order preference relation R defined earlier, element xAX is interpreted as at least as good as any other element of X. The best option is x on the basis of the preference relation R. Therefore Cb(X, Q) 5 {x}. For the greatest element rationalizability, choosing the best option x is rational. On the other hand, for the maximal-element rationalizability, choosing not inferior option to any other is rational (or good).

3.3.1.2 Maximal option and quasiorder The following lemmas about the maximal option have been presented by Sen (1970). Lemma 3.7: Lemma of maximal option. Any finite quasiordered set (S, Q) in which Q holds reflexivity and transitivity has at least one maximal element (Sen, 1970). That is, Mb(S, Q) is nonempty if S is finite and Q is quasiorder. Proof: Suppose that elements are x1 ; x2 ; . . . ; xn . First, let us assume a1 5 x1 . By the recursive rule, aj11 5 xj11 if aj11 Oxj otherwise, aj 5 aj11 : By the construction of a1 ; . . . ; an , an becomes maximal element. At least one an can be constructed by the recursive rule. Therefore the previous relation holds. This lemma suggests that the maximal-element rationalization can be executed if better relation judgment holds quasiorder. Lemma 3.8: Lemma of maximal option. Let us define Cb(S, Q) and Mb(S, Q) over finite set X. The following relation holds: Cb(S, Q)CMb(S, R). Proof: It is clear that xRy for every y in S implies that there is no y in S such that yPx. If :xRy and :yRx hold, the maximal set M(S, R) is not empty but the choice set Cb(S, Q) is empty. Therefore Cb(S, Q)CMb(S, Q) holds. It is shown that the best option and the greatest element rationalization always mean existence of the maximal element of the choice set and the maximal-element rationalization. However, the reverse relation does not hold. In this sense the maximal-element rationalization is a broader concept of rationalization.

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3.3.1.3 Theorem of the maximal-element rationalization The following theorem on the maximal-element rationalization holds (Cato, 2016). Theorem 3.5: Theorem of the maximal-element rationalization. Mb(R, S) is a choice function and is not empty if and only if R is acyclic, where the maximal-element rational choice set of Q-maximal elements of S over finite set X is defined as follows: Mb(R, Q) 5 {xAX: ’ yAS,:(yQx :(xQy))} 5 {xAX: ’ yAS,:(yOx)}. Proof: Let us assume that the M(S, Q) is empty for some SCX by the way of contradiction. Let us suppose that elements are x1 ; x2 ; . . . ; xn . Let x1 AS. There exists x2 ASnx1 such that x2 Ox1 : In the same manner, there exists x3 ASnx1 ; x2 such that x3 Ox2 . Moreover, there exists xk11 ASnx1 ; . . . ; xk such that xk11 Pxk , and xn AS such that xn Px1 because S is finite set. However, this contraposition result is that when Q is acyclic. By the way of contradiction to prove the only if proposition, let us assume that R is not acyclic relation. Then, there exist x1 Ox2 ,. . ., xk Oxk11 , and xn Ox1 . This indicates that Mb(R, Q) is empty. This indicates that if Mb(Q, S) is not empty then Q is acyclic.

3.3.2 Maximal-element irrationality and bad decision 3.3.2.1 Maximal-element irrationality and not superior option We explained the second type of rationalizability defined as the maximal-element rationalizability that requires no option in this set which is strictly preferred to any one of the chosen options. In the same manner, we can define the maximal-element irrationality at no option in this set that is strictly not superior to any one of the options. Suppose a binary relation R on a set X and a nonempty subset SCX; it is defined that x is an R-maximal element of S if xAS and for every yAS,:(yPx), that is, every yAS,:(yRx :(xRy)). The maximal element is not inferior to any other element in S and is denoted as M(X, R). This notion is in line with Pareto optimality. Let X 5 {x, y, z}. Suppose the following dispreference relation holds xRx, xRy, yRy, xPz, and yPz. In such case, we will have M(X, R) 5 {x, y}. In this definition, maximal elements are x and y. The maximal-element irrational choice can be defined as M(X, R). Assuming weak-order preference relation R defined earlier, element xAX is interpreted as at least as bad as any other element of X. The worst option is x on the basis of the dispreference relation R. Therefore C(X, R) 5 {x}. For the greatest element irrationalizability, choosing the best option x is irrational. On the other hand, for the maximal-element irrationalizability, choosing not superior option to any other is irrational (or bad).

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3.3.2.2 Maximal option and quasiorder Following lemmas about the maximal option have been presented by Sen (1970). The similar discussion can be applied to the irrational decision. Lemma 3.9: Lemma of maximal option. Any finite quasiordered set (S, R) in which R holds reflexivity and transitivity has at least one maximal element (Sen, 1970). That is, Mw(S, R) is nonempty if S is finite and R is quasiorder. Proof: Proof is the same in Lemma 3.7. Suppose that elements are x1 ; x2 ; . . . ; xn . First, let us assume a1 5x1 . By the recursive rule, aj11 5 xj11 if aj11 Pxj , otherwise, aj 5 aj11 : By the construction of a1 ; . . . ; an , an becomes maximal element. At least one an can be constructed by the recursive rule. Therefore the previous relation holds. This lemma suggested that maximal-element irrational choice can be defined that worse relation judgment holds quasiorder that satisfies reflexivity and transitivity. Lemma 3.10: Lemma of maximal option. The following lemma also holds in the same as Lemma 3.8. Let us define Cw(S, R) and Mw(S, R) over finite set X. The following relation holds: Cw(S, R)CMw(S, R). Proof: It is clear that xRy for every y in S implies that there is no y in S such that yPx. If :xRy and :yRx hold, the maximal set Mw(S, R) is not empty but the choice set Cw(S, R) is empty. Therefore Cw(S, R)CMw(S, R) holds. It is shown that the worst option and the greatest element irrationalization always mean existence of the maximal element of the bad choice set and the maximalelement irrationalization. However, the reverse relation does not hold. In this sense the maximal-element irrationalization is a broader concept of irrationalization. Therefore the definition of bad decision can be broader if we assume the maximalelement irrationalization. If we assume maximal-element rationalization and irrationalization, concepts of good and bad decisions have broader extension since Cb(S, Q)CMb(S, Q) and Cw(S, R)CMw(S, R).

3.3.2.3 Theorem of the maximal-element irrational choice The following theorem on the maximal-element irrationalization holds in a manner similar to that of the maximal-element rationalization (Cato, 2016). Theorem 3.6: Theorem of the maximal-element irrational choice.

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Mw(R, S) is a choice function and is not empty if and only if R is acyclic, where the irrational choice set of R-maximal elements of S over finite set X is defined as follows: Mw(R, S) 5 {xAX: ’ yAS,:(yRx :(xRy))} 5 {xAX: ’ yAS,:(yPx)}. Proof: The proof is same as the proof of Theorem 3.4. Let us assume that Mw(R, S) is empty for some SCX by the way of contradiction. Let us suppose that elements are x1 ; x2 ; . . . ; xn . Let x1 AS. There exists x2 ASnx1 such that x2 Px1 : In the same manner, there exists x3 ASnx1 ; x2 such that x3 Px2 . Moreover, there exists xk11 ASnx1 ; . . . ; xk such that xk11 Pxk , and xn AS such that xn Px1 because S is finite set. However, this contraposition result is that when R is acyclic. By the way of contradiction to prove the only if proposition, let us assume that R is not acyclic relation. Then, there exist x1 Px2 ,. . ., xk Pxk11 , and xn Px1 . This indicates that M(R, S) is empty. This indicates that if M(R, S) is not empty then R is acyclic. Theorem 3.5 indicates that necessary and sufficient condition of the maximalelement irrational choice is that worse relation be acyclic. Like Theorem 3.5, Theorem 3.4 also indicates that necessary and sufficient condition of the maximalelement rational choice is, better relation be acyclic. Therefore the maximalelement rationalization and irrationalization can be obtained if and only if people can make choice that holds acyclic relational judgment.

3.3.3 Maximal-element irrationality and rationality As discussed previously, there is necessary and sufficient condition for the existence of maximal-element bad and good option is that preference relation be acyclic. The following theorem focuses on the existence of the worst and the best options. Let X be a finite set to be selected and define xPy be not xRy and yRx [i.e., : xRy4 yRx], and define xOy be not xQy and yQx [i.e., (: xQy4 yQx]. Let Nb(S, Q) be Q-minimal element of S if xAS and for every yAS,:(xOy), and Nw(S, R) be R-minimal element of S if xAS and for every yAS,:(xPy). Lemma 3.11: Lemma of Maximal and Minimal Element. As given in the earlier definitions, Mb(S, Q) 5 Nw(S, R) and Mw(S, R) 5 Nb(S, Q). Proof: Mb(S, Q) is Q-maximal element of S if xAS and for every yAS,:(yOx). By the definition, Mb(S, Q) is Q-maximal element of S if xAS and for every yAS, :(xPy). This definition is the same as Nw(S, R), that is, R-minimal element of S. Similarly Mw(S, R) 5 Nb(S, Q) by the definition. The previous lemma indicates that Q-greatest element of S is equal to R-minimum element of S, and that R-greatest element of S is equal to Q-minimum element of S by the assumption of the reverse relation of R and Q. This suggests that the minimum element can be irrational choice and the greatest element can be rational choice concerning the greatest element rationalization by Q if the worse and the

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better relative judgments have a reverse relation to each other. That is, it is shown that the best option is the greatest element and the worst option is the minimum one if the worse relative judgment of R has a reverse relationship with a better relative judgment of Q. Theorem 3.7: Theorem on necessary and sufficient conditions for the existence of maximal-element irrational and rational choice. Let X be a finite set to be selected and define xPy be not xRy and yRx [i.e., : xRy4 yRx], and define xOy be not xQy and yQx [i.e., (: xQy4 yQx]. If we assume either ’ x, yASCX, xRy3yQx, or ’ x, yASCX, xPy3yOx, the necessary and sufficient conditions for the following relations hold and each relation is equivalent to each other. That is, assuming either ’ x, yASCX, xRy3yQx, or ’ x, yASCX, xPy3yOx, then the following relations hold and each relation is equivalent to each other. (a) A necessary and sufficient condition for the maximal-element choice function Mb(S, Q) derived from the binary preference relation Q is acyclic. (b) A necessary and sufficient condition for the maximal-element choice function Mw(S, R) derived from the binary dispreference relation R is acyclic. (c) A necessary and sufficient condition for the minimal-element choice function Nb(S, Q) derived from the binary preference relation Q is acyclic. (d) A necessary and sufficient condition for the minimal-element choice function Nw(S, R) derived from the binary dispreference relation R is acyclic.

Proof: Each statement of (a), (b), (c), and (d) holds by the earlier discussion of Theorems 3.5 and 3.6. The statements (a) and (d), and (b) and (c) are equivalent under the conditions of the relation of R and Q by Lemma 3.11. The statement (a) holds if and only if the statement (b) holds by Theorems 3.5 and 3.6. The statement (c) also holds if and only if the statement (d) holds by Theorems 3.5 and 3.6. Therefore the previous relations hold and each relation holds if and only if any of the other relation holds. Theorem 3.7 indicates that the maximal-element rationalization of the worst option can be obtained from the minimal-element rationalization of the best option if there is a reverse relationship between the better and the worse relative judgments. The theorem suggests that the maximal-element rational choice and the irrational choice can be obtained when the preference relation or dispreference relation holds acyclic.

3.4

Conclusion

This chapter gives a perspective on a bad decision from the point of view of rational and irrational choice by set theory. Bad decision can be defined by the greatest element rationality or the maximal-element rationality. If we see the bad decision and irrationality from the greatest element rationalization, the weak order of preference relation has a crucial role. If we see the bad decision and irrationality from the

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maximal-element rationalization, a more relaxed preference relation such as acyclic preference will be important. As discussed the same in Chapter 2, Formal Definitions of the Worst Decisions, Best Decisions, and Bad Decisions, we can consider that the bad decision is the opposite to the good decision. Although avoiding a bad decision does not equal to seeking a good decision, we can view the irrational decision by looking at the mirror image of a rational decision by assuming the opposite relation. If we see the bad decision and irrationality from the greatest element rationalization, the irrational decision can be defined as choosing the worst option. A bad decision might be defined as being irrational. If we see the bad decision and irrationality from the maximal-element rationalization, the irrational decision can be defined as choosing the minimal element of the choice set that includes the worst option. The latter definition of the bad decision indicates that the irrational and the bad decisions can be the minimal element that is not strongly preferred to any other option. Latter definition of the bad and the irrational decisions is broader and includes the worst decision. This maximal-element rationalization relates to the Pareto set and is defined as the set of maximal elements with respect to the Pareto criterion. Given a multiattributable decision-making or social decision-making, we can define the set of maximal elements of the alternatives or social preference profiles. In general, the set of maximal elements might be the empty set. However, if the preference is acyclic, the maximal and the minimal elements of the alternative are not empty under earlier described condition. Of course, the bad decision does not always imply irrational decision. The concept of bad decision can be broader than the irrationality. However, we can see the bad decision from the concept of irrationality defined in this chapter.

References Bossert, W., & Suzumura, K. (2010). Consistency, choice, and rationality. Cambridge, MA: Harvard University Press. Cato, S. (2016). Rationality and operators: The formal structure of preferences. Tokyo: Springer. Mikami, R. (1987). Keizai no Hakubutsu Shi [Natural history of economics]. Tokyo: Nihon Hyoron Sya. (in Japanese). Sasaki, K. (2002). Koten ha no keizai Jin Gainen [The classical concept of economic man]. Keizaigakushi Gakkai Nenpou, 41, 71
79. (in Japanese). Sen, A. K. (1970). Collective choice and social welfare. San Francisco, CA: Holden-Day. Simon, H. A. (1986). Rationality in psychology and economics. The Journal of Business, 59(4), S209
S224. Takemura, K. (2018). Avoiding bad decisions: From the perspective of behavioral economics. In: Keynote paper presented at the international congress of applied psychology. Montreal, Canada. Takemura, K. (2019). Foundations of economic psychology: A behavioral and mathematical approach. New York: Springer.

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Takemura, K. (2020). Behavioral decision theory. Oxford research encyclopedia of politics. Oxford: Oxford University Press. Available from https://doi.org/10.1093/acrefore/ 9780190228637.013.958. Weber, M. (1922). Soziologische Grundbegriffe. Wirtschaft und Gesellschaft (pp. 1
30). Tu¨bingen: J. C. B. Mohr. Weber, M. (1972). Wirtschaft und Gesellschaft: Grundriss der Verstehenden Soziologie, 5. revidierte Auflage. Tu¨bingen: J. C. B. Mohr.

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Preference ordering and measurement

4

In the previous chapter, I discussed rational and irrational decision-making. In this chapter, I will discuss the issue of how preference relations are represented in such decision-making. Rational choice, as discussed in the previous chapter, presupposes that we can at least choose the best option, and that we can order the options in the desired order. Also, irrational and bad decision-making is considered to be choosing the least desirable option. Since irrational choices can be thought of as mirror images of rational choices, we will discuss rational preferences, their measurement, and the problem of quantification of preference relations. In traditional economics, preference relations are discussed from the perspective of utility, and rational choice is sometimes discussed from the perspective of utility maximization. In psychology, quantitative representations of preferences are sometimes discussed from the perspective of psychological scales. Therefore in this chapter, I will introduce the concept of utility deduced from the observation of choice behavior and briefly introduce the traditional concept of ordinal utility theory. Ordinal utility theory has been postulated in many economic theories (e.g., von Neumann & Morgenstern, 1944/1947) and is also used in psychology to discuss preferences under the name of ordinal scales (e.g., Indow, 1977; Sayeki, 1973). If we assume that both rational and irrational preferences have the properties of ordinal or ordinal utility, it is convenient to be able to represents them quantitatively. In later chapters, I will present the idea of revealed preference behind utility measurement, but in this chapter, I will first introduce the idea of axiomatic measurement theory, which is the basic representation of preference relations, and the quantitative representation of preference relations based on it.

4.1

Understanding preference relationships through ordering decisions and behavioral observations

The basis of people’s decision-making is preference. Simply put, it is a preference. Judgments of preference for an object can be ordered in many cases. In this chapter, I would like to explain how the ordering judgment of preference can be measured, and how we can think of measurement. For simplicity’s sake, let us assume the following judgment situation. Ranko-san is holding an apple and a tangerine in her hands and comparing their weights. Which is heavier, the apple or the tangerine? In psychological experiments, to examine the characteristics of such comparative judgments, we sometimes Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00013-2 © 2021 Elsevier Inc. All rights reserved.

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hold several weights in our hands with our eyes closed and try to determine which one is heavier, to see how much we can tell the difference in weight. Now, let us consider a more practical and serious decision. Hanako was proposed to by Taro, whom she had been dating for a while since their college days, and at about the same time, Jiro, whom she met at her new workplace, proposed to her as well. Hanako feels a little like she is being double-timed, but she is trying to decide which one she prefers, whether she cannot decide between them, or whether she should turn them both down. In the end, she thinks that Taro, who she has been with for a long time, is better than Jiro. Let us consider another situation. On his way home from work, Taro drops by a department store and is thinking about whether to buy a new jacket. There are three brands, A, B, and C. After trying them on, he thinks the best one is brand A and the last one is brand C. Such a situation of social decision-making is also conceivable. These are preference judgments about national policies, such as whether or not the government should spend taxpayer money on public investment to develop the economy, or rather, whether or not the government should invest less in public investment to reduce the deficit. All of the previous situations are situations of preference ordering decisions. These situations may be quite common in our daily lives. Even if not in daily life, preference ordering judgments are frequently made in modern society, such as in entrance and employment examinations, personnel evaluations, and voting behavior. Furthermore, these ordering judgments are the judgments that seem to be most related to the human “mind.” In such a situation, it is possible that the stress is so great that comparisons are impossible and no ordering is possible at all, but in most cases, if there is enough time, at least an ordering can be done. What does such an order represent? In many psychological studies, quantification is done on the basis of the ranked results, but is there any point in that? Is not ordering a qualitative phenomenon, and, therefore, not amenable to quantification? I think it is reasonable to ask such a question. In this chapter, I focus on the problem of ordering, a qualitative judgment of humans, and explain how the results of this ordering can be represented in quantity. I also explain what it means to make measurements using such ordering judgments as an example, from the perspective of axiomatic measurement theory.

4.2

Aspects of ordering decisions

4.2.1 Properties of preference relations The nature of human judgment has been examined by various people in ancient India, ancient China, and ancient Greece. Basically, judgment begins with the recognition of relations. As introduced in Chapter 2, Formal Definitions of the Worst Decisions, Best Decisions, and Bad Decisions, binary relations that satisfy reflexivity and transitivity are called quasiorder, binary relations that satisfy completeness

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and transitivity are called weak order, and binary relations that satisfy completeness, transitivity, and antisymmetry are called total order. A weak order that is not a total order is sometimes called a strict weak order, and a quasiorder that is not a weak order is sometimes called a strict quasiorder. These quasiorder, weak order, and total order are collectively called order. This shows that a quasiorder contains a weak order and a weak order contains a total order. For example, the relation between the size of rational and real numbers is a total order, and the relation “not above grade” is a strict weak order. The less-than relation on the set of integers I is a quasiorder. Next, let R be an order on a set X and consider a subset Y of X. For any elements x, y( ’ x, yAX), if xRy and x; y 2 = Y, there exists some zAY such that xRz and zRy, Y is said to be R-dense order in X. For example, if we consider the relation $ on the set of real numbers, the set of rational numbers is $ dense order on the set of real numbers. The property that a rational number is R-dense order on a set of real numbers may not seem important from an empirical scientific point of view, but it has an important position in mathematical psychology and utility theory.

4.2.2 Equivalence relation A binary relation that satisfies reflexivity, symmetry, and transitivity is called an equivalence relation. An equivalence relation R is often denoted by the symbol B. If there exists an equivalence relation R on a set X, the set of elements yAX and the set of elements of X in the equivalence relation R RðyÞ 5 fxjxAX; xRyg is called the equivalence class generated from y by the equivalence relation R. The set of equivalence classes obtained by the equivalence relation R on X is called the quotient set of X by R, or the equivalence class set, and is denoted by X/R. For example, the equivalence relation R on gender divides the set of humans X into a set of equivalence classes consisting of two equivalence classes, male and female.

4.2.3 Relationship system A set and its elements, subsets, and relations on it are called a relational system or mathematical structure. For example, the binary relation R on a set X can be represented as hX, Ri. The ordering relation can also be represented as a relational system. The ordering relation also appears in the preference relation of likes and dislikes. Let us consider the preference h relations of decision makers on a set of objects X. When ðx; yÞAh, that is, xhy, we say that “x is preferred to y.” This preference relation is a binary relation. In this chapter, we will focus on the binomial relation, but we can also consider the ternary relation of a direct product X 3 X 3 X subset on a set X, or even the n-term relation in general (n is an integer greater than or equal to 1). Also, suppose

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that some set X is defined, and various relations are considered its direct product subsets, such as R1, R2, . . . , Rn. In this way the system of relations can be represented as hX, R1, R2, . . . , Rni.

4.2.4 Total order and representation theorem Next, let us consider how the ordering relation can be quantified. First, let us consider the case where the ordering relation is total order. Assume that the set of objects X is finite and the system of relations hXhT i is totally ordered, and consider that this system of relations represents preferences. By the definition of total order, the following three properties are established. 1. Completeness (compare possibilities) ’ x, yAX, xhTy 3 yhTx. Here, xhTy can be interpreted as either x is preferred over y or x and y are indiscriminate, and yhTx can be interpreted as either y is preferred over x or x and y are indiscriminate. Here, the symbol 3 is the logical symbol “or,” which means that at least one of them is valid. This completeness is equivalent to the following condition: ’ x; yAX; xhT y 3yhT x3xhT y 3 xBT y 3 x!T y: That is, for any x and y of the elements of X, one of xgTy (x is preferred over y), xBTy (x and y are indiscriminate), or x!Ty (y is preferred over x) holds. Where xgTy is the case where xhTy and yhTx do not hold. That is, ’ x, yAX, xgTy3(xhTy)4:(yhTx). The logical product “and” is represented by the symbol 4, and negation is represented by the symbol :. The symbol 3 is a necessary and sufficient condition that both the relationships between xx and WW (xx.WW), and WW and xx(WW.xx) are

satisfied. Similarly, xBTy is the case when both xhTy and yhTx hold. That is, if x

 ’ x; yAX; xBT y3 xhT y 4 yhT x : Furthermore, x!Ty is a case where yhTx and xhTy do not hold. That is, if ’ x, yAX, x!Ty3(yhTx)4:(xhTy). Thus we have the following three properties.1. Completeness (Comparability)





 ’ x; yAX; xhT y 4: yhT x 3 xhT y 4 yhT x 3


 T T T T yh x 4: xh y 3xh y3yh x 2. Antisymmetry ’ x, yAX, xBTy.x 5 y. That is, for any x and y of the elements of X, if xBTy, then x 5 y. 3. Transitivity ’ x, y, zAX, xhTy4yhTz. xhT. That is, for any x, y, z in X ( ’ x, y, zAX), if xhTy, yhTz, then xhTz holds.

The following representation theorem holds for total order satisfying above three properties.

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Theorem 4.1: Representation theorem for total order (on finite sets). If and only if a system of relations hX,hTi on a finite set X is total order, then there exists a real-valued function ϕ: X!Re on X such that ’ x; yAX; xhT y3ϕðxÞ ^ ϕðyÞ

(4.1)

In other words, the theorem implies that a judgment that is totally ordered can be represented by a real-valued function that preserves the relation between the judgments. In other words, it shows that qualitative all-order judgments can be considered quantitatively. Proof: First, we prove that ’ x, yAX, xhTy.ϕ(x) $ ϕ(y). Assume that ’ x,yAX, xhTy. For all z such that yhTz holds, the following relation holds by utilizing the property of transitivity of the total order: {z|xhTz}+{z|yhTz}. We denote the number of components of a set by ϕ and construct the function as follows: ϕ(x) 5 Card ({z| xhTz}), ϕ(y) 5 Card ({z| yhTz}), where Card ( ) is a function that represents the number of elements of the set in parentheses. Constructing the function ϕ in this way, we have ’ x, yAX, xhTy.ϕ(x) $ ϕ(y). Next, we prove that ’ x, yAX, ϕ(x) $ ϕ(y).xhTy. To prove this proposition, we only need to prove the counterpart of this proposition. The counterpart is ’ x, yAX,:(xhTy).:(ϕ(x) $ ϕ(y)). From completeness the proposition on the left is ’ x, yAX, y!Tx.ϕ(x) , ϕ(y). Here, yhTz holds for all z such that xgTz. Hence, we have {z|xgTz}C{z|ygTz}. We denote the number of components of the set by ϕ and construct the function as follows: ϕ(x) 5 Card({z|xgTz}), ϕ(y) 5 Card({z|ygTz}), where Card ( ) is a function that represents the number of elements in the set in parentheses. Constructing the function ϕ in this way, we have ’ x, yAX, y!Tx.ϕ(x) , ϕ(y). Hence, ’ x, yAX, ϕ(x) $ ϕ(y).xhTy. Therefore the theorem has been proved. The previous theorem can be extended to the case of countable infinite sets. A countable infinite set is a set that has an all-injection between it and the natural numbers. Here, an all-singular projection means that the map f: A!B has (1) f (A) 5 B (all-singular), and (2) for any two sources a1 and a2 of A, if a1 6¼ a2, then f (a1) 6¼ f(a2) (all-singular). In other words, a countable infinite set is an infinite set that has a one-to-one correspondence with the natural numbers, including the integers and the rational numbers. The real numbers are not a countable infinite set, but a noncountable infinite one. Theorem 4.2: Representation theorem for total order (on countable infinite sets). If and only if the relation hX, hTi on a countable infinite set X is total order, there exists a real-valued function ϕ: X!Re on X such that ’ x; yAX; xhT y3ϕðxÞ ^ ϕðyÞ

(4.2)

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The proof of the theorem is basically the same as for finite sets, but since we are dealing with countable infinite sets, we will construct the function ϕ related to the concentration of the set in a different way than in the finite set case. Proof: First, we prove that ’ x, yAX, xhTy.ϕ(x) $ ϕ(y). Assume that ’ x, yAX, xhTy. Let the elements of X be x1, x2, x3, . . . , xi, . . . and define a function Sij such that Sij 5 1 for xihTxj and Sij 5 0 otherwise. Furthermore, we construct the following function ϕ(xj). That is ϕðxj Þ 5

N X 1 i51

2i

Sij


 It is clear that ϕ xj converges. Constructing the function ϕ in this way, we have xihT xj.ϕ(xi) $ ϕ(xj). Therefore ’ x, yAX, xhTy.ϕ(x) $ ϕ(y) holds. Next, we prove that ’ x, yAX, ϕ(x) $ ϕ(y).xhTy. To prove this proposition, we only need to prove the counterpart of this proposition. The counterpart is ’ x, yAX,:(xhTy).:(ϕ(x) $ ϕ(y)), and from completeness, ’ x, yAX, y!Tx.ϕ(x) , ϕ (y). Similarly, if constructing the function ϕ(xj), we have xi!Txj.ϕ(xi) , ϕ(xj). Hence, ’ x, yAX, ϕ(x) $ ϕ(y).xhTy. Therefore the theorem is proved.

4.2.5 Weak order and representation theorem Now consider the case where the ordering relation is weakly ordered. Suppose that the set of objects X is finite and the system of relations hX,hi is weakly ordered, and that this system of relations represents preferences (preference relations). By the definition of weak order, the following two properties are established. 1. Completeness (comparability) ’ x, yAX, xhy3yhx. Here, xhy can be interpreted as x being preferred over y, or x and y being indiscriminate, and yhx as y being preferred over x, or x and y being indiscriminate. 2. Transitivity ’ x, y, zAX, xhy 4 yhz. xhz. That is, for any x, y, z in X ( ’ x, y, zAX), if xhy, yhz, then xhz holds.

In short, it is a property that excludes antisymmetry from the previous property of total order, and it is a situation where antisymmetry does not necessarily hold. It is more natural to think that antisymmetry does not always hold when considering actual human judgments and preferences. For example, even if the preferences are indiscriminate, the objects are not necessarily the same (see Fig. 4.1). It is known that the following representation theorem for weak order satisfying these two properties. In traditional economics, this quantity is called ordinal utility, and in traditional psychology, it is called a psychological scale. Theorem 4.3: Representation theorem for weak order (on finite sets). If and only if the relation hX,hi on a finite set X is weak order, there exists a real-valued function ϕ: X!Re on X such that ’ x; yAX; xhy3ϕðxÞ ^ ϕðyÞ

(4.3)

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Weak Order Structure

55

Whole-order structure

Figure 4.1 Comparison of weak order and total order.

In other words, the theorem implies that weak order judgments can be represented by a real-valued function that preserves the relationship between the judgments. In other words, it shows that qualitative weakly ordered judgments can be quantified. Proof: First, since antisymmetry does not hold for weak orders, we construct the set of equivalences obtained by the equivalence relation B on X, that is, the quotient set X/B by B of X. As mentioned earlier, xBy is the case where both xhy and yhx hold, that is, ’ x, yAX, xBy3(xhy) 4 (yhx). Since antisymmetry holds for this set of equivalences, it is clear that the relational system hX/B, hTi holds for all orders. Therefore using Theorem 2.1, for a system of relations hX/B, hTi on a finite set X/B, there exists a real-valued function ϕ0 : X/B!Re on X, and ’ a; bAX=B; aiT b3ϕ0 ðaÞ ^ ϕ0 ðbÞ From this ϕ0 : X/B!Re, we have ’ xAa, ’ aAX/B, and ϕ(x) 5 ϕ0 (a), so that ϕ: X!Re ’ x; yAX; xiy3ϕðxÞ ^ ϕðyÞ ’ x; yAX; xBy3ϕðxÞ 5 ϕðyÞ It is clear that this is the case. ’ The previous theorem can be extended to the case of countable infinite sets.

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Theorem 4.4: Representation theorem for weak order (on countable infinite sets). If and only if a relation hX, hi on a countable finite set X is weak order, then there exists a real-valued function ϕ: X!Re on X such that ’ x; yAX; xhy3ϕðxÞ ^ ϕðyÞ

(4.4)

Proof: First, since antisymmetry does not hold for weak orders, we construct the set of equivalences obtained by the equivalence relation B on X, that is, the quotient set X/B of X by B. Since antisymmetry holds for this set of equivalences, it is clear that there is a system of relations hX/B, hTi that satisfies the total order. Therefore using Theorem 2.2, for a relational system hX/B,hTi on a countable infinite set X/B, there exists a real-valued function ϕ0 : X/B!Re on X, and ’ a; bAX=B; ahT b3ϕ0 ðaÞ ^ ϕ0 ðbÞ From this ϕ0 : X/B!Re, we have ’ xAa, ’ aAX/B, and ϕ(x) 5 ϕ0 (a), so that ϕ: X!Re ’ x; yAX; xhy3ϕðxÞ ^ ϕðyÞ ’ x; yAX; xBy3ϕðxÞ 5 ϕðyÞ Therefore the theorem is proved. It is clear that Theorem 4.4 is for countable infinite sets, but it does not hold in general for noncountable infinite sets. The following theorem holds for noncountable infinite sets (see Krantz, Luce, Suppes, & Tversky, 1971; Roberts, 1979 for detailed proofs). Theorem 4.5: Representation theorem for weak order (on noncountable infinite sets) If and only if the relation hX, hi on a noncountable finite set X is weak order, and X/B has a hT-dense order countable subset, then there exists a real-valued function ϕ: X!Re on X such that ’ x; yAX; xhy3ϕðxÞ ^ ϕðyÞ

4.3

(4.5)

What is the measurement of preference relations?

4.3.1 Correspondence and measurement Measurement can be thought of as the assignment of numerical values to objects based on empirically observed relationships between objects, and the representation of empirically obtained relationships between objects by means of relationships between those numerical values.

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Measurement is the mapping of an empirical relational system to a particular numerical relational system (Krantz et al., 1971; Sayeki, 1973). An empirical relation is a relation between objects that is observed empirically. Empirical relations, such as preference relations, can be represented as subsets of direct products of sets of objects, and empirical relation systems can be represented as hX, Ti. In the same way, quantitative relations R (e.g., relations between large and small real numbers) can be represented as a subset of the direct product of a set of real numbers, and the quantitative relation system can be represented as hRe, Ri (Krantz et al., 1971; Sayeki, 1973). Here, the empirical relational system is hX, T1, T2i. Let us clarify what we mean by “correspond” when we say that the empirical relation system hX, T1, T2, . . . , Tni corresponds to the quantitative relation system hRe, R1, R2, . . . , Rni. Let us clarify what we mean by “corresponds to” when we say “corresponds to a system of quantitative relations hRe, R1, R2, . . . , Rni.” (1) For any xAX, one particular rARe is determined, and (2) for any subset Ti, i 5 1, . . . , n of the direct product of X, one subset Ri of the direct product of Re is determined (Sayeki, 1973). When such a correspondence can be made, hRe, R1, R2, . . . , Rni is a homomorphism hX, T1, T2, . . . , Tni. When such a correspondence is possible, hRe, R1, R2, . . . , Rni is called a homomorphism to hX, T1, T2, . . . , Tni. In this case, hX, T1, T2, . . . , Tni is represented by hRe, R1, R2, . . . , Rni. In this case, hX, T1, T2, . . . , Tni is said to be represented (or measured) by hRe, R1, R2, . . . , Rni.

4.3.2 On the measurement and representation of preference relation Measurement is the basis of analysis in any qualitative research, survey research, observation, or experiment. Measurement can be thought of abstractly as the assignment of numerical values to objects based on empirically observed relationships between objects, and the representation of empirically obtained relationships between objects by means of relationships between those numerical values. The axiomatic measurement theory is a theory that systematizes the problem of measurement axiomatically based on modern mathematical concepts such as set theory. Axiomatic measurement theory is also closely related to the quantification of ordering mentioned earlier, and to psychological measurement issues such as extensive measurement and conjoint measurement, which will be introduced in later chapters. It is also closely related to the issues of scaling, such as multidimensional scaling, and modeling of consumer utility and preference. According to this general idea of axiomatic measurement theory, measurement is the mapping of an empirical relational system to a particular numerical relational system (Coombs, Dawes, & Tversky, 1970). First, an empirical relation is a relation between objects that is observed empirically. For example, a preference relationship in which a consumer prefers brand B to brand A is an empirical relationship. For example, let the set of brands X be X 5 {brand A, brand B, brand C}. The binary direct product X 3 X, which is the set of all combinations of binary relations of the

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function (e.g., math, programing)

x, y, z Ѯ X

ȭ: X Ѝ Re

Collection of objects (Grasping the empirical relational system by observing the object)

1, 8, 21 Ѯ Re

Scale value (Expressing the empirical relational system into a quantitative relational system)

Figure 4.2 Measurement as a representation of an empirical relational system into a quantitative relational system.

elements of X, is X 3 X 5 {(brand A, brand B), (brand B, brand A), (brand C, brand B), (brand B, brand C), (brand A, brand C), (brand C, brand A)}. Here, the ordinal pair (brand A, brand B) can be interpreted as “brand A is preferred over brand B,” which can be considered an indication of all possible preferences when preference comparisons between brands are possible. Suppose that, as a result of a brand preference experiment, a consumer prefers brand A over brand B, brand B over brand C, and brand A over brand C. If we denote this preference relationship as T, then T 5 {(brand A, brand B), (brand B, brand C), (brand A, brand C)}. Thus it is clear that the preference relation T is a subset of X 3 X. Thus empirical relations such as preference relations can be represented as subsets of the direct product of sets of objects, and empirical relation systems can be represented as hX, Ti. In the same way, quantitative relations R (e.g., size relations of real numbers) can be represented by a subset of the direct product of a set of real numbers, and the quantitative relation system can be represented by hRe, Ri (see Fig. 4.2).

4.3.3 Uniqueness and measurement scale level When an empirical relational system is represented by a quantitative relational system, a scale construction becomes possible. Here, scale construction is the assignment of a numerical value to an object so that a meaningful mapping between the empirical and quantitative relational systems is possible (a mapping by homomorphism, as described in Section 4.3). The scale values of a measurement scale obtained by scale construction may be acceptable for certain transformations. The question of what transformations are acceptable, that is, the question of uniqueness of the transformations, has led to the classification of measurement scales. When an empirical relational system is homomorphism to a quantitative relational system, there can be more than one correspondence. When an empirical relational system is represented by a quantitative relational system, that is, when a homomorphic correspondence exists, the homomorphic correspondence is not necessarily only one in general, because there may be other homomorphic correspondences even with certain

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transformations. For example, for any x, yAX, there exists a real-valued function ϕ such that ϕ(x) . ϕ(y) if and only if a person decides that x is preferable to y. This means that the empirical system of relations for the elements of X is represented by a quantitative system of relations between real numbers and their sizes, and a homomorphic correspondence is established. In this case, any positive linear transformation of ϕ(x) (f(ϕ(x)) 5 αϕ(x) 1 β, α . 0) or any monotonically increasing transformation (e.g., g(ϕ(x)) 5 logϕ(x), x . 0) can represents the preference relation and establish a homomorphic correspondence. Therefore the question in measurement is to what extent a transformation that leads to a homomorphism is acceptable (Sayeki, 1973). When an empirical relational system is represented by a quantitative relational system, and a homomorphic correspondence is made, measurement becomes possible, and scale construction becomes possible. Here, scale construction is the process of assigning a numerical value to an object so that a homomorphic correspondence can be established. As mentioned earlier, the scale value of a measurement scale obtained by scale construction may be acceptable for certain transformations. The question of what transformations are acceptable, that is, the question of uniqueness of transformations, has led to the classification of measurement scales. In this regard the following four categories are commonly used: nominal scale, which is unique for transformations with arbitrary real-valued functions that give different numerical values for different objects; ordinal scale, which is unique for arbitrary monotonically increasing transformations; interval scale, which is unique for arbitrary positive unique interval scale for any positive linear transformation; and a unique ratio scale for any positive constant-doubling transformation. This is the level of scaling according to the idea of axiomatic measurement theory. In addition to these four general categories, there is also the absolute scale, which does not allow for any transformation, but since there are many aspects that are not theoretically clear, only the previous four scales will be explained in detail next. A nominal scale is a scale used to dichotomize survey targets by the presence or absence of certain characteristic expressions, or to assign targets to certain categories or groups. For example, a nominal scale is used to classify by gender (male/ female) or by blood type (type A, B, AB, O, etc.). For example, if we assign a code number of 1 to males and 2 to females, there is no quantitative difference between 1 and 2, such as 2 2 1 5 1, or a proportional relationship such as 2/1 5 2. However, it is possible to treat them as quantitative data by treating them as 1 if they fit into each category and 0 if they do not. When creating a nominal scale for grouping survey targets, it is necessary to ensure that the survey targets are included in one of the categories. This principle is called exhaustiveness of the categories. In addition, a respondent should not be included in two categories at the same time. This principle is called mutual exclusiveness. Rather than simply dividing a variable into a number of qualitatively different categories, an ordinal scale assigns to each category an order of preference, such as first, second, and so on. The rankings are directional; first place is better than second place, and second place is better than third place. In this way the ordinal scale can give superiority or inferiority to categories and calculate percentiles. For

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example, if there are 50 brands of the same type of product, and the percentile of the recall rank of the company’s most important brand is 25 from the bottom, it is immediately clear that 75% of the brands have better recall than the company. However, since rank is not a quantitative unit, it is difficult to estimate the quantitative difference between the rankings. Therefore it is not subject to addition, subtraction, or division, but in practice, it is treated quite arbitrarily, such as by calculating the mean or median. An example of this is the attempt to convert rank into a rank score and treat it like a metric. Another example of ordinal scaling is to assign a superiority or inferiority to only two categories. Even if there are three or more categories, the method of decomposing them into different combinations of two categories each and repeating the superiority/inferiority judgment is also adopted. This is called a pairedcomparison scale, in which the superior of the two categories is given a rank score of 1 and the inferior of 0. An interval scale is not simply a relationship of superiority and inferiority, but an interval scale in which the difference between superior and inferior has a quantitative meaning. For example, the difference between 45 and 50 on a thermometer is equal to the difference between 25 and 30 . Assuming that the interval scales in question have equal intervals, the difference between “very good” and “fairly good” is equal to the difference between “undecided” and “somewhat bad.” Mean and variance also have a quantitative meaning. However, because they do not have an absolute origin, 0, and because the origin and units can be determined arbitrarily, proportional relationships such as 40 being 10 four times hotter or “quite good” being twice as good as “somewhat good” cannot be established. A scale in which the intervals between units are equal and at the same time have an absolute origin is called a proportional scale. The interval scale has an arbitrary choice of zero as its base point, while the proportional scale has only one base point, the absolute zero. Not only does the difference have a quantitative meaning, but the ratio also has a meaning. For example, if the sales volume of brand A is 10 million tons and that of brand B is 20 million tons, then the sales volume of brand A is one-half that of brand B. Also, a 1-kg 3000 yen live fish is 1.5 times more expensive than a 2000 yen live fish. It is also possible to use proportional scales to divide the survey targets into different groups. Thus the proportional scale is the most advanced scale that has all the capabilities of the four types of scales. It is also possible to create a categorical scale based on a proportional scale. The constant-sum scale, which is based on the fact that percentages range from 0 to 100, can also be considered a type of proportional scale. For example, the participants are asked to guess whether they eat rice, bread, snacks, other foods, or no breakfast and allocate 100% of the total to each of the five categories. It can be used to measure attitudes toward snacks in proportion to other foods such as rice. Thus, when representing empirical relational systems obtained from observations into quantitative relations, it is important to know at what scale level they are represented to examine the quantified results. Also, as will be shown shortly in Section 4.3, once we know the nature of the empirical relational system obtained from observation, we can derive what scale it is from a mathematical

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point of view. This is treated in axiomatic measurement theory as a proof of uniqueness. In axiomatic measurement theory, for example, if a relational system hX,hi is weak order, then whether it also constitutes an ordinal scale is justified as in the proof of the following theorem. Theorem 4.6: Uniqueness theorem for weak orders (on finite sets). If and only if a system of relations hX,hi on a finite set X is weak order, then hX,hi is a real-valued function ϕ: X!Re on X, as shown in Theorem 2.3. The structure hhX,hi, hRe, $ i,ϕi is an ordinal scale, represented by hRe, $ i. Proof: Since it is clear from the proof of Theorem 4.3 that hX,hi is represented by hRe, $ i through the real-valued function ϕ: X!Re on X shown in Theorem 4.3, we prove that the structures hhX,hi, hRe, $ i, ϕi are ordinal structures. If ψ: ϕ(x)!Re is an arbitrary monotonically increasing transformation function, the composite function ψоϕ must always satisfy the following relation: ’ x, yAX, hx y3ψоϕ(x) $ ψоϕ(y). This is because, by Theorem 2.3, ’ x, yAX, ψоϕ(x) $ ψоϕ(y)3ϕ(x) $ ϕ(y)3xhy. Moreover, even assuming that ’ x, yAX, hx y3ϕ(x) $ ϕ(y), if ψ: ϕ(x)!Re is an arbitrary monotonically increasing transformation function, then ’ x, yAX, hx y3ψоϕ(x) $ ψоϕ(y). Next, we show that ψ: ϕ(x)!Re must be a monotonically increasing transformation function. If a 5 ϕ(x), b 5 ϕ(y), then ’ x, yAX, ’ a, bAϕ(X), a $ b3x hy3ψоϕ(x) $ ψоϕ(y)3ϕ(x) $ ϕ(y). This shows that an admissible transformation function ψ: ϕ(x)!Re satisfying this relation is impossible for either monotone nonincreasing or nonmonotone transformation functions, and that only monotone increasing transformation functions are possible. Therefore the structure hhX,hi,hRe, $ i,ϕi is an ordinal scale, since the admissible transformation function ψ: ϕ(x)!Re belongs to the class of monotonically increasing transformation functions. The proof takes the same form as earlier, but for the uniqueness of weak ordering on countable infinite sets and on noncountable infinite objects, the following theorem holds. Theorem 4.7: Uniqueness theorem for weak order (on countable infinite sets). If and only if a relation system hX,hi on a countable infinite set X is weak order, then hX,hi is represented by a real-valued function ϕ: hRe, $ i on X through X!Re as shown in Theorem 2.4, and the structure hhX,hi, hRe, $ i, ϕi is an ordinal scale. Theorem 4.8: Uniquness theorem for weak order (on noncountable infinite sets). The relation hX,hi on a noncountable infinite set X is weak order and X/B has a hT-dense order countable subset, then hX,hi is represented by hRe, $ i through the real-valued function ϕ: X!Re on X, and the structures hhX, hi,hRe, $ i, ϕi are ordinal scale.

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Quantitative representation of possible psychophysical laws and preference relations in terms of scale levels

4.4.1 Psychophysical laws There is a classical psychophysical approach to representing preference relations in comparative judgments and decision-making. This is important for quantitative representations of good and bad decision-making judgments. One example is the measurement of price judgment for discounts and price increases. In the field of experimental psychology the measurement of stimulus
response relationships when the stimulus can be physically measured and quantitatively described has been studied for more than 100 years. Fechner (1860) proposed the psychophysical method (sometimes translated as psychophysical measurement) and developed constant measures and scale construction methods to specify the functional relationship between stimulus intensity and psychological quantities made through judgments. He also developed a constant measure and scale construction method to identify the functional relationship between stimulus intensity and psychological quantities made through judgments, based on Weber’s law, which states that the ratio of stimulus intensity I to its discrimination threshold ΔI, ΔI/I is constant (Wada, Oyama, & Imai, 1969; Indow, 1977). In deriving Fechner’s law, he considered ΔI a derivative and assumed that ΔI 5 dI, which is proportional to the smallest unit of sensation, ΔS 5 dS, where dS 5 kdI/I (k is a constant), and took the integrals of both sides of this equation to obtain S 5 k. If the stimulus intensity at S 5 0 is I0, we can assume that C 5 2klog I0. If the stimulus intensity at S 5 0 is I0, then C 5 2klog I0, which can be thought of as S 5 klog I 2 klog I0 5 klog I/I0. If we consider I/I0 to be the stimulus intensity standardized by the stimulus threshold value I0, we obtain the so-called Fechner law. Like Fechner’s law, the law concerning the relationship between physical and psychological quantities is called the psychophysical law, and various studies have been conducted even today. There is some disagreement as to whether Fechner’s psychophysical function of the logarithmic function is really valid or not, with criticism that there is a leap in deriving it from Weber’s law, and Stevens’ theory (S 5 αIβ, where α and β are constants) that the Beki function is more valid than the logarithmic function (Wada et al., 1969). Despite this controversy, Fechner’s logarithmic function and Stevens’ power function are generally accepted as psychophysical functions for stimulus and response. In addition, many theories of value and utility, which are outside the realm of the senses, use value and utility functions similar to the psychophysical functions of Fechner and Stevens. For example, in nonlinear utility theory, such as the prospect theory of Tversky and Kahneman (1992), which describes the evaluation of monetary gain, there are many theories that use value and utility functions similar to the psychophysical functions of Fechner and Stevens. Luce (1959), a mathematical psychologist, used functional equations to develop a theory of possible psychophysical laws according to interval and proportional scales. For example, if stimulus I is on a proportional scale and stimulus II is on a

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proportional scale, then stimulus III is on an interval scale. For example, if the stimulus I is of proportional scale and the sensory quantity v(I) is also of proportional scale, according to the definition of proportional scale, even if the unit of the scale value of the stimulus I is changed and transformed by a constant factor (k-fold), the scale of the sensory quantity v(I) ( . 0) will also be correspondingly multiplied by K(k), and the correspondence will be based on homomorphism. Therefore we can assume that the following functional equation holds: vðkI Þ 5 K ðkÞvðI Þk . o; K ðkÞ . 0

(4.6)

It has been proved that the only continuous function v(I) that satisfies the previous functional equation can be the following power function: vðI Þ 5 αI β ; α . 0

(4.7)

Similarly, if we assume that the sensory quantity u(I) is an interval scale, we can assume that when we change the units of the scale value of I and make a constant multiplication transformation (k-fold), u(I) is considered to be linearly transformed by the definition of interval scale, so that the following functional equation holds: vðkI Þ 5 K ðkÞuðI Þ 1 C ðkÞ k . o; K ðkÞ . 0

(4.8)

It has been proved that there can be only two continuous functions u(I) that satisfy the previous functional equation: uðI Þ 5 αlogI 1 β uðI Þ 5 αI β

(4.9) (4.10)

This formulation of Ruth’s shows that when stimuli can be measured on a proportional scale, Stevens’ law holds when human judgments are on a proportional scale, and Fechner’s law or Stevens’ law holds when judgments are on an interval scale. However, this formulation has been criticized for its inapplicability when the unit of stimulus intensity is nondimensionalized (Indow, 1977), and researchers are still debating about the formulation of Rousse (Birnbaum, 1998). In addition, Takemura (1998, 2001) proposed the mental ruler theory, which states that the evaluation function in consumer judgments is concave near the lower limit of the possible stimuli and convex near the upper limit. He formulated the theory in such a way as to include Fechner’s law and Stevens’ law as special cases. Thus it is possible to quantify the relationship between preferences through a psychophysical approach, although the consequences of Ruth’s formulation require further study in the future. However, as discussed earlier, it should be noted that there are some axiomatic assumptions in this quantitative representation.

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4.4.1.1 Psychological scale structure of preference There are various methods of constructing measurement scales, but they can be roughly divided into representational measurement, which is based on axiomatic measurement theory in mathematical psychology, and psychometric measurement (Judd & McClelland, 1998). The former type is based on axiomatic measurement theory in mathematical psychology (Judd & McClelland, 1998). The former type of scale construction method is based on an axiomatic system in which empirical relational systems are represented by quantitative relational systems and basically attempts to construct proportional and interval scales from ordinal-scale judgments. This approach includes extensive measurement and conjoint measurement, which are described later. On the other hand, the latter type of scaling method is based on the traditional methods of econometrics and includes various types of unidimensional and multidimensional scaling. The first type of measurement, representationa measurement, is based on strict logic based on axiomatic measurement methods, but it has the problem that it does not consider sufficiently developed techniques for handling errors and checking reliability. On the other hand, the latter type of measurement, measurement psychology, is considered to be relatively easy to use from a technical point of view, but it has problems in that the preconditions for its measurement are very strict and it is not treated from the viewpoint of axiomatic measurement theory at all. Thus both approaches have their advantages and disadvantages, and there is some debate as to which approach is superior (Judd & McClelland, 1998). However, the important thing seems to be to use both approaches in a complementary manner rather than to adopt one over the other. The representational measurement approach, while rigorous, is technically difficult to use, so it is recommended that it be used as a philosophy for recognizing limitations and constraints in measuring psychometrics, or as a partial check. Although the quantitative psychological measurement approach is technically easy to use and recommended for achieving practical purposes such as marketing research, it employs rather stringent assumptions in terms of its representational measurement approach, and it would be necessary to examine these assumptions. To grasp the theoretical position of the preference relation, what follows is a brief description of the approach to representational measurement based on axiomatic measurement theory.

4.4.2 Representational measurement approach The concept of extensive measurement was originally conceived by the mathematician Ho¨lder, O., to provide an axiomatic basis for physical measurements, but it is also applicable to psychological measurements. However, it can also be applied to psychological measurements. Now consider a set X of measurement objects, and suppose that for any elements x and y of X, x is somehow higher (e.g., heavier) than y, or at least equal. Then (1) there exists a real-valued function ϕ such that ϕ(x) $ ϕ(y) if and only if the relation holds, and (2) for the concatenation of x and y, xxy, ϕ(xxy) 5 ϕ(x) 1 ϕ(y). We consider a measurement scale such that ϕ(xxy) 5 ϕ(x) 1 ϕ(y). An extensive measurement is a

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measurement scale ϕ that satisfies (1) and (2), and the structure of such a measurement scale is called an extensive structure. The extensive structure is unique with respect to the positive constant multiplication transformation and is considered to be a proportional scale. To construct an extensive-measurement measure, the judgment must satisfy qualitative conditions such as weak order, associativity, monotonicity, and positivity properties (Iverson & Luce, 1998). Therefore in constructing a scale, it is necessary to check whether the ordinal judgment of the object satisfies these qualitative conditions, and if it does, quantify it. Conjoint measurement is a measurement proposed by Luce and Tukey (1964) for constructing interval scales from ordinal scale
level judgments for multiattribute objects. Now, suppose there is a set X of objects with two different attributes A and U. That is, X 5 A 3 U. Here, for any x 5 (a,u), y 5 (b,v)AX, there are real-valued functions ϕ, ϕ1, ϕ2 such that ϕ(x) 5 ϕ1(a) 1 ϕ2(u), ϕ(y) 5 ϕ1(b) 1 ϕ2(v) if and only if x is weakly preferred (at least equal or preferred) to y, suppose that there exist real-valued functions ϕ, ϕ1, ϕ2 such that measurement scales ϕ, ϕ1, ϕ2 are constructed by conjoint measurement, and the structure of such measurement scales is called an additive conjoint structure. An additive conjoint structure is unique with respect to a positive linear transformation and is considered to be an interval scale. To construct a conjoint measure, the judgment must satisfy some qualitative conditions such as weak order, independence, and double cancellation (Sayeki, 1973; Iverson & Luce, 1998). Therefore in constructing a scale, it is necessary to check whether the ordinal judgment of the target satisfies these qualitative conditions, and if the conditions are satisfied, quantification should be performed. However, since checking these qualitative conditions is technically quite complicated, some methods have been developed to check the reliability of a scale by assuming an additive conjoint structure in advance, having the user make ordinal judgments, constructing the scale using the least squares method, and simulating it. Such a simple method is called conjoint analysis and is often used in marketing research and traffic engineering. This will be discussed in more detail in later chapters. Conjoint analysis is often used to understand consumer preferences, especially in marketing. For example, in the development of a new product, it can be used to determine which attributes of an existing product should be changed to produce a new product that is most preferred by consumers, or to calculate the market share of a new product by simulation. Conjoint analysis is currently applied to marketing in a large number of cases, but it can also be applied to the study of preference judgment, such as preference surveys for university entrance, and it is also used in the study of risk assessment by civil engineering experts. As shown in the pioneering work of Luce and Tukey (1964), conjoint analysis is an analytical technique originally developed in the field of mathematical psychology to construct an additive real-valued function (additive utility function) equivalent to an interval scale from preference data at the ordinal scale (or more precisely, a scale satisfying weak ordinality) level. The purpose is to construct an additive real-valued function (additive utility function) equivalent to an interval scale from preference data at the level of the interval scale (precisely a weakly ordinal scale). To construct such an additive real-valued function, it is known that the preference relation must satisfy a set of axioms.

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In the early days of conjoint analysis, the mainstream of utility estimation was based on the assumption of an ordinal scale for participants’ preference judgments and the application of monotone transformation methods such as MONANOVA (monotone analysis of variance) (e.g., Shepard, Romney, & Nerlove, 1972). In recent years, however, conjoint analysis using the ordinary least squares method with dummy variables has been used more frequently (Louviere, 1988; Cattin & Wittink, 1989). Although conjoint analysis using ordinary least squares strictly requires that the preference judgments be at or above the interval scale level, simulation studies have shown that the results are very similar to MONANOVA, which assumes an ordinal scale and performs a monotonic transformation (Carmone, Green, & Jain, 1978). This section provides a brief explanation of conjoint analysis using the least squares method, which is incorporated into ordinary statistical packages. In conjoint analysis the response (evaluation result) ri of a participant to the evaluation target i is represented by the following linear model. ri 5 β 0 1

p X

uj ðkji Þ

j51

However, uj(kji) is the utility (partial utility) at the kji level of factor (attribute) j in evaluation target i (denoted as ujk for simplicity next). The partial utility function uj is calculated differently with respect to the estimation of the evaluation result ri in the following cases: (1) in the case of a discrete factor where a linear or quadratic relationship between the levels of the factor cannot necessarily be assumed, (2) in the case of a linear factor where a linear relationship between the levels can be assumed, and (3) in the case of a quadratic factor where a quadratic relationship between the levels can be assumed (ideal factor). For example, in the case of the linear factor, a linear relationship can be assumed between the levels. For example, in the case of a linear factor, the estimated evaluation value changes as a linear function of the level value, while in the case of a quadratic factor, the estimated evaluation value changes as a quadratic function of the level value. Based on the specification of these functions, ujk is estimated. In the actual acquisition of data, all the profiles to be evaluated are presented to the survey participants, and evaluation scores and ranking data are collected. However, as the number of attributes and attribute levels increases, it becomes more difficult for the respondents to rank and evaluate the data. To reduce this burden, various measures must be taken. Orthogonal programming is often used to reduce the number of profiles presented to participants.

4.5

Conclusion

In this chapter, I have explained the problem of how preference relations are represented in decision-making, mainly based on axiomatic measurement theory. In this

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chapter, I introduced the concept of utility inferred from the observation of choice behavior and simultaneously introduced psychological scales as well as the traditional concept of ordinal utility theory. As mentioned in this chapter, ordinal utility and ordinal scales are mathematically the same thing, and it is known that they can be represented if the weak ordinal relation is satisfied. In this sense the preference relation can be represented quantitatively. However, the quantity of this ordinal scale is only a measure that preserves the fruit of the ordinal relation, which cannot be calculated in four arithmetic operations. If we want to represents something like the strength of preference, which is what traditional psychology deals with, we have to satisfy at least the properties of the interval scale. Therefore even if we try to represents quantitatively the goodness or badness of a decision, it is only an ordinal scale. In addition, as discussed in Chapter 3, Rational Choice, Irrational Choice, and Bad Decisions, weak order is assumed in the premise of rational decisionmaking, which seems to be a rather strict assumption in terms of axioms, but this weak order also has only the structure of an ordinal scale. To measure the strength of preference on an interval scale, as in traditional psychology (e.g., Likert method and SD method,), we can say that we are making an even more stringent assumption than the stringent assumption of perfect rationality. This implies that quantitative representations of good and bad decisions can be constructed theoretically, but only under very strict conditions in practice.

References Birnbaum, M. H. (Ed.), (1998). Measurement, judgment, and decision making. San Diego, CA: Academic Press. Carmone, F. J., Green, P. E., & Jain, A. K. (1978). Robustness of conjoint analysis: Some Monte Carlo results. Journal of Marketing Research, 15, 300
303. Cattin, P., & Wittink, D. R. (1989). Commercial use of conjoint analysis: An update. Journal of Marketing, 53, 91
96. Coombs, C. H., Dawes, R. M., & Tversky, A. (1970). Mathematical psychology: An elementary introduction. Englewood Cliffs, NJ: Prentice-Hall. Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971). Foundations of measurement Volume 1: Additive and polynomial representations. New York: Academic Press. Fechner, G. (1860). Elemente der Psychophysik. Leipzig: Breitkopf & Hartel. Indow, T. (1977). Shinri Sokutei, Gakusyu Riron [Psychological measurement, learning theory]. Tokyo: Morikita Publishing. (in Japanese). Iverson, G., & Luce, R. D. (1998). The representational measurement approach to problems. In M. H. Birnbaum (Ed.), Measurement, judgment, and decision making (pp. 1
79). San Diego, CA: Academic Press. Judd, C. M., & McClelland, G. H. (1998). Measurement. In D. T. Gilbert, S. T. Fiske, & G. Lindzley (Eds.), Handbook of social psychology (4th ed., pp. 180
232). New York: McGraw-Hill. Louviere, J. J. (1988). Analyzing decision making: Metric conjoint analysis. Beverly Hills, CA: Sage Publications, Inc. Luce, R. D. (1959). On the possible psychophysical laws. Psychological Review, 66, 81
95.

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Luce, R. D., & Tukey, J. W. (1964). Simultaneous conjoint measurement: A new type of fundamental measurement. Journal of Mathematical Psychology, 1, 1
27. Roberts, F. S. (1979). Measurement theory with applications to decision-making, utility, and the social sciences. Reading, MA: Addison Wesley. Sayeki, Y. (1973). Kourironteki apurohchi: Conjoint measurement Riron [Axiomatic approach: Conjoint measurement theory]. In T. Indow (Ed.), Shinrigaku Kenkyuu Hou 17. Moderu Kousei [Psychological research method 17: Model building] (pp. 231
247). Tokyo: Morikita Publishing., in Japanese. Shepard, R. N., Romney, A. K., & Nerlove, S. (1972). Multidimensional scaling (Vol. 1). New York: Seminar Press. Takemura, K. (1998). Jokyo izonteki isikettei no teiseiteki moderu: Shinteki monosashi riron niyoru setsumei [Qualitative model of contingent decision-making: An explanation of using the mental ruler theory]. Ninchi Kagaku, 5(4), 17
34, in Japanese. Takemura, K. (2001). Contingent decision making in the social world. In C. M. Allwood, & M. Selart (Eds.), Decision making: Social and creative dimensions (pp. 153
173). Dordrecht: Kluwer Academic Publishers. Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 5, 297
323. von Neumann, J., & Morgenstern, O. (1944/1947). Theory and games and economic behavior. Princeton, NJ: Princeton University Press. Wada, Y., Oyama, T., & Imai, S. (Eds.), (1969). Kankaku 1 chikaku shinrigaku handobukku [A handbook for sensory and perception psychology]. Tokyo: Seishin Shobo.

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In Chapter 4, Preference Ordering and Measurement, I mainly discussed the quantitative representation of preference relations from the perspective of ordinal utility. It was found that ordinal utility and ordinal scales require the property of weak ordering. In the case of interval scales, the expression “cardinal utility” is used. In this chapter, I will introduce the concept of revealed preference under the assumption of ordinal utility and the assumption of cardinal utility. The revealed preference theory theoretically guarantees the measurability of utility under the assumption of rationality. Similarly, we may consider revealed preference in the opposite sense from the assumption of irrationality as described in Chapter 3, Rational Choice, Irrational Choice, and Bad Decisions. As described in Chapter 3, Rational Choice, Irrational Choice, and Bad Decisions, complete rationality requires the weak order property to be satisfied, and if there is complete irrationality, which can be thought of as bad decision-making in the opposite sense, it also requires the weak order property. This is based on the assumptions of completeness and transitivity. Completeness means comparability, and transitivity is a relation between two alternatives, for example, if I like candy better than chocolate, and I like gum better than candy, then I like gum better than chocolate, which is a consistent preference relation property. Also, in terms of rationality in a looser sense, introduced in Chapter 3, Rational Choice, Irrational Choice, and Bad Decisions, at least acyclicity must be satisfied. Acyclicity is also assumed in models of limited attention (Masatlioglu, Nakajima, & Ozbay, 2012). Acyclicity is a looser condition than transitivity, because it means that the preference relation does not circulate in any one place. In other words, if transitivity is satisfied, acyclicity is satisfied, but the reverse relationship does not hold. In this chapter, I will focus on examples where the transitivity assumption of ordinal utility and the acyclicity assumption of weak rationality are not satisfied and introduce empirical studies.

5.1

Rationality criteria and revealed preference

As discussed in Chapter 3, Rational Choice, Irrational Choice, and Bad Decisions, the following rationality property β holds, which satisfies the weak ordering relation (Sen, 1970). Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00006-5 © 2021 Elsevier Inc. All rights reserved.

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Property β: If some elements x and y belonging to X1, a subset of the choice set X2, are the best elements in X1, and x is also the best element in X2, then y is also the best element in X2. That is, ’ x,y, [x∊C(X1, R) and X1CX2]![x∊C(X2, R)3y∊C(X2, R)] Property β says that if x and y are both best choices in X1, a subset of X2, then if one x is the best choice of X2, then the other y is also a subset of X2, and if y is the best choice of X2, then x is also the best choice of X2. Deducing this from the idea of ordinal utility, to say that property β holds, is equivalent to choosing the option with maximum utility. This shows that utility maximization is equivalent to the property β of rationality and that the preference relation is weakly ordinal. Also, as shown in the axiomatic measurement theory in Chapter 4, Preference Ordering and Measurement, if the preference relation can be measured as an empirical relation through behavioral observation, then the preference relation can be measured. This can be applied to both desirable good decision-making problems and undesirable bad decision-making problems. In other words, irrational and bad decision-making is equivalent to minimizing utility if goodness and badness are diametrically opposed. Also, if goodness and badness are not necessarily diametrically opposed, it means maximizing the badness of the decision. However, this is only true if the preference decision relation satisfies the weak ordering criterion and satisfies the properties of ordinal measure or ordinal utility (Takemura, 2019, 2020).

5.2

The concept of revealed preference

As discussed in Chapter 4, Preference Ordering and Measurement, if we can measure the preference relation as an empirical relation, then we can express ordinal utility, but what does it mean that we can measure the preference relation as an empirical relation? For example, if a person wants to buy a certain product x but chooses the lower priced y over the higher priced x due to lack of money, can it be said that the person has preferred y over x? Based on simple behavioral observations, it might be considered reasonable to judge that the person chose y over x. In social psychology a phenomenon called fundamental attribution error or correspondence bias is known. This leads people to believe, based on behavioral observations, that the behavior in question is a manifestation of their intentions or motivations. For example, a person who refrains from going out of the house due to social pressure may be considered to have a preference for staying at home rather than going out, and observers have shown that such an attributional tendency exists. However, when there are external constraints, it is more natural to assume that the intentions and preferences of the individual are not known. On the other hand, a person who makes irrational choices is choosing an undesirable action, but again, the relationship may be reversed in the presence of external constraints. In economics, there is a proposition that “people maximize utility in their decisionmaking.” This proposition seems to hold if the weak order assumption is satisfied, as

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shown earlier. However, the question of whether this proposition can be determined a priori, whether it is a proposition that can be examined empirically, or whether it is a matter that can be determined normatively is related to the problem of rationality and is also closely related to the idea of revealed preference. The idea of revealed preference allows us to interpret this proposition as an empirical proposition. According to this way of thinking, decision makers maximize utility even in reality, and the indifference curve and utility can be estimated through experiments in which income and prices are varied. Many economists seem to think of optimization propositions as empirical propositions, something that can be observed empirically. When we want to know preferences, the question is how to find out. This also leads to the question of how to infer the utility function. It is possible to ask people directly about their preferences using questionnaires, as is done in social psychology. However, there is no guarantee that people will answer honestly. On the other hand, the theory of revealed preference is a methodology to obtain information about preferences by assuming the rationality of consumers. To illustrate the concept of revealed preference theory, we first assume quantitative relationships and cardinal utility as assumed in traditional economics and then explain the indifference curve, followed by an explanation of revealed preference.

5.3

Utility functions and indifference curves

5.3.1 Indifference curve Before explaining the revealed preference theory, let us discuss the idea of indifferent curves. Let us consider the indifference curve using a simple example. For example, consider a good consisting of two items, such as grapes (x) and apples (y). Assuming that these goods are measured in kilograms, they can be denoted by an arbitrary vector of the form (grapes, apples 1 kg). This notation can be made more abstract, such as (x1,y1), (x2,y2). Given two consumption vectors, (x1,y1) and (x2,y2), we assume that consumers make comparative decisions based on their individual preferences. The preference structure hX,hi assuming that h is weak order, the relation that y is preferred over x is denoted by xgy, and xgy3xhy and :ðyhxÞ This indicates that x is preferred in a stronger sense than y. Also, x hy, we say that x is preferred in a weaker sense. Furthermore, the same degree of preference is indicated by the notation x to y. xBy3xhy and yhx and x and y are denoted as indifference. A consumption vector xi∊X and a set of indiffrence consumption vectors Ix 5 fyAXjy 2 xg

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are called the indifference set, and the set of consumption vectors that weakly prefer a certain consumption vector   Rx 5 yAXjyhx This is called the upper contour set (Takemura, 2019). Like the weights of grapes (first good) and apples (second good), the indifference curves are the vectors of consumption that are indifferent between the consumption of the first and second goods on both axes. This may be easier to understand if we consider the utility function shown earlier. The indifference curves are the ones that connect all the consumption vectors such that the utility function of a certain consumption vector is u(x,y) 5 k. As shown in Fig. 5.1, the utility is higher in the upper part of the figure, and the group of indiffrence curves in two dimensions is the projection on the two-dimensional plane as shown in Fig. 5.2 by connecting the quantities of x and y with the same utility height.

5.3.2 Perfect substitute goods When consumers are able to substitute one good for another at a certain exchange ratio, the two goods are called perfect substitutes. For example, when Company A’s wine bottle can be substituted for Company B’s wine bottle at a one-to-one

Figure 5.1 Utility functions for two goods.

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Figure 5.2 The group of indifference curves is constructed from the utility functions of the two goods. According to this figure, consumption vectors A and B are indifferent, and both have a strong preference for consumption vector C.

Number of bottles of wine (Company B)

Marginal rate

1 1 0

Slope = -1

1

2

Number of bottles of win (Company A)

Figure 5.3 Group of indiffrence curves for the case of perfectly substitutable goods.

exchange ratio, we can draw a group of indifference curves as shown in Fig. 5.3. In this case the utility curve is uðx; yÞ 5 x 1 y

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In the case of perfect substitutes, preferences are generally indicated by the following utility curve In the case of perfectly substitutable goods, preferences are generally indicated by the following utility curve uðx; yÞ 5 ax 1 by The slope of the indifference curve is 2 a/b. The slope of the indiffrence curve is sometimes called the marginal rate of substitution. The slope of the indifference curve represents the exchange ratio when consumers substitute the first good for the second good (Takemura, 2019; Varian, 2014). Next, let us explain this marginal rate of substitution in terms of marginal utility. The marginal utility for a good is the rate of change in utility ΔUx linked to a small change in the quantity of the good Δx, while the change in the quantity of other goods is fixed. Let MUx be the marginal utility for the first good. MUx 5

ΔU uðx 1 Δx;yÞ 2 uðx;yÞ 5 Δx Δx

Let MUy be the marginal utility for the second good. MUy

ΔU uðx;y 1 ΔyÞ 2 uðx;yÞ 5 Δy Δy

If the utility function is partial differentiable, MUx is the partial derivative of the utility function at x, and MUy is the partial derivative of the utility function at y. If the utility function is partial differentiable, MUx is the utility function partial differentiated by x, and MUy is the utility function partial differentiated by y. The marginal rate of substitution, expressed in terms of marginal utility, is MRS 5

Δy MUx 52 Δx MUy

5.3.3 Complete complementary goods A good that is consumed together by consumers in a certain fixed ratio is called a perfect completeness good. This is easy to understand if we consider, for example, shoes or a pair of glasses. These are goods that are almost meaningless unless both are consumed together. Alternatively, consider the left and right sides of a shoe. Consider that there is one glass of the first pair of goods and a quantity of the other glass of the second pair of goods. In such a case, a group of indiffrence curves is drawn as shown in in Fig. 5.4. In the case of a perfectly complementary good, as shown in Fig. 5.4, the utility function is: ðx; yÞ 5 minðx; yÞ: This is because utility increases only when both pairs own the same number of units. This is because utility increases only when both members of a pair own the

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Number of glasses A ⬚

⬚

O Slope = -1

Number of glass B

Figure 5.4 Group of indiffrence curves for the case of fully complementary goods.

same number of units. In the case of perfectly substitutable goods, preferences are generally indicated by the following utility curve: ðx; yÞ 5 minðax; byÞ; where a and b are positive numbers that indicate the proportion of each good consumed.

5.3.4 Indifference curve groups for noneconomic goods In general, goods satisfy the property of monotonicity, in which utility increases as quantity increases, but there are some noneconomic goods (called “bads”) or negative goods that are not preferred as quantity increases; for example, garbage and pollutants in the environment. Fig. 5.5 is an example where one good x is a noneconomic good, and Fig. 5.6 is a group of non-discriminatory curves where both goods x and y are non-economic goods. In Fig. 5.5, the utility value increases in the upper left direction, and in Fig. 5.6, the utility value increases in the lower right direction of the origin.

5.3.5 Indifference curve group of neutral goods A good utility of which does not increase at all with an increase in quantity is called a neutral good. This means that if the amount of potato chips in a hamburger store does not increase a person’s utility no matter how much the amount of chips is

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Figure 5.5 x is a noneconomic good and y is a good that satisfies monotonicity.

⬚

utility

O

⬚

Figure 5.6 Noneconomic goods for both x and y.

increased, then the chips are a neutral good. The group of indiffrence curves for the case where one good x is a neutral good and the other good y is a good satisfying normal monotonicity is shown in Fig. 5.7.

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utility ⬚

O

⬚

Figure 5.7 x is a neutral good, y is a good that satisfies monotonicity, and y is a normal good.

5.4

Revealed preference

5.4.1 What is revealed preference? Suppose there is a indiffrence curve for some goods x and y, as shown in Fig. 5.8. If the price per unit of a good x is p1 and the price per unit of y is p2, then the budget m m 5 p 1 x 1 p2 y In Fig. 5.8 the straight line to the right is this budget constraint line. In this figure the downward right line is this budget constraint line. If the indiffrence curve is convex as shown in the figure, the combination of goods with the highest utility will be the point where the indiffrence curve touches the budget constraint line. In this case, the consumption vector marked with “K” is the optimal consumption plan. The consumption vector to the left of the budget constraint line has a lower utility value. The principle of revealed preference can be shown as follows, taking into account the problem of budget constraints.

5.4.2 Principle of revealed preference Let a consumption vector (x1,y1) be a the one that is chosen under the price (p1,p2). Let (x2,y2) be another one satisfying p1x1 1 p2y1 $ p1x2 1 p2y2. Then, if the consumer tries to choose the best consumption vector, then (x1,y1) prefers (x2,y2) in a strong sense (Takemura, 2019; Varian, 2014).

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y

Optimal

O

x

Figure 5.8 Consumption vector for utility maximization under a given budget constraint.

If the budget constraint inequality p1x1 1 p2y1 $ p1x2 1 p2y2 holds and (x1,y1) and (x2,y2) are different consumption vectors, then (x1,y1) is more directly revealed than (x2,y2). It is said that (x1,y1) is more directly revealed to (x2,y2). Also, when there are three consumption vectors, (x1,y1), (x2,y2), and (x3,y3), for example, even though (x1,y1) is not directly revealed prefered to (x3,y3), (x1,y1) is directly revealed prefered to (x2,y2), and (x3,y3) is directly revealed prefered to (x2,y2), and also (x3, y3) to (x2,y2), and (x1,y1) is indirectly revealed prefered to (x3,y3) (Varian, 2014).

5.4.3 Weak axiom of revealed preference Let a consumption vector (x1,y1) be the one that is chosen under the price (p1,p2). Let (x2,y2) be another one satisfying p1x1 1 p2y1 $ p1x2 1 p2y2. Suppose that (x1,y1) is directly revealed preferred over (x2,y2), and that these consumption vectors are not identical. To express this axiom in other words, if (x1,y1) is purchased when some consumption vector (x2,y2) is available for purchase, then (x1,y1) is not available for purchase when (x2,y2) is purchased. The weak axiom of revealed preference (WARP) states that if x(p,m) is the consumption vector when the price vector is p for some arbitrary budget m (denoted by (p,m)) and x(p0 ,m0 ) is the consumption vector when the price vector is p0 for another arbitrary budget m0 (denoted by (p0 ,m0 )), then the following relation holds. In other words, when px(p0 ,m0 ) # m, x (p0 ,m0 ) 6¼ x(p,m), then p0 x(p,m) . m0 . Therefore if the WARP is satisfied, then px(p0 ,m0 ) . m or p0 x(p,m) . m0 is true, and px(p0 ,m0 ) # m and p0 x(p,m0 ) # m0 cannot be satisfied simultaneously. Therefore

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Y ⬚

⬚

⬚

x

O

⬚

Figure 5.9 An example where the weak axiom of revealed preference is satisfied. Y ⬚

⬚

⬚

x Budget line of (

)

Figure 5.10 The case where the weak axiom of revealed preference is not satisfied.

in the example of Fig. 5.9, px(p0 ,m0 ) . m and p0 x(p,m) . m0 are true and the WARP is satisfied, while in the example of Fig. 5.10, px(p0 ,m0 ) # m and p0 x(p,m) # m0 are simultaneously satisfied and the WARP is not satisfied (Takemura, 2019).

5.4.4 Strong axiom of revealed preference Let a consumption vector (x1,y1) be the one that is chosen under the price (p1,p2). Let (x2,y2) be another one satisfying p1x1 1 p2y1 $ p1x2 1 p2y2. Suppose that (x1,y1)

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is directly or indirectly revealed preferred over (x2,y2), and that these consumption vectors are not identical. When the strong axiom of revealed preference is satisfied, we can interpret that consumers are maximizing their utility. Based on the axiom of revealed preference, we can infer preferences from the actual purchase patterns of consumers (Takemura, 2019).

5.4.5 A more general definition of rationality and revealed preference Let us now give a more general definition of rationality and revealed preference. To explain the basic concept of rational choice, we can define a function C as a choice function domain of which is the set of arbitrary subsets of the set of alternatives X (set family) κ. This C can be understood as a choice function. Any SAκ is an opportunity set of choices, and C(S) can be called a choice set from an opportunity set S (Suzumura, 2009). In the following, we assume that the choice set for any opportunity set SAκ is not an empty set. Here, the revealed preference relation Rc, which can be derived from the choice function C, can be defined as follows (Suzumura, 2009): ’ x; yAX; xRcy3'SAκ; xAC ðSÞ and yAS: That is, for any elements x and y of a choice set X, the fact that x is revealed preferred to y (xRcy) means that x can be defined to be the choice from a choice function C if x and y are elements of the choice set S. This notion of revealed preference simply means that being revealed preferred is equivalent to being selected from a set of opportunities. In traditional economics, this idea of revealed preference is further extended to ensure that utility functions can be estimated from revealed preferences. On the other hand, in psychology, it is common to consider procedural rationality, but when we think of psychological measurement, we inevitably think of a function of psychological responses based on choice outcomes, and in the estimation of this function, the principle of revealed preference is implicitly assumed, just as in the estimation of utility functions in economics. In other words, in the sense that we consider a person’s desires and motivations based on the actions he or she chooses, we are understanding human beings in terms of revealed preferences, or to put it more harshly, we are understanding human behavior based on basic attribution error and response bias. Thus in psychology, procedural rationality, as Simon (1986) calls it, is taken into account theoretically, while substantive rationality is assumed for methodological requirement. This is true not only in traditional experimental psychology, but also in psychology in a broader sense, such as analytical psychology and psychoanalysis. For example, the unconscious errors and misstatements of people proposed by Freud.S also seem to assume that the unconsciousness has a rationality of purpose.

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A choice function C is said to be a rational choice function if there exists a preference relation R and it can be understood in a unified way as an action that optimizes the preference under a given set of opportunities. That is, consider a set (family of sets) κ of arbitrary subsets of a set X of alternatives, where any SAκ is an opportunity set of alternatives, and there exists a preference relation R on X (RCX 3 X) such that   C ðSÞ 5 xASj ’ yAS:xRy : When C(S) holds for any SAκ, we call C(S) a rational choice function and say that the preference relation R rationalizes the choice (Suzumura, 2009). The existence of a rational choice function means that there is a best alternative, which we discussed earlier. Theorem 5.1: Richter’s rationalizability theorem (Richter,1971) I will now introduce the relationship between the existence of this rational choice function and revealed preference. For the existence of a rational choice function, the following property of Richter’s weak axiom (Richter, 1971) is a necessary and sufficient condition. That is, a necessary and sufficient condition for the existence of a rational choice function C on a choice space (X,κ) is that C satisfies Richter’s weak axiom (Suzumura, 2009) defined as fllow: ’ S∊κ, ’ x∊S: [ ’ y∊S:xRcy.x∊C(S)]. This Richter’s weak axiom means that for any elements x and y of the choice opportunity set S, if x is revealed prefered to y, then x will be chosen from the choice opportunity set S. Proof: We first prove the necessity. If the choice function C has rationalization R, then   ’ SAκ; C ðSÞ 5 xASj ’ yAS:xRy : Now, if, for any S∊κ and any x∊S, ’ y∊S:xRcy holds, then by definition of the revealed preference relation Rc, 'S0 Aκ:xAC ðS0 Þ and yAS0 holds: That is, since C is a rational choice function and has rationalization R, xRz holds for any z∊S0 . Applying this to y∊S0 , we have xRy for x∊S and any y∊S. Since R is a rationalization of C, x∊C(S), which proves the necessity of Richter’s weak axiom. Next, we prove sufficiency. First, we assume that the choice function C satisfies Richter’s weak axiom. That is, let S∊κ be an arbitrary set of choice opportunities, and let ’ SAκ; CðS; RcÞ 5 fxASj ’ xAS:xRcyg holds: This implies that if xAS and xRcy holds for any x∊S and any y∊S implys that x∊C(S) holds by Richter’s weak axiom. This also implies that CðS; RcÞDC ðSÞ:

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Furthermore, if we assume that x∊C(S), then for any y∊S, we have xRcy, so C(S,Rc)+C(S). This implies that C is a rational choice function that rationalizes Rc, and the sufficiency is proved. ’ This shows that the necessary and sufficient condition for the existence of a rational choice function, which states that the best alternative exists, is that the revealed preference relation satisfies Richter’s weak axiom. Richter’s weak axiom is the requirement that x is chosen if x is revealed preferred to any y. Behind this preference relation, we can think of it as the assumption of completeness and acyclicity.

5.5

Irrational choice and revealed preference

According to traditional choice theory in economics, the typical idea of revealed preference is that x of an element of a choice set X is preferred to y if and only if x is chosen when element y of X is also available. Then the selected element is preferred as far as rationality is assumed. This would mean that any painful behavior, even antisocial behavior, would have been preferred when no other behavior was available. However, if we assume complete irrationality, the story is quite the opposite. Under the assumption of complete irrationality, such behavior is irrational and badly decided. Thus although the idea of revealed preference may seem to guarantee the measurement of the preference relation, if the assumption of rationality does not hold, then we cannot say that we have a preference for what we have chosen. In this way, under the assumption of irrationality, the inferred preference relation is reversed. The idea of revealed preference provides a strong theoretical basis for the high principle, but it only provides a basis under the assumption of rationality. In this way the preference relation is reversed depending on whether one assumes rationality or irrationality, and the issue becomes something of a theological debate. What can be said here is that, as in Becker (1962), one can assume rationality behind any seemingly irrational behavior, but one can also assume irrationality. In addition, as shown later, even if rationality is assumed, the estimation of preferences is complicated when the phenomenon of inattention due to limited rationality is considered.

5.6

Revealed attention

Masatlioglu et al. (2012) provide an interesting theoretical development in which preferences change with attention. The argument for revealed preference relies on the implicit assumption that the decision maker considers all viable options. However, without the assumption of full consideration of alternatives, as they preach, the idea of revealed preference can be misleading. That is, it is possible that a decision maker prefers x to y but chooses y simply because he is unaware that x is also available when x is present (Hausman, 2008; Masatlioglu et al., 2012). For example, when consumers are examining product shelves in a store, the decision maker may only pay attention to the first shelf item because it would take too long to consider all the alternatives.

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Then, they choose the best of the first shelf choices, for example, y. Thus they thought, for an outside observer, even if y is chosen when x is available, he or she may not be able to conclude that y is preferred over x. Masatlioglu et al. (2012) called this phenomenon “limited attention” and explained how to infer the decision maker’s preferences and the options to pay attention to from the observed behavior. Let me briefly introduce their theory. Basically, they postulate a filter for paying attention in decision-making. Let S be the feasible set facing the decision maker, let Γ (S) be the (nonempty) set of elements to which he pays attention, and let κ be set of all of nonempty subsets of X which is set of alternatives. Formally, Γ is a map from κ to κ with nonempty set Γ (S)CS. As a premise of the theory for their revealed attention, the following definition of decision-making is given next (Masatlioglu et al., 2012). Definition 5.1: A consideration set mapping Γ is an attention filter if for any S, Γ (S) 5 Γ (S \ x) whenever x 2 = Γ (S). Definition 5.2: A choice function c is a choice with limited attention if there exists a complete and transitive preference g over X and an attention filter Γ such that c(S) is the g best element in Γ(S). Definition 5.3: Let us assume that c is a choice by limited attention and there are k different pairs of preference and attention filter that represent c, (Γ 1,g1), (Γ 2,g2),. . .,(Γ k,gk). According to Masatlioglu et al. (2012), the following statements hold. G

G

G

x is revealed to be preferred to y if x gi y for any i, x is revealed to attract attention at S if Γ i(S) includes x for any i, x is revealed not to attract attention at S if Γ i(S) excludes x for any i.

A sufficient and necessary condition for observed behavior to be consistent with preference maximization under the full attention assumption would be the following WARP (Masatlioglu et al., 2012). WARP: WARP means that x is available and must be chosen from any set T whenever there is a choice from T in S, which is equivalent to showing that every set S has a “best” alternative x . For any nonempty S, there exists x AS such that for any T containing x , if c(T)AS, then c(T) 5 x . Given the possibility of limited attention, to conclude that x was chosen from T, we need to make sure not only that the elements chosen from T are in S and that x is available, but also that x attracts attention. According to them, this can be inferred when removing x from T changes the decision maker’s choice, which is an additional requirement for x to be selected from T. This argument implies the following assumption, which weakens the WARP condition (Masatlioglu et al., 2012). WARP with limited attention (WARP(LA), Masatlioglu et al., 2012): For any nonempty S, there exists x AS such that for any T containing x , there exists x AS such that for any T containing x , if c(T)AS and c(T) ¼ 6 c(T)x , then

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c(T) 5 x . WARP(LA) guarantees that the binary relation P defined next is acyclic and fully characterizes the class of choice functions generated by the attention filter. That is, if at any time the choices change as a result of deleting an option, the first choice will take precedence over the deleted one. Formally, we define the relation xPy as follows. That is, for any different x and y, we define xPy if there exists T such that c(T) 5 x 6¼ c(T \ y). They lead to the following theorem (Masatlioglu et al., 2012). Theorem 5.2: The necessary and sufficient condition theorem for WARP(LA) A necessary and sufficient condition for the choice function c to satisfy WARP (LA) is that P is acyclic. Proof: First, suppose that P has a period: x1Px2P?PxkPx1. Then, for each i 5 1, . . ., k 2 1, there exists a Ti such that xi 5 c(Ti) ¼ 6 c(Ti\xi11) and xk 5 c(Tk) ¼ 6 c(Tkx1). Consider the set S 5 {x1, . . ., xk}. Then, for all xAS, there exists T such that c(T \ x) ¼ 6 c(T) with c(T)AS. Since x ¼ 6 c(T), WARP(LA) is violated. On the other hand, if P is cyclic (acyclic), then S has at least one element x such that there is no y with yPx, which implies that there is no yAS with y 5 c(T) ¼ 6 c(T \ x). In other words, if c(T)AS and c(T) ¼ 6 c(T \ x), then x 5 c(T) must be, and this irrevocably shows WARP (LA). This proves the theorem. If x 5 c(T), then x 5 c(T). According to Masatlioglu et al. (2012), due to the lack of time and the complexity of the decision problem, decision makers selectively focus on a smaller set of alternatives and ignore the rest of the alternatives. even if they know that S is their entire feasible set, they still choose the alternatives optimally based on their prior beliefs about the value of the alternatives and even though he knows that S is his entire feasible set, he optimally chooses the consideration set Γ (S) based on his prior beliefs about the value of alternatives and the cost of testing. He also considered WARP(LA) as the WARP under such limited attention and proved that the necessary and sufficient condition for the choice function to satisfy it is acyclicity. Their theory shows one aspect of the irrationality of decision-making. In addition, the acyclicity of the preference relation is a weaker condition than weak order and so on. However, as for the acyclicity of the preference relation itself, Tversky’s (1969) experimental research has shown that it is not necessarily satisfied.

5.7

Empirical testing of acyclic preference relations

5.7.1 Empirical investigation of acyclicity Are rational decision-making, the strong axiom of revealed preference, and the weak order property postulated in ordinal utility theory valid in actual preference judgments and decision-making?

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$4.50

$0

Figure 5.11 Example of gambling cards used in the experiment. Source: Adapted from Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 31
48.

Tversky (1969) examined whether transitivity, which is assumed to be a weak ordering, is satisfied in decision-making through experiments. He showed the subjects two pie-chart cards like the one in Fig. 5.11 and asked them which of the two gambles they preferred. At this point, they were not allowed to express indiffrence preferences but were asked to state which one they would prefer. Thus this is a strong preference relation xgy, that is, xhy and not (yhx), where h is the preference relation. On the card the amount of the prize was written above the pie chart, and the ratio of the area of the black-filled fan to the area of the circle was expressed as the winning percentage. In the experiment, several patterns were prepared, but a typical pattern was to combine five cards as shown in Table 5.1 and ask the participants which one they preferred. In the case of comparative judgments such as a and b, and b and c, the slight difference in winning percentages was ignored and the one with the larger prize amount tended to be chosen, but in the case of combinations such as a and e, where the winning percentages differed greatly, the one with the higher winning percentage, e, tended to be chosen. This indicates the relationship agb, bgc, cgd, dge, ega, which clearly does not satisfy the transitivity condition. This indicates that the condition of acyclicity, which is a relaxation of the condition of transitivity, is also not satisfied. Tversky (1969) also presented subjects with the percentile rank scores of the intelligence, emotional stability, and social skills of five applicants to a university, as shown in Table 5.2, and asked them to answer, in a pairwise comparison, which applicant should be admitted to the university with the greatest emphasis on intelligence. In the case of comparative judgments such as a and b, or b and c, the slight differences in the evaluation of intelligence were ignored and the one with the higher evaluation of the other dimension tended to be chosen, while in the case of combinations such as a and e, where the evaluation of intelligence differed greatly, the one with the higher evaluation of intelligence, e, tended to be chosen. This result

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Table 5.1 Experimental tasks to study transitivity (Tversky, 1969). Gambling

Winning percentage

Prize (USD)

Expected value (USD)

a b c d e

7/24 8/24 9/24 10/24 11/24

5.00 4.75 4.50 4.25 4.00

1.46 1.58 1.69 1.77 1.83

Table 5.2 Experimental tasks to study transitivity (Tversky, 1969). Applicant

Intelligence (points)

Emotional stability (points)

Sociality (points)

a b c d e

69 72 75 78 81

84 78 72 66 60

75 65 55 45 35

also shows the relationship agb, bgc, cgd, dge, ega, which clearly does not satisfy transitivity and even acyclicity.

5.7.2 Nontransitivity and thresholds Acyclicity includes transitivity. Noncyclicality is a broader concept. Conversely, nontransitivity is a broader concept than circularity. In other words, nontransitivity includes cyclicality. Nontransitivity can be explained by considering that, within a certain threshold, preference relation becomes indiffrent. indifference can be defined as a binary relation I on X when we assume a strong preference relation R on the set X (i.e., a relation that can say which is preferred). That is, for x, yAS xIy3not½xRy and not½xRy: then x and y are indiffrent. Thus in judgments and decision-making, there must be a relationship in which it is impossible to say which is preferred. Therefore, when we consider a preference relation R on a set X, we can assume a real function with a threshold, which is indifferent with respect to some difference, as follows. That is, for any x, yAX xRy3vðxÞ . vðxÞ 1 δðx; yÞ However, we assume that v is a utility function and δ is a function of a threshold value that is positive and varies with the objects x and y. If we assume for

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simplicity that the threshold is constant in situation X, then the previous equation naturally becomes, that is, for any x, yAS xRy3vðxÞ . vðyÞ 1 δ However, δ is a positive constant. The necessary and sufficient condition for this equation to hold is the theorem of Scott and Suppes (1958), which states that the preference structure (X, R) is of the following semiorder. That is, for any elements w, x, y, z 1. not[xRx]. 2. wRx and yRz.[wRz or yRz]. 3. wRx and xRy.[wRz or zRy]. . .

This condition is a necessary and sufficient condition for the fact that xRy3v (x) . v(y) 1 δ.

5.7.3 A decision-making model to explain nontransitivity Tversky (1969) proposed a mathematical model called the additive difference model (ADD) to explain human preferences that do not satisfy such transitivity. In this model, first considered the set of alternatives A 5 A1 3 A2 3 ? 3 An as a set of alternatives consisting of multiple attributes as shown in Table 5.2. In addition, each choice is considered to consist of values of multiple attributes, such as x 5 (x1, x2, . . ., xn), y 5 (y1, y2, . . ., yn). The ADD is expressed as follows, where ui is a real-valued function and φi is an increasing function xhy( )

n X


 φ i u i ð x i Þ 2 ui y i $ 0

i51

However, for any attribute i, φi ð 2 δi Þ 5 2 φi ðδi Þ; δi 5 ui ðxi Þ 2 ui ðyi Þ Assuming that ϕi(δi) 5 ti(δi) and ti . 0, we have n X

n n X 
 X
 φ i ui ð x i Þ 2 ui y i 5 t i ui ð x i Þ 2 ti ui yi

i51

i51

i51

If we put vi ðxi Þ 5 tui ðxi Þ, then xhy( )

n X i51

vi ðxi Þ 2

n X
 vi yi i51

If φi can be assumed to be linear in this way, nontransitivity cannot be explained, but if φi is like a step function with a threshold (e.g., ε $ δ; then φi ðδi Þ 5 0), this ADD can explain the nontransitivity.

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Figure 5.12 Fuzzy set representation of comparative judgments when comparability in the strict sense does not hold (Takemura, 2007, 2012).

Nakamura (1992) conducted an experimental study on the conditions for deviating from transitivity and pointed out that (1) in the case of preference judgments based on a single attribute, judgments are made relatively clearly even if the differences in utility are small, (2) judgments become ambiguous when the utility of two or more attributes is trade-off-like and their differences are antagonistic, and (3) when the utility of one attribute is regarded as equal to that of another attribute, but the utility of the attribute is not regarded as equal, the effect of the attribute regarded as equal is downplayed. To explain the nontransitivity of human preferences, he proposed a preference model called additive fuzzy utility difference structure model, in which utility is assumed to be a fuzzy set with vague boundaries. In this way, we have shown that transitivity in weak order may not always hold, but empirically, comparability may not always hold either. For example, if we do not know much about the brand name of a product, it would be difficult to always show a preference relation that satisfies comparability. In the study by Tversky (1969), subjects were forced to choose between two alternatives, but it is thought that there are situations in which such a choice is difficult. Takemura (2007, 2012) extended Nakamura’s (1992) model by proposing a model in which the weight function of utility is also a fuzzy set, and tried to approximate the preference relation when comparability and transitivity are not satisfied, and actually conducted a survey on product choice. In Takemura’s model (2007,2012), the preference strength was represented by fuzzy set as shown in Fig. 5.12.

5.8

Conclusion

This chapter introduces the concept of revealed preference under the assumption of ordinal utility and the assumption of cardinal utility. Revealed preference theory theoretically guarantees the measurability of utility under the assumption of rationality. However, as we have discussed, revealed preference can be thought of in the

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opposite sense from the assumption of irrationality, so that even inferences based on revealed preference can be completely different depending on the assumptions of rationality and irrationality. Irrational decision-making has also been explained in terms of revealed attention (Masatlioglu et al., 2012). Whether we assume a choice function of rationality or irrationality, we can see that acyclicity is the key concept to show it. Noncircularity means that the preference relation does not circulate somewhere in either, which is a looser condition than transitivity, and nontransitivity is a broader concept than circularity. Of course, it should be clear that neither good nor bad can be defined unless the noncircularity of the preference relation can be assumed. In this chapter, I have discussed examples that do not satisfy the assumption of transitivity in ordinal utility, and also the weak assumption of acyclicity in rationality, and introduced empirical studies, as well as psychological models that explain nontransitive decision-making. These considerations suggest that nontransitive decision-making can also exist in the consideration of rationality and irrationality. Although nontransitive decision-making includes noncyclicality, it seems that it is only with noncyclicality that we can discuss good and bad decisionmaking. This is because otherwise the preference relation would be circular and neither good nor bad decisions could be defined.

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13. Hausman, D. (2008). Mindless or mindful economics: A methodological evaluation. In A. Caplin, & A. Schotter (Eds.), The foundations of positive and normative economics: A handbook (pp. 125
155). New York: Oxford University Press. Masatlioglu, Y., Nakajima, D., & Ozbay, E. Y. (2012). Revealed attention. American Economic Review, 102(5), 2183
2205. Nakamura, K. (1992). On the nature of intransitivity in human preferential judgments. In V. Novak, J. Ramik, M. Mares, M. Cherny, & J. Nekola (Eds.), Fuzzy approach to reasoning and decision making (pp. 147
162). Dordrecht: Kluwer. Richter, M. K. (1971). Rational choice. In J. S. Chipman, L. Hurwicz, M. K. Richter, & H. F. Sonnenschein (Eds.), Preference, utility and demand (pp. 29
58). New York: Harcourt Brace Jovanovich. Scott, D., & Suppes, P. (1958). Foundational aspects of theories of measurement. The Journal of Symbolic Logic, 23, 113
128. Sen, A. K. (1970). Collective choice and social welfare. San Francisco, CA: Holden-Day. Simon, H. A. (1986). Rationality in psychology and economics. The Journal of Business, 59 (4), S209
S224. Suzumura, K. (2009). Kousei Keizaigaku no Kiso [Foundations of welfare economics]. Tokyo: Iwanami Shoten. (in Japanese). Takemura, K. (2007). Ambiguous comparative judgment: Fuzzy set model and data analysis. Japanese Psychological Research, 49, 148
156. Available from https://doi.org/10.1111/ j.1468-5884.2007.00341.x.

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Takemura, K. (2012). Ambiguity and social judgment: Fuzzy set model and data analysis. In E. P. Dadios (Ed.), Fuzzy logic—Algorithms, techniques and implementations (pp. 1
22). In Tech: Open Access Publisher. Takemura, K. (2019). Foundations of economic psychology: A behavioral and mathematical approach. New York: Springer. Takemura, K. (2020). Behavioral decision theory. Oxford research encyclopedia of politics. Oxford: Oxford University Press. Available from https://doi.org/10.1093/acrefore/ 9780190228637.013.958. Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 31
48. Varian, H. R. (2014). Intermediate microeconomics: A modern approach (9th ed.). New York: W. W. Norton & Company.

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Most people make their purchase choices based on a number of issues such as price, design, and brand performance (Takemura, 2014, 2019). Thus most of people’s decision-making can be viewed as multiattribute decision-making. Knowing how multiattribute decision-making works is essential in relation to business policy and marketing. In this chapter, we outline the theoretical framework describing multiattribute decision-making and its analytical approach. First, we present the qualitative assumptions that allow for a mathematical representation for analyzing multiattribute decision-making. Many decision-making situations are structured to consider not only price but also many other attributes such as product quality and design. Previous theoretical studies have shown that in decision-making for two or more attributes, it is difficult to satisfy all of the assumptions, even if they include some plausible assumptions such as the multidimensionality of the attributes to be considered and their independence from Pareto and unrelated alternatives (Takemura, 2011a,b, 2014). This corresponds to the economist Arrow (1951) who, in his impossibility theorem, suggested that the basic assumptions of democracy are inconsistent with a rational social decision-making system and that autocracy is not inconsistent with a rational decision-making system. This interpretation of his impossibility theorem is what emerges. Similarly, applying this idea, it is also difficult to find a rational decisionmaking scheme that determines the worst possible decision. Rational decisionmaking in this context is the kind of decision-making that satisfies the weak order of completeness and transitivity. However, if we relax any of these weak order properties in the decision-making scheme, the contradiction will not arise. For example, with a property like acyclicity, no contradiction arises. This chapter will, thus, first give a qualitative interpretation of multiattribute decision-making. Next, this chapter considers a decision-making scheme that considers the additive number of values of multiattribute utilities. This corresponds to what is called a scalarization function in the research area of multiobjective optimization. In this chapter, we introduce the scalarization function and explain the axiomatic conditions under which such an additive decision-making scheme is possible. Although the number of additive values contains strict assumptions, we believe that, to a large extent, there is some validity in using an additive value function to make decisions. In the next and subsequent chapters, we will examine these approximate problems of additive value functions through computer simulations and experiments, but in this chapter, we will explain the theoretical representation of additive value functions. Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00012-0 © 2021 Elsevier Inc. All rights reserved.

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Plurality of values and multiattribute decision-making

There is no reason why decision-making should not extend to more important aspects of decision-making, such as personal career decisions and policy decisions. When considering practical activities in life, “decision-making” turns out to be a rather important concept. Under these circumstances, there is a growing tendency to decide how to make the best decisions. For example, there is a tendency to focus on “cost performance,” to look for the “best choice,” and to look for the “best partner.” In addition, traditional utility and social choice theories in economics state that it is a prerequisite for decision makers to make the best choice. Many people take it for granted that they want to be able to make the best choice, but the primary reason why pursuing the best choice too much may have social harmful effects is that pursuing the best decision requires us to decide on only one attribute (condition), such as money or formal procedures. This can be overwhelming. If this pursuit of the best goes hand in hand with globalization, rather than increasing the diversity of society, it may lead to a unification of value dimensions, making it impossible to make decisions with a true sense of purpose. However, is it possible to make rational decisions by integrating diverse values? As I pointed out in Chapter 1, Introduction: Escaping From Bad Decisions, Aristotle’s argument states that happiness is the highest good, but he seems to suggest that happiness is not only pleasure or virtue but is also pluralistic. Also, according to Berlin (1969, 1990), the plurality of values means that, for example, respect for human life is very important, but so is freedom, and both of these values are important in an absolute sense, and in some situations the two may be irreconcilable. In this chapter, I will start by reinterpreting Arrow’s (1951) impossibility theorem and consider it from the standpoint of value pluralism as taught by Berlin and Crowder (1994, 2002). I would like to suggest that when we take this perspective, that is, when we assume that at least the pluralistic criteria of formal rationality, happiness, justice, beauty, and virtue are satisfied, good and bad decisions are inconsistent with the rational decision-making scheme (Takemura, 2011a,b, 2018).

6.2

Difficulties of multiattribute decision-making

6.2.1 Multiattribute decision-making and information search We will assume a set of circumstances related to purchasing a product at a store. Presume, for instance, that we purchase a digital audio player. Consumers make a purchase decision after comparing multiple attributes, such as the prices, number of recordable tracks, sound performance, and designs at stores, or using catalogs. Such decision-making after considering multiple attributes is known as multiattribute decision-making. Multiattribute decision-making is presumably performed by obtaining various types of information. The methods of information search and the assessment of alternatives are closely related to each other. Decision-making in the purchase of a television, for example,

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Figure 6.1 Examples of attribute- and alternative-wise information search.

involves the assessment of various televisions. Information about what attributes of a television are sought in what order strongly affects the overall assessment of the television. As presented in Fig. 6.1, the assessment of alternatives is expected to differ clearly when information search is performed for all attributes of all alternatives and when the search is limited to the information related to a part of the attributes (Takemura, 2014, 2019). The assessment of alternatives and the results of decision-making often vary between cases, in which the most appropriate brand based on the most important attribute such as price is identified by acquiring information on, first, the prices of all brands, then on the second most important attribute (attribute-based information search) and cases in which the optimal brand is determined by searching for information related to each brand and then making a comprehensive evaluation (alternative-based information search) (Bettman, 1979; Bettman, Johnson, & Payne, 1991; Takemura, 2014, 2019, 2020). The methods of information search and the assessment of alternatives are, therefore, inseparable.

6.2.2 Multiattribute decision-making, best decision, and worst decision We make various decisions in our daily life. We make decisions on every occasion: from casual ones such as what to have for lunch to more serious decisions such as an individual’s future course and government policy. Decision-making, therefore, becomes a rather important concept when considering practical activities and making choices in life. Aristotle in the Nicomachean Ethics purportedly seeks the highest good (agathon) in people’s act of selecting. This can be made more comprehensible by asking and answering the following questions: Why do people wish to go to a good college? Because they are more likely to get a good job. Why do they wish to get a good job? Because they wish to live a good life. Why do they wish to live a good life? Because they seek something good. This good thing might be the highest good. If we seek more factors that increase the value, we might arrive at the highest good. Examining optimal decision-making reveals that rationality is necessary in the course of making the decision. A decision for which the purpose and method are contradictory is somehow not right. When we intend to make a good decision, it appears that we often

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assume that we will select the optimal alternative, that is, the best decision-making. This is what is called the “best decision-making” in the world of business. The same can be said about the worst decisions. The worst decision can easily be made if we choose an option that is inferior in any attribute. However, when the values of the various attributes are different, it is not easy to decide.

6.2.3 Multiattribute decision-making and intransitivity of preference Decision-making in many cases has a multiattribute structure. Consider the example of multiattribute decision-making in the selection of a personal computer presented in Fig. 6.2. In the purchase decision-making to select a PC from brands A, B, and C, we assume that the consumer makes the decision by comparing two brands to select one with more preferable attributes than the other and that the consumer purchases the one that remains in the end. Such a means of making a decision is often witnessed in the technique called monitoring information acquisition, which we use to analyze the process of obtaining information, and a verbal protocol for making verbal reports. It might seem that the option that will ultimately prevail would be the same irrespective of the order of selection. If we follow this procedure and compare brands A and B first, brand A prevails over brand B in the price and performance, whereas brand C outscores brand A in the performance and design in the comparison between brands A and C. If the comparison begins with brands B and C, however, brand B would remain after the final stage. Despite the preference for brand A to B and brand B to C, the transitivity by which brand A is preferred to brand C is not satisfied. Instead, the result is the reverse relation in which brand C is selected over brand A (see Fig. 6.2).

6.2.4 Difficulty of multiattribute decision-making and its psychological cause Under such circumstances, information related to the order in which the brand options are focused suggests the final result of the selection. Although Fig. 6.2 exemplifies only simulated conditions, this implies that the result of selection could not be predicted

Figure 6.2 Example of cyclic preference relation that does not satisfy transitivity and acyclicity (Ohkubo & Takemura, 2011).

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without knowing the order of processing information in the decision-making process even when it is based on the same decision-making standard. Our last research findings related to decision-making process indicate that people’s decision-making process, in fact, relies on the path. Such reliance on the circumstances or paths increases along with a larger number of options, and evidently, also with increased emotion or excitement. Such a phenomenon hints that people’s actual preference relations do not satisfy the properties of weak order (properties that satisfy both transitivity and completeness) assumed in the expected utility theory and multiattribute utility theory. The study by Tversky (1969) and Takemura (2014) indicated that people’s preference relations do not satisfy the properties of weak order and acyclic preference relation. These inference and findings further suggest that people are incapable of making the best decision, maximizing the utility, and the rational choice. This discussion is also applicable to the problem of bad decisions. If we assume the multidimensionality of decision problem, the issues of the best and the worst decision lead to be more complicated. Research toward good decision-making belongs to the field called “normative decision theory.” Conventional normative decision theory often assesses “goodness” in view of the rationality of form. I also would like to first examine decisionmaking from a pluralistic perspective based on the formal rationality in this sense. Normally, theories to consider decision-making from a pluralistic perspective include the system of the so-called multiattribute utility theory. This theoretical system concerns the method of deriving the eventual decision by trading off the value in multiple dimensions. Although such a concept is extremely important, I first would like to develop an argument from a perspective that is slightly different from the ordinary multiattribute utility theory. In other words, rather than considering the trade-offs of various values as the starting point of the argument, we first perform a normative analysis from the perspective that no values can be compared. Although this assumption might seem somewhat unnatural, it has certain significance as the starting point of the argument, considering the difficulty of trading off values and determining values of higher importance in the actual decision-making. For instance, the question of whether respect for a human life or achievement of justice is more important cannot be answered easily. Trading off one for the other would be considerably difficult because some decision of an organization is necessary even though some value trade-offs would ultimately be necessary. Although acknowledging the importance of the trade-off issue, this chapter first develops the argument without assuming the possibility of trade-offs from the beginning. This is similar to the idea of not assuming the comparison of utility among individuals as the starting point of an argument. There is also a method of normative analysis that uses game theory by setting up multiple subjects to examine the interaction among the subjects of decision-making. However, I do not perform the analysis from this type of perspective. Although the perspective of game theory allows interesting studies as to whether honest expression of preference is rational and whether individual rationality engenders collective rationality, I use an extremely simple view that the decision-making of both individuals and a group seemingly involves

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general intentions. Examination based on such assumption is likely to facilitate a general understanding of multiattribute decision-making despite the probable limitation posed by the simplification of the issue. I would like to exemplify the perspective of form that when multiattribute decision-making is viewed from the perspective stated earlier, it satisfies the rationality standards such as transitivity and completeness, and conditions considered appropriate in multiattribute decision-making contradict. This can be derived by the application of and reinterpreting the mathematical structure of the general possibility theorem of group decision-making presented by Arrow (1951) to the multiattribute decision-making defined earlier. Applying Arrow’s general possibility theorem on this assumption results in the finding that rational decision-making is possible only when it is based on one-dimensional standards, which suggests that rational decisions generally cannot be made if the pluralistic values cannot be ranked, which means that making the best decision would also be meaningless. Although the actual decision-making involves the issue of such unfeasibility of decision-making, it appears that we do not normally face the unfeasibility in the psychological aspect. The question of whether people psychologically make their problems onedimensional to avoid the confrontation with the unfeasibility of decision-making will be examined based on the theory of “mental ruler” proposed by myself. According to this theory, people reduce the difficulty of decision-making by one dimensionally viewing a multidimensional problem. Making an issue onedimensional reduces psychological burden in some respects and encourages more efficient decision-making, which, however, involves the risk of ignoring the attributes of important decision-making. I would like to claim that, from prescriptive view, one-dimensional criteria of decision-making should be avoided. If the result of decision-making is particularly important, decision based on one value only might be risky. To avoid bad decision, it is important to make the decision comprehensively by particularly addressing the plurality of values. It should be pointed out that pluralistic value must be considered based on a prescriptive view and originally a normative view, and various values must be combined or traded off even though such practice is extremely difficult. This discussion is intended to reveal the conditions that are likely to require judgment based a one-dimensional “mental ruler.” The argument will add at the end how to make a decision for which such onedimensional judgment is not necessary.

6.3

Theoretical examination when multiattribute decision-making does not satisfy weak order property of preference

Quantitative analysis is easy if the multiattribute decision-making can be represented by an additive system of utility of attributes as assumed in conjoint analysis, and the preference is a weak order. However, as explained later, multiattribute decision-making does not always have a weak order structure (Takemura, 2011a,b, 2014, 2019).

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First, we will consider preference based on the dominance principle presented later as an example of the property of completeness of a weak order.

6.3.1 Preference based on the dominance principle Preference that “x is indifferent or preferred to y” as the overall preference only when the preference relation of all attributes is “x is indifferent or preferred to y.” In other words, there is a type of preference based on the dominance principle that becomes xhy only when “xhi y for all attributes i.” The following theorem holds for the dominance principle based on this type of preference. (1) Completeness (Connectivity): Relation xhy or yhxð ’ x, yAAÞ holds for arbitrary elements x, y of the set of alternatives A that is represented by multiple attributes. In addition, the preference relation hi for different values of a given attribute i satisfies completeness. (2) Transitivity: Relation xhz holds if xhy, yhz for arbitrary elements x, y, z ð ’ x, y, zAAÞ of the set of alternatives A represented by multiple attributes. In addition, the preference relation hi for different values of a given attribute i satisfies transitivity. (3) No limitation of space for multiattribute decision-making problems: As long as completeness and transitivity are satisfied, any type of preference is applicable to each attribute value in multiattribute decision-making, and any combination of preferences can be made among the multiple attributes.

Theorem 6.1: Theorem of decision-making based on the dominance principle. Preference based on the dominance principle under the previous conditions (1), (2), and (3), that is, the preference that becomes xhy only when “xhi y for all attributes i” does not satisfy completeness, is not a weak order and involves no multiattribute value function that represents a preference relation. Proof: Suppose a case of preference based on the dominance principle in which xhk y holds for a given attribute k and y is weakly preferred to x for other attributes. In this case, completeness cannot be established because xhy and yhx do not hold to begin with. The previous theorem, therefore, holds true.’ This result suggests that such decision-making based on the dominance principle assumed for a number of psychological models would be difficult to perform even for ordinary quantitative analysis, which differs from the so-called principle of utility maximization (Takemura, 2011a,b).

6.3.2 Preference based on the principle of the maximum number of dominant attributes Preference that “x is indifferent or preferred to y” is the overall preference only when the number of attributes, preference relation of which is “x is indifferent or preferred to y,” is larger than the preference relation of which is “y is indifferent or prefered to x.” The following theorem holds also for this type of reference.

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Theorem 6.2: Theorem of decision-making based on the principle of the maximum number of dominant attributes. Preference based on the principle of the maximum number of dominant attributes under the conditions of (1) completeness, (2) transitivity, and (3) no limitation of problem space is not a weak order and does not have any multiattribute value function that represents a preference relation. Proof: If the number of attributes is an even number and the number of dominant attributes is the same, then none of them will be preferred. They will incomparable, which will not satisfy completeness. If the number of attributes is an odd number, a cyclic relation that does not satisfy transitivity can be made easily. The previous preference relation, therefore, is not weak order, which does not involve any multiattribute value function.’ This consequently suggests that decision-making would be difficult with multiple attributes. Nevertheless, people must make decisions even under such conditions. In the previous two cases (conditions for the two theorems), a decision maker can find a best alternative in a specific case. However, the probability of finding a best alternative may be very low. For instance, if we assume that there are five levels (e.g., very good, good, average, bad, and very bad) of three attributes (e.g., price, quality, and design) then the probability of existence of the best alternative is 0.8% under the equal and independent probability distribution assumption. Moreover, it might be very difficult to find the previous average alternatives for all attributes. For instance, the probability of this condition (three attributes case) is only 6.4%. If we add to five attributes, the probability of finding an above average alternative for all attributes is only 1.0%. It seems that an “above average” alternative is quite common, but it would be very difficult to find it in the multi attribute decision-making problem.

6.3.3 Impossibility theorem of multiattribute decision-making Decision-making for multiple purposes that considers pluralistic aspects such as monetary, ethical, and esthetic values has a structure called “multiattribute decision-making” in the decision theory. Multiattribute decision-making considers a multiattribute alternative x as an alternative represented by q-dimensional attributes and the set of attributes X1 , X2 , . . . , Xq expressing various values as the elements of the subspace of the Cartesian product set. In other words, xAX1 3 X2 3 ? 3 Xq : Assuming a Cartesian product Xk 3 Xk for an arbitrary attribute k, we consider that the ordered pair of this element represents the preference relation of the attribute value. If this preference relation is Rk , thenRk is a subset of Xk 3 Xk . It is

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natural to assume that Rk satisfies the properties of transitivity and completeness for each attribute as the basis of rationality. When Rq 5 R1 3 R2 3 ? 3 Rq , we assume that the function to apply the preference relation R based on multiattribute decision-making to the elements of Rq is called the multiattribute value function. In other words, the multiattribute value function U can be represented as shown next. U:Rq ! R: It is also natural to assume a weak order for the multiattribute value function. Although the definition of the multiattribute value function presented up to this point does not contradict the definition of an ordinary multiattribute utility theory, adding the following conditions would make it different from the system of an ordinary multiattribute utility theory. Such conditions are added because it would presumably be more natural as a starting point of an argument to assume that, as described in the Introduction, the incomparability (difficulty of comparison) of various values and each value can only be judged in the sense of ordinal numbers. In addition, as stated in the Introduction, one social choice theory that is used to consider decision-making of social groups is Arrow’s (1951) general possibility theorem of democratic group decision-making. The conditions presented by this theorem are of a multiattribute decision-making problem and reinterpreting the results in the general possibility theorem of the following multiattribute decision-making. This theorem indicates that composing a multiattribute value function that satisfies all the later conditions is impossible, meaning that conditions to satisfy completeness and transitivity, which are the conditions for rationality, and the following conditions presumably appropriate for rational decision-making do not hold simultaneously. Conclusion of general possibility theorem of multiattribute decision-making: We assume that the Cartesian product of sets X1 , X2 , . . ., Xq of attributes that express various values is A, and its elements (ordered set representing the q-term relations) such as x, y, and z are alternatives described by multiple attributes. If there are three or more multiattribute alternatives described by two or more attributes, there is no multiattribute value function that satisfies the following conditions, and satisfying these conditions simultaneously would be contradictory (Takemura, 2011a,b, 2014, 2019). The value function that satisfies the conditions (1), (2), (4), and (5) under this condition of three or more alternatives with two or more attributes is onedimensional or represents an imposed preference relation. In this case, being one-dimensional means that preference is represented only by a single-attribute preference relation, and being imposed means that a preference relation is determined for a given pair of alternatives irrespective of the values of attributes. (1) Completeness: The relation xhy or yhxð ’ x, yAAÞ holds for arbitrary elements x, y of the set of alternatives A that is represented by multiple attributes. Additionally, the preference relation hi for different values of a given attribute i satisfies completeness. (2) Transitivity: Relation xhz holds if xhy, yhz for arbitrary elements x, y, z ð ’ x, y, zAAÞ of the set of alternatives A represented by multiple attributes. Additionally, the preference relation hi for different values of a given attribute i satisfies transitivity.

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(3) No limitation of space for multiattribute decision-making problems: As long as the conditions of completeness and transitivity are satisfied, a preference of any type is applicable to each attribute value in multiattribute decision-making and any combination of preferences can be made among the multiple attributes. (4) Monotonicity (Pareto principle): If the preference relation of all attributes is “x is preferred to y,” the overall preference is also “x is preferred to y” (in other words, “xgi y for all attributes i” results in xgy). (5) Independence of irrelevant alternatives property: Preference for alternatives x and y is determined only by ordering the attributes of these two alternatives. In other words, they are unaffected by the attribute preference for the other alternative z. (Therefore determining whether xhy holds only requires a profile describing either one or both of xhi y and yhi x holds for those specific x, y in all cases of attribute i.) (6) Multiple goals (multidimensionality): No preference is based only on a single attribute (an attribute that always makes the overall preference of x over y if the attribute prefers x to y) (in other words, there is no attribute i that makes “xgy if xgi y” for an arbitrary preference profile). This condition demands that people make decisions for multiple goals and never make decisions only on one dimension.

If Arrow’s general possibility theorem is interpreted in this manner, then when three or more alternatives exist, no multiattribute value function satisfies all the conditions for the six axioms related to the overall preference of the decision maker described earlier. In other words, the two conditions (preferences can be comparable and transitive) for the decision maker to make a rational selection of alternatives and the four conditions suggesting the rationality of multiattribute decision-making do not hold true simultaneously, which implies that it is extremely difficult for the decision maker to make the optimal and rational decision in multiattribute decisionmaking, which suggests that even if we seek rational decision-making to achieve our welfare, it is likely impossible as long as we have multiple dimensions and multiple goals. Considering that imposed decision-making is not rational, a rational decision might require decision-making based on a one-dimensional attribute. Although this seems to be rather counter-intuitive, it might be the key to explaining why an individual seeking rationality intends to make a one-dimensional judgment. From earlier theoretical considerations, I would like to suggest that the seeking the best alternative is not practical, or ideal, and is almost illusive in real-life multiattribute decision-making situations. It is the same for the worst decision. The worst alternative can be fined in a certain situation. But it would be difficult to find the worst alternative. Therefore we, decision makers, usually can find better or worse decisions. Buchanan (1954) severely criticized the transitivity of social preferences. He severely criticized the transitivity of social preferences. According to him, the rationality or irrationality of a social group implies that it imparts its individual element to the organic existence of society. In fact, since individual preferences themselves may not be complete or transitive, it is not unnatural to think that social preferences may not be transitive or complete either. Sen (1969) and other studies of cases where social preferences do not meet the requirements of rationality have shown that there are social decision methods that satisfy Arrow’s axiom if either completeness or transitivity is relaxed. For example, if we allow for the possibility that social preferences

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are not complete, there are social evaluation methods that satisfy Arrow’s axiom (Cato, 2016; Sen, 1970). In light of this, it is suggested that even in multiattribute decision-making, by removing the condition of either completeness or transitivity from the overall preference relation regarding the previous impossibility theorem, rational, though not fully rational, decision-making is possible. Monotonicity, which can also be described as Pareto-ness, considers a decision method such that for any alternatives x, y, xRy holds only if xRiy holds for all attributes i. Such a decision method does not produce preference relations satisfying completeness but always produces transitive preference relations when there are conflicts among attributes or when there are value conflicts. In addition, Sen (1969) proposed the requirement of quasitransitivity, which imposes transitivity only on strong social preferences P, not on weak preferences R. However, there are preference relations for decision-making that satisfy Arrow’s axiom after satisfying completeness and quasitransitivity. Thus it is shown that the possibility theorem of rational preference relations can be obtained if the criterion of weak order of preferences in multiattribute decision-making is relaxed. However, further progress in social preference research has shown that this is not a great possibility (Cato, 2016; Sen, 1970), and applying these suggestions to the multiattribute decision problem, it is clear that no matter how much we relax the rationality criterion, the possibility of a rational preference relation, albeit in a weaker form than that of single-attribute decisions, is still a possibility. If we apply these suggestions to the multiattribute decision-making problem, we can say that there are some attributes that can be determined by only one attribute, although in a weaker form than the decision by only one attribute, no matter how much we relax rationality. This suggests that it is difficult to say that many attributes can be combined in a pluralistic multiattribute decision-making. However, in actual applications of decision theory, psychometric research approaches to decision-making have gained a certain degree of convenience by representing decisions in terms of simple linear functions, even though there are too many strict assumptions and theoretical problems remain. Given this, we will now consider how this additive decision-making method with linear functions can be positioned from the perspective of multiobjective optimization.

6.4

Multiattribute decision-making and multioptimization

6.4.1 Multioptimization In recent years, there has been a demand for optimization methods that support rapid and flexible decision-making under diverse and competing values and fluctuating system environments. In this context the application of multiobjective optimization, which is an optimization method based on comprehensive evaluation, is expected. Multiobjective optimization is characterized by the fact that multiple evaluation functions compete with each other and that there is no common measure for each evaluation function.

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The problem of minimizing or maximizing an objective function under constraints is called an optimization problem, and the method of solving the optimization problem is called an optimization method. Most of the currently proposed optimization methods provide a method to find the optimal solution for a single objective function. However, in many real-world problems, there are not only one but multiple required objectives. In multiattribute decision-making problems, there are often multiple objective functions when we want to find a more practical solution. Such an optimization problem with multiple objective functions with different evaluation criteria is called a multiobjective optimization problem (MOP). MOPs exist not only in engineering but also in other fields such as economics, business administration, and sociology. The Pareto optimal solution, which provides a reasonable norm for this multiobjective optimization, is generally a set of countless alternatives. Usually, in a multiattribute decision-making problem, it is required to find one or an appropriate number of alternatives in the end. In particular, the Pareto optimal solution set can be a valuable source of preference information to support the final decision. In recent years, a number of computational methods called multiobjective analysis have been developed to obtain the Pareto optimal solution set, and various applications have been reported (Ehrgott, 2005; Miettinen, 1999). The scalarization method is a classical method for finding Pareto solutions to MOPs (Ehrgott, 2005; Miettinen, 1999). In this method, multiple objective functions are somehow converted to a single objective to obtain the optimal solution. The linearized weighted sum method (aggregate objective function, AOF, Miettinen, 1999) creates a single weighted objective function by giving weights to each objective function and finds the optimal solution. It has been shown that the resulting optimal allocation is a Pareto solution of the original problem (Miettinen, 1999). AOF is very simple in concept and can easily be applied to real problems. In the past, various MOPs have been defined and many solution methods have been proposed. Most of them target optimization problems where the variables take continuous values. This is due to the fact that the optimization problem is NP-complete (nondeterministic polynomialtime complete), which makes it difficult to develop effective solutions for real problems. Because a method for computing the solutions to NP-complete problems quickly remains undiscovered, NP-complete problems are often addressed by using heuristic methods and approximation algorithms.

6.4.2 Concept of multiobjective optimization A MOP is generally formulated as the minimizing problem (Miettinen, 1999; Nakayama & Tanino, 1994). The formulation can easily be converted to the maximizing problem as follow: Multi objective problem ðMOPÞ: f ðxÞ: 5 ðf1 ðxÞ;. . .;fr ðxÞÞ!max Constraints: xAXCRn :

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Definition 6.1: Vector inequality For y1, y2ARr, y1 , y2(.y1i , y2i, ’ i 5 1,. . .,r (1) y1 , y2(.y1i , y2i, ’ i 5 1,. . .,r (2) y1 s y2(.y1 s y2, ’ i 5 1,. . .,r (3) y1 # y2(.y1 s y2, y1 6¼ y2

Definition 6.2: Pareto solution When there does not exist xAX such that f(x^ ) # f(x), we call this x^ the Pareto optimum, or simply the Pareto solution. For future analysis, it is often more convenient to think in the space of the objective function f, rather than in the space of the design variables x. x^ is a Pareto solution geometrically. If y^ (5f(x^ )) and y^ 1 Rr1 have nothing in common with f(X) except y^ . However, Rr1: 5 {yARr| y ^ 0}. The set of Pareto solutions in the space of objective functions is called the Pareto frontier or efficiency frontier. In actual decision-making, one decision must be made in the end, so usually one final solution is chosen from among these Pareto solutions, taking into account the balance of each objective. When there is no xAX such that f(x^ ) , f(x), this x^ is called weak Pareto optimal or simply weak Pareto solution. x^ is a weak Pareto solution. Weak Pareto solution is geometrically defined as y^ (5f(x^ )) with y^ 1 int Rn1 having nothing in common with f(X). A weak Pareto solution is not necessarily satisfactory from a decisionmaking point of view, since there is room to keep some of the objective functions at their values and improve others, but it often happens that only weak Pareto optimality can be guaranteed, but the Pareto optimal does not hold Pareto optimal. Scalarization has long been the most commonly used method for obtaining Pareto solutions. Since the objective function in multiobjective optimization is a vector value, it is converted to a scalar value once. The essential properties of this scalarized objective function are given by the following theorem (Miettinen, 1999; Nakayama & Tanino, 1994). Theorem 6.3: Theorem of Pareto solution (Miettinen, 1999; Nakayama, & Tanino, 1994). Let F be a scalarizing function that scalarizes the vector-valued objective function y 5 f(x). If F preserves the Pareto ordering with respect to y, that is, y1 # y2.F(y1) , F (y2) for any y1, y2Af(X) (4), then the solution x0 that minimizes F on X is a Pareto solution. Typical examples of scalarized functions are (1) F1(f(x)) 5 w1 f1(x) 1 ? 1 wrfr(x), (2) FN(f(x)) 5 min1 s i s r wifi(x), P (3) F~N(f(x)) 5 min1 s i s r wifi(x) 1 α ri51 wi fi(x)

(1) is a linear sum of weights, (2) is a Chebyshev scalarized function, and (3) is an expanded Chebyshev scalarized function. This is because (1) the linear weighted sum cannot extract Pareto solutions in depressed areas when the Pareto frontier is nonconcave, (2) the Chebyshev scalarization function may extract weak Pareto solutions, and (3) the expanded Chebyshev scalarization function is most often used.

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In this chapter, we have introduced the scalarization method as the most common approach currently used for MOPs. The scalarization method, as mentioned earlier, is to convert the original problem into an optimization problem with a single objective function by applying some device using parameters. In this scalarization method, we need to consider how to select the scalarization parameters. Since the parameters for obtaining the desired solution are unknown, the decision maker has to select them. It is also important to note that the solution depends on the parameters. In some problems the parameters that give good results are limited, and if other parameters are selected, the scalarized objective function values may diverge and no solution can be obtained. In addition, since the essence of a multiobjective problem is how to make trade-offs among multiple objective functions, it is often insufficient to seek a single optimal solution by scalarization. Solutions to MOPs have often been obtained by scalarization, where the original problem is transformed into a single-objective problem by some device. However, obtaining a single optimal solution by scalarization is insufficient as information. In addition, it is not easy to obtain the desired solution by adjusting the weights of the scalarization, since the solution can be obtained only when the Pareto surface is simple and convex. However, in traditional economics as well as in general multiattribute decision-making research, the usual case is that the Pareto surface is a simple convex shape. In this light, assuming a scalarization function also has a certain degree of practicality from the perspective of Pareto optimality. In multiattribute decision theory, such scalarization functions are called additive decision-making, and from the standpoint of high theoretical measurement theory, they are called additive conjoint systems (additive conjoint systems). In the next section, we will discuss decision-making as an additive conjoint system or additive conjoint system.

6.5

Additive conjoint structure and quasi best decision

6.5.1 Making the best decision with a single attribute and utility function Previous discussions suggest that the concept of best decision in ordinal scale setting is too ideal in multiattribute cases. Therefore we would like to set an approximate standard of the best decision by adopting the additive conjoint structure assumed in additive decision strategy. Before we consider multiattribute decision-making and additive conjoint structure, we will review single-attribute decision-making. The theorem for a weak order of preference indicates the conditions for the best decision-making and conditions for utility maximization. As described in Chapter 5, Rational Preference, Irrational Preference, and Revealed Preference, the following theorem holds.

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Theorem 6.4: Theorem for a weak order on a finite set (Krantz, Luce, Suppes, & Tversky, 1971). If the preference structure of a finite nonempty set, hA, hi, is a weak order, then there exists a real-valued function u on A (u : A ! Re) such that, ’ x; yAA; xhy3uðxÞ ^ uðyÞ: In other words, this theorem means that if the preference made is a weak order, it can be reprented with a function that takes real numbers that maintain the preference relation. Therefore this indicates that the preference relation of a qualitative weak order can be examined by quantifying it using ordinal utility. Theorem 6.5: Uniqueness theorem for a weak order on a finite set (Krantz et al., 1971) If the preference structure hA, hi of a finite nonempty set A is a weak order, then in such a case, hA, hi is represented as hRe, $ i through the real-valued function u : A ! Re indicated in the theorem stated earlier, and the structure hhA, hi, hRe, $ i, ui becomes an ordinal scale. Although this theorem assumes a finite set, we know that it also applies to countably and uncountably infinite sets (Krantz et al., 1971). In this sense, if the preference satisfies completeness and transitivity, preference or equality of an arbitrary pair of alternatives can be represented, then at least one best option can be selected, and this preference is equivalent to utility maximization. Although the best selection can be made if the preference is acyclic even if it is not a weak order, being a weak order guarantees the maximization of utility. This is true not only in the case of a single attribute, but in the preference relation of alternatives in multiattribute decision-making. This can be described as an additive conjoint system of multiattribute decision-making.

6.5.2 Multiattribute decision-making and additive conjoint structure The kinds of analysis that assumes a desire vulnerable order consist of conjoint analysis, which assumes the additivity of the operation to totalize the utility values of attributes. Conjoint evaluation is frequently used specifically for grasp preference for marketing purposes. In new product development, for example, it is used to locate out which attribute cost of a present product need to be changed to produce a new product that can appeal to customers the most. It is additionally used to calculate the market share of the new product via simulation. Currently, conjoint evaluation is used most regularly in marketing. It can also be applied to studies of preference judgment such as a survey of high school students in their determination of a university to attend. Not solely for preferences, it is also used for the research of chance assessment by means of civil engineering experts, and its plausible applicability to other fields is markedly high. As indicated in the pioneering learn about of Luce and Tukey (1964), conjoint evaluation is an analytical approach initially developed in the field of mathematical psychology to compose an additive real-valued characteristic (additive utility function) that is equal to the interval scale from choice records at the level of ordinal

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scale (or more precisely, a scale that satisfies weak order). We comprehend that the desire relation has to fulfill a group of axioms to compose such an additive realvalued function. The decision maker must have the axiomatic property of additive conjoint structure for such conjoint analysis to be feasible. When this condition is satisfied, the decision maker can make a rational decision to a certain degree. The following describes the additive conjoint structure (Krantz et al., 1971; Luce & Tukey, 1964). Let X1 , X2 ,. . .,Xq be the set of possible values of q attributes, and let the set of alternatives be the corresponding Cartesian product set, A 5 X1 3 X2 3 ? 3 Xq : A particular alternative xAA is given by x 5 ðx1 ; x2 ; . . .xq Þ, y 5 ðy1 ; y2 ; . . .; yq Þ, where x1 ; x2 ; . . .; xq ; y1 ; y2 ; . . .yq are the corresponding values of X1 ; X2 ; . . . ; Xq , respectively. If the following relation, xhy3u(x) $ u(y), holds, the following additive utility functions represent the preference structure. uð x Þ 5

q X

uj ðxj Þ

j51

uð y Þ 5

q X

uj ðyj Þ

j51

6.5.3 Axiomatic properties of additive conjoint structure From the theoretical viewpoint of measurement, the conjoint measurement shown earlier cannot be represented by the additive structure from the theoretical viewpoint if it does not have a property called additive conjoint system. In the following, we explain the viewpoint of the additive conjoint system from the perspective of the axiomatic measurement theory by Krantz et al. (1971) and the multiobjective decision theory by Ichikawa (1980). Definition 6.3: Independence The relationship h on the set X1 3 X2 is independent, the following is a necessary and sufficient condition: That is, for a; bAX1 , for some pAX2 ða; pÞhðb; pÞ implies, for any qAX2 , ða;qÞhðb;qÞ holds; and; for p;q AX2 ; ð a;pÞh ða;qÞ for some aAX1 ; implies that ðb;pÞ h ðb;qÞ for any bAX1 holds: Then, independence in each attribute is similarly defined. Definition 6.4: Independence within attributes We assume that the relationship h on the set X1 3 X2 is independent. Then, define h1 on X1 be, for a; bAX1 , ah1b holds if and only if, for some pAX2 , ða; pÞhðb; pÞ hold, and define h2 on X2 be for p; qAX2 , ph2q holds if and only if some aAX1, ða; pÞhða; qÞ holds.

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Definition 6.5: Double cancellation and Thomsen condition A double cancellation relationship h on the set X1 3 X2 indicates that, for any a; b; f AX1 and for any p; q; xAX2 , if ða; xÞhðf ; qÞ and ðf ; pÞhðb; xÞ, then ða; pÞhðb; qÞ holds. Additionally, the condition that replaced h in this weak order relationship with the indifferent relationship B is called Thomsen condition. In the Thomsen condition, for any a; b; f AX1 and any p; q; xAX2 , if ða; xÞBðf ; qÞ and ðf ; pÞBðb; xÞ, then ða; pÞBðb; qÞ holds. Fig. 6.3 shows the Thomsen condition, which states that if points A and B are indifferent and points E and F are indifferent, points C and E are indifferent. Definition 6.6: Archimedean property Real numbers have an Archimedean property, in which an integer n satisfies nx $ y for any positive number x, regardless of how small it is and for any number y, regardless of how large it is (Krantz et al., 1971). In other words, even if any other real number β . 0 is taken, by adding to a positive real number α, α , 2α , 3α , ? , ðn 2 1Þα , β # nα; the numerical sequence (1, 2, 3, . . ., n of natural numbers) stated above is finite. For a set N of consecutive integers (which can be either positive or negative, finite or infinite), the set {ai 9ai AX i ; iAN} is said to be a standard sequence for attribute X1 if and only if the following holds; that is, there is p; qAX2 , which is not pB2 q, and for any i, i 1 1AN, ðai ; pÞBðai11 ; qÞ is given. The standard sequence {ai 9ai AX 2 ; iAN} is called to be the strictly bounded if and only if, for any iAN, there exit some b,cAX1 satisfying cg1 ai g1 b. For X2 as well, a similar standard sequence can be defined. Suppose that h is an weak ordering for the set X1 3 X2. For any a; bAX1 and any p; qAX2 , when the strict bounded standard sequence is finite, the weak order relationship h on the set X1 3 X2 is Archimedean (see Fig. 6.4).

Figure 6.3 Thomsen condition.

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Definition 6.7: Unrestricted solvability A proposition that the relationship h on the set X1 3 X2 satisfies unrestricted solvability indicates that for a; bAX1 , p; qAX2 , when three elements are given, the remaining one that satisfies ða; pÞBðb; qÞ exists. Definition 6.8: Restricted solvability A proposition that the relationship h on the set X1 3 X2 satisfies restricted solvability indicates that for any a; b ; b AX1 , p; qAX2 , when (b ,q)h(a,p)h(b ,q), some bAX1 exist and ðb; qÞBða; pÞ is satisfied. Furthermore, for any a; bAX1 , p,q , q AX2 , when (b,q )h(a,p)h(b,q ) is gained, for p; q ; q AX2 , some qAX2 exists and (b,q)B(a,p) is satisfied (see Fig. 6.5).

X2

p

… q

a1

a2

a3

a4

ai

c

ai+1

X1

Figure 6.4 Archimedean property with two attributes. Source: Takemura, K., & Fujii, S. (2015). Ishikettei no shoho¯ [Prescription for decision making]. Tokyo: Asakura Shoten (in Japanese) (Takemura and Fujii, 2015). X2

p

q

B

A

D C b*

a

b

b*

X1

Figure 6.5 Restricted solvability on X1. Source: Takemura, K., & Fujii, S. (2015). Ishikettei no shoho¯ [Prescription for decision making]. Tokyo: Asakura Shoten (in Japanese).

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Fig. 6.5 shows the diagram of restricted solvability on X1. According to this diagram, if point B exists between the indifference curve passing through the point A and the indifference curve passing through point C, then point D always exists and an indifference curve passing through B and D exists. Definition 6.9: Essentiality We assume the relationship h on the set X1 3 X2. That X1 is essential means that for any a; bAX1 , pAX2 , (a,p)B(b,p) is not given. That X2 is essential means that for any aAX1 , p; qAX2 , (a,p)B(a,q) is not given. This condition means that the indifference curves are not parallel to the X1 or X2 axis. Definition 6.10: Additive conjoint structure We assume that sets X1 and X2 are nonempty sets and have a relationship h on X1 3 X2. The set of triads (X1, X2, h) is called an additive conjoint structure when it satisfies the following conditions: 1. 2. 3. 4. 5. 6.

weak order, independence (Definition 6.3), Thomsen condition (Definition 6.5), Archimedean property (Definition 6.6), restricted solvability (Definition 6.8), and each attribute is essential (Definition 6.9).

Representation theorem of additive conjoint structure (Krantz et al., 1971: Theorem 6.6) We assume that the set of triads (X1, X2, h) is an additive conjoint structure. From each of X1, X2 to real numbers, functions ϕ1 and ϕ2 exist, respectively, and for a; bAX1 , p; qAX2 , (a,p)h(b,q)( ) ϕ1 ðaÞ 1 ϕ2 ðpÞ $ ϕ1 ðbÞ 1 ϕ2 ðqÞ is obtained. Additionally, each function is unique in the range of ϕ01 , ϕ02 of the positive linear transformation. That is, ϕ01 5 αϕ1 1 β 1 , ϕ02 5 αϕ2 1 β 2 , where α . 0. This theorem shows that when the preference relation has an additive conjoint structure, the preference relation can be represented by the utility of the additive system, and even if this utility function makes a positive linear transformation, its essential characteristic is not changed. This condition means that utility measured by additive conjoint measurement is an interval scale. Multiattribute decision-making that satisfies this additive conjoint system guarantees the best decision to be made, which allows maximization of multiattribute utility. Whereas the empirical testing of the unrestricted solvability and the Archimedean conditions is nearly impossible, the weak order condition, the independence condition, and the Thomsen condition can be tested empirically. Decision-making that satisfies these conditions would be difficult even in the study of double-attribute cases, which implies the difficulty of the conditions established. In this sense, assuming an additive conjoint system in multiattribute decision-making is empirically difficult, suggesting the difficulty also of best decision-making.

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To relax the additive conjoint structure conditions, we can define more heuristic concept of additive decision strategy. If the additive conjoint structure holds, the following additive strategy holds. The additive strategy is the following: Additive strategy: A decision strategy of this type includes consideration of all alternatives at every level, which are assessed comprehensively to determine the best alternative. Additive strategies include a weighted additive strategy that places different weights on each attribute and an equal weight strategy, which is contrary.

6.6

Conclusion

Peoples often make multiattribute decisions by searching multiple attributes such as prices and functions from various pieces of information. This chapter presents a critical examination of the multiattribute decision-making, findings obtained from them, and rational decision-making. First, a basic framework is presented as normative analysis and is examined in view of rationality. By subsequently defining the version of ordinal utility theory expanded to multiattribute decision-making, we will reinterpret the rationality of multiattribute decision-making based on Arrow’s general possibility theorem. Reinterpretation of the general possibility theorem of Arrow (1951) suggests that the rational multiattribute decision-making defined here could not be performed with the exception of one-dimensional decision-making based only on specific attributes. The two conditions for decision makers to be able to select options rationally (preferences are completeness (comparable) and transitive) are not compatible with the four conditions that suggest rationality for multiattribute decision-making. This fact not only suggests that it is extremely difficult for decision makers to have optimal and rational decisions in multiattribute decision-making, but also that the quantitative analysis of decision makers as conditions for such decision-making is extremely difficult. Most studies on behavioral decision-making and quantitative analysis of marketing, including linear regression analysis, structural equation modeling, and conjoint measurement, are included in a series of models of additive conjoint systems, so they have a high probability of differing from the properties of actual consumer decision-making. There is a need for optimization methods that support rapid and flexible decisionmaking under diverse and competing values and fluctuating system environments in recent days. In this context the application of multiobjective optimization, an optimization method based on comprehensive evaluation, is expected. Multiobjective optimization is characterized by the fact that multiple evaluation functions compete with each other and there is no common measure for each evaluation function. It is not easy to obtain the desired solution by adjusting the scalarization weights, because the solution can only be obtained if the Pareto surface is a simple convex surface. However, in traditional economics and general multiattribute decision-making research, it is common when the Pareto surface is a simple convex shape. In this context the assumption of a scalarization function has some utility from the perspective of Pareto optimality. In multiattribute decision theory, such scalarization functions are called additive decisions,

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and in terms of high theory measurement theory, they are called additive conjoint systems. In the next section, we will discuss decision-making as additive conjoint systems or additive conjoint structures. This chapter also introduces the additive conjoint structures and additive decision strategy for the decision maker’s information search and information evaluation. This chapter shows that considering the decision structure of additive conjoint systems under the assumption of multiattribute decision-making is somewhat warranted in terms of Pareto optimality in MOPs, especially when the Pareto surface is convex. Considering good and bad decisions from this perspective, we find that the best decision corresponds to maximization of the additive value number, and the worst decision corresponds to minimization of the additive value number.

References Arrow, K. J. (1951). Social choice and individual values. New York: Wiley. Berlin, I. (1969). Four essays on liberty. London: Oxford University Press. Berlin, I. (1990). The crooked timber of humanity: Chapters in the history of ideas. London: John Murray. Bettman, J. R. (1979). An information processing theory of consumer choice. Reading, MA: Addison Wesley. Bettman, J. R., Johnson, E. J., & Payne, J. W. (1991). Consumer decision making. In T. S. Robertson, & H. H. Kassarjian (Eds.), Handbook of consumer behavior (pp. 50
79). Englewood Cliffs, NJ: Prentice Hall. Buchanan, J. M. (1954). Social choice, democracy, and free markets. The Journal of Political Economy, 62, 114
123. Cato, S. (2016). Rationality and operators: The formal structure of preferences. Tokyo: Springer. Crowder, G. (1994). Pluralism and liberalism. Political Studies, 42, 293
305. Crowder, G. (2002). Liberalism and value pluralism. London: Continuum. Ehrgott, M. (2005). Multicriteria optimization (2nd ed.). New York: Springer. Ichikawa, A. (1980). Tamokuteki kettei no riron to hoh ¯ o¯ [Theory and method of multiobjective decision]. Tokyo: Keisoku jid¯o seigyo gakkai, (in Japanese). Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971). Foundations of measurement volume 1: Additive and polynomial representations. New York: Academic Press. Luce, R. D., & Tukey, J. W. (1964). Simultaneous conjoint measurement: A new type of fundamental measurement. Journal of Mathematical Psychology, 1, 1
27. Miettinen, K. (1999). Nonlinear multiobjective optimization. Boston, MA: Kluwer Academic Publishers. Nakayama, H., & Tanino, T. (1994). Tamokuteki keikaku hou no riron to ouyou [Theory and application of a multi-objective planning]. Tokyo: Corona Publishing Co. Ltd., (in Japanese). Ohkubo, S., & Takemura, K. (2011). Consumer behavior and marketing (2) Measurement of the eye movement and consumer behavior [Consumer behavior and marketing (2) measurement of the eye movement and consumer behavior]. Seni seihin shohi kagaku, 52, 744
750, (in Japanese). Sen, A. K. (1969). Quasi-transitivity, rational choice and collective decisions. Review of Economic Studies, 36, 381
393.

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Sen, A. K. (1970). Collective choice and social welfare. San Francisco, CA: Holden-Day. Takemura, K. (2011a). Tazokusei ishikettei no shinri moderu to “yoi ishikettei” [Psychological model of multi-attribute decision making and good decision]. Oper¯eshonzu risachi, 56, ¯ 583
590, (in Japanese). Takemura, K. (2011b). Shirizu shohisha kodo to maketeingu (1) shohisha no tazokusei ishikettei to sono bunseki [Consumer behavior and marketing (1) consumer decisionmaking by other attributes and its analysis]. Seni seihin shohi kagaku, 52, 670
677, (in Japanese). Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical descriptions of human choice behavior, Tokyo: Springer. Takemura, K. (2018). Avoiding bad decisions: From the perspective of behavioral economics. In: Keynote paper presented at the international congress of applied psychology, Montreal, Canada. Takemura, K. (2019). Foundations of economic psychology: A behavioral and mathematical approach. New York: Springer. Takemura, K. (2020). Behavioral decision theory. Oxford research encyclopedia of politics. Oxford: Oxford University Press. Available from http://doi.org/10.1093/ acrefore/9780190228637.013.958. Takemura, K., & Fujii, S. (2015). Ishikettei no shoho¯ [Prescription for decision making]. Tokyo: Asakura Shoten, (in Japanese). Tversky, A. (1969). Intransitivity of preferences. Psychological Review, 76, 31
48.

A computer simulation of cognitive effort and the accuracy of two-stage decision strategies in a multiattribute decision-making process

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As shown in the previous chapters, most decision-making can be regarded as multiattribute decision-making. Understanding the process of multiattribute decision-making is important for predicting social behavior, marketing, management policy, and economic policy (Takemura, 2009, 2014, 2019, 2020; Tsuzuki & Matsui, 2006). Although it is generally difficult to accurately find the optimal solution to a multiattribute decisionmaking problem, as shown in Chapter 6, assuming that the value function is a concave function, the additive value functon (additive utility function), which can be regarded as a scalarization function, gives the Pareto optimal value. Therefore we will consider the additive value function (additive utility function) to represent the overall evaluation. In addition, using the additive decision strategy (especially the weighted additive strategy) corresponding to this additive value fnction (additive utility function) as a standard, we will examine how the results and the amount of processing for executing the strategy differ from various heuristic decision strategies. The content of this chapter is based on research by Takemura (2018), Takemura, Haraguchi, and Tamari (2015), and Takemura, Tamari, and Ideno (2021). In this chapter, in particular, we will examine various two-stage decision-making strategies, following the evaluation method of previous studies of decision-making strategies conducted by Payne, Bettman, and Johnson (1993). In other words, we will conduct computer simulations of decision strategy as a cognitive strategy in a multiattribute decisionmaking process and examine its psychological functions, first by comparing the accuracy criterion of Payne et al. (1993) and cognitive effort (in addition to the perspective of efficient decision-making). Other indicators of the various criteria of Payne et al. (1993) and the extent to which the worst decisions can be eliminated will be discussed in Chapter 8, A Computer Simulation of Bad Decisions and Good Decisions: An Extended Analysis of Two-Stage Decision Strategies.

7.1

Introduction

Payne et al. (1993) used computer simulations to examine the psychological functions of decision strategies and found that the psychological functions of decision Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00014-4 © 2021 Elsevier Inc. All rights reserved.

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strategies vary with the number of choices and attributes. Payne et al. (1993) used computer simulations to examine the psychological functions of decision strategies and found that the psychological functions of decision strategies differed depending on the number of alternatives and attributes. In this study, we used the framework of this study, added decision strategies that they had not dealt with, and conducted computer simulations that took into account the fact that decision strategies may be changed during the decision-making process, setting two stages in the decisionmaking process and assuming that decision strategies may change. We consider the combinations of decision strategies in the two stages and conduct computer simulations to examine which combinations of decision strategies require less cognitive effort, are relatively rational, and do not select the worst decision. Then, we examine which two-stage decision strategies are efficient in terms of Payne et al.’s (1993) accuracy criterion and cognitive effort criterion for decision-making in reallife situations.

7.2

Findings and problems of previous research on decision strategies

7.2.1 Decision strategies identified Understanding decision strategies is important because not only the criteria and conditions of a decision, but also the chronological patterns of information search and evaluation of alternatives may determine the outcome of the decision itself (Tversky, 1972). For example, the purchase of a computer is usually a multiattribute decision, and the order in which the attributes are searched for affects the evaluation of the computer. Even if each attribute is evaluated based on the same criteria, the evaluation of the alternatives may differ between the case where the information search is conducted for all attributes of all alternatives and the case where the information search and evaluation are conducted for only some alternatives. For example, if a person visits all the stores in Akihabara’s electronics district in Tokyo and chooses the cheapest laptop computer with the most satisfactory brand, and if he decides immediately on a single store, he is likely to choose a different option. In addition, to find the best brand for an attribute such as price, there are two cases: one is to search for information on the price of all brands first, and then to search for information on the second most important attribute (attribute-type information search), and the other is to search for information on each brand, and then to make a decision after a comprehensive evaluation of each brand (choicetype information search). The results of the choice often differ between the two types of information search. Previous studies have found from laboratory experiments and behavioral observations that people’s decisions are made using relatively simple decision strategies (Brandst¨atter, Gigerenzer, & Hertwig, 2006; Payne & Bettman, 2004; Simon, 1957; Takemura, 2019). Simon (1957) argues that people do not make decisions according

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to the maximization or optimization principle, rather they select the best option from the available options, as assumed in traditional economics, but according to the satisficing principle, they seek a satisfactory option at a certain point due to the limitations of their information processing capacity. In a nutshell, he pointed out that decision-making is not based on the principle of maximization or optimization, but on the principle of satisficing, which is the search for satisfactory options at a certain point due to the limitations of information-processing capacity. Since then, a number of decision strategies have been found, mainly due to the limitations of human information processing capacity, and various decision strategies are used depending on the situation (Payne et al., 1993; Takemura, 2019; Tsuzuki & Matsui, 2006). Decision strategies are also called decision heuristics, especially in the field of cognitive psychology. The concept of heuristics is in contrast to algorithms, which are execution strategies that always lead to optimal solutions. The use of heuristics often solves problems more quickly and efficiently than the use of algorithms, but in some cases they can lead to inappropriate solutions or to inconsistent and situation-dependent decisions. Typical decision strategies that have been found include the following (Payne et al., 1993; Takemura, 2014, 2019). In this decision strategy, each option is examined across all attributes, the overall evaluation of each option is made, and the option with the best overall evaluation is selected. There are two types of additive methods: weighted additive (WADD) and equally-weighted additive (EQW). For example, let us assume that there are four brands of personal computers, A, B, C, and D, and that we are considering brands based on price, function, and design as attributes to be examined. For the sake of simplicity, we assume that the values of these attributes are evaluated by scores. In this strategy, we first consider brand A and say, for example, “The price is 39,800 yen (60 points). The design is not so good (50 points).” For example, “The price is 39,800 yen (60 points), the design is not so good (50 points), and the functions are very good (90 points),” and then make a judgment such as “Overall, brand A is fairly good (total of 200 points).” Similarly, brand B is “very good” (total score: 250), brand C is “quite good” (total score: 240), brand D is “fairly good” (total score: 190), and so on. In additive difference (DIF) type decision strategy, the evaluation values of any pair of alternatives are compared for each attribute. When the number of alternatives is three or more, the winning alternatives are compared one after another in a tournament-like fashion, and the final alternative is adopted. For example, in this strategy, brand A is first compared with brand B. Brand B is superior in price, but brand A is superior in quality. For example, in this strategy, brand A is first compared with brand B. Brand B is superior in price and in design, while brand A is superior in function. For example, the difference in price between brands A and B is minus 20 points (60 2 80 points), the difference in function is also minus 20 points (50 2 70 points), and the difference in design is 20 points (90 2 70 points). The total difference between brands A and B would be minus 20 points, so if you compare brands A and B, you would choose brand B for now. Next, brands C and D are compared in the same way, and brand C is chosen first, and finally, brands B

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and C are compared, and, for example, brand B is chosen. In the additive difference type, the preference relationship between a pair of alternatives is determined by adding up the differences in the evaluation values of the attributes. In the conjunctive (CON) type, each attribute has a set of necessary conditions, and if any one of the attributes does not satisfy the necessary conditions, the information processing of the alternative is terminated and the alternative is rejected, regardless of the values of the other attributes. In the case of choosing only one option with this decision strategy, the first option that exceeds the necessary conditions across all attributes will be chosen. For example, if the required score for all attributes is 80 points or more, and the alternatives are evaluated sequentially, starting with brand A, brand B, which is the first one to meet the requirement, will be selected. In this case the remaining brands C and D are not considered. This decision strategy corresponds to the decision based on Simon’s (1957) satisficing principle. However, in the simulations of this study, multiple alternatives were left in the first stage in the manner described later. In the disjunctive (DIS) type decision-making, sufficient conditions are set for each attribute, and if any one attribute satisfies the sufficient condition, the alternative is adopted regardless of the values of the other attributes. For example, suppose that the sufficient condition for all attributes is 80 points or more. If the alternatives are evaluated sequentially, starting with brand A, brand A will be chosen immediately because it has a score of 70 or higher for function, although it does not meet this condition for price and design. In this case the remaining brands B, C, and D are not considered. In lexicographic (LEX)-type decision strategy, the option with the highest rating is chosen for the most important attribute. If there is a tie for the most important attribute, the next most important attribute is chosen. However, if a small difference within a certain range is also considered as the same rank and the next most important attribute is used for judgment, it is called lexicographic semiorder (LEX-S). For example, if price is most important in lexicographic semiordering, brand B with the lowest price will be selected. In the case of lexicographic semiorder, even a small difference is considered as the same rank, and the next attribute is selected. In either case, decisions are made based on a small number of important attributes, and information on other unimportant attributes is not taken into account. In EBA (elimination by aspects) type decision-making strategy, each attribute is examined to see if it satisfies the necessary conditions, and alternatives that do not satisfy the necessary conditions are rejected. This decision strategy is similar to the linkage type but differs from the linkage type in that it adopts an attribute-type decision strategy in which multiple alternatives are scanned for a single attribute. For example, suppose that the attributes are considered in the order of function, price, and design, with the same standard requirement as in the linkage type (70 points or more). Then, brands A, B, and C would remain for function, followed by brands B and C for price among the remaining three, and finally brand C for design, and the last remaining brand C would be selected. In majority of confirming dimensions (MCD) decision strategy, the evaluation values of any pair of alternatives are compared for each attribute in a brute force

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fashion. The evaluation method differs from the additive difference method; in that it compares the number of dominant attributes and adopts the option that has the highest winning rate in the round robin comparison. For example, in the comparison of personal computers, brand B is superior to brand A in two attributes, and brand A is superior in one attribute, so brand B is evaluated as the winner. In this way the option with the highest number of wins is selected. All of these decision strategies are classified into two types: compensatory and noncompensatory. Compensatory decision strategies are those in which a low evaluation value of one attribute is compensated by a high evaluation value of another attribute, resulting in a comprehensive evaluation. In the compensatory approach, the information of all alternatives is considered. On the other hand, noncompensatory decision strategies are different from compensatory ones in that there is no compensation relationship between attributes. Under the noncompensatory decision strategy, the order in which alternatives and attributes are considered can lead to inconsistent decision outcomes. In the conjunctive strategy, the first option that satisfies the necessary conditions is adopted, so the order in which the brands are considered is important. In the case of TV(Television) brand decision-making, even if the brand of TV that the consumer likes the most is available at another store, if the first store that the consumer visits has the one that satisfies the necessary conditions, the brand will be purchased. Therefore the consumer’s decision to purchase the brand that he likes the most is easily influenced by situational factors such as the product placement in the store and the location of the store. In addition, in actual decision-making situations, several decision strategies are often mixed, depending on the decision stage. For example, previous experimental studies have shown that decision makers often use a compensatory strategy, such as an additive strategy, to reduce cognitive effort after narrowing down the number of alternatives to a small number using an EBA type strategy (Bettman, 1979; Takemura, 1996, 2014). In this way the decision strategy itself may mutate as the decision process progresses. This kind of decision-making is called multistage decision-making (Takemura, 1993, 2014, 2019).

7.2.2 Computer simulation studies of multiattribute decisionmaking process and problems Since decision strategies are adopted depending on various situational factors, the outcome of the decision also depends on the situation, and multiattribute decisionmaking is highly dependent on the situation (Payne et al., 1993; Takemura, 2014). A typical theoretical framework to explain the mutation phenomenon of situationdependent multiattribute decision-making is the computational framework. The computational approach assumes that the decision maker adopts an appropriate decision strategy by calculating the costs (expenses) and benefits (benefits) of using the relevant decision strategy to adapt to the situation. Considered in the calculation of costs and benefits are the magnitude of the cognitive effort required to make the decision, the optimality of the decision, and so on.

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The first model based on this computational approach was the situational model by Beach and Mitchell (1978), but a model that extends the basic idea of this model and elaborates it to allow for computer simulations is the adaptive model by Payne et al. (1993). They believe that a particular decision strategy is adopted in a given situation as a result of the decision maker’s trade-off between the amount of cognitive effort required to make the decision and the optimality (accuracy) of the decision. They conducted computer simulations of the seven decision strategies and two combinations of decision strategies, varying the number of alternatives and attributes. They calculated the cognitive effort (operationally defined by the number of basic information processing operations) and the relative accuracy (RA) (operationally defined by the weighted additive type and the index that takes the value of 1 when the outcome is exactly the same as the weighted additive type and 0 when the response is completely random) of the decision outcome in each condition. Their measures of cognitive effort can be divided into the eight types as same as the previous study (Payne et al., 1993). The decision-making process and outcomes were analyzed in terms of the magnitude of cognitive effort and RA. RA is calculated by the following equation (Payne et al., 1993): Relative accuracy 5

½EVðheuristic rule choiceÞ 2 hEViðrandom rule choiceÞ ½EVðexpected value choiceÞ
hEViðrandom rule choiceÞ

(7.1)

EVexpected value choice in Eq. (7.1) is the expected value of the number of positive choices, which is a strategy to adopt the choice with the highest score, using the attribute value weighted by the importance as the score. EV(heuristic rule choice) is the expected value of the number of positive choices among the strategies to be considered. According to Eq. (7.1), we can express the accuracy ratio of the outcome of a decision strategy as 1 for the outcome of a decision based on the expected value (positive selection) and 0 for the outcome of a decision based on random selection. This analysis revealed that the strategies that can make accurate decisions generally require a large amount of information processing, and the accuracy of the results must be sacrificed to make quick decisions. From this study, Payne et al. (1993) concluded that there is a trade-off between accuracy of results and speed of processing, and that when there are few options, people tend to adopt accurate decision strategies because they do not require a lot of cognitive effort, and when there are many options and attributes, people tend to adopt quick decision strategies without complicated processing. The weighted additive type, by definition of Eq. (7.1), has a RA of 1 but requires a very large amount of cognitive effort as the number of alternatives and attributes increases (Payne et al., 1993). On the other hand, lexicographic strategy requires little cognitive effort and retains some accuracy even when the number of alternatives and attributes increases (Payne et al., 1993). In addition, noncompensatory decision strategies do not require as much cognitive effort as weighted additive strategies, even when the number of alternatives and attributes increases (Payne et al., 1993). Previous experimental studies have shown that the adoption rate of

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noncompensatory decision strategies increases as the number of alternatives and attributes increases (e.g., Bettman, 1979; Takemura, 2014), and this phenomenon can be interpreted consistently with the results of this simulation. In other words, in situations where the number of alternatives and attributes is small, compensatory strategies such as weighted additive strategies with high accuracy are likely to be used because they do not require much cognitive effort, but in situations where the number of alternatives and attributes is large, compensatory decision strategies that require a great deal of cognitive effort will not be adopted. However, in situations with a large number of alternatives and attributes, compensatory decision strategies that require a large amount of cognitive effort are less likely to be adopted, and noncompensatory decision strategies that require less cognitive effort are more likely to be adopted. Payne et al. (1993) correlated the results of this simulation with the results of a number of psychological experiments and concluded that decision makers adaptively choose decision strategies by trading off cognitive effort for accuracy of choice. Payne et al.’s model can quantitatively predict which decision strategies are likely to be adopted and which decisions are likely to be made in which situations, and it is, therefore, useful in predicting consumer behavior and supporting consumer decision-making in marketing. This perspective has also been adopted in recent decision theory of consumer behavior (Takemura, 2014, 2019). However, the computer simulation study of Payne et al. does not deal with the multistage decision-making process and only examines the EBA type and some combinations of decision strategies to see what combinations of decision strategies affect the RA of decisions and cognitive effort. It does not examine strategies that are considered to be used in practice, such as the disjunctive and additive difference types. For example, in the early stages of decision-making, the lexicographic method is used to narrow down the candidates, and the additive method is used to decide on the narrowed candidates (Takemura, 1993, 2014, 2019). We believe that it is necessary to consider this from the perspective of multistage decision-making. Therefore in this study, in addition to the decision strategies discussed in Payne et al.’s study, we will analyze the additive difference type (DIF), the disjunctive type (DIS), and the equal-weighted additive type (EQW), and combine these discussed strategies in a two-stage study. For example, we first used the lexicographic type and then used various types of strategies such as additive, lexicographic, and conjunctive strategies in the next stage.

7.3

Purpose and methods of computer simulation 1

7.3.1 Purpose of computer simulation 1 In computer simulation 1, we will study the following two problems. First, we examine the differences in RA and cognitive effort between decisions made using a single strategy and decisions made using a combination of two strategies. In other words, we measured the cognitive effort and RA of the decision outcomes when

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one decision strategy was used to narrow down the choices to a few and then another strategy was used to decide on the choices, and compared them with the decision process when only one strategy was used from start to finish without combining decision strategies. The results were compared to a decision process in which only one strategy was used from start to finish without combining decision strategies. Second, we examined how different combinations of decision strategies affect the RA and cognitive effort of decision-making when two-stage decision strategies are used.

7.3.2 Method of computer simulation 1 In the simulation of this study, we created a set of alternatives that consisted of multiple attributes. The value of each attribute could take an integer value from 0 to 1000, and the attribute values were generated using uniform random numbers. The importance of each attribute was assumed to be a real number between 0 and 1 and was generated by a uniform random number. 1. Method of creating a multiattribute decision-making task The number of alternatives from the first to the second stage was set to three, referring to Payne et al. (1993). To have more than three options in the two-stage decisionmaking, the number of options at the beginning of decision-making was set to three levels: 5, 8, and 10. The number of attributes was set at three levels (3, 5, and 8) based on Payne et al. The dispersion of importance refers to the amount of variance in importance set for each attribute, and the superior option refers to the option that has equal or better values than the other options for all attributes. In this study, the presence of the superior option was set to two levels: presence and absence. The importance of the attribute was randomly generated and applied by two different creation methods that branched according to the setting of high and low variance. For the low variance group, the importance was randomly generated from the uniform distribution in the [0, 1] interval and transformed so that the sum would be 1. For the high variance group, the weight a1 was first generated randomly from the uniform distribution in the [0, 1] interval. Next, the weight a2 was generated from the uniform distribution of [0, 1 2 a1 ]. Then, the previous operations were repeated up to attribute n 2 1, and the weight ai was generPn21 ated from the uniform distribution in the interval [0; 1 2 i51 ai21 ]. The weights an P were set to 1 2 ni51 ai . These methods are based on the study of Payne et al. (1993). 2. Simulation method We generated 3000 multiattribute decision-making tasks under the following 36 conditions: number of alternatives (three conditions), number of attributes (three conditions), variance in importance (two conditions), and the presence or absence of a superior alternative (two conditions) . In the first stage, four types of strategies were used: conjunctive (CON), disjunctive (DIS), eliminaton by aspects (EBA), lexicographic (LEX) as shown in Fig. 7.1 and moreover, decision-making using a single strategy without narrowing down the options was used (NONE). Although CON and DIS are not suitable for narrowing down the alternatives because they end the decision-making process by adopting the first alternative that satisfies the

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Figure 7.1 Two-stage decision strategy in this simulation. Note: The left figure indicates that CON is applied in the first stage and DIS is applied in the second stage. The right figure indicates that EBA is applied in the total process. conditions, we newly set them to continue the search until at most three alternatives that match the conditions appear to narrow down the alternatives. To explain the results concisely, the results of the importance variance condition and the presence/ absence of superior alternatives condition are described as a whole and not separately for each condition. In the second stage, nine strategies were used: conjunctive (CON), additive difference (DIF), disjunctive (DIS), elimination by aspects (EBA), equal weighted (EQW), lexicographic (LEX), lexicographic semiorder (LEX-S), majority of confirming dimensions (MCD), and weighted additive (WAD). The DIF and DIS were not used in Payne et al. (1993) but are often used as representative decision strategies (Bettman, 1979; Takemura, 2014). DIF and DIS are as described earlier, while EQW is an equally weighted additive strategy in which the attribute values of each option are added together and the option with the largest value is adopted. The cognitive effort for each decision strategy in the second stage, where the required attribute values for CON and EBA were set to 700 and 500, respectively, according to Payne et al. The threshold for determining whether to ignore differences used in LEX-S was also set to 50 according to Payne et al. (1993). The sufficient condition for DIS was set to 700. If none of the alternatives for CON, DIS, or EBA exceeded the set criteria, the necessary condition was multiplied by 0.9 and the study was repeated. We simulated a total of 45 combinations of strategies using five strategies for the first stage and nine strategies for the second one. From the simulations, we calculated the average cognitive effort and the RA and examined the differences between the different combinations of strategies.

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7.4

Results and discussion of computer simulation 1

7.4.1 Strategies and cognitive effort in the first-stage The average cognitive effort for each strategy used in the first stage is shown in Fig. 7.2. The standard deviation of the cognitive effort is shown in the same figure. Since the standard deviation of the cognitive effort was large, the mean and standard deviation were calculated after logarithmic transformation. The error bars in the figure represent the standard deviation. Fig. 7.3 shows that the group that used DIS or CON to narrow down the choices in the first stage showed greater cognitive effort than the other three groups. EBA and LEX, both of which showed low cognitive effort, are attribute-based strategies that look at all the alternatives by attribute. CON and DIS, which had high cognitive effort, are choice-based strategies that look at all attributes in terms of alternatives.

7.4.2 First-stage strategies and relative accuracy The mean values of RA for each type of first-stage strategy are shown in Fig. 7.3. This figure shows that the RA was lowest when DIS was used in the first stage, followed by NONE and CON at the same level, and the RA was highest when EBA and LEX were used. As with cognitive effort, attribute-type strategies tended to have higher RA, while choice-type strategies tended to have lower RA.

7.4.3 Relationship between relative accuracy and cognitive effort Fig. 7.4 shows the relationship between RA and cognitive effort in the two-stage decision-making. In Fig. 7.4 the lightest gray dots indicate that CON, black DIS,

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Figure 7.2 Mean cognitive effort across all conditions and types of strategies used in the first stage.

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Figure 7.3 Means of the types of strategies used in the first stage and their relative accuracy.

Figure 7.4 Relationship between cognitive effort and relative accuracy in two-step decisionmaking.

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dark gray EBA, the medium gray dots indicate LEX, and the darkest gray dots indicate NONE, which were used in the first stage. The figure shows the regression line obtained from the logarithmic transformation of cognitive effort and RA, respectively, with the natural logarithm. This regression line is, therefore, a product of power functions, since a linear regression was performed after log-transforming both variables. In the figure, for clarity, the values on the horizontal axis are inverted, so that the upper right corner shows higher values of RA and lower values of cognitive effort. Fig. 7.4 shows a magnified view of the dense points in Fig. 7.5. From Figs. 7.4 and 7.5 the combination using EBA and LEX in the first step is located in the upper right corner. The combinations that used CON as the first step were generally located below the regression line. In addition, the groups that narrowed down the choices using LEX and those that narrowed down the choices using EBA were almost in the same position on the scatter plot. A regression analysis was conducted using log(y) 5 a log(x), where y is the RA and x is the relative cognitive effort. As a result, a 5 0.2237 was obtained. This means that the predicted value of RA is estimated as 0.22 power of cognitive effort. The predicted values of the regression equation are considered to represent the average trade-off between cognitive effort and RA. The values that deviate from the predicted values in the positive direction can be interpreted as an adaptive decision strategy that reduces cognitive effort but maintains RA above the average value (Takemura et al., 2015). In this result the combinations that use attribute-type strategies such as LEX and EBA to narrow down the alternatives ranked high.

Figure 7.5 Relationship between cognitive effort and relative accuracy in two-stage decision-making (partial magnification). Note: ’ indicates 5 alternatives, ■ indicates 8 alternatives, and ■ indicates 10 alternatives.

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The results show that using attribute-type strategies such as EBA and LEX for narrowing down the alternatives when using a combination of decision strategies can lead to highly accurate decision-making, while using alternative-type strategies such as CON and DIS for narrowing down the alternatives can lead to a decision that requires more cognitive effort than a decision made using a single strategy without narrowing down the alternatives. The results suggest that the number of choices and the accuracy of the decision-making process are related.

7.4.4 Relationship between the number of options, cognitive effort, and relative accuracy 7.4.4.1 Relationship between the number of choices and cognitive effort Next, we examined the relationship between the number of choices and cognitive effort. Figs. 7.6 and 7.7 show the cognitive effort for each number of choices in each combination of strategies. Note that the results of using a method other than NONE to narrow down the choices showed that cognitive effort monotonically increased with the number of choices in all combinations (Fig. 7.8). Through the previous three figures, we can see that cognitive effort tends to increase as the number of alternatives increases in most of the combinations of strategies, but in the group that made decisions using only CON or DIS without narrowing down the alternatives, there was almost no change in cognitive effort depending on the number of alternatives. This result can be interpreted as a result

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Figure 7.6 Relationship between the number of alternatives and cognitive effort when NONE is used in the first stage. Note: ’ indicates 5 alternatives, ■ indicates 8 alternatives, and ■ indicates 10 alternatives.

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Figure 7.7 Relationship between the number of alternatives and cognitive effort when CON is used in the second step. Note: ’ indicates 5 alternatives, ■ indicates 8 alternatives, and ■ indicates 10 alternatives.

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Figure 7.8 Relationship between the number of alternatives and cognitive effort when DIS is used for the second step. Note: ’ indicates 5 alternatives, ■ indicates 8 alternatives, and ■ indicates 10 alternatives.

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of the fact that in CON and DIS, the search is conducted in the form of alternatives, and when an alternative is found that satisfies the necessary conditions, the search is terminated, and, thus, the effect of the large number of alternatives is lessened. On the other hand, when CON and DIS were used as the second stage of combination decision-making, the cognitive effort increased despite the fact that the combinations used the same CON and DIS because they were affected by the size of the number of alternatives at the time when the strategy was used to narrow down the alternatives in the first stage. The order of the magnitude of cognitive effort within the same number of alternatives was constant regardless of the increase or decrease in the number of alternatives.

7.4.4.2 Relationship between the number of choices and relative accuracy Next, we examined the relationship between the number of alternatives and RA. Fig. 7.9
7.11 show the RA of each combination of strategies for each number of alternatives. The group that used CON in the first stage did not have any characteristics to be discussed, so the figure is not shown. These three figures show that when the DIS was used in the first stage of decision-making, the RA decreased as the number of alternatives increased, regardless of which strategy was used in the second stage. This may be due to the fact that in the first stage of narrowing down the choices, many choices were left that had at least one high attribute value but did not have a high expected value. In 1.2

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Figure 7.9 Relationship between the number of alternatives and relative accuracy when DIS is used at the first stage. Note: ’ indicates 5 alternatives, ■ indicates 8 alternatives, and ■ indicates 10 alternatives.

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1 0.8 0.6 0.4 0.2 0 CON

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Figure 7.10 Relationship between the number of options and relative accuracy when EBA is used at the first stage. Note: ’ indicates 5 alternatives, ■ indicates 8 alternatives, and ■ indicates 10 alternatives.

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Figure 7.11 Relationship between the number of alternatives and relative accuracy when LEX is used in the first step. Note: ’ indicates 3 attributes, ■ indicates 5 attributes, and ■ indicates 8 attributes.

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addition, combinations that used attribute-type strategies such as LEX and EBA in the first stage to narrow down the choices were less affected by the increase in the number of attributes, and combinations that used attribute-type strategies such as CON and DIS in the second stage after narrowing down the choices using LEX or EBA in the first stage were less affected by the increase in the number of attributes. In the combination the RA tended to be higher when the number of options was larger.

7.4.5 Relationship between the number of attributes and cognitive effort and relative accuracy 7.4.5.1 Relationship between the number of attributes and cognitive effort First, we examined the relationship between the number of attributes and cognitive effort. Fig. 7.12 shows the magnitude of cognitive effort for each number of attributes in each combination of strategies. Fig. 7.12 shows that the cognitive effort tended to increase with the number of attributes for all strategies except for the decision-making strategy that used only DIS without narrowing down the options. This is because DIS is a strategy in which the search is continued until the first attribute value that satisfies the necessary conditions appears, and the search is terminated when a choice with an attribute that satisfies the conditions appears. Therefore it is assumed that the number of cognitive effort processes is not affected by the number of attributes that a single choice has.

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Figure 7.12 Relationship between the number of attributes and cognitive effort when NONE is used in the first step. Note: ’ indicates 3 attributes, ■ indicates 5 attributes, and ■ indicates 8 attributes.

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7.4.5.2 Relationship between the number of two attributes and relative accuracy Next, we examined the relationship between the number of attributes and RA. Fig. 7.13
7.18 show the RA of each attribute for each combination of strategies. The previous six figures show that the RA of decision-making using EBA and LEX in the first stage is less affected by the number of alternatives than that using CON and DIS in the first stage (Fig. 7.13
7.18). This may be due to the fact that EBA and LEX use attribute-type choices for the most important attributes. In the case of DIS, the RA decreased as the number of attributes increased, while in the case of CON, the RA increased as the number of attributes increased. On the other hand, with CON, the probability of having attribute values that do not meet the necessary conditions increases as the number of attributes increases, making it harder to adopt options with low RA. In CON, as the number of attributes increases, the probability of having attribute values that do not match the necessary conditions increases, making it harder to adopt alternatives with low RA. These results indicate that by increasing the number of attributes, the magnitude of cognitive effort increases regardless of the strategy, but the RA differs depending on the strategy used.

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Figure 7.13 Relationship between the number of attributes and relative accuracy when CON is used in the first step. Note: ’ indicates 3 attributes, ■ indicates 5 attributes, and ■ indicates 8 attributes.

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Figure 7.14 Relationship between the number of attributes and relative accuracy when DIS is used in the first step. Note: ’ indicates 3 attributes, ■ indicates 5 attributes, and ■ indicates 8 attributes.

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Figure 7.15 Relationship between the number of attributes and relative accuracy when EBA is used in the first step. Note: ’ indicates 3 attributes, ■ indicates 5 attributes, and ■ indicates 8 attributes.

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Figure 7.16 Relationship between the number of attributes and relative accuracy when LEX is used in the first step. Note: ’ indicates 3 attributes, ■ indicates 5 attributes, and ■ indicates 8 attributes.

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Figure 7.17 Relationship between the number of attributes and relative accuracy when CON is used in the second step. Note: ’ indicates 3 attributes, ■ indicates 5 attributes, and ■ indicates 8 attributes.

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Figure 7.18 Relationship between the number of attributes and relative accuracy when DIS is used in the second step. Note: ’ indicates log EIP in which the number of left alternatives in the second stage is 2, ■ indicates that for 3 alternatives, and ■ indicates that for 4 alternatives.

7.5

Purpose and method of computer simulation 2

7.5.1 Purpose of computer simulation 2 Based on the results of computer simulation 1, we conducted a new computer simulation 2. The purpose of simulation 2 was to examine how RA and cognitive effort change by mutating the number of options left from the first to the second stage of a two-stage decision-making process. In other words, we examined the effects of the number of options left when narrowing down from the first to the second stage on cognitive effort and RA. The number of alternatives and attributes was fixed, while the number of alternatives left in the second stage was varied, and the decision-making process and results were examined.

7.5.2 Method of computer simulation 2 For a multiattribute decision-making task with three attributes and five alternatives, we narrowed down the alternatives and adopted the alternatives using the top seven combinations that were located above the regression curve in the previous computer simulation. The number of alternatives left in the second stage was set at three levels: two or less, three or less, and four or less, which are around the values used in Payne et al. (1993). One trial is a sequence of narrowing down the options using

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a strategy and then adopting one of the options using the strategy. This was repeated for 3000 trials in each of the three conditions: narrowing the choices to two or fewer, narrowing the choices to three or fewer, and narrowing the choices to four or fewer. From the results, we calculated the average of cognitive effort and RA and compared them with each combination of strategies. For the group that made decisions using only LEX without combining strategies, we did not consider the number of options to be left in the second stage, because they did not narrow down the options.

7.6

Results and discussion of computer simulation 2

7.6.1 Relationship between the number of options left in the second-stage and cognitive effort Fig. 7.19 shows the relationship between cognitive effort and the number of options left in the second stage. Fig. 7.19 shows that the effect of the number of alternatives left in the second stage on cognitive effort is smaller for the combination using EBA to narrow down the alternatives than for the combination using LEX. This may be due to the fact that, due to the nature of EBA, the number of options to be advanced to the second stage may be smaller than the specified number, and the variation in the number of options to be left for the second stage is smaller than that of LEX.

Figure 7.19 Relationship between the number of alternatives left in the second stage and cognitive effort. Note: ’ indicates log EIP in which the number of left alternatives in the second stage is 2, ■ indicates that for 3 alternatives, and ■ indicates that for 4 alternatives.

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7.6.2 Relationship between the number of alternatives left in the second-stage and relative accuracy Next, Fig. 7.19 shows the RA for each number of options left in the second stage. The figure shows that when the same strategies are combined in decision-making, the RA is not affected by the number of options left in the second stage. The reason for this is that in the attribute-type strategy, when the same strategies are combined, the options are looked at again from exactly the same perspective, so there was no difference in the results no matter how many options were left in the second stage. In the case of the combination using WAD in the second stage, the RA tended to be higher when the number of choices left in the second stage was large. This tendency can be considered due to the fact that the probability of excluding alternatives with high RA from consideration by narrowing down the alternatives before adopting alternatives with high RA by WAD becomes low. In addition, when EBA was used after narrowing the choices with LEX, or when LEX was used after narrowing the choices with EBA, there was a tendency for the RA to decrease as more choices were left in the second stage. This may be because LEX and EBA are more likely to adopt the option with the highest evaluation for only the most important attributes when making a choice among many options (Fig. 7.20).

7.7

General discussion

The results obtained from the computer simulations so far indicate that using an attribute-based strategy, such as EBA or LEX, for narrowing down the alternatives in a two-stage decision-making process will result in higher RA with the same cognitive effort as a single strategy. The RA of the strategies tended to be higher than

Figure 7.20 Relationship between the number of options left in the second stage and relative accuracy.

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that of the single strategy. In previous research on the decision-making process, decision makers have been reported to reduce cognitive effort by first narrowing down the number of alternatives to a small number using a decision strategy such as LEX, and then making a weighted additive decision (Bettman, 1979; Takemura, 2014). Our findings support this interpretation. The present finding supports this interpretation. For example, in the case of purchasing a personal computer, for example, a decision is made to rank the brands according to their functions, such as CPU, and then to narrow down the list to two or three brands with the best functions. As revealed by Payne et al. (1993) and confirmed in this study, the accuracy of the lexicographic type alone is about 80% of that of the weighted additive type. According to Payne et al. (1993) and confirmed in this study, the accuracy of the lexicographic type alone is 80% of that of the weighted addition type, but the combination of the lexicographic type and the weighted addition type is suggested to improve the accuracy. The fact that such a strategy is often used in multistage decision-making by actual participants in experiments suggests that humans are trying to minimize cognitive effort as much as possible, while at the same time trying to make decisions with accuracy similar to the weighted additive type. The results of our computer simulations show that two-stage decision-making using alternative decision strategies such as CON and DIS as the first stage consumes more cognitive effort than decision-making using a single strategy and also reduces RA. This result can be interpreted to mean that in multiattribute decisionmaking in general, without considering the situation of the decision task such as the number of alternatives or the number of attributes, narrowing down the alternatives using an attribute-type strategy and then using another strategy is the most likely method to lead to quick and accurate decision-making. CON is a decision-making method that corresponds to Simon’s (1957) satisficing principle, but it deviates considerably from the accuracy of the weighted addition strategy. This result suggests that decision-making based on the satisficing principle is a decision-making strategy that differs considerably from the weighted-additive strategy in terms of decision outcomes. In social psychology, the weighted additive type represents a style of integrating weighted information such as that postulated in the multiattribute attitude model, and in decision theory, in multiattribute decision theory and expected utility theory. The results suggest that such a decision strategy differs considerably not only in terms of cognitive effort but also in terms of decision outcome from the conjunctive type based on the satisficing principle. In contrast, the results of the lexicographic type were relatively close to those of the weighted addition type. Next, in the second simulation study, when the number of alternatives was manipulated in the decision-making process, the combination in which the number of alternatives was narrowed down by attribute-type alternatives was less affected by the increase of alternatives than the other combinations. In the present multiattribute decision-making task with 5
10 alternatives, the RA of the strategies and the ranking of cognitive effort did not change depending on the number of alternatives. This suggests that if we use attribute-type strategies to narrow down the choices and then use choice-type strategies, decision-making becomes easier regardless of

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the number of choices. In previous experimental studies of multiattribute decisionmaking, it has been found that after narrowing down the choices using an attributetype strategy, a choice-type strategy is more likely to be used (Takemura, 1993, 2014). Takemura (1993, 2014) suggests that humans use attribute-type refinement and then choice-type strategies to cope with information overload, such as an increase in the number of choices. The results of an experiment in which the number of attributes was manipulated showed that the RA of decision-making using CON increased as the number of attributes increased, but conversely the RA of decision-making using DIS decreased. This can be interpreted to mean that when people try to make decisions by considering a large number of attributes to adopt a better option, they are more likely to adopt an option with high RA when using CON, but they are more likely to adopt an option with low RA when using DIS. In fact, the previous multiattribute decision-making method was used. In fact, previous research on multiattribute decision-making has reported that when many attributes are presented to experimental participants, the decision results deviate significantly from the weighted additive type (Bettman, 1979). This phenomenon can be explained consistently if we interpret that the experimental participants were using a strategy like the disjunctive type. However, this interpretation is not supported by previous studies of weighted additive models, which have not examined the nature of information processing and decision strategies.

7.8

Conclusions and problems of this study

In this chapter, we used the basic framework of Payne et al.’s (1993) computer simulation of decision strategies and added decision strategies that they did not deal with, and also set up two stages in the decision-making process, taking into account the fact that decision strategies may change during the decision-making process. In addition, we set up two stages in the decision-making process to take into account the fact that the decision strategies may be changed during the decision-making process and conducted computer simulations assuming that the decision strategies change during the decision-making process. In other words, we considered combinations of the two stages for all of the decision strategies discussed and conducted computer simulations. In this computer simulation, we examined which decision strategies and combinations of decision strategies are less cognitive effort and relatively accurate, and which two-step decision strategies are relatively less cognitive effort and more accurate for realistic decision-making. In this study, we examined the psychological functions of the two-stage decision-making strategy. In this study, we examined a two-stage decision-making strategy, and found that narrowing down the choices to two using LEX and then comparing them using WAD was relatively accurate with low cognitive load. If we consider this in a practical situation, the decision maker can make a decision with relatively little cognitive effort and close to the result of the weighted additive method from the

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beginning if he narrows down the choices to the attributes that are most important to him, narrows down the choices to the next ones when he cannot decide, and then narrows down the final candidates to two and makes a decision in the weighted additive method. This is because the decision-making process is relatively low cognitive effort. Previous research on multiattribute decision-making has shown that many people exhibit such a decision-making process (Bettman, 1979; Takemura, 2014). This suggests that many consumers who exhibit a multistage decisionmaking strategy are making relatively rational decisions. However, it is important to note that RA was measured by a weighted additive type in this study, similar to the Payne et al. study (Payne et al., 1993). The question remains from normative decision theory whether the weighted additive approach is really a rational and accurate decision strategy. From the viewpoint of multiobjective optimization, there is a restriction on the conditions under which the weighted additive type becomes Pareto optimal, and in this sense, it cannot necessarily be said that the weighted additive type is optimal and rational. In addition, the assumption that all attribute values can be numerically weighted is also a problem that should be fully considered, given the axiomatic conditions of the weighted additive type (Krantz, Luce, Suppes, & Tversky, 1971; Takemura & Fujii, 2015). In the simulations of the present study, we have examined how two-stage decision-making changes cognitive effort and outcome accuracy in each condition. In the current experiment, the CON, DIS, and EBA groups, which are strategies using the necessary condition, were set to continue searching until the number of remaining options was less than three when narrowing down the options. Therefore it is assumed that there were cases where the average number of choices left in the second stage was actually less than three. To allow the participants to make decisions in the second stage among the three options each time, we should have set the second stage so that there were always exactly three options left. In this study, we also tested the effect of varying the number of alternatives left in the second stage when narrowing down the choices using LEX with relatively good performance and concluded that the effect of the number of alternatives left in the second stage on RA depended on the combination of strategies. However, we believe that it is necessary to further investigate combinations of decision strategies other than those examined in this study. In addition, the decision strategies examined in this study are basically only representative and do not cover all decision strategies in real-life situations. Although actual decision strategies have been examined by process tracking methods such as verbal protocol methods and information monitoring methods, their identification is difficult and there is ambiguity in their measurement (Takemura, 2014, 2019). Therefore there is a limit to the consideration of decision strategies in this study only by computer simulation. It is necessary to reexamine this issue experimentally using process tracking techniques. For example, we can conduct a correlation analysis study of multistage strategies and their psychological states in actual decisionmaking by using the process tracking technique. In the next chapter, we will examine this two-stage decision-making using the criteria of bad decision-making and various alternative evaluation criteria.

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References Beach, L. R., & Mitchell, T. R. (1978). A contingency model for the selection of decision strategies. Academy of Management Review, 3, 439
449. Bettman, J. R. (1979). An information processing theory of consumer choice. Reading, MA: Addison Wesley. Brandst¨atter, E., Gigerenzer, G., & Hertwig, R. (2006). The priority heuristic: Making choices without tradeoffs. Psychological Review, 113, 409
432. Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971). Foundations of measurement Volume 1: Additive and polynomial representations. New York: Academic Press. Payne, J. W., & Bettman, J. R. (2004). Walking with the scarecrow: The information-processing approach to decision research. In D. J. Koehler, & N. Harvey (Eds.), Blackwell handbook of judgment and decision (pp. 110
132). Malden, MA: Blackwell Publishing. Payne, J. W., Bettman, J. R., & Johnson, E. J. (1993). The adaptive decision maker. Cambridge: Cambridge University Press. Simon, H. A. (1957). Administrative behavior: A study of decision making process in administrative organization (2nd ed.). New York: McMillan. Takemura, K. (1993). Protocol analysis of multistage decision strategies. Perceptual and Motor Skills, 77, 459
469. Takemura, K. (1996). Ishikettei no Shinri: Sono Katei no Tankyu [Psychology of decision making: Investigation of its process]. Tokyo: Fukumura Shoten (in Japanese). Takemura, K. (2009). Koudou Ishi Ketteiron: Keizai Kodo no Sinrigaku [Behavioral decision theory: Psychology of economic behavior]. Tokyo: Nihon Hyoron Sya (in Japanese). Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical descriptions of human choice behavior. Tokyo: Springer. Takemura, K. (2018). Avoiding bad decisions: From the perspective of behavioral economics. In: Keynote paper presented at the international congress of applied psychology, Montreal, Canada. Takemura, K. (2019). Foundations of economic psychology: A behavioral and mathematical approach. New York: Springer. Takemura, K. (2020). Behavioral decision theory. Oxford research encyclopedia of politics. Oxford: Oxford University Press. Available from 10.1093/acrefore/9780190228637.013.958. Takemura, K., & Fujii, S. (2015). Ishikettei no shoho¯ [Prescription for decision making]. Tokyo: Asakura Shoten (in Japanese). Takemura, K., Haraguchi, R., & Tamari, Y. (2015). Tazokusei Isikettei Katei ni okeru Kettei Houryaku no Ninchiteki Doryoku to Seikakusa: Keisanki Simyureisyon wo Mocihita Koudou Ishiketteironteki Kentou [Cognitive effort and accuracy of decision strategies in multi-attribute decision making process: A behavioral decision theoretic approach using computer simulation technique]. Ninchikagaku, 22, 368
388. (in Japanese). Takemura, K., Tamari, Y., & Ideno, T. (2021). Simulation and experiment of bad decision making: Examination of two stage decision strategy. Unpublished Manuscript, Department of Psychology, Waseda University. Tsuzuki, T., & Matsui, H. (2006). Tazokusei Ishikettei ni okeru Bunmyaku Kouka ni kansuru Moderu Kenkyu no Doukou [New trends in modeling studies on context effects in multiattribute decision making]. Rikkou Daigaku Shinrigaku Kenkyu: The Japanese Journal of Psychology, 48, 69
79. (in Japanese). Tversky, A. (1972). Elimination by aspects: A theory of choice. Psychological Review, 79, 281
299.

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A computer simulation of bad decisions and good decisions: an extended analysis of two-stage decision strategies

8

This chapter is based on computer simulation studies of decision strategy as a cognitive strategy in multiattribute decision-making process by Takemura (2015, 2018) and Takemura, Tamari, and Ideno (2021). The analysis in Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute Decision-Making Process, was based on the analysis of Payne, Bettman, and Johnson (1993) with the addition of various two-stage decision strategies. The research in that chapter examined two-step decision strategies and found that narrowing down the choices to two using LEX and then comparing them using WAD exhibited relatively low cognitive load and was accurate. If we consider this in a practical situation, the decision maker can make a decision with relatively little cognitive effort and close to the result of the weighted additive method from the beginning if he narrows down the choices to the attributes that are most important to him, then to the next ones when he cannot decide, and finally to the final candidates to two and makes a decision in the weighted additive method. However, the question remains whether such a strategy really leads to the avoidance of worst-case decisions. In this study, using the basic framework of computer simulation for the decision-making strategy in Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute Decision-Making Process, we will add various indices to the decision-making indices used in that chapter and further study them in terms of avoidance of bad decisions and efficient decision-making.

8.1

A comparison between additive strategy (WAD) and lexicographic strategy (LEX) in multiattribute decision-making

In this chapter, we compare additive (WAD) and lexicographic strategies (LEX) for multiattribute decision-making. In the machine simulation study the two-stage decision strategy was examined, and it was found that narrowing down the choices to two using LEX and then comparing them with WAD is relatively accurate with low cognitive load, and that LEX is relatively inaccurate and has low cognitive load (Payne et al., 1993). Because of this, in this section, we will consider LEX and WAD. Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00001-6 © 2021 Elsevier Inc. All rights reserved.

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In lexicographic (LEX) decision-making, it has been empirically used in the field of marketing science to represent consumers’ attributes as hierarchical models, such as nested logit models, when the importance of the attributes is obtained in advance. However, the hierarchical model can be used only when the importance of attributes is known, and the problem of determining the order of importance of attributes is NP(non-deterministic polynomial) problem due to combinatorial explosion when the number of attributes and levels is large (Martignon & Hoffrage, 2002). Therefore in econometric analysis of decision-making in consumer behavior and social behavior, the objective of calculating the partial utility of each level of attributes from the data and calculating the importance of each attribute from this information is usually not supported. For this problem, Yee, Dahan, Hauser, and Orlin (2007) showed that Greedoid-Languages, a type of greedy algorithm, can replace the NP-hard problem with a polynomial-time approximation algorithm. In more than half of consumer decisions, noncompensatory models without such a complementary relationship are not used for estimation more than compensatory models that can compensate the negative part of the other attribute with the positive part, such as additive models. The predictive power of the noncompensatory model was higher than that of the compensatory model in the hold-out sample. This suggested that an additive (WAD) model can approximate a lexicographic (LEX) model, but not necessarily in a strict sense. It has been empirically known that noncompensatory models such as LEX can be approximated by compensatory models in terms of econometric models, but the specific mathematical conditions have not been known. To address this issue, Kohli and Jedidi (2007) showed that lexicographic decision-making can be represented by a linear model with constraints on the parameters if the level of attributes is discrete. They obtained necessary and sufficient conditions for an additive (WAD) decision strategy and the corresponding linear utility function to represent a standard lexicographic model, but not all WADs can be represented by LEX, and the two are not compatible unless the weights of the most important attributes have a large superiority with respect to the weights of the other attributes. They studied and simulated an algorithm to estimate the best fitting lexicographic model from preference data for multiattribute alternatives. The simulation results suggest that the greedy algorithm is effective in recovering the true attribute order and that the proposed method of assigning alternative preference models to consumers is robust. A survey of consumer preferences for laptops showed that two-thirds of the subjects favored the use of the lexicographic strategy. They also found that the lexicographic strategy, which does not take into account trade-offs between attributes, is the most suitable rule to describe the preferences of a significant proportion of subjects. Finally, they have developed a method for hierarchical clustering of consumers using lexicographic analysis and interpreting the clustering as a collection of market structures. While the correspondence of LEX with WAD can be fully expected from previous theoretical analyses and econometric studies, this chapter examines whether the use of various indicators of decision-making can produce findings similar to those in Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of

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Two-Stage Decision Strategies in a Multiattribute Decision-Making Process. In particular, we will examine how the probability of choosing the worst option is affected by the decision strategy.

8.2

Methodology of this study

This study will use the same method as the computer simulation in Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute Decision-Making Process. In other words the target strategies are as follows.

8.2.1 Target decision strategy We used the following decision strategies. At first, additive strategy was used. There are two types of additives: one in which different weights are placed on each attribute (weighted additive type: WADD) and the other in which no weights are placed (equal weight type: EQW). Additive difference (ADF), conjunctive (CON), disjunctive (DIS), lexicographic (LEX) types were used, whereas, if a small difference in a certain range is also considered to be of the same rank and the next most important attribute is used for judgment, this type is also set as lexicographic semiorder (LEX-S). Elimination by aspects (EBA) and majority of confirming dimensions (MCD) types are also used. In addition, the setting of the two-stage decision strategy and the other conditions are the same as in Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute Decision-Making Process.

8.2.2 Indicators of decision-making First, in this study, as in Payne et al. (1993), the cognitive effort involved in implementing each strategy [elementary information processes (EIP): operationally defined by the number of basic information processing operations] and the relative accuracy (RA) of the decision outcome (RA: operationally defined as a weighted additive index that takes a value of 1 when the outcome is exactly the same and 0 when the response is completely random) were calculated in each condition. In other words, we first used the following indices. RA is defined by Payne et al. (1993) as (EV(heuristic rule choice) 2 EV(random rule choice))/ (EV(expected value choice) 2 EV(random rule choice)). However, this index can tell us the RA based on the expected value, but it cannot tell us how much of the time we are choosing the most desirable and best option. Therefore we calculated the probability of that choice for each condition. Since the Payne et al.’s (1993) index is based on random choices and does not have the perspective of using the value of the least desirable choice as a criterion, we obtained the following index as an alternative index.

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RA based on the minimum value is defined as (EV(heuristic rule choice) 2 EV(the minimum value))/ (EV(expected value choice) 2 EV(the minimum value)). In addition, as a measure of bad decision-making, we also calculated the percentage of choices that chose the lowest expected value. This is the rate of choosing the option with the lowest expected value in the name of the set of options in question. This can be interpreted as the rate of adoption of the worst option. In addition, in Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute Decision-Making Process, EIP was displayed in logarithmic form, but in this chapter, RA divided by EIP is displayed to facilitate comparison of the efficiency of the strategies. To summarize, this study used (1) the elementary score of EIP, (2) the adoption rate of the worst alternative, (3) the RA defined from the lowest expected value, (4) the RA defined from Payne et al. (1993) (duplicated in Chapter 7: A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute Decision-Making Process), and (5) the efficiency index of RA divided by EIP.

8.2.3 Method of computer simulation In the simulation of this study, as in Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute Decision-Making Process, we created a set of alternatives consisting of multiple attributes. The value of each attribute can take an integer value from 0 to 1000, and the attribute values were generated using uniform random numbers. The importance of each attribute was assumed to be a real number between 0 and 1 and was generated by a uniform random number. To create a multiattribute decision-making task the number of options from the first stage to the second stage was set to three, referring to Payne et al. (1993). To have more than three options in the two-stage decision-making the number of options at the beginning of decision-making was set to three levels: 5, 8, and 10. The number of attributes was set at three levels (3, 5, and 8) based on Payne et al. (1993), and the presence or absence of a dominant option in each decision task. The importance of the attributes was randomly generated and applied using two different creation methods that diverged according to the setting of high and low variance. We generated 3000 multiattribute decision-making tasks with a total of 36 conditions: number of alternatives (3 conditions) 3 number of attributes (3 conditions) 3 variance of importance (2 conditions) 3 presence of superior alternatives (2 conditions). In the first stage, five types of strategies were used: conjunctive (CON), disjunctive (DIS), elimination by aspects (EBA), lexicographic (LEX), and decision-making using a single strategy without narrowing down the options (NONE). In the second stage, as in Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute DecisionMaking Process, we used nine strategies: conjunctive (CON), additive difference (DIF), disjunctive (DIS), elimination by aspects (EBA), equal weighted (EQW), lexiicographic (LEX), lexicographic semiorder (LEX-S), majority of confirming dimensions (MCD), and weighted additive (WAD) strategies.

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We simulated a total of 45 combinations of strategies using 5 strategies for the first stage and 9 strategies for the second stage. From the simulations, we calculated the average cognitive effort and the RA defined for each species and the percentage of the best and worst choices under the expected value index.

8.3

Results and discussion of computer simulation

8.3.1 Cognitive effort (elementary information processes) In this chapter, we will examine the effects of combinations of decision strategies by showing the EIP in real values rather than in logarithmic form; to examine the two-stage strategy, we will first show the results for different numbers of alternatives when we narrowed down the choices to two in the first stage. The average cognitive effort for each strategy used in the first stage is calculated and shown in Fig. 8.1. The results for the three options in the first stage are also shown in Fig. 8.2. It can be seen that the group that narrowed down the choices using CON and EBA in the first stage showed greater cognitive effort than the other groups; the high CON and EBA may be due to the time taken to process the cases where the narrowing did not go to the planned number of choices in the narrowing that met the necessary conditions. Of course, WAD, EQW, and ADF take less cognitive effort. Similarly, the results for different numbers of attributes are shown in Figs. 8.3 and 8.4. Furthermore, the results for different dispersion levels when the number of options remaining at the end is two and three are shown in Figs. 8.5 and 8.6, and the results with and without dominance are shown in Figs. 8.7 and 8.8 and 1.00

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Figure 8.1 Average EIPs in the two-stage decision-making when the number of alternatives left in the second stage is two for the different numbers of alternatives. EIP, elementary information processes.

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Figure 8.3 Average EIPs in the two-stage decision-making when the number of alternatives left in the second stage is two for the different numbers of attributes. EIP, elementary information processes.

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Figure 8.4 Average EIPs in the two-stage decision-making when the number of alternatives left in the second stage is two for the different numbers of attributes. EIP, elementary information processes.

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Figure 8.5 Average EIPs in the two-stage decision-making when the number of alternatives left in the second stage is two for the different dispersion levels. EIP, elementary information processes.

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Figure 8.6 Average EIPs in the two-stage decision-making when the number of alternatives left in the second stage is three for the different dispersion levels. EIP, elementary information processes.

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Figure 8.7 Average EIPs in the two-stage decision-making when the number of alternatives left in the second stage is two for the different dominance levels. EIP, elementary information processes.

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Figs. 8.9 and 8.10 for the overall average values, respectively. These figures show that compensatory decision strategies require more cognitive effort, while decision strategies such as LEX and LEX-S require less cognitive effort. In addition, it is generally less cognitive effort to choose the last two options than to choose the last three. 1.00

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DIS

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Figure 8.8 Average EIPs in the two-stage decision-making when the number of alternatives left in the second stage is three for the different dominance levels. EIP, elementary information processes.

Elementary Information Processes

1.00

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Figure 8.9 Overall average EIPs in the two-stage decision-making when the number of alternatives left in the second stage is two. EIP, elementary information processes.

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8.3.2 Choice rate of the worst option In this chapter, we calculated the rate of choosing the least expected value among the alternatives as the rate of choosing the worst alternative in each condition. Fig. 8.11 shows the results for different numbers of alternatives when the number 1.00

Elementary Information Processes

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EQW LEX LEX−S MCD WAD

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Figure 8.10 Overall average EIPs in the two-stage decision-making when the number of alternatives left in the second stage is three. EIP, elementary information processes. 0.15

N Alt: 5

0.05

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2nd STR CON DIF

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DIS 8

EBA EQW LEX

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LEX−S MCD WAD

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Rate of choosing the alternative with the minimum expected value

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Figure 8.11 Rate of choosing the alternative with the minimum expected value in the twostage decision-making when the number of alternatives left in the second stage is two for the different numbers of alternatives.

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of alternatives is reduced to two in the first stage to examine the two-stage strategy. The results of narrowing down the choices to three in the first stage are also shown in Fig. 8.12. Similarly, the results at different numbers of attributes are shown in Figs. 8.13 and 8.14. Furthermore, the results at different dispersion levels for the 0.15

N Alt: 5

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2nd STR CON DIF

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EBA EQW LEX

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LEX−S MCD WAD

0.00 0.15

0.10 10

Rate of choosing the alternative with the minimum expected value

0.10

0.05

0.00 CON

DIS

EBA

LEX

LEX−S

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1st STR

Figure 8.12 Rate of choosing the alternative with the minimum expected value in the twostage decision-making when the number of alternatives left in the second stage is three for the different numbers of alternatives. 0.15

N Att: 3

0.05

0.00 0.15

2nd STR CON DIF

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EBA EQW LEX

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LEX−S MCD WAD

0.00 0.15

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Rate of choosing the alternative with the minimum expected value

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0.00 CON

DIS

EBA

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Figure 8.13 Rate of choosing the alternative with the minimum expected value in the twostage decision-making when the number of alternatives left in the second stage is two for the different numbers of attributes.

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last remaining options of two and three are shown in Figs. 8.15 and 8.16, and the results with and without dominance are shown in Figs. 8.17 and 8.18 and Figs. 8.19 and 8.20, respectively. As can be seen from these figures, it is clear that the compensatory decision strategy does not choose the worst option, but even the 0.15

N Att: 3

0.05

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EBA EQW LEX

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LEX−S MCD WAD

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Rate of choosing the alternative with the minimum expected value

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Figure 8.14 Rate of choosing the alternative with the minimum expected value in the twostage decision-making when the number of alternatives left in the second stage is three for the different numbers of attributes.

0.10 Dispersion: High

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EBA EQW

0.15

LEX LEX−S MCD WAD

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Rate of choosing the alternative with the minimum expected value

0.15

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0.00 CON

DIS

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LEX

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Figure 8.15 Rate of choosing the alternative with the minimum expected value in the twostage decision-making when the number of alternatives left in the second stage is two for the different dispersion levels.

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0.10 Dispersion: High

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Rate of choosing the alternative with the minimum expected value

0.15

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0.00 CON

DIS

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LEX

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Figure 8.16 Rate of choosing the alternative with the minimum expected value in the twostage decision-making when the number of alternatives left in the second stage is three for the different dispersion levels.

0.10 Dominance

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2nd STR CON DIF DIS

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LEX LEX−S MCD WAD

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Rate of choosing the alternative with the minimum expected value

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Figure 8.17 Rate of choosing the alternative with the minimum expected value in the twostage decision-making when the number of alternatives left in the second stage is two for the different dominance levels.

noncompensatory strategies with two or three options in LEX and LEX-S are less likely to choose the worst option. In particular, when the second stage of processing is done with a compensatory strategy such as WAD, it is difficult to choose the worst possible outcome, and when the decision strategy such as LEX and LEX-S

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0.10 Dominance

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Rate of choosing the alternative with the minimum expected value

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DIS

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LEX

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Figure 8.18 Rate of choosing the alternative with the minimum expected value in the twostage decision-making when the number of alternatives left in the second stage is two for the different dominance levels.

Rate of choosing the alternative with the minimum expected value

0.15

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2nd STR CON DIF DIS EBA EQW LEX LEX−S MCD WAD

0.05

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DIS

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Figure 8.19 Overall rate of choosing the alternative with the minimum expected value in the two-stage decision-making when the number of alternatives left in the second stage is two.

requires little cognitive effort, the total cognitive effort is low and the worst possible option is difficult to choose. The probability of choosing the worst option depends on the number of options, the number of attributes, the variance in the importance of the attributes, and the presence or absence of a superior option, but surprisingly, this tendency was generally observed in all conditions.

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Rate of choosing the alternative with the minimum expected value

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DIS

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Figure 8.20 Overall rate of choosing the alternative with the minimum expected value in the two-stage decision-making when the number of alternatives left in the second stage is three.

On the other hand, when DIS was used to narrow down the first stage, throughout, or in the second stage, the probability of choosing the worst option was also decreased. The DIS strategy suggests that the worst possible option is likely to occur if people are blinded by salient attribute features. This feature of DIS suggests that when people make biased decisions based on attention to events, they are more likely to make bad decisions. In sum, the probability of choosing the worst option depends on the number of options, the number of attributes, the variance in the importance of the attributes, and the presence or absence of a superior option, but surprisingly, this tendency was generally observed in all conditions.

8.3.3 Relative accuracy defined by the difference from the minimum value and by Payne et al In this chapter the RA defined from the difference from the minimum value was calculated for each condition, and the RA of Payne et al. (1993) was also calculated for comparison. For the RA defined by the difference from the minimum value, Fig. 8.21 shows the results for different numbers of alternatives when the number of alternatives was reduced to two in the first stage to examine the two-stage strategy. The results of narrowing down the choices to three in the first stage are shown in Fig. 8.22. Similarly, the results at different numbers of attributes are shown in Figs. 8.23 and 8.24. Furthermore, the results at different dispersion levels for the last remaining options of two and three are shown in Figs. 8.25 and 8.26, and the results with and without dominance are shown in Figs. 8.27 and 8.28 and Figs. 8.29 and 8.30, respectively. Similarly, the RA as defined by Payne et al. (1993) was obtained in Figs. 8.31
8.40. Although these two indices are different in concept,

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EQW LEX

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LEX−S MCD WAD

0.00 1.00

0.75

10

Rate of choosing the alternative with the maximum expected value

0.75

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0.00 CON

DIS

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Figure 8.21 Relative accuracy defined by the minimum expected value in the two-stage decision-making when the number of alternatives left in the second stage is two for the different numbers of alternatives. 1.00

N Alt: 5

0.50

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2nd STR CON

0.75

DIF DIS

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8

EBA EQW LEX

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LEX−S MCD WAD

0.00 1.00

0.75

10

Rate of choosing the alternative with the maximum expected value

0.75

0.50

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0.00 CON

DIS

EBA

LEX

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Figure 8.22 Relative accuracy defined by the minimum expected value in the three stage decision-making when the number of alternatives left in the second stage is two for the different numbers of alternatives.

the results of the analysis show almost similar patterns. As can be seen from these figures, it is clear that compensatory decision strategies have high RA, but even noncompensatory strategies such as LEX and LEX-S, which limit the number of options to two or three, are less likely to choose the worst option. In particular,

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N Att: 3

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LEX−S MCD WAD

0.00 1.00

0.75

0.50

8

Rate of choosing the alternative with the maximum expected value

0.75

0.25

0.00 CON

DIS

EBA

LEX

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1st STR

Figure 8.23 Relative accuracy defined by the minimum expected value in the two-stage decision-making when the number of alternatives left in the second stage is two for the different numbers of attributes. 1.00

N Att: 3

0.50

0.25

0.00 1.00

2nd STR CON

0.75

DIF DIS

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5

EBA EQW LEX

0.25

LEX−S MCD WAD

0.00 1.00

0.75

0.50

8

Rate of choosing the alternative with the maximum expected value

0.75

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

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1st STR

Figure 8.24 Relative accuracy defined by the minimum expected value in the two-stage decision-making when the number of alternatives left in the second stage is three for the different numbers of attributes.

when the second stage of processing is performed in the compensatory type such as WAD, the RA is high. The pattern of RA is shown in Fig. 8.1. The pattern of RA varied depending on the number of alternatives, the number of attributes, the variance in the importance of the attributes, and the presence or absence of a superior

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1.00

Dispersion: High

0.50

0.25

2nd STR CON DIF DIS

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EBA EQW

1.00

LEX LEX−S MCD WAD

0.75

Low

Rate of choosing the alternative with the maximum expected value

0.75

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.25 Relative accuracy defined by the minimum expected value in the two-stage decision-making when the number of alternatives left in the second stage is two for the different dispersion levels. 1.00

Dispersion: High

0.50

0.25

2nd STR CON DIF DIS

0.00

EBA EQW

1.00

LEX LEX−S MCD WAD

0.75

Low

Rate of choosing the alternative with the maximum expected value

0.75

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.26 Relative accuracy defined by the minimum expected value in the two-stage decision-making when the number of alternatives left in the second stage is three for the different dispersion levels.

alternative, but surprisingly, this tendency was generally observed in all conditions. On the other hand, when DIS was used to narrow down the first stage, throughout, or in the second stage, the RA of the results was also low. It is easy to get the worst results as well as low RA, as shown earlier.

Computer simulation of bad decisions and good decisions

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1.00

Dominance

0.50

0.25

2nd STR CON DIF DIS

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EBA EQW

1.00

LEX LEX−S MCD WAD

0.75 Non Dominance

Rate of choosing the alternative with the maximum expected value

0.75

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.27 Relative accuracy defined by the minimum expected value in the two-stage decision-making when the number of alternatives left in the second stage is two for the different dominance levels.

1.00

Dominance

0.50

0.25

2nd STR CON DIF DIS

0.00

EBA EQW

1.00

LEX LEX−S MCD WAD

0.75 Non Dominance

Rate of choosing the alternative with the maximum expected value

0.75

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.28 Relative accuracy defined by the minimum expected value in the two-stage decision-making when the number of alternatives left in the second stage is three for the different dominance levels.

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Rate of choosing the alternative with the maximum expected value

1.00

0.75

2nd STR CON DIF DIS EBA

0.50

EQW LEX LEX−S MCD WAD

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.29 Overall relative accuracy defined by the minimum expected value in the twostage decision-making when the number of alternatives left in the second stage is two.

Rate of choosing the alternative with the maximum expected value

1.00

0.75

2nd STR CON DIF DIS EBA

0.50

EQW LEX LEX−S MCD WAD

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.30 Overall relative accuracy defined by the minimum expected value in the twostage decision-making when the number of alternatives left in the second stage is three.

8.3.4 Relative accuracy divided by cognitive effort (an index of efficiency) To examine the efficiency of the decision strategy, the value of RA divided by cognitive effort by Payne et al. (1993) is shown in Fig. 8.41 for different numbers of

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0.75 N Alt: 5

0.25

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DIF DIS

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8

Relative Accuracy defined by Payne, Bettman, Johnson (1993)

0.50

EQW LEX

0.25

LEX−S MCD WAD

0.00 1.00

0.75

10

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.31 Relative accuracy defined by Payne et al. (1993) in the two-stage decisionmaking when the number of alternatives left in the second stage is two for the different numbers of alternatives.

1.00

0.75 N Alt: 5

0.25

0.00 1.00

2nd STR CON

0.75

DIF DIS

0.50

8

Relative Accuracy defined by Payne, Bettman, Johnson (1993)

0.50

EBA EQW LEX

0.25

LEX−S MCD WAD

0.00 1.00

0.75

10

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.32 Relative accuracy defined by Payne et al. (1993) in the two-stage decisionmaking when the number of alternatives left in the second stage is two for the different numbers of alternatives.

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1.00

0.75 N Att: 3

0.25

0.00 1.00

2nd STR CON

0.75

DIF DIS

0.50

EBA

5

Relative Accuracy defined by Payne, Bettman, Johnson (1993)

0.50

EQW LEX

0.25

LEX−S MCD WAD

0.00 1.00

0.75

8

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.33 Relative accuracy defined by Payne et al. (1993) in the two-stage decisionmaking when the number of alternatives left in the second stage is two for the different numbers of attributes.

1.00

0.75 N Att: 3

0.25

0.00 1.00

2nd STR CON

0.75

DIF DIS

0.50

5

Relative Accuracy defined by Payne, Bettman, Johnson (1993)

0.50

EBA EQW LEX

0.25

LEX−S MCD WAD

0.00 1.00

0.75

8

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.34 Relative accuracy defined by Payne et al. (1993) in the two-stage decisionmaking when the number of alternatives left in the second stage is three for the different numbers of attributes.

Computer simulation of bad decisions and good decisions

163

1.00

Dispersion: High

0.50

0.25

2nd STR CON DIF DIS

0.00

EBA EQW

1.00

LEX LEX−S MCD WAD

0.75

Low

Relative Accuracy defined by Payne, Bettman, Johnson (1993)

0.75

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.35 Relative accuracy defined by Payne et al. (1993) in the two-stage decisionmaking when the number of alternatives left in the second stage is two for the different dispersion levels.

1.00

Dispersion: High

0.50

0.25

2nd STR CON DIF DIS

0.00

EBA EQW

1.00

LEX LEX−S MCD WAD

0.75

Low

Relative Accuracy defined by Payne, Bettman, Johnson (1993)

0.75

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.36 Relative accuracy defined by Payne et al. (1993) in the two-stage decisionmaking when the number of alternatives left in the second stage is two for the different dispersion levels.

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Escaping from Bad Decisions

1.00

Dominance

0.50

0.25

2nd STR CON DIF DIS

0.00

EBA EQW

1.00

LEX LEX−S MCD WAD

0.75 Non Dominance

Relative Accuracy defined by Payne, Bettman, Johnson (1993)

0.75

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.37 Relative accuracy defined by Payne et al. (1993) in the two-stage decisionmaking when the number of alternatives left in the second stage is two for the different dominance levels.

1.00

Dominance

0.50

0.25

2nd STR CON DIF DIS

0.00

EBA EQW

1.00

LEX LEX−S MCD WAD

0.75 Non Dominance

Relative Accuracy defined by Payne, Bettman, Johnson (1993)

0.75

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.38 Relative accuracy defined by Payne et al. (1993) in the two-stage decisionmaking when the number of alternatives left in the second stage is three for the different dominance levels.

Computer simulation of bad decisions and good decisions

165

Relative Accuracy defined by Payne, Bettman, Johnson (1993)

1.00

0.75

2nd STR CON DIF DIS EBA

0.50

EQW LEX LEX−S MCD WAD

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.39 Overall relative accuracy defined by Payne et al. (1993) in the two-stage decision-making when the number of alternatives left in the second stage is two.

Relative Accuracy defined by Payne, Bettman, Johnson (1993)

1.00

0.75

2nd STR CON DIF DIS EBA

0.50

EQW LEX LEX−S MCD WAD

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.40 Overall relative accuracy defined by Payne et al. (1993) in the two-stage decision-making when the number of alternatives left in the second stage is three.

alternatives when the number of alternatives is first narrowed down to two in the first stage to examine the two-stage strategy, as before. The results for the case where the options were narrowed down to three in the first stage are also shown in Fig. 8.42. Similarly, the results at different numbers of attributes are shown in

166

Escaping from Bad Decisions

1.00

0.75 N Alt: 5

0.50

0.25

0.00 1.00

2nd STR CON DIF DIS

0.50

8

RA / EIP

0.75

EBA EQW LEX

0.25

LEX−S MCD WAD

0.00 1.00

0.75

10

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.41 RA/EIP in the two-stage decision-making when the number of alternatives left in the second stage is two for the different numbers of alternatives. EIP, elementary information processes; RA, relative accuracy.

1.00

0.75 N Alt: 5

0.50

0.25

0.00 1.00

2nd STR CON DIF DIS

0.50

8

RA / EIP

0.75

EBA EQW LEX

0.25

LEX−S MCD WAD

0.00 1.00

0.75

10

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.42 RA/EIP in the two-stage decision-making when the number of alternatives left in the second stage is three for the different numbers of alternatives. EIP, elementary information processes; RA, relative accuracy.

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167

Figs. 8.43 and 8.44. Furthermore, the results at different dispersion levels for the last remaining options of two and three are shown in Figs. 8.45 and 8.46, and the results with and without dominance are shown in Figs. 8.47 and 8.48 and Figs. 8.49 and 8.50, respectively. 1.00

0.75 N Att: 3

0.50

0.25

0.00 1.00

2nd STR CON DIF DIS

0.50

5

RA / EIP

0.75

EBA EQW LEX

0.25

LEX−S MCD WAD

0.00 1.00

0.75

8

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.43 RA/EIP in the two-stage decision-making when the number of alternatives left in the second stage is two for the different numbers of attributes. EIP, elementary information processes; RA, relative accuracy. 1.00

0.75 N Att: 3

0.50

0.25

0.00 1.00

2nd STR CON DIF DIS

0.50

5

RA / EIP

0.75

EBA EQW LEX

0.25

LEX−S MCD WAD

0.00 1.00

0.75

8

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.44 RA/EIP in the two-stage decision-making when the number of alternatives left in the second stage is three for the different numbers of attributes. EIP, elementary information processes; RA, relative accuracy.

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1.00

0.75 Dispersion: High

0.50

0.25

2nd STR CON

RA / EIP

DIF DIS

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EBA EQW

1.00

LEX LEX−S MCD WAD

0.75

Low

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.45 RA/EIP in the two-stage decision-making when the number of alternatives left in the second stage is two for the different dispersion levels. EIP, elementary information processes; RA, relative accuracy.

1.00

0.75 Dispersion: High

0.50

0.25

2nd STR CON

RA / EIP

DIF DIS

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EBA EQW

1.00

LEX LEX−S MCD WAD

0.75

Low

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.46 RA/EIP in the two-stage decision-making when the number of alternatives left in the second stage is three for the different dispersion levels. EIP, elementary information processes; RA, relative accuracy.

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0.75

Dominance

0.50

0.25

2nd STR CON

RA / EIP

DIF DIS

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EBA EQW

1.00

LEX LEX−S MCD WAD

0.75 Non Dominance

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.47 RA/EIP in the two-stage decision-making when the number of alternatives left in the second stage is two for the different dominance levels. EIP, elementary information processes; RA, relative accuracy.

1.00

0.75

Dominance

0.50

0.25

2nd STR CON

RA / EIP

DIF DIS

0.00

EBA EQW

1.00

LEX LEX−S MCD WAD

0.75 Non Dominance

0.50

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.48 RA/EIP in the two-stage decision-making when the number of alternatives left in the second stage is three for the different dominance levels. EIP, elementary information processes; RA, relative accuracy.

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1.00

0.75

2nd STR CON

RA / EIP

DIF DIS EBA

0.50

EQW LEX LEX−S MCD WAD

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

NON

1st STR

Figure 8.49 Overall RA/EIP in the two-stage decision-making when the number of alternatives left in the second stage is two. EIP, elementary information processes; RA, relative accuracy.

1.00

0.75

2nd STR CON

RA / EIP

DIF DIS EBA

0.50

EQW LEX LEX−S MCD WAD

0.25

0.00 CON

DIS

EBA

LEX

LEX−S

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Figure 8.50 Overall RA/EIP in the two-stage decision-making when the number of alternatives left in the second stage is three. EIP, elementary information processes; RA, relative accuracy.

As can be seen from these figures, WAD is relatively efficient among the compensatory decision strategies, but the two-step strategy using WAD after narrowing down the number of alternatives to two or three in the noncompensatory LEX and LEX-S is the most efficient. When the number of alternatives is narrowed down

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using a strategy that requires less cognitive effort, such as LEX and LEX-S, the total cognitive effort is also lower and it is easier to select alternatives with high RA, indicating high efficiency. This tendency varies depending on the number of choices, the number of attributes, the variance in the importance of the attributes, and the presence or absence of a superior option. However, unexpectedly, the efficiency trend of the lexicographic strategy was generally observed in all conditions. On the other hand, when DIS was used to narrow down the first stage, DIS was used throughout, or DIS was used in the second stage, the efficiency of the decision strategy was also low. The DIS is a strategy to adopt an option if even one of the attributes to which attention is directed exceeds the sufficient condition.

8.3.5 Best choice rate In this chapter, we calculated the rate of choosing the maximum expected value among the alternatives as the rate of choosing the best alternative in each condition. Fig. 8.51 shows the results for different numbers of alternatives when the number of alternatives is reduced to two in the first stage to examine the two-stage strategy. The results of narrowing down the choices to three in the first stage are also shown in Fig. 8.52. Similarly, the results at different numbers of attributes are shown in Figs. 8.53 and 8.54. Furthermore, the results at different dispersion levels for the last remaining options of two and three are shown in Figs. 8.55 and 8.56, and the results with and without dominance are shown in Figs. 8.57 and 8.58 and Figs. 8.59 and 8.60 for overall average values, respectively. As can be seen from these figures, it is clear that the compensatory decision strategy does not choose the worst option, but even the noncompensatory strategies with two or 1.00

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Figure 8.57 Rate of choosing the alternative with the maximum expected value in the twostage decision-making when the number of alternatives left in the second stage is two for the different dominance levels.

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Figure 8.60 Overall rate of choosing the alternative with the maximum expected value in the two-stage decision-making when the number of alternatives left in the second stage is three.

three options in LEX and LEX-S are likely to choose the best option. In particular, when the second stage of processing is done with a compensatory strategy such as WAD, it is difficult to choose the best possible option, and when the decision strategies such as LEX and LEX-S require little cognitive effort, the total cognitive effort is low and the worst possible outcome is difficult to choose. The probability of choosing the best option depends on the number of options, the number of attributes, the variance in the importance of the attributes, and the presence or absence of a superior option, but surprisingly, this tendency was generally observed in all conditions. On the other hand, when DIS was used to narrow down the first stage, DIS was used throughout, or DIS was used in the second stage, the probability of choosing the best option was also decreased. The DIS strategy suggests that the worst possible outcome is likely to occur if people are blinded by salient attribute features. This feature of DIS suggests that when people make biased decisions based on attention to events, they are more likely to make bad decisions. The probability of choosing the best option depends on the number of options, the number of attributes, the variance in the importance of the attributes, and the presence or absence of a superior option, but surprisingly, this tendency was generally observed in all conditions. This pattern of the result is a mirror image of the worst decision cases.

8.4

General discussions

The results obtained from the computer simulations so far indicate that using an attributebased strategy such as LEX or LEX-S for narrowing down the options in a two-stage decision-making process, which searches across multiple options for a single attribute,

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can lead to relatively accurate decisions with the same cognitive effort as decisions made with a single strategy. The results show that the RA of the attributive strategies is higher with the same cognitive effort as the single strategy. In previous research on the decision-making process, decision makers have been reported to first narrow down the options to a small number using a decision strategy such as LEX and then make a weighted additive decision to reduce cognitive effort (Bettman, 1979; Takemura, 1993, 2014, 2019), but this study’s Brandst¨atter, Gigerenzer, and Hertwig (2006) proposed a strategy similar to LEX, called priority heuristics. They proposed a strategy similar to LEX, called priority heuristics, which is characterized by its low cognitive load, high RA, and difficulty in choosing the worst option, but it turns out that the two-step decision strategy from LEX to WAD, which is often taken by ordinary people, is highly efficient (Brandst¨atter et al., 2006). In view of the goal of this book, which is to avoid the worst decision, it is suggested that it is desirable to narrow down the options to a few with the most important attributes according to the decision maker’s values and then to consider them in an additive manner. If there is a time crunch or an emergency, it may be acceptable to use only the lexicographic (LEX) method of decision-making. In this chapter’s research, unlike Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute Decision-Making Process, the number of options left in the first stage was two and three, a combination of all strategies, but nevertheless, the results suggest that the two-stage strategy from LEX to WAD is highly efficient and avoids the worst decisions. In this experiment the CON, DIS, and EBA groups, which are strategies that use necessary conditions, were set to continue searching until there were only three options left when narrowing down the choices, and this may have resulted in relatively high EIP for these strategies. It is necessary to take this point into consideration in the future.

8.5

Conclusion

In this study, using the basic framework of Payne et al.’s (1993) computer simulation of decision strategies, we examined multistage decision strategies that they did not deal with, defining the rate of choosing the worst option and other decision efficiency indices. In this study, we set two stages in the decision-making process, taking into account that the decision strategy may change during the process, and conducted computer simulations assuming that the decision strategy changes during the decision-making process. In other words, as in Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute Decision-Making Process, we considered combinations of two stages for all of the decision strategies discussed and conducted computer simulations. In this computer simulation, we examined which decision strategies and which combinations of decision strategies are efficient in avoiding the worst decisions, and we discussed the psychological functions of these strategies.

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In this study, we examined two-stage decision strategies and found that narrowing down the choices to two using LEX and then comparing them with WAD is efficient in that it exhibited relatively low cognitive load and is accurate, and it is also good in that it avoids the worst choices. Considering this in a realistic situation, the decision maker can make a decision similar to the result of weighted additive decision-making from the beginning if he narrows down the options by the attribute that is most important to him, by the next when he cannot decide, and the final candidates to two. In this chapter the RA is also measured by the weighted additive method, as in the research of Payne et al. As discussed in Chapter 6, Multiattribute DecisionMaking, Multiobjective Optimization, and the Additive Conjoint System, it can be considered a scalar function in a multiobjective optimization problem and can be interpreted as having a certain degree of rationality.

References Bettman, J. R. (1979). An information processing theory of consumer choice. Reading, MA: Addison Wesley. Brandst¨atter, E., Gigerenzer, G., & Hertwig, R. (2006). The priority heuristic: Making choices without tradeoffs. Psychological Review, 113, 409
432. Kohli, R., & Jedidi, K. (2007). Representation and inference of lexicographic preference models and their variants. Marketing Science, 26, 380
399. Martignon, L., & Hoffrage, U. (2002). Fast, frugal and fit: Simple heuristics for paired comparisons. Theory and Decision, 52, 29
71. Payne, J. W., Bettman, J. R., & Johnson, E. J. (1993). The adaptive decision maker. Cambridge: Cambridge University Press. Takemura, K. (1993). Protocol analysis of multistage decision strategies. Perceptual and Motor Skills, 77, 459
469. Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical descriptions of human choice behavior. Tokyo: Springer. Takemura, K. (2018). Avoiding bad decisions: From the perspective of behavioral economics. In: Keynote paper presented at the international congress of applied psychology, Montreal, Canada. Takemura, K. (2019). Foundations of economic psychology: A behavioral and mathematical approach. New York: Springer. Takemura, K., Haragichi, R., & Tamari, Y. (2015). Tazokusei Isikettei Katei ni okeru Kettei Houryaku no Ninchiteki Doryoku to Seikakusa: Keisanki Simyureisyon wo Mocihita Koudou Ishiketteironteki Kentou [Cognitive effort and accuracy of decision strategies in multi-attribute decision making process: A behavioral decision theoretic approach using computer simulation technique]. Ninchikagaku, 22, 368
388. (in Japanese). Takemura, K., Tamari, Y., & Ideno, T. (2021). Simulation and experiment of bad decision making: Examination of two stage decision strategy. Unpublished Manuscript, Department of Psychology, Waseda University. Yee, M., Dahan, E., Hauser, J. R., & Orlin, J. (2007). Greedoid-based noncompensatory inference. Marketing Science, 26, 532
549.

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This chapter is based on experimental enemy research by Takemura (2018) and Takemura, Tamari, and Ideno (2021) on decision strategy as a cognitive strategy in multiattribute decision-making processes. In Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two-Stage Decision Strategies in a Multiattribute Decision-Making Process, and Chapter 8, A Computer Simulation of Bad Decisions and Good Decisions: An Extended Analysis of Two-Stage Decision Strategies, I added various second-stage decision strategies to the analysis of Payne, Bettman, & Johnson (1993) and analyzed them based on various indicators of decision-making. It was also found that the second-stage decision strategy, lexicographic screening, and the additive evaluation on a few alternatives, is effective in avoiding worst case decisions. However, we examined whether such a second-stage strategy is really effective in actual decision-making tasks, and how it compares with compensatory strategies such as additive strategies, using the information monitoring method, a technique for tracking the decision-making process.

9.1

Implementation of the additive decision strategy and bad decision: a pilot study

9.1.1 Previous research on the choice accuracy and its problem The additive decision strategy was considered to be a normative strategy as in the previous computer simulation study (Payne, Bettman, & Johnson, 1993; Takemura, Haraguchi, & Tamari, 2015; Thorngate, 1980). The additive strategy has been used as basis of decision accuracy index in empirical research (Hahn, Lawson, & Lee, 1992; Jacoby, Speller, & Berning, 1974; Jacoby, Speller, & Kohn, 1974; Malhotra, 1982; Takemura, 2014, 2019). A decrease in choice accuracy in actual decision-making was associated with an increase in the number of alternatives (Hahn et al., 1992; Jacoby et al., 1974; Malhotra, 1982). It has also been reported that there is a nonlinear relationship (inverted U-shape) between the number of alternatives and choice accuracy, and that time pressure is a condition for the occurrence of information overload (Hahn et al., 1992). Several studies have provided examples of a positive relationship between selection accuracy and the number of attributes (Jacoby et al., 1974; Malhotra, 1982; Malhotra, Jain, & Lagakos, 1982). Lurie (2004) also reported that accuracy decreases as the number of alternatives or attributes increases, or as the distribution of attribute levels becomes more uniform. However, previous studies have not examined worst case decision-making, nor have they fully examined the impact of each strategy on decision quality. Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00010-7 © 2021 Elsevier Inc. All rights reserved.

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9.1.2 Purpose of the experiment The weighted-additive decision strategy (WAD) is a compensatory decision strategy, and as pointed out in Chapter 6, Multiattribute Decision-Making, Multiobjective Optimization, and the Additive Conjoint System, it is regarded as a relatively rational decision-making strategy due to its correspondence with the scalarized arithmetic of multiobjective optimization. In addition, WAD is generally regarded as a rational decision strategy and is also used as a criterion for the index of relative accuracy of decision-making in the study by Payne et al. In this study, as a preliminary study, we will first examine the results of having subjects actually perform the WAD.

9.1.3 Method Participants: Thirty-two male and female at Waseda University undergraduates enrolled in the introductory psychology course participated in the experiment. Task: The stimuli were information matrices representing six different laptop computers. Laptop computers were chosen as the choice sets because most university students are involved and familiar with them. Each row of the matrix represented one attribute of laptop computers, and each column was labeled with a letter representing each laptop computer (e.g., product A). Attributes were chosen on the basis of an exploratory study involving 52 undergraduates. Six attributes most frequently listed as important in selecting a laptop computer were used in the present study. These were (1) price, (2) weight, (3) warranty, (4) battery type, (5) CPU, and (6) memory. There were three levels of value on each attribute: above average, average, and below average. In the standard introduction the experimenter told the participants that they should try to apply their tasks to them as accurately as possible in making choices among the sets of laptop computers. Participants were instructed not to deviate in any way from their prescribed strategies. They were forewarned that they would be questioned on how they executed the decision strategies afterward. The subjects were then given a leaflet in which each decision strategy was described in general terms. Participants were also asked to rate attribute importance and preference order of alternatives to perform conjoint analysis. We compare the results of conjoint analysis and output of selecting alternative by participants.

9.1.4 Result and discussion Interestingly, 19% of additive strategy chose the worst and second worst alternatives and 28% of the additive strategy chose the below average alternative, although 25% of the additive strategy chose the best alternative. Although most of the participants understood what additive strategy is, they could not perform additive strategy. These results indicated that it was very difficult to perform additive strategy assumed in the additive conjoint structure.

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Those findings imply that additive rule is not practical and may not lead the best decision in real lives. In addition, past studies in social psychology reveal that people seeking rationality tend to be rather susceptible to depression and a low level of subjective welfare (Schwartz et al., 2002). Considering these aspects, in the author’s opinion, purposely placing oneself in the multidimensional confusion to consider multiattribute decision-making while recognizing rationality as an important standard might lead to “good decision” and avoiding “bad decision.” But it is a paradoxical relation between the aim and performance.

9.2

How to examine the effect of a second-stage decision-making strategy using process tracking on the bad decisions

9.2.1 Issues to be examined and the purpose of this study Takemura et al. (2015) considered that in everyday decision-making situations, there are not only cases in which only one strategy is used, but also cases in which multiple options are narrowed down using one decision-making strategy and then compared using another strategy. In this study, we extended research Payne et al. (1993) and conducted a computer simulation study on the case where two decision strategies are combined as second-stage decision-making. As a result, it was shown that in multiattribute decision-making, it is easier to make a faster and more accurate decision if the decision strategy that looks at attributes is used to narrow down the options and then another strategy is used to make the decision. In addition, as shown in Section 9.1, it was suggested that implementing the typical additive decision strategy of the compensatory type is difficult even with a not so large number of alternatives and may instead lead to the worst possible choice. However, although computer simulations of second-stage decision-making have been studied, it is not clear to what extent people are convinced of the difficulty of the decision or that they have made a good choice when they actually make such a decision, and to what extent the simulations reflect the senses of people searching for information. It is not clear to what extent the simulation reflects the senses of the information seekers. In this study, we examined the decision-making process by having people experimentally perform a choice task with a decision-making strategy as a simulation of first- and second-stage decision-makings. By comparing the results of computer simulations with those of actual human decision-making, we examined the characteristics of both and considered how the decision-making strategies affect the decision-making process and the psychological state after decisionmaking. In this study, we further developed the experiment by using information monitoring software to present and use an information presentation board with a touch panel system and examined which attributes subjects focused on and whether they actually used the strategy correctly.

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9.2.2 Method of monitoring information acquisition as a process tracking technique As a method for examining decision-making strategies, the process tracking technique has been developed (Takemura, 2014, 2019). The hypothetical tracking technique is mainly based on the following two methods: (1) the verbal protocol method, in which experimental participants are asked to dictate their internal thoughts during the decision-making process in a choice situation, and the recording is used to examine what decision-making strategies were used; and (2) the eye gaze method, in which an eye camera is used to track the gaze of experimental participants during the decision-making process. In this study the verbal protocol method is used to examine the decision-making strategies used, the eye gaze method is used to track the gaze of the participants in the decisionmaking process, and the method of monitoring information acquisition is used to present the choices and attributes in a matrix format and allow the participants to search for information. In this study the information monitoring acquisition method is used. In this study, we use the method of monitoring information acquisition. The method of monitoring information acquisition is a method that clarifies which attributes of which choices and in what order the experimental participants acquired the information from the group of choices until they reached a decision. Usually, in this method, information about each option is not given to the participants at the beginning of the decision task. In this method the participants are not given any information about the options at the beginning of the decision-making task but are given information about the attributes of each option from an information board. In this information board the choices are arranged in columns and the attributes in rows, in a matrix format. The information monitoring method allows us to see which choices and attributes the participants paid attention to, and in what order they explored the information, because the participants freely and independently explore the information they want to see.

9.2.3 Overview of the experiment In this study, we asked participants to perform two tasks: a multiattribute decisionmaking task using the information monitoring method and a questionnaire, after specifying the decision strategy. In the multiattribute decision-making task the participants were asked to choose a decision strategy after the decision strategy was specified in advance. To check and analyze whether the participants were able to use the decision strategies specified by the experimenter, we used an information monitoring program in Visual Basic. This program was implemented on a PC with an information presentation board that could record the changes in the attributes that the participants paid attention to when the stimuli were presented. For the stimuli, we used a decision-making task in which participants were asked to purchase a laptop computer. A combination of decision strategies was created in advance for the participants to make a second-stage decision.

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Using the results of the questionnaire the importance of the attribute and the satisfaction level of each level were multiplied to calculate the score for each option, and the options with the highest satisfaction level (the best option) and the lowest satisfaction level (the worst option) were estimated for each participant. After that the probability of choosing the best and worst options for each strategy (best option adoption rate and worst option adoption rate) was calculated. We also calculated the probability that the worst option existed when we narrowed down the options to two choices in the first-stage (crisis rate). The general flow of this experiment is shown in Fig. 9.1. Before starting the experiment the experimenter explained to the participants that they had to choose an option according to the specified decision method, and that the decision-making task was to purchase a “laptop computer.” Next, the decision-making strategy used in this trial was explained on the computer screen. The participants were instructed on the decision strategy to be used for each of the second-stages: narrowing down the six choices to two (first-stage) and deciding on one of the two choices (second-stage). After the strategies were explained the experimenter checked that the participants had no questions and confirmed their understanding of the strategies. Specifically, each time the strategy was changed, and the experimenter presented the “confirmation of understanding of the decision strategy” questionnaire to the participants and asked them to choose the strategy to be used from the options to confirm their understanding of the strategy. The participants were asked to select the strategy to be used from a list of options and to confirm that they understood

Figure 9.1 Flow of the experiment.

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the strategy. The procedure of explanation and confirmation of the strategy was repeated until the participants were able to select the specified strategy. After the confirmation the touch panel used in the decision-making task was explained, and a practice trial was conducted. The subject of the practice trial was a task assuming the scene of renting an apartment. After the practice trial was over, we moved to the main trial. The experimenter instructed the participants that “the task from here on is to be performed assuming the situation of purchasing a laptop computer” and had them performed the choice task using the decision strategy that had been taught beforehand. After completing the choice task in this trial, the participants were asked to answer the “postdecision questionnaire.” In the “postdecision questionnaire” the participants were asked to indicate the choices they made using the specified decision strategy, as well as the difficulty and confusion they felt when using the specified strategy, the uncertainty in the choice process, and the uncertainty in deciding on the choice, using Takemura’s (1996) “decision-making scale.” As soon as they had completed this form, we moved on to the next trial. After the choice task was performed for all combinations of strategies (36 combinations), the participants were asked to answer the questionnaire “evaluation of the decision-making task,” and the experiment was terminated with a reward. The “evaluation of the decision-making task” consisted of three items: the degree of satisfaction with the value of each level (0
100 points), the degree of importance placed on each attribute when performing the product selection task (7-point scale), and the evaluation scores for the 18 PC options. To conduct conjoint analysis the combinations of attributes and levels used in the experiment were created using R software. This was done to identify the “good” options that differed among individuals and to check whether the participants were able to choose the “good” one from the group of options when they actually used the decision strategy. The average experimental time per participant was 2.5 hours.

9.2.4 Methods of the experiment 9.2.4.1 Participants in the experiment The participants of the experiment were 40 university students (15 males and 25 females, mean age 21.28 years, standard deviation 5 1.58).

9.2.4.2 Experimental equipment In this experiment, we used Visual Basic program software for information monitoring for the stimulus presentation and the information search board. For time measurement, we used the stopwatch application of iPhone.

9.2.4.3 Tasks and strategies used in the experiment In this study, we used a multiple-choice, multiple-attribute decision-making task (6 options 3 6 attributes) and two types of questionnaires.

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In the multiattribute decision-making task, the experimenter specified the decision-making strategy in advance and taught it to the participants before having them performed the choice task. In the multiattribute decision-making task the experimenter specified the decision strategy in advance and taught it to the participants. For the choice task, we used as stimulus subjects a decision task that assumed a situation, in which the participants rented an apartment in the practice trial, and a situation in which they purchased a laptop computer at an electronics retail store in the main trial. Two types of questionnaires were used: the “postdecision question” and the “evaluation of the decision-making task.” The “postdecision questionnaire” was administered between trials, and participants were asked to describe the difficulty and confusion they felt when using the specified strategy, the uncertainty in the selection process, and the uncertainty in deciding on the alternatives. The “evaluation of the decision-making task” was conducted after all the trials were completed, and the participants were asked to answer whether they were able to choose a “good” option from a group of alternatives when they used the decision strategy. In this experiment, as in Takemura (1996), the following eight strategies were used: equal-weighted (EQW), weighted-additive (WAD), additive diffrence (DIF), majority of confirming dimension (MCD), conjunctive (CON), disjunctive (DIS), lexicographic (LEX), and elimination by aspects (EBA). Four of the eight strategies, CON, DIS, EBA, and LEX, were used in the second-stage, and all eight of them were used in the third stage. Although there are 32 possible combinations, we excluded combinations in which the same strategy is used in both the first and second-stages (e.g., CON 1 CON and DIS 1 DIS) because they are unnatural as choices in multistage decision-making in our daily lives and used 28 second-stage strategies. We also used eight first-stage strategies for each strategy. The order in which the 36 strategies were used was randomized among the subjects to avoid order effects and learning effects.

9.2.4.4 Experimental stimuli In this experiment a computer screen was used as an information presentation board, and a table with six alternatives and six attributes that each alternative had in common was presented. Fig. 9.2 shows the actual stimulus screen. Table 9.1 shows the attributes and levels of the stimuli. The attributes are “price,” “weight,” “battery life,” “warranty period,” “CPU,” and “memory capacity,” which can be expressed numerically and have a monotonic relationship with the level. The levels of the attributes of the laptops used as choices were scored as 1, 2, and 3 points for each of the three levels using the EQW strategy, and the scores were balanced among the choices so that any choice would have 12 points. To avoid the order effect of the trials, the presentation position of each option was randomized in each trial.

9.2.4.5 Instruction The following instruction was given when the experiment was conducted. In the following the experimental procedure and instruction are shown

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Figure 9.2 Example of stimulus presentation screen (in Japanese).

Table 9.1 Attributes and their levels. Attribute Price (yen) Weight (kg) Battery duration (h) Warranty period (year) CPU (GHz) Memory capacity (GB)

Level 60,000 0.8 5 1 1.5 4

80,000 1.2 10 2 2.0 8

100,000 1.6 15 3 2.5 16

according to the time sequence of the experiment. The instructions are shown in italics. Thank you very much for taking time out of your busy schedule to participate in this experiment today. The experiment you will participate in today is an experiment on product selection. It will take about 2.5 hours, including the explanation, with two breaks in between. If there is anything you do not understand during the explanation, please do not hesitate to ask. Also, if you feel unwell during this experiment, you can immediately stop the experiment, so please do not hesitate to ask for help. If you agree to participate in this experiment, please fill out the consent form at hand.

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9.2.4.6 Instruction of information monitoring method The experimenter gave the following instructions while switching between computer screens. What we are going to ask you to do now is to decide on one option that you think is the best among the multiple options presented on the computer screen. In doing so, you will be asked to make a choice according to the method we have specified. Now, please proceed to the actual screen. Press the up arrow key to go to the next slide, and press the down arrow key to go back to the previous slide. (Have them read the screen.)

As soon as the participants finished reading the explanation of the experiment, the experimenter gave them the following instructions and explained the actual strategy and combination of strategies to be taken on the computer. (Repeat the process Kx for 36 times.) KThe following is the explanation of the strategy. As before, please read at your own speed. If there is anything you do not understand, please do not hesitate to ask for help. (Have the experimenter read through the screen.) After finishing the explanation, the experimenter gave a detailed explanation and checked whether there were any questions or doubts. When there were no questions or doubts, the experimenter checked whether the participants had understood the strategy correctly. At that time, the following instruction was given. I will now confirm the strategy to be used in this experiment. Please answer these questions. (Show them the questionnaire.)

At this point the experimenter showed the participants the confirmation questionnaire with the explanation of each strategy and asked them to orally answer the correct number as the explanation of the strategy to be used in the first and secondstages, respectively. If the answer was correct, the participant proceeded to the next stage. If the answer was incorrect, the explanation was given again to ensure the participant’s understanding. When the participants understood the decision strategy, we moved on to the practice trials. At that time, we gave the following instruction: Now, I would like you to perform the practice task once. Using this touch panel, please choose an option according to the strategy specified earlier. As you can see, the specific values of the features of all the choices are hidden, but if you tap the button of the feature you want to see, you can see the specific value, such as “70,000” for “price” or “30 square meters” for “size.” Tap on the button you want to see, and proceed to examine the features. Also, please signal me twice, when you have narrowed down the choices to two, and when you have decided on one. Now touch the panel at any time to begin.

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The experimenter checked whether the participants understood the content of the decision strategy and the flow of the trial and moved on to the main trial. At that time, the following instruction was given. I will ask you to follow the flow you have just followed for the main trial. Do you have any questions? (Receiving questions) Now we will start the main trial. Please make a choice based on the assumption that you are actually going to purchase a laptop. As before, please signal me twice, when you have narrowed down the choices to two, and when you have decided on one. Now touch the panel at any time to start.

At this time, the experimenter pressed the stopwatch at the same time as the participant started and measured the time until the cue or response was given. The time measured was written on the recording sheet.

9.2.4.7 Questionnaire The experimenter administered the questionnaire method as soon as the participants confirmed the signal that they had decided on one of the options. At that time, the following instructions were given: (※From 1st to 35th trial) xThank you for your time. Next, please answer this questionnaire. (※From 1st to 35th trial)

After confirming that the participants had finished filling out the questionnaire, the following instruction was given and the participants returned to the part K. Now, I will ask you to choose the best option in the same way using a different strategy. ( 36th time)

After confirming that the participants had finished filling out the questionnaire, the following instructions were given to them, and they were asked to answer questions about the order of the attributes they considered important, the degree of importance of each attribute, the degree of satisfaction with the values of each level, and the evaluation of the alternatives. When the participants had finished filling out the form, we told them that the entire experiment was over and gave them a reward to end the experiment.

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Results and discussion of the experiment

9.3.1 Indicators used in the analysis As indicators used in the analysis, “decision time” was calculated by the information monitoring method, and “best option” and “worst option” were calculated by the questionnaire method. In addition, the indicators of “adoption rate of the best option,” “adoption rate of the worst option,” and “crisis rate” were calculated using both the information monitoring method and the questionnaire method and used in the analysis. Table 9.2 shows the list of indicators used in the analysis and their summary.

9.3.2 Relationship between decision time and worst choice adoption rate Figs. 9.3 and 9.4 show scatter plots of the worst option adoption rate and decision time for each decision strategy. The horizontal axis shows the decision time and the vertical axis shows the adoption rate of the worst option. The different levels of gray letters in the figure indicate the decision strategy used in the first-stage, and the letters indicate the decision strategy used in the second-stage. The WAD, DIF, and EQW strategies used in the first-stage strategy had long decision times and high worst choice adoption rates. In contrast, DIS, LEX, and EBA, which were used in the first-stage strategy, had shorter decision times but tended to have lower adoption rates. In addition, the second-stage strategy using the EQW strategy in the second-stage generally showed a high adoption rate. In the weighted worst alternative adoption rate, the WAD, DIF, and EQW strategies used in the first-stage strategy had long decision times, and among them, the EQW, first-stage strategy, had a high adoption rate. In contrast, DIS, LEX, and EBA, which were used in the first-stage strategy, had shorter decision times, but their adoption rates tended to be lower. In addition, the strategy that used LEX in the first-stage tended to have a shorter decision time and a lower adoption rate than the strategy that used CON in the first-stage. In Figs. 9.3 and 9.4, when WAD, DIF, and EQW were used in the first-stage strategy, the decision time was longer, but the adoption rate tended to be higher. In contrast, when LEX, DIS, and EBA were used in the first-stage strategy, the decision time was shorter, but the adoption rate tended to be lower. This indicates that the adoption rate of the worst option does not decrease in proportion to the decision time. When EBA was used in the first-stage, the decision time was short and the adoption rate was low in both graphs, indicating that the strategy did not allow the experimental participants to choose the worst option efficiently. This may be due to the fact that the EBA strategy “exclude attributes of importance that are less than the desired level” was used to exclude the worst options. In both figures the adoption rate was less than 0.2 in both cases. In other words, it was difficult to select the worst option regardless of which strategy was used. However, even EBA 1 EQW, which selected the worst option by conjoint analysis the most, selected the worst option only five times, and we could not analyze the

Table 9.2 List of indicators used for the analysis. Analysis method Information monitor ring method Questionnaire method

Index

Explanation of indicators Decision time

Best choice

Best choice based on conjoint analysis Best choice based on weight estimation

Worst choice

Worst choice based on conjoint analysis Worst choice based on the weight

Indicators obtained by the information monitoring acquisition method and the questionnaire method

Best choice rate

Worst choice rate

Crisis rate

Best option adoption rate by conjoint analysis The weight of the best choices acceptance rate by weight estimation Worst option adoption rate by conjoint analysis Worst option adoption rate by weight estimation Crisis rate based on conjoint analysis Crisis rate based on weight estimation

Time required for participants to make a decision from the start of the choice task to make decision Choices were evaluated by questionnaire, choices that the sum of the utilities of each level is the highest Scores are given for each option according to “degree of importance for each attribute satisfaction of each level value of the attribute” and the option with the highest value of the total score The option with the lowest score. The sum of the utilities was evaluated using a questionnaire The option with the lowest score according to “degree of importance for each attribute and satisfaction level value of the attribute” Percentage of all trials with the best option from conjoint analysis Percentage of all trials in which the best option adoption rate based on weight estimation Percentage of worst option adopted based on conjoint analysis Percentage of worst option adopted based on weight estimation Probability that the worst option existed at the second-stage based on conjoint analysis Probability that the worst option existed at the second-stage based on weight estimation

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Figure 9.3 Relationship between worst choice adoption rate based on conjoint analysis and time taken for decision (decision time).

Figure 9.4 Relationship between worst choice adoption rate based on weight estimation and time taken for decision (decision time).

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adoption rate of the worst option sufficiently. Therefore, as a future task, we can increase the number of worst choice adoptions by increasing the sample size of the experimental participants.

9.3.3 Worst choice rate 9.3.3.1 First-stage strategy Fig. 9.5 shows a graph of the adoption rate of the worst option for each first-stage strategy. First, we conducted a correlation analysis between the adoption rate of the worst option by conjoint analysis and the adoption rate of the worst option with weight estimation, and found no significant correlation with a correlation coefficient of 0.08. Although this is a very low value and raise a methodological problem, we considered that the two values are different indicators. Fig. 9.5 shows that MCD and EBA had the lowest adoption rates among the first-stage strategies, both by conjoint analysis and by weighted options (subjective

Figure 9.5 Worst option choice rate based on the first-stage strategy.

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worst options). In terms of the adoption rate of the worst option by conjoint analysis, WAD and EQW had the highest adoption rate, followed by DIF and LEX. In the weighted worst option adoption rate, CON, EQW, DIS, and LEX had the highest adoption rates in that order. The correlation between the two worst options was 0.08, and there was a difference in the order of the two adoption rates. The common denominator of the two worst adoption rates was that MCD and EBA had the lowest adoption rates among all first-stage strategies to the same extent, and EQW had the highest adoption rate in both cases. First, the reason for the low adoption rate of MCD is that the worst option was omitted because the option with “more superior attributes” was left in the tournament format in the “strategy of choosing two arbitrary options and comparing the attributes one by one and leaving the option with more superior attributes.” The reason for the low adoption rate of EBA is that the participants selected the remaining choices after looking at the most important attributes and eliminating the choices that did not meet their criteria, so they adopted the choices that were superior in the features they considered important, making it difficult to select the worst choices. On the other hand, the reason why the adoption rate of EQW was high is that this strategy is based on the addition of the scores of the goodness of the characteristics without weighting, so the attributes that the participants considered important were also calculated with the same weight, which is thought to have resulted in the inclusion of many worst choices.

9.3.3.2 Second-stage strategy Fig. 9.6 shows the adoption rates of the second-stage strategy for the conjoint analysis and the weighted worst option. Fig. 9.6 shows that the strategies with the lowest adoption rates in both the conjoint analysis and weighted worst choice adoption rates are DIS 1 WAD, followed by LEX 1 WAD, LEX 1 CON, and CON 1 LEX. Also, in both conjoint analysis and weighted worst choice adoption rate, the combination of LEX as the first-stage strategy tended to have the lowest adoption rate in general. The reason for this is that in LEX, the most important features are compared and the best choice is selected, so the best choice in terms of the features that are definitely important is left in the second-stage, which is thought to have led to the result that it is difficult to select the worst choice. On the other hand, DIS 1 WAD did not choose any of the worst options. Furthermore, the adoption rate of the DIS combination was also lower than expected in the firststage; the reason for the low adoption rate of DIS 1 WAD is thought to be that it did not choose the worst option because WAD was performed in the second-stage. However, this result was different from that of the computer simulation.

9.3.3.3 Rate of the worst option choice for each strategy of a combination of the first- and second-stage strategies Fig. 9.7 shows the adoption rates of the conjoint analysis and the weighted worst choices for the one- and second-stage strategies. Note that “single” in the graph refers to the first-stage strategy.

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Figure 9.6 Worst option choice rate for each second-stage decision strategy.

Fig. 9.7 shows that DIS 1 WAD has the lowest adoption rate for both the worst choice by conjoint analysis and the worst choice by weighting, when comparing the first- and second-stage strategies side by side. EBA 1 EQW had the highest adoption rate by conjoint analysis, followed by CON 1 DIF, EBA 1 CON, EQW, and WAD. This is because, as discussed in the first-stage strategy, EQW cannot be used to omit the worst option. In addition, since EBA 1 CON is a strategy without comparison, it is thought that many of the experimental participants chose the worst option because their baseline was low. In addition, the adoption rate of the firststage strategy, WAD, was low for the weighted worst option, while the adoption rate was high for the conjoint analysis. From this, it is thought that the experimental participants weighted the choices differently from the original weighting when they were performing the WAD. This may be due to the complexity of the WAD calculation method, which may have prevented the WAD strategy from being perfectly implemented. In addition, the adoption rate of DIS 1 WAD is zero because the

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Figure 9.7 Worst option choice rate for each decision strategy.

WAD was conducted with the DIS strategy narrowing down the choices to two, so it is thought that the WAD was conducted correctly.

9.3.4 Correlation between decision time, worst choice adoption rate, and questionnaire A correlation matrix representing the correlation coefficients between the worst choice adoption rate, the decision time, and the seven items in the questionnaire was calculated, but no significant correlation was found between the worst choice adoption rate, the questionnaire items, and the decision time. There was no significant correlation between the worst option adoption rate and the questionnaire items or the decision time. In the case of “difficulty” of decision-making, there was little correlation between the worst option and the adoption rate, and a strong correlation was found with the decision time (r 5 0.93). The first-stage strategies WAD and DIF had a higher degree of difficulty, but also a higher adoption rate. In addition, both first- and second-stage strategies tended to have a high degree of difficulty, but there was no trend toward a low adoption rate. In addition to that, the second-stage strategy using WAD in the second-stage tended to have a higher adoption rate of the worst option, except for DIS 1 WAD. This suggests that the second-stage strategy using WAD in the

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Figure 9.8 Time taken for decision (decision time) and subjective difficulty for implementing each strategy.

second-stage may result in poor decision-making. The first-stage strategy, EBA, was shown to be the best strategy to avoid making bad decisions in a short period of time, since it has the lowest category of worst choice adoption rate, despite having the lowest difficulty. This is a big difference from the results of the computer simulation. Fig. 9.8 shows that there is a strong positive correlation between decision time and difficulty. The single-stage strategies, WAD and EQW, had longer decision times and higher difficulty levels. In addition, both first- and second-stage strategies tended to have longer decision times and higher levels of difficulty when using the compensatory strategy. On the other hand, the first-stage strategy using the noncompensatory type tended to have a shorter decision time and a lower degree of difficulty. This may be because the noncompensatory strategy did not require a stage to narrow down the choices and required less information than the second-stage strategy. In addition, when comparing WAD and DIF, the decision time of WAD was longer than the degree of difficulty, while the decision time of DIF was shorter, but the degree of difficulty tended to be higher.

9.3.5 Crisis rate by strategy Fig. 9.9 shows a graph of the crisis rate and the worst choice rate for each strategy. If the participants were confused between the option they were looking at just before the decision and the option they adopted, we included it in the graph as the crisis rate.

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Figure 9.9 Choice rate of the worst and the critical options by the conjoint analysis for each decision strategy.

Fig. 9.9 shows that MCD in the first-stage strategy has the highest crisis rate, followed by DIS 1 DIF, DIS 1 EBA, DIS 1 LEX, and first-stage EQW. In addition, the strategy with DIS as the first-stage tended to have a high crisis rate. On the other hand, the second-stage strategy using LEX in the first-stage tended to have a low crisis rate. Since the strategy using EBA in the first-stage also tended to have a low haircut rate, it is thought that the worst option was eliminated when it was narrowed down to two by making an uncompromising choice on the most important option in the first-stage. In addition, the fact that the crisis rate of the first-stage strategy EQW was the highest is thought to be due to the fact that the last option compared was included in the crisis rate when it was the worst option. The reason why the crisis rate of the second-stage strategy that used DIS in the first-stage was high is thought to be that DIS could not narrow down the worst choices because it leaves two choices that meet the criteria even if they have one attribute. For each strategy, we also calculated the percentage of the best option that was included when we narrowed down the choices to two, regardless of the disagreement with the weighted worst option (crisis rate). Fig. 9.10 shows a graph of the crisis rate and the worst adoption rate for each strategy. Fig. 9.10 shows that the crisis rate of the first-stage strategy MCD is the highest, followed by the first-stage CON and DIS 1 DIF. EBA 1 EQW had both the highest crisis rate and the worst selection rate. In contrast to the graph in the conjoint analysis, the second-stage strategy using EBA in the first-stage also had a high haircut

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Figure 9.10 Choice rate of the worst and the critical options by the weight estimation analysis for each decision strategy.

rate. This may be due to the fact that some of the respondents left out the worst option due to the low desirability of the EBA when performing the “exclude attributes that are less than desirable in terms of importance.” In Figs. 9.9 and 9.10 the second-stage strategy that used LEX in the first-stage tended to have a low crisis rate.

9.3.6 Best choice rate for each strategy 9.3.6.1 First-stage strategy Fig. 9.11 shows a graph of the adoption rate of the best option in the first-stage strategy. First, we conducted a correlation analysis between the adoption rate of the best option by conjoint analysis and the adoption rate of the best option with weights and found that the correlation coefficient was 0.64, which is a moderate correlation. Fig. 9.11 shows that the adoption rate of the best option by conjoint analysis was higher for DIF, CON, LEX, and EBA, in that order. For the weighted best option the adoption rate was higher for LEX, DIF, WAD, and CON, in that order. First, for DIS, the adoption rate was the lowest regardless of whether the best option was produced by conjoint analysis or weighted analysis. In other words, it is expected that DIS makes it difficult to adopt the best option because even if an attribute is not considered important, it will be adopted if it meets one of the criteria. On the other hand, for DIF, LEX, and CON, the adoption rate tended to be high regardless of whether the best option was given by conjoint analysis or with weight.

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Figure 9.11 Best choice rate by first strategy.

For DIF, it is thought that the possibility of adopting the best option for oneself increases because all attributes are examined carefully while weighting them based on one’s subjectivity. The fact that the adoption rate of the best option for LEX was high suggests that people’s best choice depends on whether or not they are greatly satisfied with the attributes they consider important. As for the WAD, the adoption rate of the best option by weighted analysis was high, but the adoption rate of the best option by conjoint analysis was low. The reason for this is that in WAD, all the options are carefully examined with weighting based on one’s own subjectivity, so it is reasonable that the weighted (subjective) best option is more likely to be adopted. The adoption rate of the best option was 0.69 (the weighted best option adoption rate of LEX) at the highest in this experiment, and the adoption rate increased significantly.

9.3.6.2 Second-stage strategy Fig. 9.12 shows the adoption rate of the best option in the second-stage strategy. Fig. 9.12 shows that the adoption rates of the best option by conjoint analysis and with weights were both high for the strategies that used CON and LEX in the firststage. In particular, the LEX 1 compensation-type strategy tended to have the highest adoption rate. This was the same as the result of computer simulation. In other words, in the second-stage strategy, after narrowing down the best option in the most important feature, as in the case of LEX, it was suggested that comparing and scrutinizing the two options in the compensatory type would lead to good decision-making. On the other hand, when DIS was used in the first-stage, the adoption rate tended to be lower than when other noncompensatory types were used in the first-stage.

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Figure 9.12 Best option choice rate for each second-stage decision strategy.

The reason for this may be that DIS adopts an option as soon as it finds one attribute that satisfies its own criteria, so the possibility that the best option is not included in the two options narrowed down in the first-stage increases. In addition, no matter what strategy was used in the first-stage, the adoption rate tended to be higher when a compensatory strategy was used in the second-stage. This suggests that in the stage of narrowing down the choices from two to one, a close examination of all the attributes, such as the compensation type, with weighting and scoring, leads to the selection of the best choice.

9.3.6.3 Best choice rates of combination of first- and secondstage strategies Fig. 9.13 shows a bar graph of the adoption rate of the best option for all strategies used in this experiment. Fig. 9.13 shows that for the two criteria of the best option adoption rate by conjoint analysis and the best option adoption rate with weights, the adoption rates were high for the CON 1 compensation type, the LEX 1 compensation type, and the compensation type of the first-stage strategy. Among them, CON 1 WAD  LEX  WAD (50.58) had the highest adoption rate.

9.3.7 Correlation between decision time, best option choice rate, and questionnaire A weak correlation was found between the weighted best option adoption rate and the best feeling (r 5 0.36). The scatter plot is shown in Fig. 9.14, along with the

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Figure 9.13 Best choice rate for each decision strategy for single-stage strategy and secondstage strategy.

regression line. There was a significant difference between the adoption rate of the best option with weight estimation and the rating of best choice. Fig. 9.14 shows that the adoption rate of EBA 1 CON, which had the highest value for best feeling, was generally not high. On the other hand, the adoption rate of the first-stage strategy LEX was high, although the best feeling was not high. In addition, when the CON strategy was used in the first-stage, both the adoption rate and the best feeling were high, while when the DIS strategy was used in the firststage, both the adoption rate and the best feeling tended to be low. This result was generally similar to the findings of computer simulations. Based on these results, it was shown that people do not feel that they have made a good choice unless they examine at least the most important attributes when they first narrow down their choices, and that choosing the highest level of the most important attributes without compromise leads to a good choice. As for the first-stage strategy, the compensatory type tended to have a high sense of best, while the noncompensatory type tended to have a low sense of best. Fig. 9.15 shows a scatter plot of the correlation between decision time and best choice rating (r 5 0.56). Fig. 9.15 shows that when the LEX or EBA strategy is used in the first-stage, the decision time tends to be shorter than when the best feeling is high. In

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Figure 9.14 Best choice rate based on weight estimation and best choice rating for each decision strategy.

Figure 9.15 Time taken for decision and best choice rating for each decision strategy.

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particular, EBA 1 CON was the strategy with the highest sense of best. On the other hand, when the DIS strategy was used in first-stage, the decision time tended to be longer in addition to the lower sense of best. These results indicate that taking more time does not necessarily result in the best feeling. As for the first-stage strategy, the compensatory type tended to have a longer decision time but a higher best feeling, while the noncompensatory type tended to have a shorter decision time and a lower best choice rating.

9.4

Conclusion

The main purpose of this study was to examine the decision-making strategies of real people, focusing on “how to prevent people from making bad decisions.” For this purpose, this study incorporated two new indices: the “worst choice adoption rate” and the “crisis rate.” From this study, as well as the results of computer simulations, it was confirmed that the DIS strategy makes it easier to choose the worst option. In addition, from the decision time and the worst choice adoption rate, it was observed that the decision time became longer and the adoption rate of the worst choice became higher when the compensatory type was used in the one-stage strategy. This tendency was especially pronounced when EQW was used. In addition, in the two-stage strategy, the adoption rate tended to be the highest when EBA 1 EQW was used. In addition, from the crisis rate, it was recognized that the crisis rate was higher when MCD or EQW was used in the first-stage strategy, and the crisis rate was higher when DIS was used in the first-stage. These results suggest that EBA 1 EQW is the worst and most inefficient method. EBA 1 EQW was a strategy to eliminate the attributes that did not meet one’s own criteria for the most important attributes in the first-stage, and then to select the option with the highest sum of scores without weighting the attributes in the second-stage. This was the strategy. From this, it can be seen that the method of “excluding the ones that do not meet my criteria for the most important attribute” in the first-stage and then “selecting the one with the highest total score by focusing only on the level value of the attribute” in the second-stage was the most time-consuming method for the participants. In other words, they had to compromise and scrutinize. In other words, it is a half-hearted strategy that does not allow for compromise and scrutiny and also takes a lot of time. In any case, the “worst option choice rate” was 0.20 at the highest, and it was not necessarily appropriate as an index to be used in this study, because there was not much correlation between the one by conjoint analysis and the one by weighted analysis. In addition, the highest “crisis rate” was 0.28, suggesting that the use of less desirable decision strategies does not lead to the worst decision. But the values 0.20 and 0.28 are considered to be still high in the case of emergent important decision-making activities. Therefore, the findings of this study seem to be important from a practical point of view. The purpose of this study was to examine the information-seeking process in decision-making by conducting experiments using specific decision strategies and

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to compare the results obtained with those of previous computer simulations. The relationship between the decision time and the adoption rate of the best option suggests that the decision time is longer but the adoption rate is higher in the strategy using the compensation type, that the adoption rate is higher and the decision time is relatively shorter when the compensation type is used in the second-stage, and that the adoption rate is higher and the choice can be made in a shorter time in the strategy using LEX in both the one- and two-stage strategies. These results suggest that the adoption rate is higher and the decision time is relatively shorter for the one- and two-stage strategies, respectively. These results are generally consistent with the findings of previous computer simulations (Payne et al., 1993; Takemura et al., 2015; Thorngate, 1980). The correlations between decision time and items related to the psychological state of the experimental participants when they used the decision strategy, such as best option adoption rate and best feeling, revealed the following. When the LEX or EBA strategy was used in the first-stage, the decision time tended to be shorter than the best feeling was high. In addition, when the uncompensated strategy was used in the first-stage, the decision time was shorter and the best feeling was lower. These results suggest that the one-stage LEX strategy is a relatively easy and efficient way to select the best option, since the decision time is short and the adoption rate of the best option is high. LEX is a step-by-step method to confirm that the most important attribute is the best one, and if it is not decided there, the second most important attribute is also compared and the best one is chosen. This was a strategy. This suggests that the method of “choosing the most important attribute and the highest value of the second most important level without compromise” to secure the least important option is the best and most efficient choice for the participants. For the first-stage decision strategy, LEX, the adoption rate was 0.69, which is very high. However, for the first-stage LEX, the number of attributes to be examined and the decision time was short, so the graded sense of best decision-making was low. This suggests that choosing the best decision without compromising on the attributes that are important, such as LEX, leads to good decision-making. The final implications of this study are as follows. First, using a compensatory decision-making strategy such as WAD may seem desirable at first glance because it focuses on various attribute information and integrates complex information, but in actual decision-making, it is quite difficult to perform and did not always lead to the best decision and there are some cases that led to the worst decision. WAD is a decision-making strategy that is not recommended, especially in emergency situations. Second, a strategy such as DIS, which requires less information processing but tends to shift attention to less important attributes, is more likely to lead to bad decisionmaking and less likely to lead to good decision-making. Such decisions are more likely to occur in emergencies, and I believe that the reason why many people made poor decisions during the spread of the COVID-19 epidemic was that many people used the DIS strategy. Finally, it was suggested that a decision-making strategy such as LEX, which focuses on the most important attributes, requires less cognitive effort and makes it relatively easier to avoid the worst decision and choose the best option. This is also generally consistent with the findings of the computer simulation.

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In Chapter 9, Process Tracing Study of Decision Strategies and Bad Decisions, we experimentally examined bad decisions by asking participants to use a specific strategy. The results showed that using compensatory decision strategies, such as additive decision strategies, not only fails to produce the best decisions but can also result in the worst decisions. The results also suggest that the use of noncompensatory decision strategies such as disjunctive is likely to result in the worst decisions. Conversely, it was suggested that noncompensatory decision-making such as lexicographic screening is likely to avoid the worst decision-making. However, the extent to which bad decisions occur in normal decision-making tasks is not well understood. In this chapter, we take up food decision-making, which is also important in risk communication, and examine how much bad decision-making occurs in a process tracking technique using eye-tracking equipment. Finally, we also report the results of an additional questionnaire survey on the food decision-making problem.

10.1

The problem of risky food decision-making and the assumptions of this study

The concept of risk is a broad concept, the scope of which ranges from nuclear power to food safety. In this chapter, we adopt the National Research Council (1989) definition of risk, rather than the usual definition of risk as a situation with a known probability distribution that is used in decision theory. According to that definition, risk is “expressed as the product of two factors: how serious the harm is and how likely it is to occur” (National Research Council, 1989). This definition is a broad definition of risk. To date, most risk communication research has adopted this definition because it is known that people’s attitude toward risk (risk perception) is composed of these two elements (Kikkawa, 1999). Of the two elements, according to Kikkawa (1999), the former, the severity of damage, is called hazard and is defined as “an action or phenomenon that has the potential to cause damage to people or property.” In other words, according to this definition, risk is the expected value of how likely a hazard is to occur. Risk communication, defined by the National Research Council (1989) as “the process of exchanging information and opinions about risk among individuals and groups,” is basically a process that respects the independent judgment of Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00015-6 © 2021 Elsevier Inc. All rights reserved.

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individual decision-makers and does not take a paternalistic perspective like nudges in behavioral economics. There is no paternalistic perspective in the original concept of risk communication, which also does not necessarily assume that the correct and right knowledge will be given as in boost because of uncertainty, ignorance, and lack of knowledge. From this point of view if risk communication is good, even if the outcome of a decision is bad, it is not necessarily a bad decision. However, given enough time, good risk communication is unlikely to result in a bad outcome. In the field of risk communication, there seems to be a tendency for people to “believe in zero risk (Nakayachi, 2008),” but in real life, in modern society, it is impossible to choose to take no risk at all. In this respect, food has the power to help us make choices that risk taking more deadly risks, which we tend to fall into because of our belief in zero risk. Since the decision of which food to eat is directly related to the life of each individual, it is the most familiar decision, but because of its familiarity, complementary decisions are not made. This can be seen in the behavior of purchasing and consuming foods that do not have hygiene control (maintained by chemical seasoning) because of the emphasis on “additive-free” and “chemical seasoning-free” processed foods. Safety is not obtained by seeking out zero-risk options, but by seeking out options that minimize various risks (risk tradeoff). In this way, safety is a “relative concept” (Nakanishi, 2010). In food safety, if we do not realize this and pursue zero risk and make decisions focusing only on seemingly conspicuous risks, there is a problem that more deadly actual harm will occur. For example, according to Nakanishi (2010), as a result of stopping chlorination in Peru in 1991 to reduce the carcinogenic risk to zero, 800,000 people became ill with cholera and 7000 people died. Thus in a situation where there is a high probability of death due to food poisoning if a certain food is eaten immediately, or where death will occur immediately if appropriate measures are not taken, such as in the case of earthquake or tsunami condemnation, the situation becomes a crisis communication rather than a risk communication. In such a situation the situation becomes crisis communication rather than risk communication, and some degree of paternalistic response may be necessary. In this study, in a situation where there is a risk in both options, the participants had to choose one of two options: “There is a risk in food safety that people consider to be a risk, but not a fatal risk” and “There is a risk in food safety that people consider to be a risk, and a fatal risk.” The purpose of this study is to examine how people would make decisions if they had to choose between the two options. For example, eating the food with the risk of food poisoning is called “bad decisionmaking.” There may be some disagreement with this assumption, and from a completely liberal perspective, the person may have the right to choose even if the risk of immediate death is very high, and the decision may not necessarily be considered a bad decision. However, in this study, we will conduct our experiment under the assumption of the value that human life support is important and valuable. As mentioned earlier, in food safety, it is important not to pursue zero risk, but to make decisions that minimize various risks as a whole. In addition, since the personality tendency of an individual is considered to be related to the risk he or she

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values and the information he or she values as a basis for decision-making, this study has developed a food selection problem (a problem created in this study in which both options have risks, one of which is “the risk that people consider to be a risk in food safety” and the other is “the risk that people consider to be fatal”). In this study, we examined the relationship between social behavioral tendencies as indicated by scores on formalism and other scales and the results of decisionmaking in a food choice problem (a problem created in this study in which participants had to choose between two options, one of which was “there are some things that people consider risks in food safety, but there are no fatal risks” and the other was “there are no things that people consider risks in food safety, but there are fatal risks”). In addition, we will examine the relationship between decision-making outcomes as indicated by the scores on the Formalism scale and other scales and social behavioral tendencies. In addition, we will also examine the relationship between the decision-making results and eye-tracking data and scales that measure personality tendencies that may be related to risk communication and decision-making.

10.2

Method of the eye-tracking experiment

10.2.1 Participants The participants of the eye-tracker experiment were 46 undergraduate and graduate students at Waseda University [13 males, 33 females, 18
39 years old, mean age 5 21.84, standard deviation (SD) 5 4.36, of which 1 participant was eliminated due to missing values].

10.2.2 Experimental setup The equipment used in this study was an eye-tracking system from EyeLink. In the experiment a personal computer manufactured by Dell and a display (FlexScan S1901-B) manufactured by EIZO were used to present the stimuli. In addition, one EyeLink CL Illuminator TT-890 (hereinafter referred to as “eye tracking”) from SR Research was used to measure eye movements. In addition, a measuring tape, a chin rest, and a chin rest fixation device were used to accurately position the participants from the eye tracking (see Figs. 10.1
10.3). In addition, a controller was used to input the decision of the choice. We also prepared questionnaires for each participant in the experiment. In addition, several target stickers (attached to the forehead of the face holder) were used to set the target of the eye tracking.

10.2.3 Decision-making issues Referring to the nine food items that should be secured in Ministry of Health, Labor and Welfare’s (MHLW’s) (2011) efforts to ensure food safety, we made a list of foods with these risk factors. Then, for each food, we created 15 selection tasks: “Food A (not a bad option), which people regard as a risk in food safety but

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Figure 10.1 Eye-tracking equipment in this study.

Figure 10.2 Eye-tracking equipment and related equipment in this study.

not fatal” and “Food B (bad option), which people regard as a risk in food safety but fatal.” Six of these were used as stimuli for the eye tracking, and six were used as experimental stimuli: “liver,” “spinach,” “rice,” “water,” “lettuce,” and “mushroom.” The problem of the difference in the number of letters between the stimuli was solved by focusing on the frequency of gazing (frequency) rather than the

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gazing time on the eye-tracker data. Fig. 10.4 shows an example of the six foodrelated stimuli (introduction and choice task) used in the experiment. The experimental tasks A and B were presented with offsetting order effects in the figure. In the example of Fig. 10.4, choice A is beef liver from Fukushima, where there was a nuclear power plant accident, but it has been tested for radiation, and although we do not receive individual management information from the producer, it is cooked and eaten, so there is no immediate health risk. Option B is Matsuzaka beef, which is famous for its delicious taste, and has undergone radiation testing and has information on the producer’s individual management, but since it is eaten raw, there is a risk of food poisoning. In fact, in April 2011, there was a food poisoning incident at a yakiniku (grilled meat) restaurant in Toyama Prefecture that resulted in the deaths of five people, with a total of 181 victims, most of whom were found to have suffered from food poisoning due to eating raw meat such as yukke. Since 2012 it has been prohibited to serve raw beef liver in restaurants in Japan, and no matter how delicious and radiation-free it is, there is still a risk of death by food poisoning, so option B is worse than A in terms of health hazards and risk to life. Similar questions have been created for other assignments.

Figure 10.3 Eye-tracking equipment and participant in this study. Example: Beef liver task Beef liver A

Attribute

Beef liver B

Fukushima Beef

Raw materials

Mie Beef (Matsuzaka Beef)

Cleared inspection

Radioactive inspection

Cleared inspection

Not received

Individual management of

Received

Cook and eat

How to cook

information

Figure 10.4 Example of food decision.

Eat raw

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10.2.4 Experimental procedures The experimental procedure consists of instruction, practice trials, setup and calibration of the eye tracker, and the main trial, in that order.

10.2.4.1 Instruction First, we briefly explained the outline of the task to the experimental participants, and after obtaining their consent, we seated them in a chair in front of a PC with an eye tracking. At that time, the height of the chair was adjusted so that the height of the participants’ eyes was about 120 cm vertically from the floor. Then, the distance between the display and the participant was adjusted so that the distance between the eye-tracking lens and the eye was 50
60 cm. For these determinations a facial retainer (chin stand) was used. Next, an explanation of the experiment was given. The information necessary for the explanation was presented on a computer splay, and after the experimenter gave a verbal explanation, the experimenter participants were encouraged to ask questions. After the experimenter gave a verbal explanation, the experimenter encouraged questions from the participants and supplemented the explanation when there were questions. At the controller the experimenter operated the right and left triggers used for decision-making and the buttons used to advance to the next screen.

10.2.4.2 Practice trial After the instruction the experimental participants underwent a practice trial. The “introduction” refers to the screen of the explanation of terms before the selection task, the “selection task” refers to the screen of the food selection, and the “feedback” refers to the screen of the feedback of the experimental participant’s selection.

10.2.4.3 Eye-tracker setup and calibration In the setup and calibration of the eye tracking the focus and pupil size were adjusted after obtaining the approval of the experimental participants. Calibration (adjustment of gaze and eye capture by the eye tracking) was performed in a posture where the center of the monitor was in front of the participants. After successful calibration, validation (adjustment for accurate distance and time measurement) was performed.

10.2.4.4 Experimental trial After completing the setup and calibration, we started the task of this trial. The “screen that prompts for preparation” refers to the screen that prompts for preparation before the selection task of the experiment starts. The trial consisted of six sets of “introduction” . “selection task” . “feedback.”

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At first, the introduction section was displayed, and when the participant thought that he or she was ready, he or she pressed a button on the controller to move to the task selection screen. Next, the stimulus pairs for the task were presented on the display, and the participant chose which food to eat after viewing each condition, and then input the chosen food using the left or right trigger of the controller.

10.2.5 Content of instruction The instructions given during the experiment were discussed in the following sections.

10.2.5.1 Introductory instruction Thank you very much for your cooperation in today’s experiment. The purpose of this experiment is to investigate “how we make choices when selecting foods” by measuring eye movements with an eye tracking. What we would like you to do in the experiment is as follows What we would like you to do in this experiment is to choose which of the two foods that appear on the screen with the same item but different conditions you would like to eat after looking at each condition. (Change the screen with the spacebar) You are at home and want to eat one of two foods, A or B. Which will you choose? Which one will you choose? In the screen that you are about to see, two foods of the same item, but with different conditions, are displayed on the left and right sides of the respective condition items (showing the bottom columns of the figure). You are then free to decide which of the two you want to eat. (Change the screen with the spacebar) In the experiment, as shown in this screen, there is food A on the left and food B on the right, with the conditional items for those foods shown in the center. On this screen, decide whether you want to eat A or B, and enter A or B with the controller. (Use the spacebar to change the screen.) You will be asked to press the button after you are instructed to do so, but now you will be asked to enter your choice. If the food you have chosen and determined is A, press the left trigger on your controller; if it is food B, press the right trigger. (Experimental participant, press the right trigger or the left trigger) Your choice will be displayed in this way. Do you have any questions? If you have any questions, we would like to move on to the practice trials.

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10.2.5.2 Practice trials Now, as a practice experiment, I will ask you to choose a food called dashi. Since this is a practice, please don’t be nervous and learn how to look at the screen and how to decide your selection. As is true for the entire experiment, the length of time is not important, so please look at the information as you normally would and make your decision. The conditional items are “00,” “00,” and “00” here. In this experiment, it is not possible to go back to the previous screen, so please read and understand the explanation on the side of this screen. When you are ready, the next screen will start. To proceed to the next screen, press the button on the surface of the controller. (Experimental participant, press the button on the controller. The task selection screen appears. (Experimental participant, press the right or left trigger on the controller. The feedback screen will appear. Is the food you have chosen as shown here? (Use the spacebar to change it.)

10.2.5.3 Eye-tracking setup This concludes the exercise. Do you have any questions? If you have any questions, I would like to move on to the eye tracking setup. From now on, we would like you to keep your eyes only on the screen, so please do not take your eyes off the screen. (Use the spacebar to change. On the white screen, press the Enter key to set up. If the calibration and validation are successful, select “setup exit.” The experiment will start).

10.2.5.4 Experimental trial Please listen to the screen as you see it. Now we would like to start the main experiment. From the next screen, a total of six selection tasks will start. Note that each time you move to the next task, a black circle will appear in the center of the screen. Look at it, then press the button on the surface of the controller to move on to the next screen. When you are ready, please press the button on the controller to move to the next screen. The participant presses the button on the controller. The task selection screen will appear. Experimental participant presses the right or left trigger on the controller. The feedback screen will appear.

10.3

Results and discussion

10.3.1 Choice results and decision time in the food decision-making task Fig. 10.5 shows the results of the choices made in the food decision-making task. It shows that many of the experimental participants chose relatively bad options.

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However, this decision-making task is a problem reminiscent of the radiation damage in Fukushima, as was the case with the beef liver decision-making task, but there is a lethal risk, such as that of the O157 bacteria, from eating raw meat, even if the producer information is controlled by a delicacy such as Matsuzaka beef. We can assume that many experiment participants ignored the lethal information and made decisions based on the information of other easily visible attributes. In this light, it seems likely that many experimental participants used the disjunctive (DIS) strategy. The results of this experiment suggest that even in actual decision-making, people may make decisions based only on superficial images and attributes that are easy to pay attention to, and ignore critical information. Then, for the eye-tracking data, the mean decision time and SD for each food item were produced and shown in Fig. 10.6.

Figure 10.5 Number of worse and better option choice for each decision task.

Figure 10.6 Mean decision time (ms) for each decision task.

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10.3.2 Results of the number of times a region was viewed for each food For the eye-tracking data the average number of times each area was looked at and the average number of times each attribute item was looked at were tabulated for each food item and are shown in Tables 10.1
10.6. As can be seen, the attributes that are critical for health hazards were relatively unnoticed. For example, in the beef liver decision-making task, the information about beef from Mie Prefecture (7.31 times) and beef from Fukushima Prefecture (6.56 times) were viewed the most frequently, more frequently than the critical information about eating raw (4.51 times) and cooking (5.40 times). Overall, among the four attributes, the focus on the place of production was the highest, and the focus on the cooking method was the third. This also suggests that many of the experimental participants were using the DIS strategy. Table 10.1 Mean eye gaze times and its standard deviation for each attribute. Decision Task 1

Spinach

Standard deviation

Mean eye gaze Product area Food status (frozen or not) Quarantine Inspection of radioactivity Pesticide residues

9.22 11.02 16.49 12.55 7.89

2.82 3.14 3.09 3.08 2.85

Note: Single-asterisk symbol indicates important attribute and double-asterisk symbol indicates critically important attribute.

Table 10.2 Mean eye gaze times and its standard deviation for each attribute. Decision Task 2

Mushroom

Standard deviation

Mean eye gaze Product area Cultivation methods How to get it Mushroom name (unknown)

11.20 23.20 14.51 7.84

7.54 7.56 2.52 2.77

Note: Single-asterisk symbol indicates important attribute and double-asterisk symbol indicates critically important attribute.

Table 10.3 Mean eye gaze times and its standard deviation for each attribute. Decision Task 4

Beef liver

Standard deviation

Mean eye gaze Product area Inspection of radioactivity Information control of producer How to cook (raw meat or cooked meat) Note: Double-asterisk symbol indicates critically important attribute.

15.42 12.69 11.69 12.24

3.18 2.64 3.31 4.52

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Table 10.4 Mean eye gaze times and its standard deviation for each attribute. Decision Task 3

Lettuce

Standard deviation

Mean eye gaze Product area Cultivation method Pesticide residues Bacteria attached

8.60 14.27 10.18 9.11

2.84 3.10 1.72 2.77

Note: Single-asterisk symbol indicates important attribute and double-asterisk symbol indicates critically important attribute.

Table 10.5 Mean eye gaze times and its standard deviation for each attribute. Decision Task 5

Rice

Standard deviation

Mean eye gaze Product area Inspection of radioactivity Hygiene inspection

14.64 13.24 5.78

3.05 2.28 3.48

Note: Single-asterisk symbol indicates important attribute and double-asterisk symbol indicates critically important attribute.

Table 10.6 Mean eye gaze times and its standard deviation for each attribute. Decision Task 3

Water

Standard deviation

Mean eye gaze Product area Acceptable levels of carcinogenicity Hygiene inspection (bacteria)

13.84 28.60 10.18

8.32 8.51 4.35

Note: Single-asterisk symbol indicates important attribute and double-asterisk symbol indicates critically important attribute.

10.3.3 Relationship between questionnaire food choice scores and eye-tracking data (average number of gazes per area) To see the relationship between the total score of the questionnaire food selection questions and the eye-tracking data (average number of gazes per area), the correlation between the total score of the Q1 food selection questions and the percentage of average number of gazes per area was determined. We found that participants who tended to choose bad choices with fatal risks were more likely to pay attention to the test for radioactive materials in the beef liver question, and the more times they paid attention to the cultivation method of lettuce, such as organic cultivation without the use of synthetic pesticides, the higher their tendency to make bad choices in the food selection question. For water, it was also found that the tendency to use carcinogens was higher. In the case of water, the higher the number of times they watched for carcinogens, natural water from mountain springs, etc., the higher their tendency to make poor decisions on food selection issues. While these items are undoubtedly also important for health risks, we found that participants in

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the experiment who made more fatal choices were more likely to overlook fatal risks such as food poisoning and bacterial infection.

10.3.4 Comparison of gazed behavior between worse decision and better decision The experimental participants who made worse fatal decisions and also who made better decisions were divided into two groups for each decision-making task, and the number of times they gazed and the areas they gazed were examined for each food to see if there was any difference between them.

10.3.4.1 Spinach task First, for the spinach task, those who had made a fatal decision gazed more frequently than the average number of times they gazed at food A, “Made in China” [t (43) 5 1.717, P , .05]. However, it can be seen that participants who did not make a fatal decision paid more attention to the information of Chinese production, but in the end, they took it positively rather than negatively.

10.3.4.2 Mushroom task For the mushroom task, there was a similarly significant difference in the average number of times that “produced in China” was noted in food A [t(43) 5 4.057, P , .01]. There was also a significant difference in the average number of times “fungus bed cultivated (cultivated by planting fungi in sawdust with nutrients)” and was gazed at [t(43) 5 2.308, P , .05]. There was also a significant difference in the mean number of times they looked at “I bought it at the supermarket” [t(43) 5 2.556, P , .05] in domain 3 and “shiitake mushroom” in domain 4 [t(43) 5 3.063, P , .01].

10.3.4.3 Rice task Regarding the rice task, the experimental participants who did not make a bad decision looked at more information about food A “produced in China (imported rice)” [t(43) 5 3.516, P , .01], and they also looked at more information about food A “passed the inspection of the Ministry of Health, Labor and Welfare” [t(43) 5 1.864, P , .05].

10.3.4.4 Beef liver task For the beef liver task the experimental participants who made poor decisions tended to pay more attention to “passed the inspection of the Ministry of Health, Labour and Welfare” for food B [t(43) 5 2.631, P , .05].

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10.3.4.5 Lettuce task In the lettuce task, experimental participants who made poor decisions were more likely to pay more attention to “produced in China” [t(43) 5 2.573, P , .05] for food A, and more likely to pay more attention to “grown with synthetic pesticides” [t(43) 5 2.225, P , .05], “with pesticide residues” for food A [t(43) 5 2.631, P , .05]. In addition, the experimental participants who made less bad decisions were more likely to choose “no bacteria attached” for food A [t(43) 5 3.003, P , .01], and “from Nagano” for food B [t(43) 5 2.620, P , .01], “organically grown without synthetic pesticides” for food B [t(43) 5 3.696, P , .05], and “no pesticide residue” for food B of “almost no pesticide residues” [t(43) 5 2.773, P , .01] were more closely watched. Experimental participants who made poor decisions also paid more average attention to the label “place of production” in domain condition 1 [t(43) 5 3.886, P , .01] and more average attention to the label “possible pesticide residue” in domain condition 3 [t(43) 5 4.021, P , .01]. Basically, the results suggest that in the lettuce task, the experimental participants who made poor decisions saw more information than those who made poor decisions.

10.3.4.6 Water task In the water task the experimental participants who made a not-so-bad decision looked at the “tap water” of food A more than the experimental participants who made a bad decision [t(43) 5 4.152, P , .01]. They also paid more attention to “with chlorine sterilization treatment” for food A [t(43) 5 3.235, P , .01].

10.3.5 Relationship between the eye-tracker experiment and the questionnaire experiment To examine the correspondence between the experimental participants who made bad and not-so-bad choices in the eye-tracker experiment and those who made similar choices in the questionnaire survey conducted in conjunction with the eyetracker experiment, the correlation between the scores in the six and eight questionnaire tasks was determined. When we correlated the number of times, the participants were able to select food A in the eye-tracker experiment (their total score) with the number of times they were able to select food A in the questionnaire (their total score on the food selection questions), no significant correlation was found. This suggests that the tendency to make bad decisions is not necessarily stable but varies from task to task.

10.4

Questionnaire survey

The results of the experimental study showed that in the six decision-making tasks, most of the experimental participants chose the option that was considered to have a

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higher degree of health damage. The results of this study were based on a limited sample, so we will examine the results with a larger sample of participants and additionally examine the relationship with other social behavioral tendencies and attitudes.

10.4.1 Survey participants The survey participants were 149 undergraduate and graduate students of Waseda University (46 males, 50 females, 53 unidentified, aged 18
39, mean age 5 21.04, SD 5 2.78, of which 7 were eliminated due to missing values). The survey was conducted in a laboratory and a small classroom after recruitment.

10.4.2 Methodology of the questionnaire survey 10.4.2.1 Tasks for selecting foods Referring to the nine food items that should be secured in MHLW’s (2011) efforts to ensure food safety, we listed foods with these risk factors. Then, for each food, 15 selection tasks were made: “Food A, which people regard as a risk in food safety but not fatal risk” and “Food B, which people regard as a risk in food safety but fatal risk.” As a result of the consultation, six of the items that were easy to choose were used as stimuli for the eye tracking, and eight of the remaining items were included in the questionnaire survey. As for the nine food items that should be ensured safety, the following items are included in the questionnaire: ensuring the safety of imported food, pesticide residues in food (positive list system), measures against contaminants in food; ensuring the safety of food additives; ensuring the safety of health food, measures to prevent food poisoning, measures against bovine spongiform encephalopathy; ensuring the safety of genetically modified food; and ensuring the safety of utensils. The following issues were selected. From there the selected topics were: mushrooms, liver, water, spinach, lettuce, rice (these are the ones used for the eye tracking), puffer fish, clams, bread, fish, salt, ham, soup stock, tofu (these are the ones used for the questionnaire).

10.4.2.2 Scales for social behavior 1. Scale for attitude toward risk Individual risk attitudes toward various risks were surveyed using a 6-point scale ranging from “not at all dangerous” to “very dangerous.” 2. Formalism scale The formalism scale used in the experiment conducted by Takahashi, Takemura, Ideno, Ohkubo, and Tamari (2010). The survey was conducted using a 5-point scale ranging from “not at all applicable” to “frequently applicable.” 3. The regret and pursuer scale

The Japanese version of the regret and pursuer scale by Isobe et al. (2008) was used. The survey was conducted using a four-point scale ranging from “not applicable” to “applicable” to find out what was applicable to their daily behavior, feelings, and thoughts.

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10.4.2.3 Evaluation of knowledge about food safety We used the nine items of food items that should be ensured safety, which were mentioned in the aforementioned MHLW’s (2011) efforts to ensure food safety. The level of knowledge about food safety was surveyed using a five-point scale from “not at all familiar” to “familiar.”

10.4.2.4 Knowledge confidence survey items The confidence levels of knowledge on the risk events were used based on the information of Ministry of Health, Labour and Welfare, Saitama City, Nuclear Waste Management Center Food Safety Commission Bureau of Social Welfare and Public Health, Tokyo Metropolitan Government, National Institute of Health and Nutrition, Fukushima Prefecture Disaster Countermeasures Headquarters, and the Fukushima Prefecture Disaster Countermeasures Headquarters.

10.4.2.5 Information sources to be referred The following sources of information were used as reference in thinking about food risks: (1) television programs and newspaper articles; (2) stories from family, friends, and acquaintances; (3) school lessons; (4) general magazines; (5) specialized books and magazines; (6) talks and lectures by experts; (7) information magazines of mini-comic newspapers and NGOs; (8) information obtained in the course of work; (9) visits to science museums; (10) information obtained from work; (11) visits to science museums; (12) corporate advertisements, TV commercials, pamphlets, etc.; (13) government bulletins, white papers, pamphlets of local governments; (14) information obtained from the Internet; (15) other; (16) nothing in particular.

10.4.2.6 Randomization and counterbalancing of the questionnaire For randomization, two types of questionnaires were prepared, one with randomized order for the food selection task and the other with randomized order for the subsequent scale. The counterbalancing was performed by distributing the same number of each of the two types of questionnaires to the experimental participants.

10.4.3 Results and discussion of the questionnaire survey 10.4.3.1 Food choice task in Question 1 The results (percentage of correct answers out of a total of 142 respondents) of Question 1, which asks the participants to choose between food A, which poses no intrinsic risk, and food B, which poses intrinsic risk, for eight food items, are shown in Fig. 10.7. As shown in this figure, the percentage of fatal bad decisions is relatively high, ranging from 30% to 70%, even in other decision-making tasks.

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0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1

2

3

4

5

6

7

8

Food decision item

Figure 10.7 Ratio of bad decision in the questionnaire.

10.4.3.2 Relationship between other question items and food choice problems When the total score for the food choice question in the questionnaire (2 points for choosing a bad choice and 1 point for choosing a not-so-bad choice) was calculated, the mean score was 4.11. This indicates that, overall, the responses were almost equal. In the questionnaire survey the participants were divided into two groups: those who scored above average on the food selection question in Q1 and those who scored below average. t-tests were conducted for each scale. The results showed that there was no significant difference between the two groups on the scale of attitude toward risk. In the case of the fomalism scale, a significant difference was obtained in the score of the item “I think that anyone who violates even one rule is a bad person” [t(140) 5 1.993, P , .05], and a significant difference was obtained in the score of the item “I feel safer with products packaged in chain stores and supermarkets than with products packaged in privately owned stores obtained” [t(140) 5 2.047, P , .05], and formalistic people were less likely to make bad decisions. For the regret/pursuer scale a significant difference was obtained in the scores for the item “I pursue my favorite things, celebrities, singers, etc. to the fullest extent” [t(140) 5 2.321, P , .05], and a significant difference was also found in the scores for the item “I always try to choose the best when selecting products” [t (140) 5 2.115, P , .05], and those with a higher propensity to pursue were less likely to make bad decisions. Regarding the scale of confidence in food safety knowledge, a significant difference was found in the score of the item “Carcinogens in food” [t(140) 5 2.364, P , .05], and those who were confident in their knowledge of this item tended to make worse decisions. This result may be consistent with the idea that people who think about food safety risks in a detailed and strict way can avoid fatal risks, rather than people who make decisions in a general way. However, the effect of individual difference

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factors on decision-making in this study is not very strong. In addition, the results of this study focus on fatal risks, and the question remains as to whether they are truly bad decisions as considered by decision-makers.

10.5

Conclusion

In this chapter, we have discussed food decision-making, which is also important in risk communication, and examined the extent to which bad decisions are generated by the process tracking technique using eye-tracking equipment. Finally, we have reported the results of an additional questionnaire survey on food decision-making problems. Our findings suggest that in multiattribute decision-making for foods, despite the presence of fatal risks, participants tended to ignore the attribute information and make decisions based on the characteristics of other secondary attributes of interest. This finding was also suggested by the eye-tracking data. Such results occur even in a very small number of decision-making tasks (two choices), suggesting that bad decision-making can occur even in everyday life itself. This suggests that decisions based on the DIS strategy are likely to occur in food decisions as well, when interpreted from the perspective of the decision strategy. In this chapter, we also defined an option that could cause fatal health damage as a bad option as an experimental manipulation, but this definition still has interpretive problems. If the decision-maker herself/himself prioritizes delicious food over health hazards, even if she/he takes a fatal risk and gets food poisoning, it may not be a bad decision for him. In addition, the findings of this study can be interpreted as a rational choice of a seemingly bad option in terms of manifested preference theory, and there is much room for interpretation. However, it can be said that there is a great possibility that many people may make decisions that are not, even though their health and life are the most important. It is possible that people’s reactions to Great earthquake disaster of East Japan, to Covid-19, and many other fatal risks were based on not essential and not very important information, as shown in the findings of this study.

References Isobe, A., Hisatomi, T., Matsui, Y., Ui, M., Takahashi, N., Ohba, T., & Takemura, K. (2008). Ishi Kettei ni okeru Nihonban Koukai Tuikyuusya Syakudo no Sakusei no Kokoromi [Construction of a Japanese version of the “Regret and Maximization Scale” in decision making]. Shinrigaku Kenkyu: The Japanese Journal of Psychology, 79, 453
458. (in Japanese. Kikkawa, T. (1999). Risuku Komyunikeishon: Sougorikai to Yoriyoi Ishikettei wo Mezashite [Risk communication: Toward better decision and mutual understanding]. Tokyo: Fukumura Shuppan. (in Japanese. Kousei Rodoh Shou [Ministry of Health, Labor and Welfare, Japanese Government]. Syokuhin no Anzen Kakuho ni kansuru Torikumi [Food safety]. (2011). http://www. mhlw.go.jp/topics/bukyoku/iyaku/syoku-anzen/dl/pamph01.pdf. (in Japanese).

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Nakanishi, J. (2010). Shoku no Risuku Gaku: Hanran suru Anzen Anshin wo Yomitoku Shiten [Risk research of foods: A perspective that protects the flood of safety and security]. Tokyo: Nihon Hyoron Sya. (in Japanese). Nakayachi, K. (2008). Anzen demo Anshin Dekinai: Shinrai wo Meguru Shinrigaku [Safety, but I can’t rest assured: The psychology of trust]. Tokyo: Chikuma Shobo. (in Japanese). National Research Council. (1989). Improving risk communication. Washington, DC: The National Academy Press. Takahashi, N., Takemura, K., Ideno, T., Ohkubo, S., & Tamari, Y. (2010). Aimai Jitai Ni Okeru Keishikisei Tsuikyuu Keikou Ga Soshikinai Deno Ihan Ni Taisuru Ishiki To Shakai Handan Ni Ataeru Eukyou [Effect of tendency to seek formality in ambiguous situations on the awareness of violation in an organization and social judgment]. In: Paper presented at the 51st conference of the Japanese Society of Social Psychology (pp. 762
763) (in Japanese).

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The previous chapters have dealt with the problem of bad decision-making in personal judgments and decisions about individual behavior. According to the results, there is a certain degree of possibility that bad decisions will be made in individual behavior, and decision-making that involves comprehensive evaluation, such as the additive type, is difficult because of the cognitive load. It was recommended to use a simple decision-making strategy such as lexicographic (LEX) to narrow down the choices and then conduct a comprehensive evaluation as a way to avoid bad decisions. In addition, it was suggested that a decision strategy such as disjunctive was less likely to focus on the most important attributes and more likely to lead to poor decision-making. In view of social life, individual behavior is often defined by group discussions and collective decision-making. In this chapter, I will examine whether the decision-making strategies that have been developed for individuals can be extended to groups and whether they are effective in avoiding bad decisions through group psychological experiments (Takemura, Takahashi, & Mitani, 2021). In this chapter, we define decision-making strategies [weighted-additive decision (WAD), LEX, and disjunctive (DIS)] for groups in meeting situations, specify how to proceed with discussions (decision-making strategies) when having groups discuss and make decisions, examine what kind of decisions are made as a result, and report and discuss the results. In this study, we used both a definition of bad decision-making based on the researcher’s predetermination in the discussion and a definition based on the results of bad decisions made by the experimental participants.

11.1

Group decision and groupthink

In today’s society, many meetings are held in a variety of forms. The word “meeting” tends to be associated with formal meetings such as those held in companies, but in a broader sense, everyday discussions such as those held with friends and family can also be called meetings. However, in such meetings, good decisions are not always made. In the course of discussions, there are times when people are preoccupied with factors other than what they are focusing on and neglect the most important factors. For example, in Japan, there was a decision not to carry out seismic reinforcement work on buildings with low seismic resistance to protect the honor of architects. This is an example of a decision to neglect the safety of the building, which should have Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00009-0 © 2021 Elsevier Inc. All rights reserved.

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been emphasized, because of the concern for the honor of the architect. Such a decision deviates from the original important purpose of the project and can be considered an irrational decision and a bad decision for the residents. Janis (1982) proposed the concept of “groupthink” as an explanation for this phenomenon. Groupthink refers to the fact that when a group of people make a decision, they make a more foolish decision than when they make a decision individually. In the decision-making, we do in our daily lives, decisions made by considering information on multiple attributes of alternatives, such as price and function, are called multiattribute decision-making (Takemura, 2014, 2019). As shown in Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of TwoStage Decision Strategies in a Multiattribute Decision-Making Process, and Chapter 8, A Computer Simulation of Bad Decisions and Good Decisions: An Extended Analysis of Two-Stage Decision Strategies, we have studied multiattribute decision-making using a single decision strategy among a group of alternatives, and we have found that the decision strategy is more effective than the alternatives. In these chapters, we focus on decision strategies and compare how relative accuracy and cognitive effort are affected by multiattribute decisionmaking tasks using simulations. Relative accuracy refers to the degree of accuracy among a group of alternatives and is expressed as a percentage of the accuracy of the outcome of the decision strategy, with 1 being the exact same outcome as the WAD and 0 being the outcome of a completely random decision. Also in the same chapters, we will discuss the use of concatenative, additive difference, DIS, elimination by aspects (EBA), equal-weighted, lexicographic (LEX), semilexicographic (LEX-S), and majority of confirming dimensions (MCD) methods in computer simulations, lexicographic type (LEX), lexicographic-semiorder type (LEX-S), majority of confirming dimensions type (MCD), and weighted addition type (WAD). As a result, contrasting results were found for WAD, LEX, and DIS. Basically, this simulation study showed that the effects of the two levels differed depending on the combination of the two levels, but to simplify, the relative accuracy of WAD was 1 by operational definition, and the relative accuracy was generally high for WAD followed by LEX and DIS. In addition, WAD, LEX, and DIS were found to be desirable in avoiding choosing bad choices, in that order. In terms of cognitive effort, WAD, LEX, and DIS were higher in that order. WAD was a decision strategy that avoided bad choices with high cognitive effort and also with high relative accuracy, while LEX was a decision strategy that prevented bad choices relatively well with low cognitive effort and high relative accuracy to some extent. DIS was a decision strategy with low cognitive effort, but with fairly low relative accuracy. The psychological experiments conducted in Chapter 9, A Process Tracing Study of Decision Strategies and Bad Decisions, also indicated that WAD is relatively difficult to implement, does not lead to the best decision, and may instead lead to the worst choice. Based on this research on decision-making in personal behavior, this chapter focuses on and examines decision-making strategies as factors that lead to poor decision-making in meeting situations. The decision strategies discussed are WAD, LEX, and DIS, which are the three decision strategies that produced contrasting

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results in the studies in Chapters 7
9. If the effects of the decision strategies obtained for individuals are the same as those obtained for groups, DIS, LEX, and WAD, in that order, should be more likely to lead to bad and irrational decisions, so these hypotheses were also considered in this study.

11.2

Method of the experiment

11.2.1 Overview of the experiment The purpose of this experiment is to examine whether the way a discussion is conducted (decision-making strategy) affects the likelihood of irrational decisionmaking (bad decision-making). In this study, irrational decision-making was defined as the adoption of a bad option by the group or the difference between the option chosen by the group and the option that the individual wanted to choose (i.e., the individual’s opinion is not reflected in the group’s decision-making). In addition, two types of worst case options were operationally defined here. For the first one, Takemura et al. (2021) had a discussion before the experiment and decided that it was the worst option. For the second definition, we conducted a questionnaire survey on how people perceive decision-making as a preliminary investigation, and the results showed that this was the option that most people judged to be the worst. The discussion was conducted in accordance with three different decisionmaking strategies (WAD, LEX, and DIS). First, the WAD method was used to discuss and select options from all perspectives. Next, the LEX method was used to choose the most important point of view after deciding which one was the most important. Finally, the DIS method was used to decide the minimum points that should be satisfied for each perspective, and then choose the option that satisfied at least one of those points. In the experiment the participants were asked to discuss the presented topic with each other and to choose one of the options for the group decision-making on the topic. The participants were asked to discuss the topic in accordance with three different decision strategies (WAD, LEX, and DIS) and also asked to evaluate the process and results of the discussion and the relationship between the decision strategies, and the results were examined. In the following, we describe the experiment, the procedure before the experiment, the method of the experiment, and the instruction in this order. Fig. 11.1 shows the flow of the procedure before conducting the experiment.

Instruction

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Practice trial

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Pre experiment procedure

Figure 11.1 Outline of the experiment.

Interview and questionnaire

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Experiment

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In this experiment the participants were asked to read the agenda, viewpoints, and options; discuss them; and fill out the questionnaire repeatedly. First, the participants were asked to read silently the agenda, perspectives, and options for one agenda item (hereafter referred to as the agenda paper). After that the participants were asked to follow a different procedure for each condition and to write the results of the discussion and their evaluation of the discussion on a questionnaire. The participants were asked to follow three different decision-making strategies (WAD, LEX, and DIS), and 32 agenda items were presented for each strategy. Thirty-two topics were presented for each decision strategy. Before conducting the experiment, we explained the experiment to the participants and had them practice the discussion. Then, we conducted a preliminary survey on the perspectives of the agenda and tabulated the results. After these processes the experiment was conducted.

11.2.2 Participants in the experiment A total of 12 Waseda University students (2 males and 10 females) participated in the study. The mean age of the experimental participants was 21.67 years (standard deviation 5 1.84 years). The experimental participants were divided into four groups of three, and the composition of the group members was not changed. The participants of this experiment did not overlap with the participants of the interview survey, questionnaire survey, and preliminary experiment.

11.2.3 Procedures before conducting the experiment To conduct the experiment, we first explained to the participants how to proceed with the discussion in the experiment. After the explanation the participants were asked to practice the discussion. To prepare additional materials to be distributed to the participants during the experiment, we conducted a preliminary survey on the perspectives of the agenda.

11.2.3.1 Preliminary explanation of the experiment A PowerPoint presentation was given to all participants in the experiment. The contents of the explanation were the decision-making strategies used in individual decision-making and the three types of discussion procedures (WAD, LEX, and DIS) used in this experiment. During the explanation of each strategy, the participants were asked to deepen their understanding of the explanation by using practice agenda 1.

11.2.3.2 Experimental practice Following the explanation of the experiment, the participants were asked to practice the experiment. In this experiment the participants were asked to discuss the agenda 1 and 2 as they would in the real experiment.

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11.2.3.3 Preliminary survey The survey was conducted using Google Forms. In the presurvey, 32 agenda items and perspectives were presented, and a survey was conducted to ask the importance of each perspective and the minimum standards to be met for each perspective. The former was conducted for additional materials to be distributed at the WAD and LEX meetings, and the latter was conducted for additional materials to be distributed at the DIS meeting. In the survey the respondents were asked to select the level of importance they attached to each perspective. In addition, in the survey, the respondents were asked about the minimum standards that should be met for each viewpoint, for example, “To what extent do you want the enjoyment of the camp to be preserved? Please indicate the minimum standard you think should be met.” For example, in agenda item 3, “How low would you like the risk of suspension to be? How low would you like the risk of inactivity to be?”

11.2.4 Experimental stimuli The stimuli presented in the experiment were an agenda paper, additional materials to be distributed during the discussion, and a procedure manual.

11.2.4.1 Distributed agenda forms Each agenda sheet contained one topic, six perspectives on that topic, and four options. Four options were selected for each agenda item based on the results of the questionnaire survey on the perception of decision-making—one option was chosen as a bad option and three options were chosen as not bad options. A bad choice is a decision that does not solve a problem that is considered to be a problem in the situation indicated by the agenda, while a not bad choice is a decision that does not apply to that situation, that is, a decision that is not a bad choice. As a way of selecting the options, the bad options presented in this experiment were those that the experimenter assumed to be bad options in advance. In addition, the three options that had the lowest number of bad decisions in the questionnaire survey were used as the not-bad options in this experiment. As for the agenda, out of the 35 agendas used in the questionnaire survey, 32 agendas were adopted except for agendas 2, 27, and 29, which had less than three bad choices. In terms of perspectives, we developed six perspectives that could be used in discussion situations based on the content of the agenda. The perspectives had to be related to at least one of the options. In this way the same agenda paper was prepared for all groups for 32 agenda items. Appendix 4.2 shows the agenda paper.

11.2.4.2 Additional materials A total of 96 formats for additional materials were prepared for 32 agenda items: 1 for WAD, 1 for LEX, and 1 for DIS. In the formats the perspectives of the agenda items, such as health of new students and cancellation fees, were entered in advance. Then, the individual responses obtained from the presurvey were aggregated by group, and the aggregated results were entered into the format. In this way

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the following documents were created: additional WAD documents describing the importance of each perspective in the agenda and in the group, additional LEX documents describing the priority of the perspectives in the agenda and in the group, and additional DIS documents describing the minimum standards to be met for each perspective in the agenda and in the group. In the case of the WAD the average of the importance levels (1: not at all important to 7: very important) was calculated for each group and rounded to the first decimal place. In the case of the LEX the mean of the importance of the individual responses was calculated for each group, and the groups were prioritized according to the perspective with the highest value. In the case of DIS the most stringent criterion of the group was used as the criterion for the group to include all the criteria.

11.2.4.3 Procedures Three types of forms (procedure manuals) were prepared for WAD, LEX, and DIS, each of which described how to proceed with the experiment from the time the agenda paper and questionnaire were handed out until the questionnaire was completed. The following is an excerpt from the instructional part of the WAD, LEX, and DIS procedures on how to proceed with the discussion. For example, the instructions on how to proceed with the discussion in the WAD were as follows. For each option, choose the one with the highest rating, taking into account the importance of all the perspectives. In doing so, be sure to evaluate all of the options. Once you have selected one option, proceed to (3). However, scoring options is not allowed (e.g., thinking that “Option A is worth 90 points and Option B is worth 80 points” is not allowed). Please refer only to the content of the “Additional Materials,” not to the content of the answers each of you provided in the Google Form in advance.

In addition, the following instructions were given on how to proceed with the discussion at LEX. Evaluate each option based only on the most important aspects, and choose the option with the highest rating. Choose the one with the highest rating. In doing so, be sure to evaluate all the options. Once you have selected one option, proceed to (3). However, if there are multiple options with the same evaluation as a result of the evaluation from the perspective with the highest priority, evaluate the next option based on the perspective with the next highest priority (if there are still multiple options with the same evaluation, evaluate the next option based on the perspective with the next highest priority, and repeat this process)). Please refer only to the content of the “Additional Materials,” not to the content of the answers each of you provided in the Google Form in advance.

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Finally, the following instructions were given on how to proceed with the discussion at DIS. From the first option you see, evaluate whether it satisfies the “minimum standards” for each viewpoint, and if so, select the option that satisfies the standard. Once you have selected one option, go to (3). However, when evaluating the options, please start with the perspective you see first. After that, do not look at perspectives or options that you have not considered. Please refer only to the content of the “Additional Materials,” not to the content of the answers each of you provided in the Google Form in advance.

11.2.5 Questionnaire A questionnaire consisting of items related to the results of the discussion and items to evaluate the discussion was prepared. There was only one type of questionnaire, and all participants answered the same questionnaire.

11.2.5.1 Items related to the results of discussions We created an item that asks which option was adopted by the group and which option the individual wanted to choose. Specifically, the participants were asked to describe which option was chosen in the discussion, the reason for choosing that option, and which option they themselves wanted to choose in the course of the discussion.

11.2.5.2 Evaluation items for the discussion The evaluation of the discussion consisted of three items. The first was whether or not the discussion process was appropriate, the second was whether or not they were confident in the outcome of the discussion, and the third was their level of satisfaction with the discussion as a whole. The first item, asking whether the discussion process was appropriate, was answered using a 7-point scale ranging from “1: not at all to 7: very much so.” The second item, asking whether they were confident about the outcome of the discussion, was answered using a 7-point scale ranging from “1: not at all to 7: very much.” The third item, which asked the degree of satisfaction with the discussion as a whole, was answered using a 7-point scale ranging from “1: not at all satisfied to 7: very satisfied.”

11.2.6 Experimental procedures One classroom per group was used for the experiment. The participants were seated at desks facing each other in the classroom. To prevent infection by the new coronavirus, the experimenter wore a mouth guard and ventilation was ensured. The experimental participants also wore masks. An IC recorder and a Motorola recording application were used for recording. The duration of the experiment was about

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4
8 minutes per trial, with a 5-minute break every 30 minutes. A total of 5
32 trials were conducted in one experiment. First, after the participants were instructed, a procedure manual, an agenda sheet, and a questionnaire were distributed to each participant, and the participants were asked to read the agenda sheet silently according to the procedure manual. As soon as the participants finished reading the paper, the procedure of the discussion and additional materials, which were different for each group, were distributed one by one to each participant, and the participants were asked to discuss the paper and the additional materials. After the discussion the participants were asked to answer the questionnaire when they had decided which option to adopt. When they finished answering, the agenda paper, questionnaire, and additional materials were collected. If there was a change in the way the discussion was conducted, the procedure manual was also collected. After the last trial, we explained the purpose of this study. To maintain counterbalance the order of agenda and procedure was randomized for each group.

11.2.7 Instruction The instruction of the survey was as follows: [Greeting] [Before starting, place a sheet of paper on the subject’s desk explaining the experiment, and start recording when you are ready. Thank you very much for your cooperation in today’s experiment. My name is Moe Takahashi (Nanako Mitani), and I am a fourth-year student in the Takemura Seminar. I look forward to working with you. [Experiment description] In the experiment that you are about to participate in, you will be asked to discuss the presented agenda by referring to the “Procedures” that will be distributed to you. Please check the detailed procedure later. One more thing, there is a paper in your hand explaining the experiment. The experimental data will be processed statistically, and no individual will be identified. We will record the discussion, but the recording will not be used for any purpose other than research and we promise to keep it confidential. In addition, we have determined that there is no effect on the human body. Furthermore, if you feel unwell during the experiment, please let us know and we will stop the experiment at any time. Please don’t hesitate to let us know. Do you have any questions so far? If you have no questions, please leave it at that. First of all, please fill out this consent form. I’ll be handing out the consent forms. Please check the box next to “I do not consent to disclosure. I will collect the consent form and explanation sheet.

Decision strategies and bad group decision-making: a group meeting experiment

[Experiment started] Now we will begin the experiment. To begin, I will hand out the agenda paper, the procedure manual, and the questionnaire. I will hand them out while explaining which one is the agenda paper, the procedure manual, and the questionnaire. If you have any questions, please contact the experimenter. If you have any questions, please ask the experimenter. After the subject has read the agenda paper (Step 2) I will now hand out some additional materials. (In the case of a trial discussion at the WAD) This document contains the perspectives of this agenda item and the importance of each perspective. The level of importance is expressed in the range of 1 to 7, with higher numbers indicating higher importance and lower numbers indicating lower importance. (In the case of an attempt to discuss in LEX) This document contains the perspectives of this agenda item and the priority of the perspectives. (In the case of an attempt to have a discussion at DIS) This document contains the perspectives of this agenda item and the minimum standards to be met for each perspective. This is an aggregate of the answers we received from you via Google Form. I will distribute additional materials. After completing the questionnaire (Step 4) Since this is the end of the discussion on this topic, please collect the “agenda paper,” “additional materials,” and “questionnaire” (and the “procedure manual” after one strategy/experiment is completed). If you need to take a break, please do so at this time, and when you have completed the entire agenda, proceed to the “End of Experiment” instruction. [Moving on to the next experiment. We will now move on to the next item on the agenda. I will hand out a new “agenda sheet” and “questionnaire” (and a “procedure sheet” if the strategy changes). Distribute the agenda papers, questionnaires, and procedures, and repeat from the instruction after ( ). [30 minutes after the start of the experiment Please come back to your seats in five minutes. Please come back to your seats in five minutes. Let’s stop recording and take a five-minute break.

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We will now resume the experiment as five minutes have passed. Are you ready? We will now resume the experiment. At the beginning, I will hand out the agenda paper and the questionnaire (and the “procedure” if the strategy is changed). I will hand out the agenda paper, questionnaire, and procedure, and repeat from the instruction after ( ). Once you start writing the questionnaire for the last attempt. This is the last item on the agenda, so please answer question 7 at the end of the questionnaire as well. [Experiment terminated] This concludes today’s experiment. Thank you very much for your cooperation in this experiment. Stop recording. Explanation of the experiment Finally, I would like to explain the content of this study. The purpose of this study is to examine what kinds of discussions tend to lead to bad decision making. In social psychology, there is a phenomenon called groupthink, and it is said that this phenomenon does not necessarily lead to good decisions even when excellent people gather together. In our daily lives, it seems that we are sometimes so preoccupied with other factors, such as club meetings, that we neglect the most important factors. In this study, we focused on “how to proceed” in the discussion as one of the factors. In this study, we focused on one of the factors, “how to proceed” in the discussion, and asked the participants to discuss a text containing various elements in three different ways, to see how the group makes decisions and how the individuals evaluate the discussion. I have given you a brief explanation. If you have no questions, please leave it at that, if you do, please answer. Thank you very much for your cooperation in today’s experiment. Stop recording.

11.3

Results and discussion

11.3.1 Outline of analyzing the experimental results The purpose of this study was to examine the factors that lead to irrational decision-making in meetings, and the main factor was decision-making strategies. We conducted an experiment in which participants were asked to follow and discuss three types of decision strategies (WAD, LEX, and DIS). The participants were divided into four groups, and 32 agenda items were presented for each decision strategy. In this study, we also analyzed the group’s choice of the bad option

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and the difference between the group’s choice and the individual’s preferred choice. Two operational definitions of bad choices were used. The first is the option that was judged to be bad before the experiment by the researcher’s consensus, and the second is the option that was chosen as the bad option by the most number of confident participants in the questionnaire survey on the perception of decision-making among the four options used in the experiment. These two defined bad options were examined as separate indicators, although, of course, there were quite a few cases of overlap. The option that was interpreted as the one that the individual wanted to choose the most was the option that was chosen the most in the group (hereafter referred to as the option chosen by majority vote). Furthermore, for the majority-choice option, we analyzed data in which all participants in the group wanted to choose different options, either by excluding them from the analysis because it was not possible to narrow down to one option by majority vote or by using them in the analysis. However, since there was no difference in the results of the two analyses, we only show the results of the case in which the data in which the choices that individuals wanted to make differed from participant to participant were excluded from the analysis. The following sections describe, in order, the agreement rate between the two bad options, the tabulation of irrational decisionmaking, the tabulation of the ease of choosing the bad option in the option chosen by majority vote, the logistic regression analysis on irrational decision-making, and the multiple regression analysis on the evaluation of the discussion.

11.3.2 Agreement rate between the two bad choices The agreement rate between the options judged as bad by the experimenter and the options judged as bad based on the results of the questionnaire survey was 71.88%. From this, it can be concluded that the two types of bad choices were in agreement for about 70% of the agenda items.

11.3.3 Tabulations of bad decisions To examine the ease of choosing bad options in a group, the number of bad options chosen by the group was counted for each decision strategy. The results are shown in Fig. 11.2. In this figure the bad choices are described as “bad choices as defined by the researcher (defined by the researcher)” when they are the choices judged to be bad by the experimenter and as “bad choices as defined by the participants (defined by the participants)” when they are the choices judged to be bad based on the results of the questionnaire survey. The ease of choosing the bad option was evaluated by the following formula. As for the ease of choosing the bad option, the results suggest that WADs tend to be less likely to choose the bad option both when the bad option is defined as the option judged as bad by the experimenter and when the bad option is defined as the option judged as bad based on the results of the questionnaire survey. However, for each decision strategy, using 32 agendas, two-thirds of the decisions were the worst decisions according to the researcher’s definition, and about half of the decisions were the worst decisions in both cases

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Numbers of worst choice

according to the experimental participants’ definitions. This result is markedly different from the results of the individual decision-making task. It is not clear whether this is due to a problem in the way the decision-making strategies are taught or a characteristic of group decision-making, but it is possible that a different decision-making process occurs in group decision-making than in individual decision-making. To examine the difference between the group’s choice and the majority’s choice, we counted the number of differences between the group’s choice and the majority’s choice for each decision strategy. The results are shown in Fig. 11.3. It was

Worst choice defined by researchers

Worst choice defined by participants

Number of people

Figure 11.2 Number of bad choices made by the group for each decision strategy.

Figure 11.3 Number of differences between the group’s choice and the majority choice for each decision strategy.

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suggested that the difference between the group’s choice and the majority choice was more likely to occur in the case of DIS. This suggests that the DIS decisionmaking strategy leads to a group decision-making process that is significantly different from a process such as majority rule.

11.3.4 An examination of the ease of choosing the bad option in a majority-based choice In this study, choosing the bad option in a group and the difference between the option chosen by the group and the option the individual wanted to choose were considered decision-making considerations, but whether the option chosen by majority vote was the bad option was also considered. Table 11.1 shows the results when the bad choices were defined by the researcher, and Table 11.2 shows the results when the bad choices were judged to be bad based on the results of the questionnaire survey. Comparing the results with Fig. 11.2 and Table 11.2, respectively, it is suggested that the participants tend to be less likely to choose the bad option when they choose individually than when they choose as a group. Interestingly, LEX has relatively good decision results for individuals in the previous chapters, but not so good results for groups. The reason for this is not clear, but it may be that there are different psychological processes or group-specific interaction processes at work in the individual and group decision-making processes.

11.3.5 Logistic regression analysis on irrational decision-making 11.3.5.1 Analysis of the ease of choosing a bad option A logistic regression analysis was conducted to examine the effects of three factors: decision strategy, the group to which the participant belonged to, and the type of Table 11.1 Numbers of worst choice and not worst choice defined by researchers. Decision strategy

Worst choice

Not the worst choice

WAD LEX DIS

14 21 11

112 105 107

DIS, Disjunctive; LEX, lexicographic; WAD, weighted-additive decision.

Table 11.2 Numbers of worst choice and not worst choice defined by participants. Decision strategy

Worst choice

Not the worst choice

WAD LEX DIS

6 16 7

120 110 111

DIS, Disjunctive; LEX, lexicographic; WAD, weighted-additive decision.

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agenda on the likelihood of choosing a bad option. Specifically, we conducted a logistic regression analysis in the framework of a generalized linear model with the dependent variable being whether or not to choose the bad option (choosing the bad option 5 1, not choosing the bad option 5 0) and the independent variables being the decision strategy, the group to which the participant belonged to, and the type of agenda. The models were then evaluated using the Akaike information criterion (AIC). The models examined were a model that predicts whether or not to choose the bad option based on the intercept alone (model number 1), a model that predicts based on the intercept and the decision strategy (model number 2), a model that predicts based on the intercept and the group to which the participant belongs to (model number 3), a model that explains based on the intercept and the type of agenda (model number 4), and a model that predicts based on the intercept, the decision strategy, and the type of agenda (model number 5), and decision strategy, and the group to which the participant belongs to (model number 5), intercept and decision strategy, and the type of agenda (model number 6), intercept and the group to which the participant belongs to, and the type of agenda (model number 7), intercept and decision strategy, and the group to which the participant belongs to, and the type of agenda (model number 8). There were eight models: a model that predicts by the group the participant belongs to, the type of agenda (model number 7), the intercept and decision strategy, the group the participant belongs to, and the type of agenda (model number 8). We also compared the odds ratio of the decision strategy in the model with the lowest AIC among the four models that included the decision strategy. The worst option defined by the researcher was analyzed. The AIC of each model was compared and ranked, and the results are shown in Table 5.3. The model with the lowest AIC was the model that predicted whether to choose the worst option based only on the type of agenda (model number 4), with an AIC of 368.62. In other words, among the eight models examined, the model that predicted whether to choose the bad option based only on the type of agenda was the model with the highest predictive ability. Table 11.3 shows the odds ratio of the decision strategy in the model with the lowest AIC among the models, including the decision strategy. The partial Table 11.3 Akaike information criterion (AIC) rank and odds ratio for decision strategy, group, and agenda. Item

Model number

Model

AIC rank

DIS

WAD

LEX

Worst decision (researchers) Worst decision (participants) Difference from majority voting

6

Intercept 1 decision strategy 1 agenda Intercept 1 decision strategy 1 group 1 agenda Intercept 1 decision strategy 1 group

3

1.00

0.83

1.06

2

1.00

0.51

0.86

1

1.00

0.13

0.11

8 5

Notes: Group: group in which participants belonged to, agenda: type of agenda. DIS, Disjunctive; LEX, lexicographic; WAD, weighted-additive decision.  P , .001.

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regression coefficients for DIS were 20.18 for WAD and 0.06 for LEX, and no significant difference was found between WAD and LEX and DIS. The odds ratios were 0.83 for WAD and 1.06 for LEX. The odds ratios were 0.83 for WAD and 1.06 for LEX, indicating that WAD was 0.83 times more likely to choose the worst option than DIS, and LEX was 1.06 times more likely to choose the worst option than DIS. This result is contrary to the expectation that the worst group decision is more likely to be made in the case of DIS.

Examination of the worst option defined by the experimental participants The options that the experimental participants judged to be the worst from the results of the questionnaire survey conducted to select the bad options were defined as the bad options and analyzed. The AIC of each model was compared and ranked, and the results are shown in the upper part of Table 11.3. The model with the lowest AIC was the model that predicted whether participants would choose the bad option based on the group they belonged to and the type of agenda (model number 7), with an AIC of 299.57. In other words, among the eight models examined, the model that predicts whether participants will choose the bad option based on the group to which they belong to and the type of agenda is the model with the highest predictive ability. The odds ratio of the decision strategy in the model with the lowest AIC is shown in the lower part of Table 11.3. The partial regression coefficients using DIS as a standard, were, 20.68 for WAD and 20.15 for LEX, and there was no significant difference between WAD and LEX. The partial regression coefficients for WAD and LEX were 20.68 and 20.15, respectively, and there was no significant difference between WAD and DIS. The odds ratios were 0.51 for WAD and 0.86 for LEX, suggesting that WAD was 0.51 times more likely to choose a bad choice than DIS and that LEX was 0.86 times more likely to choose a bad choice than DIS. When the bad option was defined based on the results of the questionnaire survey of the experimental participants, the results were also contrary to the expectation that the worst group decision was more likely to be made in the case of DIS, similar to the results of the analysis of the worst option as defined by the researchers.

11.3.5.2 Analysis of the difference between the options chosen by the group and the options chosen by majority vote A logistic regression analysis was conducted to examine the effects of three factors: the decision-making strategy, the group to which the participant belonged to, and the type of agenda item, on the difference between the choice made by the group and the choice that the individual wanted to make. Specifically, we conducted a logistic regression analysis in the framework of a generalized linear model, with the dependent variable being whether or not there was a difference between the options chosen by the group and by majority vote (difference 5 1, no difference 5 0), and the independent variables being the decision-making strategy, the group to which the participant belonged to, and the type of agenda. The model was evaluated by

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AIC. Then, the models were evaluated by AIC. The models examined were a model that predicted whether differences would occur based on the intercept alone (model number 1), a model that predicted based on the intercept and the decision strategy (model number 2), a model that predicted based on the intercept and the group to which the participant belonged to (model number 3), a model that explained based on the intercept and the type of agenda (model number 4), and a model that explained based on the intercept and the decision strategy, a model predicting by intercept, group participants belonged to (model number 5), a model predicting by intercept, decision strategy, and agenda type (model number 6), a model predicting by intercept, group participants belonged to, and agenda type (model number 7), a model predicting by intercept, decision strategy, group participants belonged to, and agenda type (model number 8). There were eight models a model that predicts by the group the participant belongs to, the type of agenda (model number 7), the intercept and decision strategy, the group the participant belongs to, and the type of agenda (model number 8). We also compared the odds ratio of the decision strategy in the model with the lowest AIC among the four models that included the decision strategy. As a result of comparing and ranking the AIC of each model for the difference between the option chosen by the group and the option chosen by majority vote, the model with the lowest AIC was the model that predicted whether the difference would occur based on the decision strategy and the group to which the participant belonged to (model number 5), with an AIC of 314.02. In other words, among the eight models examined, the model that predicts the likelihood of differences based on the decision strategy and the group to which the participant belongs to can be judged to be the model with the highest predictive ability. The partial regression coefficients for DIS were 22.02 for WAD and 22.25 for LEX, indicating that WAD and LEX had a significantly negative effect on the likelihood of differences compared to DIS. The odds ratios were 0.13 for WAD and 0.11 for LEX. The odds ratios were 0.13 for WAD and 0.11 for LEX, suggesting that WAD was 0.13 times more likely than DIS and LEX was 0.11 times more likely than DIS to cause a difference between group decision-making and majority decision-making, and that DIS was more likely than WAD and LEX to cause a difference. Furthermore, the fact that the DIS showed introspection with the content “the first option seen was often chosen” suggests that the DIS is more likely to cause differences than the WAD and LEX.

11.3.5.3 Multiple regression analysis of discussion evaluation Multiple regression analysis was conducted to examine the effects of three factors (decision-making strategy, group to which participants belonged to, and type of agenda) on individuals’ evaluation of the discussion process, evaluation of the discussion results, and overall satisfaction with the discussion. Specifically, multiple regression analysis was conducted with the evaluation of the discussion process, the evaluation of the discussion results, and the overall satisfaction of the discussion as the dependent variables, and the decision-making strategy, the group to which the

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participants belonged to, and the type of agenda as the independent variables. The models were evaluated by AIC. The models examined were a model predicting by intercept only (model number 1), a model predicting by intercept and decision strategy (model number 2), a model predicting by intercept and participant’s group (model number 3), a model explaining by intercept and agenda type (model number 4), a model predicting by intercept, decision strategy, and participant’s group (model number 5), a model predicting by intercept, decision strategy, and agenda type (model number 6), a model predicting by intercept, group participants belong to, and agenda type (model number 7), a model predicting by intercept, decision strategy, group participants belong to, and agenda type (model number 8), an interaction between the intercept and the decision strategy, the group to which the participant belongs, the decision strategy and the group to which the participant belongs (model number 9), an interaction between the intercept and the decision strategy, the type of agenda, the decision strategy and the type of agenda (model number 10), and an interaction between the intercept and the group to which the participant belongs, the type of agenda, the group to which the participant belongs and the type of agenda (model number 11). We compared the partial regression coefficients of the decision strategy in the model with the lowest AIC among the six models that included the decision strategy. Multiple regression analysis was conducted to examine the influence of the three factors of decision-making strategy, the group to which the participants belonged to, and the type of agenda on the evaluation of the discussion process. As a result of comparing and ranking the AIC of each model, the model with the lowest AIC was the model that predicted the evaluation of the discussion process by the interaction of the decision strategy, the group to which the participants belonged to, and the decision strategy and the group to which the participants belonged to (model number 9), with an AIC of 2767.89. In other words, among the 11 models examined, the model that predicts the evaluation of the discussion process by the interaction of the decision strategy, the group to which the participant belongs to, and the group to which the participant belongs to with the decision strategy can be judged to be the model with the highest predictive ability. The partial regression coefficients for the decision strategies in this model are shown in Table 5.6. The partial regression coefficients for DIS as the reference were 20.07 for WAD and 20.02 for LEX. There was no significant difference between WAD and DIS for either WAD or LEX [WAD: t(1140) 5 20.63, n.s.; LEX: t (1140) 5 20.18, n.s.]. There was no significant difference between WAD and DIS [WAD: t(1140) 5 20.63, n.s.; LEX: t(1140) 5 20.18, n.s.]. This suggests that when comparing WAD and DIS, and LEX and DIS, the ratings of the discussion process did not change, respectively. Multiple regression analysis was conducted to examine the influence of the three factors of decision-making strategy, the group to which the participants belonged to, and the type of agenda on the evaluation of the outcome of the discussion. The lowest AIC model predicted the evaluation of the discussion process by the interaction of the decision-making strategy and the group to which the participants belonged to (model number 9), with an AIC of 3439.48. In other words, among the

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11 models examined, the model that predicts the evaluation of the outcome of the discussion by the interaction of the decision strategy, the group to which the participant belongs to, and the group to which the participant belongs to with the decision strategy can be judged to be the model with the highest predictive ability. The partial regression coefficients for the decision strategies in this model are shown in Table 5.6. The partial regression coefficients for DIS as the reference were 20.19 for WAD and 20.06 for LEX. There was no significant difference between WAD and DIS for either WAD or LEX [WAD: t(1140) 5 21.21, n.s.; LEX: t(1140) 5 20.41, n.s.]. There was no significant difference between WAD and DIS [WAD: t(1140) 5 21.21, n.s.; LEX: t(1140) 5 20.41, n.s.]. This suggests that when comparing WAD and DIS, and LEX and DIS, the evaluation of the results of the discussion did not change, respectively.

Analysis of overall satisfaction for discussion Multiple regression analysis was conducted to examine the impact of the three factors of decision-making strategy, the group to which the participants belonged to, and the type of agenda on overall discussion satisfaction. As a result of comparing and ranking the AIC of each model, the model with the lowest AIC predicted the satisfaction of the entire discussion by the interaction of the decision strategy and the group to which the participant belonged to (model number 9), with an AIC of 3096.21. In other words, among the 11 models examined, the model that predicts the satisfaction of the entire discussion by the interaction of the decision strategy, the group to which the participant belongs to, and the group to which the participant belongs to with the decision strategy can be judged to be the model with the highest prediction ability. The partial regression coefficients of the decision strategies in this model are shown in Table 11.4, where the partial regression coefficients for DIS were 20.11 for WAD and 20.04 for LEX [LEX: t(1140) 5 20.31, n.s.]. This suggested that the overall satisfaction with the discussion did not change when comparing WAD to DIS and LEX to DIS, respectively.

Table 11.4 Akaike information criterion rank and partial regression coefficient o for decision strategy, group, and agenda. Item

Model Model number

Process evaluation

9

Outcome evaluation

9

Satisfaction

9

Intercept 1 decision strategy 1 group 1 decision strategy 3 group Intercept 1 decision strategy 1 group 1 decision strategy 3 group Intercept 1 decision strategy 1 group 1 decision strategy 3 group

DIS

WAD

LEX

1.00

0.07

0.02

1.00

0.19

0.06

1.00

0.11

0.04

Notes: Group: group in which participants belonged to, decision strategy 3 group: interaction between decision strategy and group, process evaluation: evaluation of the discussion process, outcome evaluation: evaluation of outcome, and satisfaction: satisfaction level of discussion. DIS, Disjunctive; LEX, lexicographic; WAD, weighted-additive decision.

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243

Conclusion

The purpose of this study was to examine the factors that lead to the worst group decision-making in meetings. In this study, we mainly focused on decision-making strategies and examined the influence of decision-making strategies on the likelihood of making a bad group decision. As a preliminary survey, we conducted an interview survey to collect candidates for the alternatives to be presented in the experiment and a questionnaire survey to extract bad decisions from the answers obtained in the interview survey. Then, to examine the effect of decision strategies on the likelihood of making a bad group decision, an experiment was conducted in which the participants were asked to discuss in accordance with three types of decision strategies (WAD, LEX, and DIS). In the experiment, each group was asked to discuss according to all three decision strategies. The participants were divided into four groups, and 32 agenda items were presented for each decision strategy. We analyzed the effects of the decision strategy, the group to which the participants belonged to, and the type of agenda on the likelihood of the worst group decision. In doing so, we also examined the adoption of bad options by the group and the difference between the options chosen by the group and the options that individuals wanted to choose. We also considered two different definitions of bad choices, one by the researcher and one by the experimental participants. That is, the former was the option that the researcher judged to be bad through a prior council, and the latter was the option that most of the experimental participants judged to be bad based on the results of their questionnaire survey. The worst decision by the researcher’s definition was not defined by the decision maker himself, even though it was made through deliberation among the researchers. In addition, the worst decision as defined by the participants in the experiment is only a definition made by a majority of the participants in the experiment and does not correspond to all the personal judgments of all the decision makers. This point should be further examined in the future. The results of the analysis of bad group decision-making in this chapter showed that there was not much difference between WAD and DIS, and LEX and DIS, respectively, in adopting the bad option in a group for either of the two definitions of the worst option. Furthermore, the fact that the model with the highest predictive ability was the one that predicted whether or not the bad option would be chosen based only on the type of agenda item suggests that the decision strategy may not have much effect on the ease of choosing the bad option in the group. However, with regard to the difference between the option chosen by the group and the option that the individual wanted to choose, that is, the option chosen by majority vote, the results for both WAD and DIS, and LEX and DIS suggested that the difference was most likely to occur in the case of DIS. This result is consistent with the expectation that the worst group decision is most likely to occur in the case of DIS. As a result, the number of bad choices was lower than the number of group choices, regardless of the type of bad choice. The number of bad choices was lower when the group made decisions than when the individual made decisions. This suggests

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that the discussions in this experiment may have caused a decrease in the quality of decision-making like groupthink. We also analyzed the evaluation of the process of the discussion by individuals, the evaluation of the result of the discussion, and the satisfaction of the discussion as a whole. The results showed that there was no difference between WAD and DIS, and LEX and DIS in the evaluation of the process, the evaluation of the result, and the level of satisfaction. This suggests that the evaluation of the discussion and the level of satisfaction do not change regardless of which decision-making strategy is used. As a result, we found that there was no significant difference between WAD and DIS, and between LEX and DIS in terms of the ease with which the group chose the bad option, while there was no significant difference between WAD and DIS in terms of the ease with which the group chose the bad option. However, there was not much difference in the ease of choosing the bad option in the group between WAD and DIS, and between LEX and DIS. The nature of DIS corresponds to the introspection of the participants in the experiment, who said that the first option they saw was often chosen. However, since DIS is a decision that depends on the situation according to the attention span of various individuals, the difference between group decision-making and individual decision-making may be easy to appear. The implication of this study is that, unlike in the case of individual decisionmaking, decision-making strategies do not necessarily influence the worst choice in the case of group decision-making. In addition, apart from the abovementioned decision-making, we also examined whether the option that individuals wanted to choose was the worst option, and the results suggest that people are more likely to choose the bad option in group decision-making than in individual decisionmaking. For this reason, caution should be exercised in applying findings obtained so far in individual decision-making to group decision-making. One of the problems in this study was the content of the agenda, the options, and the perspectives. The agenda was a sentence describing a situation in which a decision must be made. As for the options, four were selected for each topic, and one was a bad option and three were not bad options. For each of the topics and options, we found that the content was ambiguous in this experiment. In addition, for the perspectives, we created six perspectives for each topic that might be used in discussion situations. Thus it is possible that each group interpreted the same topic differently during the discussion because the topics and options were ambiguous and some perspectives were difficult to understand. Therefore it may be necessary to conduct additional research on the content of the agenda to create a more sophisticated agenda in the future. In this study, we focused on decision-making strategies as a factor in bad group decision-making, and the results suggest that decision-making strategies have little effect on the group’s adoption of bad options, unlike the results of individual decision-making. This suggests that the process of group decision-making is quite different from that of individual decision-making. However, this result may be due to the fact that the experimental manipulation of the group decision-making strategy is slightly different from the manipulation and instruction methods of the individual decision-making strategy, and this is a subject for further study.

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References Janis, I. L. (1982). Groupthink: Psychological studies of policy decisions and fiascoes (2nd ed.). Boston: Houghton Mifflin. Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical descriptions of human choice behavior. Tokyo: Springer. Takemura, K. (2019). Foundations of economic psychology: A behavioral and mathematical approach. New York: Springer. Takemura, K., Takahashi, M., & Mitani, N. (2021). Shudan Ishikettei Houryaku to Warui Sentaku [Group decision strategies and bad choice]. Unpublished Manuscript, Department of Psychology, Waseda University (in Japanese).

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In Chapter 11, Decision Strategies and Bad Group Decision-Making: A Group Meeting Experiment, we examined the effect of decision strategy on bad decisions in group decision-making. The decision strategies manipulated in the experiment were additive difference model, lexicographic, and disjunctive, but unlike in the case of individual decision-making, there was little effect of decision strategy. It is possible that the decision strategies defined and manipulated in this study are group decision strategies, which are different from individual decision-making. This may have led to a different process of group interaction. Since the psychological process of group decision-making is different from that of individual decision-making, it is not clear how the psychological process of group decision-making leads to the worst choice. Therefore in this chapter, we will examine this issue. The first possibility is that in the cognitive process of group decision-making, some members have lost the ability to recognize that they are choosing the worst option or that they think that the option adopted by the group is the worst, but in the consensusbuilding process, they did not take the option they wanted. In this chapter, we will discuss the results of this experiment. Here, the participants in the experiment are asked to watch a video of a group decision-making process and consider whether they would consider it unsuitable or undesirable if the members of the group decided on an option that was clearly the worst in the video. This experiment was reported in part by Ideno et al. (2016).

12.1

Cognitive processes and groupthink in group decision-making

Imagine yourself participating in a meeting or discussion in some community. Do you feel, “There is something strange about this meeting,” “Should we really be discussing this now?,” or “By the way, what was this meeting originally about?” Or are you watching a live broadcast of the Diet on TV and wondering, “What are these people discussing?” You may be thinking, “What are they discussing?” or “The debate in the Diet is ridiculous.” As you can see, decision-making groups, even if they are made up of the best people, do not always make good decisions. However, Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00007-7 © 2021 Elsevier Inc. All rights reserved.

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despite the fact that we often feel this way in our daily lives, there has been little research on such “irrational meetings” or “ridiculous meetings.” The reasons for this may be as follows. Frankfurt (2005), author of On Bullshit, points out that one of the salient features of modern culture is that it is heavily covered with bullshit and flat logic. This is a well-known fact, and we may all find ourselves in this situation. However, we accept this situation without question. Many people tend to be confident that they can easily see through a coherent argument and believe that they will not be deceived. As a result, this phenomenon has received little conscious attention and has rarely been examined on an ongoing basis. By addressing “irrational meetings” in this study, cannot people really see “irrational meetings” as Frankfurt described them? I would like to examine what causes it, and whether people correctly understand the agenda of meetings and discussions in the first place. I hope that this research will lead to more efficient discussions that will benefit society. Many social psychological studies have pointed out that group decision-making can be distorted by social pressures such as conformity and authority. However, the implicit assumption of those studies has been that each individual is capable of making rational judgments and decisions as long as such social pressures do not exist. We tested this implicit assumption (Ideno et al., 2016). We first tested this assumption through two experiments. In everyday life, there are situations in all kinds of meetings where people find themselves straying from the original purpose of the meeting and talking about irrelevant things, or getting so hung up on details and rules that it seems as if the original purpose may not be achieved. This is also true in the case of a group of extremely talented members, who may make inferior decisions as a group than they would make as individuals. Janis (1972, 1982) called this kind of “stupid decisionmaking process by groups” “groupthink.” He examined the records of the Pearl Harbor attack, the Korean War, the Vietnam War, the Bay of Pigs Invasion, and the Watergate scandal to model the group psychological tendencies that lead to bad policy decisions, and the symptoms and preventive measures were examined. As slightly described in Chapter 11, Decision Strategies and Bad Group DecisionMaking: A Group Meeting Experiment, this concept of “groupthink” proposed by Janis (1972, 1982) has attracted the attention of many people and continues to generate many related papers. The earlier examples show that groups with a strong tendency to seek unanimity tend to show signs of groupthink. He concludes that when highly cohesive groups have organizational structural defects and are placed in stimulating situations, they show signs of groupthink and make flawed decisions. Organizational structural deficiencies include a lack of impartial leadership that gives members an equal opportunity to speak, a lack of norms that require orderly procedures, and uniformity in the social background and identity of members. An irritating situation also refers to a situation where there is a strong threat from outside the group, and no solution can be expected beyond the leader’s opinion. There are nine signs of a group that are said to be in a groupthink situation (Janis, 1972, 1982): (1) a sense of invincibility leading to optimism; (2) a callous belief that their group is inherently moral (the earlier two are signs of group overestimation); (3) a tendency to collectively rationalize past decisions and underestimate

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warnings; (4) a stereotypical belief that enemy leaders are too bad to negotiate with or too weak to fight back or stupid (the earlier two are signs of narrow-mindedness); (5) direct pressure to disagree; (6) direct pressure on members with opposing views; (7) self-censorship to stay within the bounds of group decisions; (8) majority opinion and the shared illusion that it is the consensus; (9) emergence of members who take on the role of “mind guard” to protect the group from information that contradicts the group’s views (the last four are signs of pressure for unity). These nine signs give concrete, observable attributes to the somewhat abstract concept of the “tendency to seek consensus.” Groups showing signs of groupthink are more likely to not fully consider possible options, tend not to consider rejected options, and are more likely to make “stupid” decisions. In this study, we decided to create meeting videos in three conditions, including actual videos of such “silly” meeting scenes, and conduct an exploratory study on people’s evaluation of meetings, including whether people can see through such “silly” discussions and, if not, what factors are involved.

12.2

Pilot Study 1

12.2.1 Purpose of Pilot Study 1 The purpose of Pilot Study 1 was to investigate whether there were any problems with the experimental procedure and the stimuli created prior to the main experiment.

12.2.2 Overview of the experiment Participants watched three videos of five students having a meeting and were asked to rate each video on a questionnaire. The experiment was conducted in the following order: watching a goal deviation video, answering the questionnaire, watching a procedural justice video, answering the questionnaire, watching a video that served the purpose, answering the questionnaire, and ending the experiment.

12.2.3 Making videos of a meeting scene (making experimental stimuli) The videos used as experimental stimuli were made by Waseda University students of a group decision-making acting scene with a scenario. Five students’ meeting scenes were filmed and three types of videos (goal deviation condition, procedural justice condition, and purposeful agreement condition) were made. The content of each video was a meeting scene between five executives of a club for the purpose of deciding where to hold a camp. The goal deviation condition was that as the meeting progressed, they deviated from the agenda of deciding where to hold the camp and eventually decided on the type of emergency water to keep in the club room. The procedural justice condition is that the meeting is properly held in response to the agenda, but the original majority opinion is not understood due to adherence to

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the set rules (the method of deciding the camp is a voting format). The conditions that match the purpose are meetings where the meeting proceeds suitably to the agenda and the original purpose of the camp is finally decided. The length of each video was as follows: goal deviation condition (4 minutes and 11 seconds), procedural justice (unnecessary rules) condition (7 minutes and 30 seconds), and goal matching condition (2 minutes and 40 seconds). Fig. 12.1 shows a scene from one of the actual conference videos displayed on the screen in Pilot Study 1.

12.2.4 Method Participants: A total of 13 university students (5 males, 8 females, mean age 21.23 years, SD 5 1.69) participated in the experiment. Procedures: The experiment was conducted in a small class room of Waseda University. The experimenter stood in front of a large number of experimental participants, gave instructions, and then presented the images on a screen to conduct the experiment. Therefore the experimental participants watched the images from their respective seats, and the distance between the screen and the experimental participants was not controlled. The experiment was conducted by presenting the videos in the following order: goal deviation condition, procedural justice condition, and goal agreement condition. After each video, participants were asked to answer a questionnaire, and the next video was presented paying attention to the timing when all participants had completed their answers. The duration of the experiment was about 30 minutes. Items on the questionnaire: After watching each video the participants were asked to score the desirability of the meeting’s decision (1 point: very undesirable to 7 points: very desirable) and the suitability of the meeting’s purpose and discussion (1 point: very unsuitable to 7: very suitable) and to write freely about the content and impression of the meeting.

Figure 12.1 A scene from the video used in Pilot Study 1.

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12.2.5 Results A total of 13 subjects (5 males, 8 females, mean age 21.23 years, SD 5 1.69) were analyzed. Figs. 12.2 and 12.3 show graphically the mean values of desirability and suitability of group decisions for the three meetings. Since no missing values were found, the analysis was conducted for all participants in the experiment. The mean values of the questionnaire item for the videos were calculated, and the mean values of desirability and suitability for the three videos are shown in Figs. 12.2 and 12.3. These show that the desirability items 7 6 5 4 3 2 1 0

Goal deviaon

Procedual jusce

Goal matching

Figure 12.2 Desirability of group decision in Pilot Study 1. 7 6 5 4 3 2 1 0

Goal deviaon

Procedual jusce

Figure 12.3 Suitability of meeting process in Pilot Suitability 1.

Goal matching

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were rated higher in the order of goal matching . procedural justice meeting . goal deviation, and the suitability items were rated higher in the order of procedural justice meeting . goal matching meeting . goal deviation. Next, we conducted a correlation analysis between desirability and suitability of the decision-making process in each video. A significant strong positive correlation was found between the desirability and suitability of the group decision (r 5 0.92, P, .001). There was also a significant strong positive correlation between desirability and suitability of the procedural justice condition (r 5 0.88, P, .001). In addition, there was a significant strong positive correlation between the desirability and suitability of the fitness-for-purpose condition (r 5 0.78, P, .01). There was also a significantly negative correlation between the desirability of the procedural justice condition and the desirability for goal matching (r 5 20.56, P, .05). Furthermore, a significant moderate negative correlation was found for suitabilitiy ratings between procedual justice and goal matching (r 5 20.53, P, .10). We also see the difference in the mean value of each video. Therefore we performed an analysis of variance (ANOVA) using ANOVA with the type of videos as an intrasubject factor. Regarding desirability items between each video, a significant difference tendency was observed at the 10% level. In addition, significant difference for the suitability items is also found at the 1% level. Furthermore, multiple comparisons are performed, and then there was a difference between the regular meeting, the goal deviation meeting, and the goal matching meeting.

12.2.6 Discussion From the results of Pilot Study 1, it was found that the participants noticed that they had lost the purpose of the meeting and could evaluate it correctly. However, there was no significant difference between procedural justice and the desirability and suitability to agenda, so even if the meeting did not come to a correct conclusion, if the meeting procedure was procedual justice. In addition, a significant strong positive correlation was found between the desirability and suitability of each video, so it can be said that the more desirable the meeting is, the more suitable the meeting is on the agenda. The result showed a significant negative correlation between procedural justice and goal matching, suggesting that those who highly value goal matching value procedural justice bound by rules as undesirable. However, it should be noted that in Pilot Study 1, the number of samples is as small as 13, which makes the result unreliable. It will be necessary to increase the number of samples and control the experiments in the future.

12.3

Pilot Study 2

12.3.1 Purpose 

The purpose of Pilot Study 2 is to further increase the sample size using the experimental design and experimental stimuli that were improved in Pilot Study 1 and to find out if there are any improvements that can be made.

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12.3.2 Overview of Pilot Study 2 In Pilot Study 2, five students watched three videos of a meeting and were asked to rate each video on a questionnaire. The experiment was conducted in the following order: watching the goal deviation video, answering the questionnaire, watching the procedural justice video, answering the questionnaire, watching the video that met the goal or objective, answering the questionnaire, and then completing the experiment. Creation of conference videos (creation of experimental stimuli): The videos used in Pilot Study 2 were taken in a small classroom at Waseda University. Five students’ conference scenes were filmed and three types of videos were created (conditions for goal deviation, conditions for procedural justice, and conditions for goal matching). The first half of each video had in common that the purpose of the meeting was to decide on a training camp, and the importance of selecting a candidate site with safety in mind. In the second half, we created a goal deviation condition, a procedural justice condition, and a unanimity of purpose condition, in much the same flow as the videos used in Pilot Study 1. The length of each video was set to about 6 minutes and 30 seconds, consisting of the goal deviation condition (6 minutes and 45 seconds), the procedural justice condition (unnecessary rule condition) (6 minutes and 35 seconds), and the goal matching condition (6 minutes and 32 seconds). Fig. 12.4 shows the scene of the conference video actually displayed on the screen in Pilot Study 2.

12.3.3 Method of Pilot Study 2 12.3.3.1 Participants of the experiment A total of 47 university students and professional trainees (15 males, 32 females; mean age: 26.15 years, SD 5 9.09) participated in the experiment. The experiment took place at a vocational school.

Figure 12.4 A scene from the video used in Pilot Study 2.

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Apparatus: The experimenter stood in front of a large number of experimental participants, gave them instructions, and then presented the images on a screen to conduct the experiment. Therefore as in Pilot Study 1, the experimental participants watched the videos from their respective seating positions, and the distance between the screen and the experimental participants was not controlled.

12.3.3.2 Questionnaire items After viewing each video, participants were asked to score their desirability for the meeting (1 point: very undesirable to 7 points: very desirable) and the sutability of the meeting’s purpose and discussion (1 point: very unsuitable to 7 points: very suitable) and asked for a free description of the meeting and their impressions. Furthermore, after all the videos were completed, the order of the meetings that I thought was good and the one that the people in the videos were satisfied with was calculated (ranking system).

12.3.3.3 Procedure The experiment was conducted by presenting the videos in the following order: goal deviation condition, procedural justice condition, and goal congruency condition. After each video, participants were asked to answer a questionnaire, and the next video was presented, paying attention to the timing when all participants had finished answering.

12.3.4 Results The data of 10 participants with missing values were deleted, and the analysis was conducted on 37 participants (9 males, 28 females, mean age 25.65 years, SD 5 9.12). Figs. 12.5 and 12.6 show the mean values of the three meeting desirability and their suitability to the agenda. From Figs. 12.5 and 12.6 the desirability items showed higher ratings in the order of desirability of the meeting: goal matching .procedural justice . goal deviation, while the suitability items showed higher ratings in the order of procedural justice . goal matching . goal deviation. Figs. 12.7 and Fig. 12.8 summarize the ranking results of good meetings and satisfactory meetings. Fig. 12.7 shows that the ranking results of good meetings are in the order of goal matching meetings . procedural justice meetings . goal deviation meetings. In addition, Fig. 12.8 indicates that satisfaction with the meetings was highly evaluated in the order of goal deviation meetings . goal matching meetings . procedural justice meetings. The results showed that there was a significant moderate positive correlation at the 0.1% level (r 5 .56, p , .001) between the desirability of attending a goal deviation meeting and the suitability of attending a goal deviation meeting. There was also a moderate positive correlation between the desirability for procedural

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7 6 5 4 3 2 1 0 Goal deviaon

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Figure 12.5 Desirability of group decision in Pilot Study 2. 7 6 5 4 3 2 1 0 Goal deviaon

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Figure 12.6 Suitability of meeting process in Pilot Study 2.

justice meetings and the suitability for procedural justice meetings, which was significant at the 0.1% level (r 5 .67, p , .001). There was also a strong positive correlation at the 0.1% level (r 5 .78, p , .001) between the desirability for meetings with goal matching and the desirability of meetings with goal matching. In addition, there was a moderate positive correlation at the 1% level between desirability for deviation meetings and desirability for the goal matching (r 5 .44, p , .01). There was also a significant weak negative correlation at the 5% level between suitability for procedural justice meetings and suitability for goal deviation meetings (r 5 20.36, p , .05).

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30 Goal deviaon

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Figure 12.7 Goodness rating of meeting in Pilot Study 2.

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Figure 12.8 Rating of satisfaction with meeting in Pilot Study 2.

12.3.5 Discussion Noteworthy in Pilot Study 2 are the results of asking the video performers the order of meetings they were satisfied with, shown in Figs. 12.7 and 12.8. Here the most appreciated meeting was the goal matching meeting, however some participants described the goal deviation meeting as being very favorable in the free description question. This may be due to the friendly atmosphere of the video scene that stimulated the experiment. It was suggested that even if the original goal is not reached,

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people may be satisfied with the meeting if the atmosphere of the process seems enjoyable and all members can exchange their opinions. Therefore, the improvements obtained in Pilot Study 2 are as follows.

12.3.5.1 Creation of a meeting video The following four changes were made to the video: First, we changed the lines that might affect the participants in the experiment; second, we changed the shooting range to only the upper body because some people said that the movement of their feet bothered them during the experiment; third, we unified the background color of the video; fourth, we unified the atmosphere in all the videos, because we thought that the harmonious atmosphere of the irregular meeting might have affected the results.

12.3.5.2 Experimental procedure We made the following three changes to the experimental procedure. The first change was the experimental environment; in the preliminary experiment, a large number of participants were exposed to the experiment at once, but in the main experiment, the experimenter and participants were exposed to the experiment oneon-one. The second change was to randomly change the order of the videos in this experiment for counterbalance (there were six ways to present the three types of videos). The third change was the addition of psychological load items. Half of the participants were asked to watch the video while counting the number of times one of them nodded as a mental load. Figs. 12.5 and 12.6 show that the desirability items were rated higher in the order of goal matching . procedural justice . goal deviation, and the desirability items were rated higher in the order of procedural justice . goal matching . goal deviation. In addition, Figs. 12.7 and 12.8 show the mean values of the order in which the participants thought the meeting was good and the order in which the performers in the video thought the meeting was satisfactory. Figs. 12.7 and 12.8 show that the order of the meetings that the participants thought were good was goal matching . procedural justice . goal deviation, and the order of the meetings that the actors were satisfied with was goal deviation .goal maching . procedural justice. The results of the correlation analysis showed a significant moderate positive correlation (r 5 0.56, P, .001) between the desirability and suitability of goal deviation. There was also a significant moderate positive correlation between the desirability of procedural justice and desirability (r 5 0.67, P, .001). In addition, there was a significant strong positive correlation between the desirability of goal congruence and desirability (r 5 0.71, P, .001). There was a significant moderate positive correlation between the desirability of goal deviation and the desirability of congruence (r 5 0.44, P, .01), and a significant weak negative correlation between the desirability of procedural justice and the desirability of goal deviation (r 5 20.36, P, .05). Furthermore, analysis of variance was conducted using ANOVA to examine the difference between the means of desirability and suitability for the agenda in each

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video. The results showed that there was a significant trend (P, .10) in the difference in the desirability item according to the type of video. In addition, there was a significant difference (P, .001) between the two types of videos in the item of desirability. In addition, multiple comparisons between video types showed that there were significant differences between procedural justice and goal deviation, and goal congruence and goal deviation. The results showed that there were significant differences between procedural justice and purposefulness, and between purposefulness and goal deviation. This may have been due to the congenial atmosphere of the video, which was the stimulus for the experiment. The results suggest that even if people do not reach the original goal, they may feel satisfied with the meeting if the atmosphere of the process is enjoyable or if all members can share their opinions.

12.4

Method of the experiment

12.4.1 Creation of experimental stimuli for the experiment The video for this experiment was taken in a small classroom at Waseda University. Five students filmed a meeting scene and made three kinds of videos. The contents of each video were generally the same as those used in the preliminary Experiment 2 and were filmed taking into account the improvements mentioned earlier. The length of each video was approximately 6 minutes, consisting of 6:02 minutes for the goal deviation condition, 6:05 minutes for the procedural justice condition, and 5:42 minutes for the goal mathcing condition. The procedural justice video was replaced later due to problems with some of the dialogs. Fig. 12.9 shows a scene from a conference video that was actually shown on the screen in this experiment.

Figure 12.9 A scene from the video used in the expeiriment.

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12.4.2 Implementation of the experiment A total of 100 undergraduate and graduate students (46 males and 54 females, mean age 20.6 years, SD 5 1.62, including 3 with missing data) participated in the experiment. The mean age was 20.6 years, SD 5 1.62, of which 3 were missing data. In the first half of the experiment, 51 participants (24 males, 27 females, mean age 20.53 years, SD 5 1.57) did not receive any mental load (control group) (Experiment 1). Forty-seven participants (22 males, 25 females, mean age 20.79 years, SD 5 1.69) in the latter half of the experiment (experimental group) were subjected to mental stress (experimental group) (Experiment 2). The experiment was conducted by showing a video on a screen in the laboratory. Fig. 12.10 shows the experimental site. The size of the screen was 110 cm (length), 215 cm (width), 320 cm (distance from the participant), and the viewing angle was 36
38 degrees. After watching the videos of the meetings, the participants were asked to rate how desirable the meeting was (1 point: very undesirable to 7 points: very desirable) and how suitable the purpose and discussion of the meeting were (1 point: very unsuitable to 7 points: very suitable). After the completion of all the videos, the participants were asked to rank the three meetings in order of how good they thought the meeting was and how satisfied they were with the meeting (ranking method). In this experiment, three videos were presented in a random order. To make it easier for the participants to see the videos on the screen, the lights in the room were turned off during the presentation of the videos and turned on again when they filled out the questionnaire. In addition, half of the participants were asked to

Figure 12.10 A view of the experiment room. Note: The position of the participant sitting represents the participant.

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watch the video while counting the number of nods of one of the video actors as a mental load. The duration of the experiment was about 40 minutes. The video used in the experiment is corresponding to the condition of goal deviation, procedural justice, and goal matching, respectively. In the instruction of the experiment, the experimenter called the videos in the numbers such as Videos 1, 2, and 3. An example of video scene is shown in Fig. 12.10. The instruction was as follows.

12.4.2.1 General instructions Thank you very much for your cooperation in this experiment. Thank you very much for your cooperation in this experiment. My name is xxx, a fourth-year student of the Takemura Seminar. Thank you very much for your cooperation. The experiment that you are going to participate in today is to watch a video about a meeting and to evaluate it. The experiment is expected to take about 40 minutes. After the experiment, we will give you a 500 yen book card for a small fee.

12.4.2.2 Experimental instructions In this experiment, you will watch three videos about a certain meeting scene. In this experiment, you will be asked to watch three videos of a meeting scene, and after watching each video, you will answer a questionnaire. If we were to name them Video 1, Video 2, and Video 3 in order from the beginning (the video 1,2,3 is corresponding to each experimental condition such as goal deviation, procedural justice and goal matching, but presentation order is counterbalanced. The example is shown in Fig. 12.9), the order would be Video 1, Questionnaire 1, Video 2, Questionnaire 2, Video 3, Questionnaire 3, and the rest of the questionnaires. Please do not open the next page of the questionnaire until you are instructed to do so. Do you have any questions so far? If you have any questions so far, please ask them to fill out the consent form. Fill out the consent form. (If there are no questions about the experiment) The experimental data will be processed statistically, and no individual will be identified. The experimental data will be processed statistically, and no individual will be identified. Also, there will be no effect on the human body. If you feel sick during the experiment, please do not hesitate to inform us so that we can stop the experiment. First of all, please fill out this consent form. (Confirm the contents of the consent form. The content of the consent form must be explained.) Start the experiment. We will now begin the experiment. Now, let’s start the experiment. (Start playing Video 1) [End of Video 1] Yes.

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Yes, please turn the cover of the questionnaire and answer the first question. (End of Questionnaire 1) Yes, I will play the next video. [End of video 2] Yes, please turn the cover of the questionnaire and answer the second questionnaire. [End of Questionnaire 2] Yes, that’s right, the next video will be played. [End of video 3] Yes, please turn the cover of the questionnaire and answer the third questionnaire. Please answer the rest of the questionnaires. Yes, this is the end of the experiment. Thank you very much. If you have any comments about this experiment, please let us know. End of Experiment This is the end of the experiment. Thank you very much for your cooperation in this experiment. Gratitude Procedure Please fill out this form to receive a 500 yen library card as a reward. Please fill out this form. The following post-experiment debriefing will be conducted at the end of the experiment or in parallel with the gratuity procedure. I will briefly explain the contents of this research. The purpose of this study was to explore the problems that can be observed in a discussion situation. In social psychology, a phenomenon called groupthink is known, and it is known that good decisions are not always made even when excellent people gather together. Even in our daily lives, we often get sidetracked from the original purpose of a group meeting and end up discussing irrelevant things, or we become obsessed with details and rules and do not always achieve the original purpose. So I decided to make a video of the conditions for sticking to the rules, getting sidetracked, and following the purpose of the meeting, and see how we evaluate meetings. Now that I’ve given you a brief overview, do you have any questions? [End].

In the experiment with psychological load, before playing the video, we asked the participants to watch the video while counting the number of nods of the man

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sitting in front of them on the right. In the experiment with psychological load, before playing the video, we added the following instruction: “Please watch the video while counting the number of nods of the man sitting in front of you on the right.” The following instruction was added.

12.5

Result of experiment

12.5.1 Experiment 1 12.5.1.1 Overall results Fig. 12.11 shows the mean values of the desirability and suitability of the three meetings. Fig. 12.11 shows that the participants rated the meeting highly in the order of congruence of purpose . procedural justice . goal deviation for the desirability and suitability items. Furthermore, Figs. 12.12 and 12.13 show the order of meeting desirability and meeting satisfaction in the control group of Experiment 1. From the abovementioned figures, it was found that the desirability of the meeting was highly evaluated in the order of congruence of purpose . procedural justice . goal deviation. As for the satisfaction of the meeting, the order of evaluation was goal matching . goal deviation . procedural justice.

12.5.1.2 Correlation analysis The results of the correlation analysis showed that there was a significant strong positive correlation between the desirability and suitability of goal deviation (r 5 0.73, P, .001). There was also a significant moderate positive correlation between the desirability of procedural justice and desirability (r 5 0.57, P, .001). 6 5 4 Desirability

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Figure 12.11 Desirability and suitability rating in Experiment 1.

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50 45 40 35 Goal deviaon

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Figure 12.12 Ranking judgment of meeting desirability in Experiment 1.

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Figure 12.13 Ranking judgment of meeting satisfaction in Experiment 1.

There was also a significant strong positive correlation between the desirability of congruence of purpose and desirability (r 5 0.72, P, .001). Furthermore, there was a significant low positive correlation between the desirability of goal deviation and the desirability of congruence (r 5 0.28, P, .05). Correlation analysis was also conducted for each desirability item, but no significant correlation was found between any of the videos.

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12.5.1.3 Analysis of variance We also conducted an ANOVA to see the differences in the mean values of the meeting evaluations for each video. The results of multiple comparisons showed that there was a significant difference between all the videos, both for the desirability and suitability items.

12.5.2 Experiment 2 12.5.2.1 Overall results Fig. 12.14 shows the mean values of the desirability and suitability items for the three meetings in the order of goal matching . procedural justice . goal deviation. Furthermore, Figs. 12.15 and 12.16 show the order of meeting desirability and meeting satisfaction in the experimental group of Experiment 2. In terms of meeting desirability, we found that the order of evaluation was as follows: goal matching . procedural justice . goal deviation. As for the satisfaction of the meeting, the order of the evaluation was goal matching . goal deviation . procedural justice.

12.5.2.2 Correlation analysis The results of the correlation analysis showed that there was a significant strong positive correlation between the desirability and suitability of goal deviation (r 5 0.78, P, .001). There was also a significant moderate positive correlation between the desirability of procedural justice and desirability (r 5 0.42, P, .01). In addition, there was a strong positive correlation between the desirability of goal congruence and desirability (r 5 0.74, P, .001). There was also a significant low 6

5

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Figure 12.14 Desirability and suitability rating in Experiment 2.

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45 40 35 30 25

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Figure 12.15 Ranking judgment of meeting desirability in Experiment 2. 40 35 30 25 Goal deviaon 20 Procedual jusce

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Figure 12.16 Ranking judgment of meeting satisfaction in Experiment 2.

positive correlation between the desirability of goal deviation and the desirability of goal matching (r 5 0.32, P, .05). Correlation analysis was also conducted for each suitability item, but no significant correlation was found between any of the videos.

12.5.2.3 Analysis of variance We also conducted an ANOVA to see the difference in the mean values of the meeting evaluations for each video. The results showed that there were significant

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differences among the videos for both the agreeableness and disagreeableness items, and the multiple comparison results showed that there were significant differences among all the videos for the agreeableness item. The results of multiple comparisons showed that there were significant differences between all the videos for the desirability item. For the desirability item, there were significant differences between goal matching and goal deviation, and between procedural justice and goal deviation.

12.5.2.4 Interaction between control and experimental groups An ANOVA was conducted to examine the interaction between the control and experimental groups. As a result, there was a significant trend in the interaction between mental load and video. Therefore when we looked at the simple main effect, we found a significant difference between mental load (experimental group and control group) and goal deviation. Analysis of variance was also conducted for the worthiness items, but no significant difference was found in the interaction.

12.6

Discussion

12.6.1 Experiment 1 In Experiment 1, 51 participants (24 males and 27 females) who were not subjected to mental stress were analyzed as the control group. In Experiment 1, 51 participants (24 males and 27 females) who were not subjected to mental load were analyzed. In the order of desirability of group decision-making, the participants rated the level of desirability as goal matching . procedural justice . goal deviation, and in the order of satisfaction, the participants rated the level of satisfaction as goal matching . goal deviation . procedural justice. From the open-ended comments, many participants emphasized the importance of “whether the discussion was conducted well” in their satisfaction with the meeting. In the procedural justice video the participants spent a lot of time on the lottery procedure and did not discuss much, which may have led to the reversal of the rating of goal deviation . procedural justice. Correlation analysis showed positive correlations in all videos for the desirability and suitability items, indicating that people rated meetings as more desirable when they were suitable to the agenda. Analysis of variance showed significant differences among the videos for both the desirability and suitability items, and multiple comparisons showed significant differences among all videos. Since it can be said that there was a difference in the mean of the meeting evaluations of each video, people were able to discriminate between goal deviation, procedural justice, and goal congruence, and they also rated goal matching decision-making highly and goal deviation due to excessive promotion of goal deviation and procedural justice

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low. This suggests that the participants in the experiment are able to recognize bad group decision-making to some extent.

12.6.2 Experiment 2 In Experiment 2, we analyzed 47 participants (22 males and 25 females) who were subjected to psychological load as the experimental group. The results of the analysis showed that the desirability for the meeting of the agenda was highly evaluated in the order of goal matching . procedural justice . goal deviation. This suggests that people correctly evaluate desirable and suitable meetings even under psychological stress and can detect group decisions that deviate from the goal. In the order of desirability, participants rated the meeting as goal matching . procedural justice . goal deviation, and in the order of participant satisfaction, participants rated the meeting as goal matching . goal deviation . procedural justice. This result is also the same as that of the control group, indicating that people correctly judge desirable meetings to some extent even under psychological stress and evaluate meetings with lively discussions as highly satisfactory. The results of the correlation analysis showed that all the videos were positively correlated for the items of desirability and sutability, indicating that people evaluate meetings as more desirable when they are suitable to the agenda, even under psychological stress. A significant positive correlation was also found between goal deviation and procedural justice, which means that people who highly valued rule-bound procedural justice meetings highly valued goal deviation meetings that deviated from the agenda.

12.6.3 Interaction between control and experimental groups An interaction between mental load and video was found, as well as a significant difference between mental load and goal deviation. This suggests that people may be more likely to rate the meeting of goal deviation highly when they are given a mental load.

12.7

Conclusion

Bad decisions and irrational meetings are often hidden in our daily lives (Frankfurt, 2005). There have not been many studies on this topic. Frankfurt (2005) points out that, although modern society is full of poop arguments, people are so convinced that they are not fooled that this phenomenon has not caused much conscious attention and has rarely been subjected to continuous examination. However, the conclusion that can be drawn from this study is that people are able to pay attention to the process of irrational argumentation and are able to recognize what is an suitable argument for the purpose. Considering this, it seems that people are not so “stupid as Frankfurt suggested.

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In this chapter, I have examined whether the ability to recognize the worst option in the cognitive process of group decision-making is lost in some members by conducting an observational experiment using video. They noticed when discussions in group decision-making deviated from the objectives or pursued procedural justice so much that they resulted in decision processes that were different from the goals or purposes and rated them lower than discussions that were consistent with the goals or objectives. It is true that people tended to evaluate superficial procedural justice issues more highly, especially in situations of high mental load, but in general, people seemed to be able to evaluate the development of discussions reasonably well from the standpoint of an observer. Janis (1972, 1982) called “groupthink” the “foolish decision-making process by groups” that occurs in meetings and other situations and pointed out that groupthink occurs in many important policy-making situations. The consequence of this study is that, while it may be true that even experts sometimes engage in groupthink in important decision-making, people can check the process of irrational discussion well enough if they follow the discussion from the standpoint of an observer. Indeed, the response of government agencies to Covid-19 that has unfolded around the world shows many signs of such groupthink intervening. However, if there is transparency in the discussion of policy making, citizens can check the policy making process during and after the decision-making process and evaluate the policy at least after the fact, which can be used for future policy making. For example, in Japan, the government’s expert meetings, expert subcommittees, and other important policy decision-making processes for Covid-19 are not disclosed in public documents. Although there may be many states and local governments that keep such decision-making processes secret, the implication of this study is that it would be desirable for the processes of meetings that have important consequences for citizens to be made public, even after the fact, since people can fully evaluate the processes and may be able to contribute to better decision-making or avoid bad decisions. It is desirable that the process of meetings that have important consequences for citizens be made public even after the fact.

References Frankfurt, H. G. (2005). On bullshit. Princeton, NJ: Princeton University Press. Ideno, T., Sakagami, T., Fujii, S., Karasawa, K., Hatori, T., Hayashi, M., . . . Takemura, K. (2016). Mokuteki kara Itudatsu shita kaigi no Hyouka ni kansuru Kentou [A study on the evaluation of meetings deviating from the purpose]. In: Poster presented at the 57th annual meeting of the Japanese Society of Social Psychology, Kwansei Gakuin University, Hyogo, JP. Janis, I. L. (1972). Victims of groupthink. Boston, MA: Houghton Mifflin. Janis, I. L. (1982). Groupthink: Psychological studies of policy decisions and fiascoes (2nd ed.). Boston, MA: Houghton Mifflin.

Revisiting the group decision-making experiment

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In Chapter 12, An Observational Experiment in Group Decision-Making: Can People Detect Bad Group Decisions?, three conditions were established: the procedural justice condition, in which bad decisions are made because rules are too important; the goal deviation condition, in which meeting process deviate from the original purpose; and the goal matching condition, in which discussions are conducted in accordance with the goals. The participants were asked to evaluate the meeting after viewing the video of group decision-making. The theme of the meeting was to decide the location of a club camp. The study in Chapter 12, An Observational Experiment in Group Decision-Making: Can People Detect Bad Group Decisions?, was about whether people can detect when a meeting in group decision-making is not in line with its original purpose. The research in this chapter examined whether people can notice when the outcome of a decision is unreasonable and evaluate it as undesirable. The research in this chapter was conducted by Takemura, Ideno, Miyajima, Okuma, and Sakagami (2021).

13.1

Irrationality and bad decision-making in group decision-making

There are many kinds of meetings in our daily life. The term “meeting” can mean anything from a small one, such as deciding which restaurant to go to with friends, to a large one, such as discussing a bill in the Diet. Frankfurt (2005) points out that irrational meetings are often held as a characteristic of modern culture and compares them to “poop discussions.” Why do irrational meetings take place? One possible reason is the concept of groupthink proposed by Janis (1972, 1982). Groupthink refers to the fact that when a group of people make a decision, they make a more foolish decision than when they make a decision individually. In a situation where several people are gathered, it is easy to imagine that they are unable to express their own opinions because they are concerned about others and are influenced by the atmosphere of the place. In addition, Frankfurt (2005) stated that many people think they can spot irrational meetings, so they are not seen as a problem and little consideration has been given to irrational meetings. The results of the research in Chapter 12, An Observational Experiment in Group DecisionMaking: Can People Detect Bad Group Decisions?, showed that people can properly evaluate the process of a meeting if it is not in line with its purpose. Therefore this study examines whether people can detect when the outcome of group Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00004-1 © 2021 Elsevier Inc. All rights reserved.

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decision-making is irrational, rather than the process of irrational meetings. In addition, we will examine how people evaluate irrational group decision-making and also the factors that lead people to evaluate that a group decision is irrational. In Chapter 12, An Observational Experiment in Group Decision-Making: Can People Detect Bad Group Decisions?, the participants were asked to watch a video of a meeting under three conditions: procedural justice, goal deviation, and goal matching, and to evaluate the video of a scene in which a group makes a group decision about the destination of a club camp. The procedural justice condition was that the meeting proceeded according to the agenda until the middle of the meeting, but when deciding the destination of the camp by majority vote, the meeting adopted the minority opinion instead of the majority opinion because of the insistence on the majority vote method. The method of majority vote was to fold the hair in two when voting, and votes that did not follow this rule were considered invalid. The deviation from the purpose condition was a meeting that went off the topic in the middle of the meeting, resulting in losing sight of the purpose of the meeting and deciding on other matters instead of deciding on the camp destination. The goal matching condition was that the meeting proceeded properly until the end and the campsite could be decided. The results of the experiment showed that the participants evaluated the meetings as desirable in the order of the goal matching condition, procedural fairness condition, and goal deviation condition. This suggests that people are able to judge irrational meetings appropriately in Chapter 12, An Observational Experiment in Group Decision-Making: Can People Detect Bad Group Decisions?, and do not necessarily overlook irrational meetings as suggested by Frankfurt (2005). In the present study, we examined whether people can detect irrational group decision-making by a group rather than the process of a meeting, and to examine the factors that contribute to this, we conducted an experiment in which real-life decision-making situations that are evaluated as irrational were adopted as meeting agendas and people or participants were asked to evaluate the meeting situations. Second, we conducted a preliminary survey using a questionnaire to examine the so-called bad group decision-making situations in which people are not able to make rational decisions in their daily lives that satisfy the earlier settings. In addition, we made the following three changes to the research in Chapter 12, An Observational Experiment in Group Decision-Making: Can People Detect Bad Group Decisions?, regarding the setting of the experiment. The first factor is the outcome of the decision, which is risky (high hazard) or riskless (low hazard), and the second factor is the difference in the emphasis of the risk. The third factor is whether or not there is rule compliance instruction. To examine the effects of these factors, we divided the two factors into four conditions each and created eight different videos. Specifically, we set up a scene in which a meeting was held to decide the ingredients for dinner at a seminar camp by majority vote. The two options were Matsuzaka beef that was 5 days past its expiration date and cheap imported beef purchased at a supermarket. The second change is that the number of participants in the experiment was changed to multiple participants; in the study of Chapter 12, An Observational

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Experiment in Group Decision-Making: Can People Detect Bad Group Decisions?, the experiment was conducted with one participant for each experimenter, and the environment was quiet and conducive to concentration, so the environment may have been very different from the actual meeting. In an actual meeting, there are several factors that may distract the participants from concentrating, such as noise and the actions of the people around them. Therefore in this study, we conducted an experiment with three to five participants for each experimenter. This setting would allow the participants to watch the video in a situation more similar to a meeting, which would make it easier for them to evaluate irrational decisions favorably. The third change is that the experimental design was changed from a withinsubjects to a between-subjects design. Specifically, in the previous studies, participants were made to watch videos in all the three conditions, but in this study, participants were made to watch only one of the eight videos. This change was expected to allow the experimental participants to make their evaluations without being influenced by the other videos. If people are able to detect irrational meetings, it is expected that they will give higher ratings to the decisions in which imported cattle from supermarkets are the final outcome of the decision, regardless of the emphasis of the risk and whether or not they comply with the rules. This study allows us to infer and verify the causes of irrational and bad group decision-making.

13.2

Preliminary survey

13.2.1 Purpose of the preliminary survey The purpose of the preliminary study was to determine the agenda to be used in the video of the meeting. We investigated how people judge decisions that seem to be good decisions but are irrational when considered carefully. The following sections describe the questionnaire used in the survey, the implementation of the preliminary survey, and the results and discussion of the preliminary survey, respectively.

13.2.2 Questionnaire To determine the agenda of the meeting, we devised a questionnaire consisting of 16 items, which were based on the decision-making cases in which the end result or trade-off occurred. For each item, we used a questionnaire with two types of questions: “How good do you think the decision is?” The questionnaire was divided into two parts. A 7-point scale was used, ranging from “1: completely disagree” to “7: strongly agree.” The specific items were as follows: Item 1: “At Junior High School A, a change of clothes will take place from July, and the wearing of blazers will be prohibited. However, one day in July, the school was hit by a cold wave and a student wore a blazer to school. In the morning staff meeting, it was decided that the student would be instructed to take off his blazer. How good (or bad) a

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decision do you think it was?”; Item 9: “The members of my club went out to buy something for the camp. We bought everything we needed with the camp fee collected from the members, but if we buy another 5000 yen, the parking fee of 1000 yen will be waived. After some discussion, we decided to buy another 5000 yen worth of snacks. How good (or bad) a decision do you think it is?" and so on. The order in which the decision-making events were presented was the same for all participants in the experiment.

13.2.3 Implementation of the preliminary survey The survey was conducted among 100 students (33 males and 67 females) at Waseda University. The mean age of the survey participants was 20.02 years (standard deviation (SD) 5 1.39 years). Fifty survey participants were assigned to each of the “good decision” and “bad decision” questionnaires. In this study, we asked survey participants to answer two patterns: how good and bad the decisions were. To facilitate the interpretation of the analysis results, the questionnaire items for good decisions were treated as reversal items. Specifically, the scores obtained from the respondents were subtracted from eight and converted into the degree to which they perceived the decision to be bad. In this way the higher the score of an item in both questionnaires, the more correctly the survey participants judged the corresponding decision as a “bad decision.”

13.2.4 Results and discussion of the preliminary survey Fig. 13.1 shows the mean and the standard deviation of the poorness of the decision results for each decision case. The horizontal axis shows the number of irrational decisions. 8 7 6 5 Good decision

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Figure 13.1 Mean and standard deviation of badness for decision.

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For the agenda of the meeting to be visualized, we chose the items that had a large variation in evaluation among the participants. The first criterion was that the item should have a large SD, and the second criterion was that the mean value should be close to 4.0. Based on these criteria, Item 5 with a mean value of 4.14 and an SD of 2.06 were adopted as the agenda item in the video for this experiment. The participants of the experiments were asked to respond the following task: “We are going to have barbecue at the seminar camp. There was a member of the group who said that he had some expensive Matsuzaka beef in his refrigerator that was 5 days past its expiration date. After discussing whether to eat this Matsuzaka beef or go to the supermarket to buy inexpensive beef, it was decided to have them bring the Matsuzaka beef from home and eat it. The question is How good (or bad) a decision do you think it was?”

13.3

Method for group decision-making experiment

13.3.1 Experimental design In this study, we used a two-level between-subjects factorial design for each of the three factors: decision outcome of the meeting, risk emphasizing, and rule compliance. The levels of decision outcomes were risky (high hazard) and riskless (low hazard) decision outcomes. Second, the level of risk emphasis was defined as high risk (strongly emphasized risk) and low risk (weakly emphasized risk), with the high risk case having one more sentence of dialog that emphasized the risk of death strongly than the low risk case. Third, the level of rule compliance was defined as rule compliance (following rule) and rule noncompliance (not following rule) and, thus, deals with whether or not the rules are followed in the instruction. For each of the three factors, we created eight videos: four combinations of rule compliance and decision outcomes, and four combinations of high risk (risk emphasized) and low risk (risk unemphasized) conditions and decision outcomes (risky decision outcome and riskless decision outcome).

13.3.2 Stimulus creation The videos were filmed in a small classroom at Waseda University. Twelve undergraduate students of the psychology course in the Faculty of Letters, Arts and Sciences of Waseda University participated in the filming of the videos, and all eight videos were filmed in a meeting of those students. Fig. 13.2 shows a scene from the video, in which the 12 students were seated at their desks in a U-shape, and the chairman sat in the center. The scene setting for all the eight videos was a scene in which 12 students belonging to the same seminar decided on the ingredients for the dinner at the seminar camp by majority vote. In all the videos the two dishes for the dinner ingredients were Matsuzaka beef, which was 5 days past its expiration date, and cheap imported beef purchased at a supermarket, although it was still within its expiration date. In the high risk (risk emphasized) and low risk (risk unemphasized) conditions, we created a total of four videos: two in which the decision outcome was imported beef and Matsuzaka

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Figure 13.2 A scene from the video used in the experiment.

beef in the low risk (risk unemphasized) condition and two in which the decision outcome was imported beef and Matsuzaka beef in the low risk (risk unemphasized) condition (Fig. 13.3). In the low risk (risk unemphaized condition, the risk of eating expired Matsuzaka beef was mentioned three times. On the other hand, in the high risk (risk emphasized) condition, the risk of eating Matsuzaka beef was mentioned four times. In the nonrisk condition, the participants only stated the risk of eating Matsuzaka beef as an individual thought, but in the high risk condition, one additional dialog was about searching the Internet for the risk of eating expired beef and telling the results to everyone. For the rule compliance (following rule) condition, we created a total of four videos: two in which the decision outcome was imported beef and Matsuzaka beef in the rule compliance condition, and two in which the decision outcome was imported beef and Matsuzaka beef in the rule noncompliance (not following rule) condition (Fig. 13.4). In the rule compliance condition, when the majority decided whether to choose Matsuzaka beef or imported beef, they were so concerned about the voting rules that they decided on the minority opinion instead of the majority opinion. On the other hand, the rule noncompliance condition that did not follow the rules was the one that abandoned adherence to the rules to decide on the majority opinion.

13.3.3 Questionnaire The participants answered a questionnaire about the evaluation of the video. Items for the evaluation of the video were created for the desirability of making decisions in meetings and the desirability of the way meetings are conducted. The response method was a 7-point scale (1: not at all agree to 7: agree very much).

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Figure 13.3 Contents of the videos for the four high and low risk conditions.

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Figure 13.4 Contents of the four videos for the rule compliance condition.

We created an item to determine how much importance people attach to the way discussions are conducted and the results of decisions when they make decisions in groups. The response method was a 7-point scale (1: not at all to 7: very much). We also created an item to ask whether they trust the opinions of the group when making decisions and also asked them to answer using a 7-point scale (1: not at all to 7: very much).

13.3.4 Implementation of the experiment 13.3.4.1 Participants Total 125 students (36 males and 89 females) of Waseda University participated in the experiment. The mean age of the participants was 20.58 years (SD 5 1.17 years). About 15
16 students were tested at each level of the video. The experiment was conducted in a small classroom at Waseda University.

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Figure 13.5 Participants and screen layout in the experiment.

13.3.4.2 Procedure The video was presented using a projector and a screen. The projector was an EB-435w made by EPSON. The size of the screen was FS-100V made by PLUS, 215 cm in width and 135 cm in height. The distance between the subject and the screen was about 180 cm when the subject was seated in the first row and about 290 cm when the subject was seated in the second row. Fig. 13.5 shows the actual experimental scene. The experiment was conducted in small groups of three to seven participants each time, with only four seats in the first row used for experiments with three to four participants, and seats in the second row for experiments with five to seven participants. The time required for the experiment was about 15 minutes. After the participants were instructed, they were asked to watch a video on the screen, evaluate the meeting on the video, and answer the questions about their attitudes toward everyday decisions. Afterward, they were asked to write freely about their introspection. After the experiment, we debriefed the participants about the purpose of this experiment.

13.3.4.3 Instruction The instruction of the experiment was as follows: [Greeting and experiment contents] Thank you very much for your cooperation in the experiment today. My name is xx, a fourth-year student of the Takemura Seminar, and I look forward to working with you. In the experiment you are about to participate in, you will be asked to

Revisiting the group decision-making experiment

watch a video of a seminar meeting and evaluate it. The duration of the experiment is expected to be about 15 minutes. The experimental data will be processed statistically, and no individual will be identified. In addition, we believe that there will be no impact on the human body. In addition, if you feel sick during the experiment, we will stop the experiment. Please do not hesitate to let us know. Are there any questions so far? (If you have no questions, please answer them.) First, please fill out this consent form.

Distribution of questionnaire and consent form: [Fill out the consent form.] Confirm the contents of the consent form. [Start the experiment.] We will now start the experiment, and we will play the video, so please look at the projector in front of you. Please look at the projector in front of you. [The video is finished.] This is the end of the video. Now, please turn the cover of the questionnaire and answer the questions. [End of questionnaire] Thank you very much. If you have any impressions about this experiment, please write them in the box at the end of the questionnaire. [End of experiment] This is the end of the experiment. Thank you very much for your cooperation in this experiment.

After the experiment, the following debriefing will be given: Finally, I would like to explain the contents of this research. The purpose of this study is to explore the problems that can be observed in discussion situations such as meetings. In social psychology, there is a phenomenon called groupthink, and it is said that this phenomenon does not necessarily result in good decisions even when excellent people gather together. In our daily lives, we often emphasize a certain point in a meeting of a group and get pulled into that point of view, or we are so concerned about details and rules that we fail to achieve our original goal. Therefore in this study, we decided to make a video for the conditions of emphasizing the risks and sticking to the rules at the time of voting and see how we evaluate the meetings.

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We will try to see how we evaluate the meetings. We have given a brief explanation, but do you have any questions?

13.3.6 Outline of the analysis In this experiment, out of 125 experimental participants (36 males, 89 females, mean age 20.58 years, SD 5 1.17 years), 124 were subjected to the analysis, excluding 1 participant with missing values. To examine the effects of the factors, the analysis of variance and calculation of correlation coefficients were conducted for each of the two factors among the experimental participants.

13.4

Results

To examine the factors that cause irrational meetings, we created eight videos of meeting scenes and conducted an experiment. Then, analyses were conducted to examine the effects of the outcome of the meeting decision, the emphasis of the risk, and the compliance with the rules on the desirability of the meeting decision and process. Specifically, comparison of means, analysis of variance, analysis of covariance, and analysis of correlation were conducted.

13.4.1 Analysis of the desirability of a meeting decision First, we calculated the means of the desirability of the decision in each video. In Fig. 13.6 the first left item 1 indicates the low risk and risky outcome (Matsuzaka beef) condition. The other numbers of items are follows: Item 2 for the high risk 7 6 5 4 3 2 1 0 1

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Figure 13.6 Mean and standard deviation (SD) for the desirability of decision in each condition.

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and risky outcome condition, Item 3 for the low risk and riskless outcome (Imported beef), Item 4 for the high risk and riskless outcome condition, Item 5 for the rule noncompliance and risky outcome condition, Item 6 for the rule compliance and risky outcome condition, Item 7 for the noncompliance and riskless outcome condition, and Item 8 for the rule compliance and riskless outcome condition. For clarity, when the final decision result was Matsuzaka beef, the bar graph was set to “Matsuzaka” and colored black, and when the final decision result was imported beef, the bar graph was set to “Import” and colored white. Fig. 13.6 shows the mean and the SD for the desirability of decision regardless of the emphasis of the risk or the compliance with the rule; the desirability of the decision of the meeting tended to be higher at the level where the outcome of the decision was imported cattle. Next, we conducted a two-level analysis of variance for each of the two between-subjects factors separately for risk intensity and decision outcome and for rule compliance and decision outcome. To examine the influence of the degree of risk and the decision of the meeting on the desirability of the decision, we conducted a two-level analysis of variance for each of the two between-subjects factors of risk (high risk vs low risk) and decision outcome (Matsuzaka beef (risky outcome) vs imported beef (riskless outcome)). As a result, a significant main effect was found for the decision outcome in the meeting (F(1,59) 5 21.25, P, .001). Regardless of the emphasis of the risk, the final decision for imported beef was evaluated as more desirable than that for Matsuzaka beef. Next, to examine the effects of rule compliance and decision outcome on the desirability of the decision, we conducted a two-level analysis of variance for each of the two between-subjects factors of rule compliance (rule compliance vs rule noncompliance) and decision outcome (Matsuzaka beef vs imported beef). As a result, a significant main effect was found for the decision outcome in the meeting (F(1,57) 5 4.98, P, .05). Regardless of whether the rule was adhered to or not, the final decision for imported beef was evaluated as more desirable than that for Matsuzaka beef. In the multiple regression analysis of the desirability of the decision outcome of the meeting, since it was not possible to analyze the three factors together due to the experimental design, the decision outcome (Matsuzaka beef vs imported beef), risk (high vs low), and compliance with the rule (control vs rule compliance vs rule noncompliance) were used as independent variables. Multiple regression analysis was conducted to predict the desirability of the decision from these independent variables. The control condition for the presence or absence of rule compliance was used as the low risk condition, in which there was no conflict over the rule in the majority vote. The results showed a positive partial regression coefficient that was significant at the 0.1% level (t 5 4.81, P, .001). In other words, it was recognized that the outcome of the meeting was more desirably evaluated when the final decision was made for imported cattle. There was a significant negative partial regression coefficient at the 5% level in the noncompliance condition (t 5 22.07, P, .05). In other words, the condition in which the decision was overturned due to noncompliance with the rules was rated as significantly less desirable than the control condition of rule compliance.

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We conducted an analysis of covariance with the decision outcome as the predictor variable, the desirability of the process in the meeting as the covariate, and the desirability of the decision in the meeting as the dependent variable. The results showed that the desirability of the meeting decision was significantly higher in the condition in which the decision outcome was imported beef than in the condition in which the decision outcome was Matsuzaka beef (t 5 5.18, P, .001). Next, we conducted an analysis of covariance with risk intensity as the predictor variable, desirability of the meeting process as the covariate, and desirability of the meeting decision as the dependent variable. The results showed that there was no effect of risk intensity on the desirability of meeting decisions (t 5 1.30, n.s.).

13.4.2 Analysis of the desirability of the meeting process Fig. 13.7 shows the mean and SD of the desirability of the meeting process for each video as a bar graph. The numbers of items indicate the same conditions as mentioned in the previous section. Unlike the desirability of the decision, no difference was found between the decision results of Matsuzaka and imported cattle. In addition, regardless of the final decision result, the evaluation tended to be higher in the rule compliance condition than in the rule noncompliance condition. Next, we conducted a two-level analysis of variance for each of the two between-subjects factors, dividing the results into the emphasis of risk and decision outcome, and the presence or absence of rule compliance and decision outcome. To examine the influence of risk emphasis and decision outcome on the desirability of the process, we conducted a two-level analysis of variance for each of the two between-subjects factors: risk (high vs low) and decision outcome (Matsuzaka vs imported beef ). The main effects of risk (high vs low) and decision outcome

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Figure 13.7 Mean and SD for the desirability of meeting process in each condition.

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(Matsuzaka vs imported beef) on the desirability of the process in the meeting and their interactions were not significant (F(1,59) 5 0.02, n.s., F(1,59) 5 0.40, n.s.). Next, to examine the influence of rule compliance and decision outcome on the desirability of the process, we conducted a two-level analysis of variance between subjects for rule compliance (adherence vs nonadherence) and decision outcome (Matsuzaka beef vs imported beef). A two-level analysis of variance was conducted for each factor. As a result, no factor was found to affect the desirability of the process in the meeting. As in the multiple regression analysis of the desirability of decision-making, we conducted a multiple regression analysis to predict the desirability of the process in the meeting from the three factors of decision outcome, risk intensity, and rule compliance. As a result, no independent variable was found to influence the dependent variable (for all t ,2.00, n.s.). An analysis of covariance was conducted with the rule compliance factor as the predictor variable, desirability of meeting decisions as the covariate, and desirability of meeting process as the dependent variable. The results of the analysis of covariance showed that there was no effect of the factors of noncompliance (t 5 21.39, n.s.) and compliance (t 5 0.69, n.s.) on the desirability of the meeting process.

13.4.3 Correlation analysis Next, we calculated the correlation coefficients between the eight conditions and the desirability of the decision and the desirability of the process in the meeting. As a result, a significant moderate positive correlation was found when the decision outcome was Matsuzaka beef (high risk!Matsuzaka) in the high risk (risk emphasized) condition (r 5 0.57, P, .05). A significant, moderate, positive correlation (r 5 0.66, P, .01) was also found when the decision result was imported beef (low risk!imported) in the low risk condition. In the rule compliance condition a significant, moderate, positive correlation was found regardless of the decision outcome (Matsuzaka beef: r 5 0.53, P, .05; imported beef: r 5 0.52, P, .05).

13.5

Discussion

To reproduce the phenomenon of irrational meetings by a group and examine the factors involved, three factors were set up in this study: the outcome of the meeting decision, the emphasis of the risk, and the presence or absence of rule compliance. To examine the influence of these factors on the desirability of meeting decisions and processes, we mainly conducted an analysis of variance and multiple regression analysis. The following discussion is divided into the decision of the meeting and the process in the meeting.

13.5.1 Desirability of the meeting decision The desirability of the decision of the meeting in each video was evaluated as more desirable when the decision result was imported beef than when it was Matsuzaka

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beef, regardless of the emphasis of the risk or the presence or absence of rule compliance. In addition, in the condition where the decision result was overturned and in the condition where the rule was not followed, it was recognized that the decision result was evaluated as less desirable than the other conditions. These results suggest that experimental participants can evaluate meeting decisions correctly regardless of the emphasis of the risk or the presence of rule compliance. In Chapter 12, An Observational Experiment in Group Decision-Making: Can People Detect Bad Group Decisions?, the decision outcome was judged more desirable in the goal matching condition than in the procedural justice condition. The results in this study are similar to those in the previous study, where no effect of rule compliance was found. The present study, in which the factors were modified from the previous study, could not replicate irrational decision-making in everyday situations. The reason for the lack of effect of risk intensity may be that the differences in the dialog between conditions were small. In the high risk (risk emphasized) condition, the participants were only told that expired Matsuzaka beef was dangerous, and no new information was added to the low risk (riskunemphasized) condition. Furthermore, since the participants in the experiment watched only one type of video, it is assumed that they were not able to create criteria for evaluation.

13.5.2 Desirability of the meeting process The desirability of the meeting process in each video shows no difference between Matsuzaka beef and imported beef due to the difference in decision results. On the other hand, although there was no significant difference, the evaluation of the rule compliance condition was higher than that of the rule non compliance condition. These results suggest that adherence to rules enhances the evaluation of the meeting process. It is possible that the results partially reproduce everyday situations in which people make irrational decisions because they are too concerned about the rules. The reason why the influence of the three factors on the desirability of the process was not observed is that many of the participants in the experiment had doubts about the original setting of the meeting. In the introspection, there were also questions such as, “Even though there is a budget problem, in the case of this video, I thought it would be better to buy fresh meat from the supermarket and prepare both Matsuzaka beef and supermarket meat and let people choose when they eat it.” And “Why are not the hands raised? I was worried about people who did not have any lines.” And “Why did not they raise their hands?” It is true that in an actual meeting, only a few people would not speak the same number of times. Also, it might be more natural to buy imported beef at the supermarket in addition to expired Matsuzaka beef and eat the expired one you want at your own risk. Furthermore, if the members of the seminar have a friendly relationship with each other, they would not bother to set up a troublesome rule of filling out a paper and voting but would vote by a show of hands. Therefore if we want to examine whether or not people comply with the rules, we need to consider more formal situations such as meetings in companies.

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13.5.3 Correlation coefficient between desirability of decision and desirability of process in meetings In the rule compliance condition, there was a positive correlation between the desirability of the meeting decision and the desirability of the process, regardless of the outcome of the decision. In the rule compliance condition, the higher the score of the process, the higher the evaluation of the decision will be. This suggests that adherence to the rules affects the desirability of the meeting. As before, it is possible that the results partially reproduce everyday situations in which people make irrational decisions because they are too concerned about the rules. Further investigation of this point is desirable in future research.

13.6

Conclusion and future prospects

To reproduce the phenomenon of irrational meetings by groups in daily life and examine the factors that contribute to this phenomenon, this study set up three factors that affect the evaluation of meeting scenes and examined their effects on the desirability of meeting decisions and the desirability of the meeting process. However, in both desirability of the meeting decision and desirability of the process, the results basically suggested that the experimental participants could evaluate irrational meetings correctly. This is consistent with the finding in Chapter 12, An Observational Experiment in Group Decision-Making: Can People Detect Bad Group Decisions?, that people can detect irrational and bad group decision-making. One of the reasons why we were not able to obtain the same kind of responses as in everyday situations in this study was that the participants in the experiment were not able to watch the video of the meeting with a sense of ownership and involvement. It is necessary to make the participants feel more involved in the meeting. In the case of using the same agenda as in this study, it is also necessary to ask the experimental participants about their usual awareness of consumption deadlines. In addition, the number of participants in the experiment for each condition was very small (about 15), which may be the reason why the effect of the factors was not recognized. In the future, we should ask for the cooperation of more participants in the experiment. It is also possible that the participants in the experiment did not interact with each other as they do in everyday group decision-making situations. In the present study, it was suggested that the experimental participants were able to make adequate judgments about the meeting process and irrational group decision-making. However, we believe that irrational meetings still surround us. What is the cause of this remains to be seen. However, the fact that the participants in the experiment were able to detect irrational and bad group decision-making seems to be a hint to avoid bad group decision-making.

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References Frankfurt, H. G. (2005). On bullshit. Princeton: Princeton University Press. Janis, I. L. (1972). Victims of groupthink. Boston: Houghton Mifflin. Janis, I. L. (1982). Groupthink: Psychological studies of policy decisions and fiascoes (2nd ed.). Boston: Houghton Mifflin. Takemura, K., Ideno, T., Miyajima, M., Okuma, M., & Sakagami, T. (2021). Fugouri na Syuudan Ishikettei no Kansatsu Jikken [Observational experiment of irrational group decision]. Department of Psychology, Waseda University, Unpublished manuscript.

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In Chapter 13, Revisiting the Group Decision-Making Experiment, I examined whether people can notice when the outcome of a group decision is irrational and evaluate it as irrational, rather than the progress of the meeting. The research in this chapter uses the same decision-making task as in Chapter 13, Revisiting the Group Decision-Making Experiment, to examine how individuals thought about bad outcomes and risks and how they would vote if observers actually voted rather than simply observing the meeting. The experimental study in this chapter was conducted by Takemura, Ideno, Oguni, Saito, and Sakagami (2021). Based on the results of this study, we also show that people can detect irrational meetings and the worst group decisions well enough in an independent situation with no interaction and can make decisions to avoid the worst decisions.

14.1

Detection of bad group decision-making and groupthink

In Chapter 12, An Observational Experiment in Group Decision Making: Can People Detect Bad Group Decisions?, and Chapter 13, Revisiting the Group Decision-Making Experiment, we have examined whether people can detect “bullshit" arguments as pointed out by Frankfurt (2005) through surveys and experiments. Previous research has suggested that under conditions of no interaction between individuals, many people are able to detect meeting processes that are incompatible with their goals and irrational bad decisions. One of the possible causes of such irrational conferencing situations is groupthink. Groupthink is the deterioration of mental states, reality checks, and moral judgments due to social pressures that arise in cohesive groups (Janis, 1972, 1982). Janis (1972, 1982) states that the pressure to unify groups can subvert the basic purpose of meetings. In the social psychology tradition, research on groupthink has suggested that in social influence processes, such as peer pressure, people are more likely to fall into groupthink and become less able to detect irrational meeting processes and bad decisionmaking. Then, we have been examining whether we can really make appropriate decisions in situations where there is no particular social interaction. In Chapter 13, Revisiting the Group Decision-Making Experiment, a preliminary survey using a questionnaire was conducted on students at Waseda University, and a situation in which people make seemingly good but actually irrational decisions in their daily lives was adopted as the agenda for a meeting. The agenda was to decide Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00011-9 © 2021 Elsevier Inc. All rights reserved.

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on foodstuffs at a seminar camp. The life-threatening decision was to choose expensive Matsuzaka beef that was 5 days past its expiration date, and the safe decision was to choose cheap imported beef purchased at a supermarket within the expiration date. In this study, we used three factors-between-subjects factorial design in which each factor has two levels. The three factors are as follows: decision outcome of the meeting, risk emphasis, and rule compliance. Each levels for each factor was as following: a highrisk condition that emphasized the risk of making a life-threatening decision; a low risk condition that did not emphasize the risk, a rule compliance condition (rule following condition) that determined whether or not the participants adhered to detailed rules; and risky outcome decision for a dangerous decision with high hazard (food poisoning) and a riskless decision for a safer decision wih low hazard (no food poisoning). In addition, the experiment was conducted in small groups of three to seven participants each time to give the participants a greater sense of involvement. As a result, the participants in the experiment evaluated the conditions under which the outcome of the decision would be imported beef as desirable, regardless of the emphasis of the risk or whether or not the rules were followed. In this study, people were able to evaluate meetings rationally. However, in the real world, it is possible to observe that irrational meetings occur on a daily basis. In the experiment of the previous study, the participants did not have a sense of involvement in the experiment; therefore their evaluation of the meeting was different from that of the actual society. Therefore in the research of this chapter, the process of having the participants actually vote was added to the experiment of Chapter 13, Revisiting the Group Decision-Making Experiment, in Experiment 1. In Experiment 2, based on the results of Experiment 1, a PowerPoint presentation was given to encourage the participants to give importance to the results or the rules before the video was played. The flow of the rest of the experiment was the same as in Experiment 1. In Experiment 1, we used the video of a meeting in which irrational decisions were made, as used in Chapter 13, Revisiting the Group Decision-Making Experiment. The meeting in the video was a scene in which a majority vote was used to decide on foodstuffs at a seminar camp. The two choices were Matsuzaka beef, which was 5 days past its expiration date, and cheap imported beef sold in supermarkets, which was still within its expiration date. The video was played until the scene where the majority vote was taken, at which point the video was stopped and the participants were asked to actually vote for Matsuzaka beef or imported beef. The video was then played again, and the participants were asked to evaluate the desirability of the outcome and process of the meeting. To examine the factors that affect the desirability of the meeting, two factors were set. The first factor was the decision outcome of the meeting, which was defined as risk-oriented and riskaverse options. The second factor was whether the rule was followed or not, and it was set to the case where the rule was followed or not in the majority vote. In Experiment 2, before playing the video, the participants were encouraged to consider the result or the rule as important. In the experimental design, three factors were set. The first and second factors were the same as in Experiment 1, and the third factor was the type of instruction that prompted the participants to emphasize the importance of the decision or rule compliance, that is, to emphasize the result or the rule.

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There were two differences in the experimental study of Chapter 13, Revisiting the Group Decision-Making Experiment the first difference was that the participants actually voted, and the second difference was that in Experiment 2, before the video of the meeting was shown, the participants were instructed to emphasize the importance of the outcome or rule compliance. If people can detect irrational decisions, the second and third factors are expected to have no effect on desirability. In addition, it is expected that the decision outcome would be evaluated as more desirable if the decision outcome is an imported beef, regardless of whether there is any teaching or rule compliance that encourages people to consider the decision or rule compliance as important. Therefore we expect that meetings in the rule compliance condition will be evaluated more highly regardless of the decision outcome. By examining the factors that affect irrational meetings in this experimental study, we may be able to provide suggestions on how to avoid irrational meetings in actual society.

14.2

Method of Experiment 1

To examine the factors that cause irrational meetings, we conducted an experiment using the video of the meeting scene created in Chapter 13, Revisiting the Group Decision-Making Experiment. The following sections describe the experiment in the following order: experimental outline, experimental design, stimuli, questionnaire, implementation of the experiment, and teaching.

14.2.1 Outline of Experiment 1 The experiment consisted roughly of video viewing, voting, and a questionnaire survey. The flow of the experiment consisted of having the participants watch one of four different videos for each condition, stopping the video in the middle and actually voting, and then playing the video again and answering the questionnaire. Fig. 14.1 shows the form used for the voting. To achieve counterbalance, we used two series in which the order of the selected items for Matsuzaka beef and imported beef was switched.

At the meeting you have just seen, which would you vote for, Matsusaka beef or imported beef? Please circle the one you would vote for in the box below.

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Figure 14.1 Voting sheet in the group decision experiment.

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14.2.2 Experimental design This study was a between-subjects factorial design with two levels of each of two factors: the decision outcome of the meeting (risk-oriented decision outcome vs risk-averse decision outcome) and the presence or absence of rule compliance (rule compliance vs rule noncompliance). Specifically, for the decision outcome of the meeting, the condition in which the final decision outcome was Matsuzaka beef was considered a risk-oriented decision, and the condition in which the final decision outcome was imported beef was considered a riskless decision. On the other hand, as for the specific flow of the level of compliance with the rule, in the case of compliance with the rule, the number of valid votes between the majority and the minority was reversed because the rule to invalidate named votes was observed first. Then, the meeting adopted the opinion of the minority instead of that of the majority, which was decided at the beginning by a majority vote. We used four types of videos each with two levels of two factors, in which the rule compliance and the decision result were combined.

14.2.3 Experimental stimuli The same video used in the experiment of Chapter 12, An Observational Experiment in Group Decision Making: Can People Detect Bad Group Decisions?, was used as the experimental stimulus. The scene setting was the same for all four types of videos (Fig. 14.2): 12 students in a seminar decided the ingredients for dinner at the seminar camp by a majority vote. In all the videos the two candidates for dinner ingredients were Matsuzaka beef, which was 5 days past its expiration date, and cheap imported beef purchased at a supermarket, although it was still within its expiration date. For the rule compliance condition, we created a total of four videos: two in which the decision result was Condition

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Figure 14.2 Contents of the four videos for the rule compliance condition.

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either imported beef or Matsuzaka beef in the rule compliance condition and two in which the decision result was either imported beef or Matsuzaka beef in the rule noncompliance condition. In the condition where the rule was observed, when deciding whether to choose Matsuzaka beef or imported beef by majority vote, the decision was made according to the minority opinion instead of the majority opinion because the rule was observed to invalidate the votes with names. On the other hand, the condition of not observing the rule (rule noncompliance condition) was to abandon the adherence to the rule to decide the majority opinion. The condition that questioned the rule to invalidate a registered vote resulted in foregoing the application of the rule and adopting the original majority opinion.

14.2.4 Questionnaire The questionnaire consisted of six parts: confidence in one’s own vote, evaluation of the video, items used in everyday decision-making, sensitivity to expiration dates, decision-making scale (Ideno, Ohkubo, Tamari, Abe, & Takemura, 2012), and formality-seeking scale (Takahashi, Takemura, Ideno, Ohkubo, & Tamari, 2010). The details of each question are discussed next. Confidence in one’s own vote: When the video was stopped in the middle and the participants were asked to vote, they were asked to answer their own confidence in their vote. The response method was a 7-point scale (1: not at all positive to 7: very positive). The participants were asked to rate the desirability of the decision of the meeting and the desirability of the meeting process for the video. They were asked to respond to the desirability of the decision-making process and the desirability of the meeting process of the video using a 7-point scale (1: not at all to 7: very much). The respondents were asked how many days after the expiration date they thought they could still eat the raw meat stored in the refrigerator. The response method was free. When making decisions in a group, the participants were asked to indicate the degree of importance they attach to the way the discussion proceeds and the outcome of the decision. The response method was a 7-point scale (1: not at all to 7: very much). In addition, they were asked to indicate whether they trust the opinions of the group when making decisions. The response method was a 7-point scale (1: not at all to 7: very much). The specific item was “Do you think that decisions made by a group are better than decisions made by individuals?” The participants were asked to respond to a decision-making scale (Ideno et al., 2012) using a 7-point scale (1: not at all true to 7: very true). The specific items included item 1, “I examine all options.” Formality-seeking scale: The participants were asked to answer the formalityseeking scale (Takahashi et al., 2010) using a 7-point scale (1: not at all to 7: very much). The specific items included item 2, “I think that rules are meaningful only when they are strictly followed.” The results of the analysis of the relationship between the decision-making scale and the formal-pursuit scale are omitted in this chapter.

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14.2.5 Implementation of the experiment The experiment was conducted on 104 students (32 males, 71 females, and 1 unknown) at Waseda University. The mean age of the participants was 20.54 years (standard deviation (SD) 5 1.31 years). The experiment was conducted in a small classroom in the psychology course at the Toyama Campus of Waseda University. The video was presented using a projector, screen, and speakers. The projector was an EB-435W made by EPSON, and the screen was an FS-100V made by PLUS, which was 215 cm in width and 135 cm in height. The speakers were Panasonic RP-SPC300. The distance between the subject and the screen was about 180 cm when the subject sat in the first row, and about 290 cm when the subject sat in the second row. The experiment was conducted in small groups of three to seven subjects each time, with only four seats in the first row used for three or four subjects and the seats in the second row used for five to seven subjects. The time required for the experiment was about 20 minutes. After the participants were instructed, they watched one of the videos on the screen, stopped in the middle, handed out ballots, and were asked to indicate whether they would vote for Matsuzaka beef or imported beef. In addition, after collecting the ballots, the participants were asked to evaluate their own choice. After watching the video, the participants were asked to answer the rest of the questionnaire. After the experiment the purpose of this study was explained to the participants

14.2.6 Instruction The instruction of the experiment was as follows: [Greetings and contents of the experiment] Thank you very much for your cooperation in today’s experiment. My name is XXX. I am XXX, and I look forward to working with you. In the experiment you are about to participate in, you will watch a video of a seminar meeting scene and answer a simple questionnaire. There is a paper explaining the experiment in your hand, but it is very long, so I will just explain the important parts in brief. The experimental data will be processed statistically, and no individual will be identified. In addition, we have determined that there is no effect on the human body. Furthermore, if you feel sick during the experiment, we will stop the experiment. Please do not hesitate to contact us. Are there any questions so far? (If you have no questions, please answer them.) First, please fill out this consent form. Please check the box next to "I do not consent to disclosure. if you have any questions, please leave them blank. Collect the consent form and explanation paper.

The detection of bad decisions and a voting experiment

In this experiment, we will stop the video and ask you to answer the first question. After that, you will be asked to watch the rest of the video and answer the questions again at the end. The duration of this experiment is expected to be about 20 minutes. [Start of the experiment] We will now begin the experiment. (video starts playing) (video stops) In the meeting that you have seen so far, which would you vote for, Matsuzaka beef or imported beef? I will now hand out the ballots. Please wait until you have made your choice. (Make sure that everyone has voted). I will now collect the ballots. (Confirm that everyone has voted) Now, please turn the cover of the questionnaire and answer the first question. When you have answered the question, please wait and do not proceed to the next page. (Make sure that everyone has been rated) Now, let’s play the rest of the video. (Make sure you have rated everyone.) Now, let’s continue with the video. [End of video] That’s it for the video. Now, please fill in your name, etc. on the front cover of the questionnaire, turn the pages, and answer the remaining questions to the end. [End of questionnaire] Thank you very much. If you have any comments about this experiment, please write them in the box at the end of the questionnaire. [End of experiment] This is the end of the experiment.

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After the experiment the following debriefing will be given: In the end, I will explain the contents of this study. The purpose of this study is to explore the problems that can be observed in discussion situations such as meetings. In social psychology, there is a phenomenon called groupthink, and it is said that this phenomenon does not necessarily result in good decisions even when excellent people gather together. In our daily lives, it seems that we sometimes fail to achieve our original goals because we are too concerned about the details and rules in meetings of clubs. Therefore, in this study, we decided to make a video of the conditions for sticking to the rules when voting, and to see how we make decisions and how we evaluate meetings. If you have any questions, please feel free to contact me. Thank you very much for your cooperation in this experiment. 3.

14.3

Results and discussion of Experiment 1

In this chapter, we conducted an experiment using four types of videos of meeting scenes created in the experiment mentioned in Chapter 13, Revisiting the Group Decision-Making Experiment, to examine the factors of irrational decision-making in council situations such as meetings and to reproduce real-life meeting scenes. In this study, as a new procedure, participants were asked to vote for either Matsuzaka beef or imported beef as a member of the meeting in the video. Then, we calculated and compared the means and conducted analysis of variance and analysis of covariance to examine the effects of the outcome of the meeting decisions and the adherence to the rules on the desirability of the meeting decisions and processes. Correlation analysis was also conducted to examine the relationship between evaluations of meeting decisions and evaluations of the process. Then, a comparison of the two groups was conducted to examine whether there was a difference in the number of votes cast for Matsuzaka beef and imported beef and to examine the effect of sensitivity to expiration dates on the desirability of meeting decisions. In addition, a study was conducted to examine the impact of agreement and disagreement between the results of voting and the results of decisions made in meetings on the evaluation of meeting decisions and processes.

14.3.1 Correlation analysis Correlation coefficients between the desirability of meeting decisions and the desirability of the process were calculated. The results showed that the correlation coefficient was 0.38, indicating a weak positive correlation. It was suggested that those

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who evaluated the decision of the meeting as desirable also evaluated the process of the meeting as desirable, and the result was similar to the result of Chapter 13, Revisiting the Group Decision-Making Experiment.

14.3.2 Analysis of the desirability of decisions in meetings Fig. 14.3 shows the mean and SD of the desirability of the decision for each video. The item for number 1 indicates the rule noncompliance and risky outcome (Matsuzaka beef) condition. The number 2 item indicated the rule noncompliance and riskless outcome (Imported beef) condition, the number 3 item indicates the rule compliance and risky outcome condition, and the number 4 item indicates the rule compliance and riskless ouctome condition. It was found that the desirability of the decision tended to be higher at the level where the outcome of the decision was an imported beef, regardless of whether the rule was followed or not (hereafter referred to as rule compliance or not). This result was similar to the result in Chapter 13, Revisiting the Group Decision-Making Experiment. This study examined the effects of rule compliance and decision outcomes on the desirability of decisions made in meetings. Specifically, the desirability of the decision at the meeting was set as the dependent variable, and a two-level analysis of variance was conducted for each of the two between-subject factors: decision outcome (Matsuzaka beef vs imported beef ) and rule compliance (rule compliance vs rule noncompliance) (F(1, 100) 5 20.42, P , .001). The results suggest that regardless of rule compliance, the final decision to have imported beef for dinner at the seminar camp was more likely to be evaluated as desirable. This suggested that participants in the experiment were able to judge the meeting as irrational. This 7

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Figure 14.3 Mean and standard deviation of desirability for decision in each condition.

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result is similar to the result in Chapter 13, Revisiting the Group Decision-Making Experiment, which showed that many people do not highly evaluate decisions that are too irrational to comply with the rules. Next, the correlation coefficient between the desirability of the decision outcome and the desirability of the process was 0.38. Since a correlation was found, an analysis of covariance between rule compliance and the decision outcome of the meeting was conducted to remove the effect of the correlation. Therefore to remove the influence of this relationship, we conducted an analysis of covariance between the presence of rule compliance and the outcome of the meeting. The results showed a significant trend in the decision outcome (F(1,99) 5 3.29, P , .10). The results suggested that the outcome of the meeting was more desirably evaluated when the final outcome was imported beef. Thus as in the analysis of variance for desirability of meeting decisions, it was suggested that the participants were able to judge irrational meetings. This is because in introspection, the participants said, “I watched the meeting as a complete outsider. (I did not intend to eat the meat).” It is possible that many of the experimental participants were able to judge the meeting objectively because they were watching the meeting from the perspective of a third party.

14.3.3 Analysis of the desirability of the meeting process Fig. 14.4 shows the mean and SD of the desirability of the meeting process for each video. The condition numbers on the horizontal axis in Fig. 14.4 are the same as in Fig. 14.3. Unlike the desirability of the decision, there was no difference in the mean values of the desirability of the process due to the difference in the decision results

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Figure 14.4 Mean and standard deviation of desirability of the meeting process.

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between Matsuzaka and imported beef. In addition, regardless of the final decision outcome, there was a tendency for evaluations to be higher in the rule compliance condition than in the rule noncompliance condition. To examine the effects of rule compliance and decision outcome on the desirability of the process, we conducted a two-level analysis of variance for each of the two between-subjects factors of decision outcome (Matsuzaka beef vs imported beef) and rule compliance (following the rules vs not following the rules). A twolevel analysis of variance was conducted. As a result, a significant trend was observed in the presence or absence of rule compliance (F(1, 100) 5 3.39, P , .01). Regardless of the decision outcome, it was suggested that rule compliance was more likely to be evaluated as more desirable than rule noncompliance. This is different from the results in Chapter 13, Revisiting the Group Decision-Making Experiment, where no significant main effects were found for either decision outcome (Matsuzaka beef vs imported beef) or rule compliance (following the rules vs not following the rules). Next, since the correlation coefficient between the desirability of the decision outcome and the desirability of the process was 0.38, an analysis of covariance between the presence or absence of rule compliance and the desirability of the meeting process was conducted to remove the effect of the correlation. Therefore to remove the influence of this correlation, we conducted an analysis of covariance between the presence or absence of rule compliance and the desirability of the meeting process. The presence or absence of rule compliance factor was the independent variable, the desirability of the decision in the meeting was the covariate, and the desirability of the meeting process was the dependent variable. The results showed that there was no significant main effect of rule compliance (F(1,99) 5 0.06, n.s.). This result was similar to the experiment of Chapter 13, Revisiting the Group Decision-Making Experiment. On average across conditions, meetings in which the decision outcome was imported beef were rated as relatively more desirable, regardless of the rule compliance condition. This suggests that the rule compliance factor does not affect the desirability of the process but is evaluated by the final decision outcome. The analysis of variance of the presence/absence of rule compliance and the desirability of the process showed a significant trend in the presence/absence of rule compliance, but not in the covariance analysis of the desirability of the process. These results suggest that desirability of process in meetings is rated higher than adherence to rules and regulations in meetings, if the final decision outcome is desirable. This result is contrary to the expectation that people can detect irrational the meeting processes. This is a result of the fact that in introspection, “I felt uncomfortable that the results of group decision-making could be overturned on the grounds that votes with names on them were invalid.” I did not understand why the rule “the vote of the person whose name is written on the ballot is invalid’ was set in the first place.” It is thought that the results of the decision of the meeting were more important than the compliance with the rule when evaluating the meeting because many of the participants questioned the rule itself. The fact that many of the participants questioned the rules can be attributed to the fact that there was a difference between the experimental scene and the content of the video. Specifically, the ballots distributed to the experiment

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participants had a column for selecting Matsuzaka beef or imported beef. On the other hand, in the video, it was decided that a majority vote would be taken in the middle of the experiment, and the participants were given blank sheets of paper to vote on. Therefore in the video, there was no paper prepared for the participants to choose Matsuzaka beef or imported beef in advance. Therefore there was a difference between the reality and the video, and it was difficult for the participants to have a sense of involvement.

14.3.4 Analysis of the sensitivity of the consumption deadline

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To analyze the relationship between the desirability of the decision and the desirability of the process in the meeting and the sensitivity to the consumption deadline, the scores of the sensitivity to the consumption deadline, the desirability of the decision, and the desirability of the process were plotted, respectively. If the final result was Matsuzaka beef, it was indicated by a black dot, and if the final result was imported beef, it was indicated by a white dot. The results are shown in Figs. 14.5 and 14.6. Next, we conducted a regression analysis to predict the desirability of the decision and the desirability of the process, respectively, based on the sensitivity of the expiration date. In addition to regression analysis of consumption deadline awareness and desirability of decision outcome to examine the effect of consumption deadline

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Figure 14.5 Desirability of decision and number of days elapsed between consumption dates.

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Figure 14.6 Desirability of meeting process and number of days elapsed between consumption dates.

sensitivity on the desirability of a decision, we conducted another regression analysis to predict the desirability of a decision from consumption deadline sensitivity. As a result, when the decision result was Matsuzaka beef, there was a significant trend in the sensitivity to expiration date at the 1% level (t(50) 5 1.91, P , .10). In the case of imported beef, the sensitivity to expiration date was significant at the 0.1% level (t(50) 5 23.22, P , .001). This suggests that those who were more sensitive to the expiration date evaluated the decision outcome lower when the decision outcome of the meeting was Matsuzaka beef and evaluated the decision higher when the decision outcome was imported beef. In addition to regression analysis of consumption deadline awareness and process desirability to examine the effect of consumption deadline sensitivity on process desirability, we conducted another regression analysis to predict process desirability from consumption deadline sensitivity. The results showed that regardless of the decision outcome, there was no effect of expiration date sensitivity on process desirability (Matsuzaka beef: t(50) 5 0.39, n.s.; imported beef: t(50) 5 20.77, n.s.). This suggests that in the case of Matsuzaka beef, where the decision outcome is risk-oriented, even risk-sensitive individuals evaluate the process as desirable. Considering the results of the regression analysis between the sensitivity to the expiration date and the desirability of the decision outcome, it is suggested that the sensitivity to the expiration date affects the desirability of the decision outcome but not the desirability of the process. This may be because the decision outcome was a life-threatening choice; therefore

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expiration date sensitivity may have had more influence on the desirability of the decision outcome.

14.3.5 Analysis of voting As a result of the voting, 23 out of 103 experimental participants voted for Matsuzaka beef, and 80 voted for imported beef. Fig. 14.7 shows the total number of people who voted, and Fig. 14.8 shows the number of people who voted for Matsuzaka beef and imported beef in each condition. The items numbered in Fig. 14.8 are the same as in Figs. 14.3 and 14.4. Black bars indicate the final decision to

Figure 14.7 Result of voting. 25

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go for Matsuzaka beef and white bars indicate the final decision to go for imported beef. To examine the effect of voting on the desirability of decision outcomes and processes, we conducted t-tests on the desirability of decision outcomes and processes with and without voting. There was no significant difference in the evaluation of the decision outcome and process (decision: t(225) 5 1.11, P 5 .27; process: t(225) 5 1.76, P 5 .08). This suggests that the presence or absence of a procedure that allows individuals to vote does not have an effect on the evaluation of the meeting. This suggests that we were not able to reproduce the real-life situation of the meeting. This may be because many of the participants questioned the rules of the meeting itself.

14.4

Method of Experiment 2

In Experiment 1, we conducted an experiment using a video of the same meeting scene as in Chapter 13, Revisiting the Group Decision-Making Experiment, with the aim of examining the factors that cause irrational meetings. As a result, it was suggested that the participants of the experiment detected the irrational meeting process. Therefore we thought that by teaching the participants that rules were important before the meeting, we could make them aware that there were other things to pay attention to in the meeting besides the outcome, and thus make the meeting more like an actual meeting. Therefore we thought that by explaining the importance of the results and the rules before playing the video, more people would be aware of the importance of following the rules, and even if the meeting was irrational, they would evaluate it highly if they followed the rules. Therefore in Experiment 2, in addition to the same plan as in Experiment 1, we added a change in the stage before the video was shown to the participants. Specifically, we set up two conditions, one in which the results of the meeting were taught to be more important and the other in which the rules and regulations of the meeting were taught to be more important, and examined the differences in the evaluation of the meeting between these conditions and the control condition of Experiment 1. Since the outline and design of the experiment were basically the same as those of Experiment 1, we will now describe in detail the main changes made in Experiment 2.

14.4.1 Overview of the experiment The experiment consisted roughly of instruction to emphasize the importance of consequences or rule compliance, video viewing, voting, and a questionnaire survey. The flow of the experiment was the same as in Experiment 1.

14.4.2 Experimental design To the process of Experiment 1, we added the instruction to emphasize the importance of the outcome and rule compliance. This instruction was given using a

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PowerPoint presentation before the video was played, under the condition of placing importance on the outcome and the condition of placing importance on rule compliance. Voting was conducted as in Experiment 1, and the same ballot paper was used as in Experiment 1.

14.4.3 Stimuli As in Experiment 1, we used four types of videos with and without rule compliance conditions created in Chapter 13, Revisiting the Group Decision-Making Experiment. Figs. 14.9 and 14.10 show the results and a PowerPoint presentation of the instruction to reinforce rule compliance that was given before the videos were played.

14.4.4 Questionnaire We used the same questionnaire as in Experiment 1. The questionnaire consisted of six items: confidence in one’s own vote, items for evaluating the video, items for sensitivity to expiration dates, items for everyday decision-making, a decision-making scale (Ideno et al., 2012), and a formality-seeking scale (Takahashi et al., 2010). There was only one type of questionnaire, and all participants answered the same questionnaire.

14.4.5 Implementation of the experiment A total of 167 regular students of Waseda University, 11 students of Gakushuin University, 2 students of Chuo University, 1 student of Tokyo University of Science, 1 student of Shirayuri Women’s University, 1 student of Ritsumeikan University, 3 students of Waseda University Senior High School, 8 students of Clark Memorial International High School, 5 office workers, 3 housewives, and 1 self-employed person participated in the experiment. A total of 100 males and 104 females participated in the study. The mean age of the participants was 21.64 years (SD 5 5.52 years). Precisely 25
26 participants were tested at each level, with one level being the combination of the type of video and the type of instruction. In recent years, it has become important for groups to think carefully about what the final outcome will be in their decision making. In recent years, it has become more and more important to consider the final outcome of group decisions.

Figure 14.9 Instruction of emphasizing decision outcome. In recent years, it has become important for groups to think carefully about following the rules of decision making. There have been reports of cases where significant losses were created for the group if all members did not follow the rule

Figure 14.10 Instruction of emphasizing following rules of decision-making.

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Figure 14.11 Participants in the experiment at Gakushuin University and the arrangement of the screen.

The experiment was conducted in a small classroom in the psychology course at the Toyama Campus of Waseda University and in a small classroom at Gakushuin University. The video was presented using a projector, screen, and speakers. At Waseda University the projector was an EPSON EB-435W, and the screen was a PLUS FS100V with a width of 215 cm and a height of 135 cm. At Gakushuin University the projector was a Panasonic PT-RZ570JW and the screen was a KIC SK-AF100W with a width of 231.4 cm and a height of 210 cm. The speaker was a Panasonic RPSPC300. The distance between the subject and the screen was about 180 cm when the subject sat in the first row, and about 290 cm when the subject sat in the second row. Fig. 14.11 shows the actual experimental scene at Gakushuin University. The experiment was conducted in small groups of three to seven participants each time, using only four seats in the first row for three or four participants, and the seats in the second row for five to seven participants. The time required for the experiment was about 20 minutes. As the procedure of the experiment, the participants were instructed and shown a slide that reinforced decision or procedural justice. After that the participants watched one video on the screen, stopped in the middle, and were given ballots to vote for either Matsuzaka beef or imported beef. In addition, after collecting the ballots, the participants were asked to answer the evaluation of their choice. Then, we played the rest of the video until the end. After that the participants were asked to answer the following questions: evaluation of meetings, sensitivity to consumption deadlines, awareness of everyday decisions, decision-making scale, and formality-seeking scale. In addition, the participants were asked to write freely about their introspection afterward. After the experiment the purpose of this study was explained to the participants.

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14.4.6 Instruction The instruction of the experiment was as follows: [Greetings and experimental details] Thank you very much for your cooperation in today’s experiment. My name is XXX. I am XXX, and I look forward to working with you. In the experiment you are about to participate in, you will watch a video of a seminar meeting scene and answer a simple questionnaire. There is a paper explaining the experiment in your hand, but it is very long, so I will just explain the important parts in brief. The experimental data will be processed statistically, and no individual will be identified. Also, we have determined that there is no effect on the human body. Furthermore, if you feel sick during the experiment, we will stop the experiment. Please do not hesitate to contact us. Are there any questions so far? (If you have no questions, please answer them.) First, please fill out this consent form. Please check the box next to "I do not consent to disclosure. If you have any questions, please feel free to contact me. (Collect the consent form and explanation paper.) In this experiment, we will stop the video and ask you to answer the first question. After that, you will be asked to watch the rest of the video and answer the questions again at the end. The duration of this experiment is expected to be about 20 minutes. [Start of the experiment] Now, let’s start the experiment. First of all, I would like to explain the important things about the conference. I’m going to start by explaining the important things for a meeting. Now, I will play the video, so please look at the screen in front of you. (video starts playing) (video stops) In the meeting that you have seen so far, which would you vote for, Matsusaka beef or imported beef? I will now hand out the ballots. Please wait until you have made your choice. (Make sure that everyone has voted).

The detection of bad decisions and a voting experiment

I will now collect the ballots. (Confirm that everyone has voted) Now, please turn the cover of the questionnaire and answer the first question. When you have answered the question, please wait and do not proceed to the next page. (Make sure that everyone has been rated) Now, let’s play the rest of the video. (Make sure you have rated everyone.) Now, let’s continue with the video. [End of video] That’s it for the video. Now, please fill in your name and other information on the cover page of the questionnaire, turn the pages, and answer the remaining questions to the end. [End of Questionnaire] Thank you very much. If you have any comments about this experiment, please write them in the box at the end of the questionnaire. [End of experiment] This is the end of the experiment. Thank you very much for your cooperation in this experiment.

After the experiment the following debriefing will be given: I would like to explain the contents of this research. The purpose of this study is to explore the problems that can be observed in discussion situations such as meetings. In social psychology, there is a phenomenon called groupthink, and it is said that this phenomenon does not necessarily result in good decisions even when excellent people gather together. In our daily lives, it seems that we sometimes fail to achieve our original goals because we are too concerned about the details and rules in meetings of clubs. Therefore, in this study, we decided to make a video of the conditions for sticking to the rules when voting, and to see how we make decisions and how we evaluate meetings. I have given a brief explanation.

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Results and discussion of Experiment 2

To examine the factors that contribute to irrational decision-making in a discussion situation such as a meeting, we conducted an experiment using four types of videos of meeting scenes created in the experiment mentioned in Chapter 13, Revisiting the Group Decision-Making Experiment. In this experiment, we added to the experimental design of Experiment 1 the instruction that it is important to follow the rules and the instruction that the final result is important before having the participants watch the video. The data of 306 participants were analyzed together with the data of Experiment 1. Specifically, we calculated and compared the means and conducted an analysis of variance to examine the effects of the type and presence of the instruction, the outcome of the meeting decision, and the compliance with the rules on the desirability of the meeting decision and process. Correlation analysis was also conducted to examine the relationship between evaluations of meeting decisions and evaluations of the process and meetings. A test of the difference between the ratios of the two groups was conducted to examine whether there was a difference in the number of votes for Matsuzaka beef and imported beef, and a regression analysis was conducted to examine the effect of sensitivity to expiration dates on the desirability of meeting decisions.

14.5.1 Correlation analysis Next, we calculated the correlation coefficient between the desirability of the decision and the desirability of the process in the meeting. A significant weak positive correlation was found (r 5 0.36). This result was similar to the result in Chapter 13, Revisiting the Group Decision-Making Experiment. It was suggested that those who evaluated the decision of the meeting favorably also evaluated the process of the meeting highly.

14.5.2 Analysis of the desirability of decisions We examined the effects of decision outcomes, compliance with rules, and the type and presence of instruction on the desirability of decisions in meetings. Specifically, the desirability of the decision in the meeting was set as the dependent variable, and the analysis of variance was conducted for three factors among the subjects: rule compliance (following the rule vs not following the rule), decision result (Matsuzaka beef vs imported beef), and instruction (no instruction vs result vs rule). The results showed that there was a significant main effect for decision outcome in the meeting (F(1, 294) 5 86.02, P , .001). The results suggest that regardless of the presence or absence of rule compliance and the presence and type of instruction, the final decision to have imported beef for dinner at the seminar camp was evaluated as more desirable. This result was similar to the result of the experiment in Chapter 13, Revisiting the Group Decision-Making Experiment. It is possible that the participants in the experiment judged the meeting as desirable if

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they were satisfied with the result of the decision, even if the meeting did not follow the rules.

14.5.3 Analysis of the desirability of the meeting process To examine the influence of the decision result of the meeting, the presence or absence of compliance with the rules, and the type and presence or absence of instruction on the desirability of the meeting process, the following questions were asked: What is the effect of compliance with the rules (following the rules vs not following the rules), the decision result (Matsuzaka beef vs imported beef), and the instruction (none vs result vs rules) on the desirability of the meeting process? To examine this questions, the analysis of variance was performed. When the result of the decision was imported beef, the evaluation of the process tended to be higher regardless of whether the rule was followed or not and regardless of the instruction (F(1, 294) 5 8.91, P , .005). Regardless of the decision outcome, the rule compliance condition tended to result in relatively higher evaluations of the meeting process (F(1, 294) 5 3.86, P , .01). This result was different from the results of the experiment in Chapter 13, Revisiting the Group Decision-Making Experiment, where no significant main effects were found for the factors of decision outcome and rule compliance. The reason for this is presumed to be that the newly added instruction in Experiment 2 resulted in higher evaluations of rule compliance meetings and rational decision outcomes. In addition, although the final result of imported beef was evaluated more desirably, the addition of the instruction that encouraged the participants to place importance on the result or rule compliance suggested that the rule compliance condition was evaluated relatively more desirably. Overall, however, the desirability of the meeting process was also evaluated more favorably for meetings in which the decision outcome was an imported beef, suggesting that the experimental participants were able to detect irrational group decision processes even when rule compliance was emphasized. In multiple comparisons the analyses of variance of decision outcomes, rule compliance, and teaching in the desirability of the process were examined by conducting multiple comparisons using Ryan’s method. The results suggest that the condition of rule compliance is more highly valued when there is instruction that encourages the participants to place importance on the outcome or rule compliance. This was interpreted to mean that they became more aware of rule compliance conditions when they evaluated the meeting by providing instruction that encouraged them to place importance on the outcome or rule compliance conditions.

14.5.4 Analysis of consummation sensitivity To examine the relationship between the desirability of decisions and the desirability of processes in meetings and the sensitivity of consumption deadlines, we conducted a regression analysis to predict the desirability of decisions and the desirability of processes from the sensitivity of consumption deadlines, respectively.

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As a result, when the decision result was imported beef, the effect of expiration date sensitivity on the desirability of the decision was observed (t(150) 5 20.05, P , .05), while no significant effect was observed for Matsuzaka beef (t(304) 5 2 0.05, n.s.). This suggests that when the decision outcome is Matsuzaka beef, sensitivity to expiration date has no effect on the desirability of the decision, but those who are sensitive to consumption date evaluate the decision more highly when the decision outcome is imported beef. Next, we conducted a regression analysis to predict the desirability of the process from the sensitivity of the consumption deadline and found no effect of the sensitivity of the consumption deadline on the desirability of the process regardless of the decision outcome (Matsuzaka beef: t(304) 5 2 0.97, n.s. Imported beef: t(150) 5 21.57, n.s.). This suggests that in the case of Matsuzaka beef, where the decision outcome is risk-oriented, even risk-sensitive individuals evaluate the process as desirable if they comply with the rules. Given the regression analysis of expiration date sensitivities and decision outcomes, expiration date sensitivities affected only the evaluation of the decision outcome in the case of the final decision to go with imported beef.

14.5.5 Analysis of voting As a result of the voting, 59 out of 306 experimental participants voted for Matsuzaka beef, and 247 voted for imported beef. Fig. 14.12 shows the total number of people who voted. Fig. 14.13 shows the number of people who voted for Matsuzaka beef and imported beef by level, with black bars indicating that the final decision was Matsuzaka beef and white bars indicating that the final decision was imported beef. The items numbered in Fig. 14.13 are the same as in Fig. 14.3, Fig. 14.4, and Fig. 14.8.

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14.6

Conclusion and future prospects

In the experimental study in this chapter, we examined the factors that contribute to irrational group decision-making in collegial situations such as meetings through two experiments. We used videos that reproduced real-life situations of irrational decision-making meetings as stimuli and conducted experiments on how these meetings were evaluated. In Experiments 1 and 2 the video was paused at the scene of majority voting to simulate a real-life meeting, and the participants were asked to vote for either Matsuzaka beef or imported beef. In addition, in Experiment 2, before the video was played back, a PowerPoint presentation was shown on the PC screen to encourage participants to emphasize the importance of the outcome or rule compliance. The purpose of this was to make the participants aware that there were other things to pay attention to when evaluating the meeting besides the outcome of the decision. As a result of adding the voting stage to the experimental study in Chapter 13, Revisiting the Group Decision-Making Experiment, the evaluation of the decision and process of the meeting was significantly higher when the decision result of the meeting was the imported beef, regardless of whether the rule was followed or not, as in the previous study. In addition, no difference was found in the results compared to the study in Chapter 13, Revisiting the Group Decision-Making Experiment, although the task of having the participants actually cast their votes was conducted. This suggests that experimental participants do not make irrational decisions when they are allowed to vote in a situation without interaction.

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When participants were taught to emphasize the importance of outcomes or rule compliance in meetings, differences were found in their evaluations of the desirability of the meeting process. When the instruction was given, participants rated the rule compliance condition higher, and when the instruction was not given, they rated the rule noncompliance condition higher. This suggests that the teaching of the importance of the outcome of the meeting or the compliance with the rules in the evaluation of the process of the meeting helped the participants to think that there were other important points to be considered in the meeting besides the outcome of the decision. On the other hand, the desirability of the outcome of the meeting was more highly evaluated in the case of imported beef. When the desirability of the outcome of the meeting and the desirability of the process are combined, it is thought that the participants were able to judge the meeting rationally based on the final outcome of the decision while placing importance on whether or not the rules were followed when evaluating the desirability of the process. In addition, they evaluated the desirability of the outcome of the meeting more highly when the outcome of the meeting was an imported beef, regardless of the presence or absence of rule compliance, the outcome, or the instruction that encouraged them to place importance on rule compliance. Thus even when evaluating the desirability of meeting decisions, the experimental participants were relatively able to detect meetings that were irrational and had bad outcomes, suggesting that they were able to make rational decisions that were somewhat in line with their objectives. In the present study the experimental participants were relatively able to judge irrational meetings. However, irrational meetings seem to occur in actual society. In addition to the factors examined in this study, there may be other factors that affect meetings in reality. For example, in meetings at companies, there is a clear time constraint, and it is important to make good decisions and finish the meeting in time. To finish the meeting on time, it is effective to set the rules in advance. In fact, a participant of the experiment, who was a company employee, said in his introspection, “I felt that my way of thinking has changed a little between when I was a student and when I was working. Compared to the past, I found myself becoming stricter about rules and regulations. I was more strict about rules and regulations than I used to be.” Janis (1972, 1982) found that the factors that influence groupthink, including the time constraint and the reasoning behind giving instructions that emphasize adherence to rules, which may result in meetings and group decision-making that place less emphasis on the outcome of decisions. Janis (1972, 1982) cites the lack of norms requiring systematic procedures and the lack of leadership as factors that lead to groupthink. The video used in this study contains detailed rules for majority voting and scenes of the chairperson exercising leadership, which may have made it difficult for groupthink to occur. However, through the course of these series of experimental studies, it seems that most people are capable of detecting when a group meeting is not in line with their objectives in an independent situation where there is no concerted action and of avoiding the worst decisions that focus on the consequences of group decision-making when they lead to serious consequences such as food poisoning.

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References Frankfurt, H. G. (2005). On bullshit. Princeton, NJ: Princeton University Press. Ideno, T., Ohkubo, S., Tamari, Y., Abe, S., & Takemura, K. (2012). Ishikettei Katei ni Kansuru Shitumonshi Shakudo no Kaihatsu [Development of questionnaire scales of decision making process]. In: Paper presented at the Joint Workshop of Behavioral Economic Society and Conference of Experimental Social Science, Aoyama Gakuin University, Tokyo, JP. Janis, I. L. (1972). Victims of groupthink. Boston, MA: Houghton Mifflin. Janis, I. L. (1982). Groupthink: Psychological studies of policy decisions and fiascoes. (2nd ed.). Boston, MA: Houghton Mifflin. Takahashi, N., Takemura, K., Ideno, T., Ohkubo, S., & Tamari, Y. (2010). Aimai Jitai ni okeru Keishikisei Tsuikyu Keikou ni kansuru Yobiteki Kentou [Preliminary study on the tendency to pursue formalism in ambiguous situations]. In: Proceedings of the 74th annual convention of the Japanese Psychological Association, Osaka University, Osaka, JP. Takemura, K., Ideno, T., Oguni, E., Saito, H., & Sakagami, T. (2021). Fugouri na Syuudan Ishikettei no Kansatsu to Touhyou Jikken [Observation of irrational group decision and voting experiment]. In: Unpublished Manuscript, Department of Psychology, Waseda University.

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Situation dependence of group and individual decision making and bad decisions

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Chapters 1
9 of this book have been devoted to theoretical and experimental investigations of individuals’ irrational and bad decision-making. These have shown that some individual decision strategies, despite their relatively low cognitive load, make it easier to choose the best option and harder to choose the worst one. When we apply these decision strategies to group decision-making in Chapter 11, Decision Strategies and Bad Group Decision-Making: A Group Meeting Experiment, and conduct experiments, we find that similar decision strategies in groups do not produce desirable results. The results were not so desirable. In Chapters 12
14, we examined the latter possibility by experimenting with the question of whether individuals can detect irrational meeting processes and worst case choices that deviate from the goal in group decision-making and meetings in the absence of interaction. The results suggest that even in group meetings and group decision-making, individuals can detect irrational meetings and worst choices if they observe them in a situation without interaction. These considerations suggest that the reason why the worst choice is made in group decision-making is that the cognition, judgment, and decision of irrational meetings and decisions are distorted due to the influence of interaction among group members. In this chapter, I will point out the phenomenon of preference reversal due to situation-dependent decision-making, which is known as the framing effect, and attentional shifts as distortions of cognition, judgment, and decision-making under such interactions. In addition, by reinterpreting the jury theorem in group decision-making, I will discuss the possibility that group decision-making may be distorted by these situationdependent effects.

15.1

Decision-making strategies for individual decision-making and group decision-making by majority rule

In Chapter 7, A Computer Simulation of Cognitive Effort and the Accuracy of Two Stage Decision Strategies in a Multiattribute Decision-Making Process, and Chapter 8, A Computer Simulation of Bad Decisions and Good Decisions: An Extended Analysis of Two Stage Decision Strategies, we performed computer simulations of individuals’ decision strategies and found that when individuals narrow Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00016-8 © 2021 Elsevier Inc. All rights reserved.

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down the number of choices to about two using a decision strategy such as lexicographic strategy (LEX) and then make a decision using a compensatory decision strategy such as additive strategy (ADD), the accuracy of the decision strategy is about the same as that of the ADD strategy, although the cognitive effort is considerably lower. It was also found to be effective in avoiding choosing the worst possible option. In addition, in Chapter 9, A Process Tracing Study of Decision Strategies and Bad Decisions, we examined the two stage decision-making strategy by having the experimental participants actually execute it and found that the earlier two stage decision-making strategy, which was considered to be highly effective in the computer simulation, was effective in both the decision-making performance of the experimental participants and in avoiding the worst decision. In addition, compensatory decision strategies such as ADD can lead to information overload due to the high level of cognitive effort when participants are actually asked to make a decision, leading them to choose the worst option or making it difficult to choose the best option. In addition, the first step was to use a system like disjunctive strategy (DIS). In addition, when a decision-making strategy such as DIS was used in the first stage, the actual decision-making of the participants in the experiment in the computer simulation was less likely to choose the best option than the other decision-making strategies. It was found that they were less likely to choose the best option and more likely to choose the worst one. Let us now consider the following method of consolidating the opinions of group members in group decision-making. For example, in the first stage, after narrowing down the options to two or three, the group members will decide which option is best for them. For example, let us assume that in the first stage, after narrowing down the options to two or three, the individual chooses the most desirable option by using a strategy such as ADD. After that, it is assumed that the option with the highest number of votes is adopted by majority vote. What would be the result in such a case? For the sake of simplicity, let us assume that the decision-making process of one member is independent of the decision-making process of another member, and that independence is maintained among all members. Given these assumptions, let us consider how group decision-making works. For the sake of simplicity, let us consider three group members. This chapter is based on a three-person version of the computer simulation conducted by Payne, Bettman, and Johnson (1993) (Nakamaru, Tamari, & Takemura, in preparation; Takemura, Tamari, & Nakamaru, in preparation). Under these conditions, we considered all combinations of one-step decision strategies and calculated the rate of choosing the worst and best options in terms of weighted additive expectation, as shown in Figs. 15.1 and 15.2, respectively (Nakamaru, Tamari, & Takemura, in preparation; Takemura, Tamari, & Nakamaru, in preparation). In both the figures the vertical axis is the rate of choosing the option with the largest expected value (the probability of choosing the best option), and the horizontal axis is the rate of choosing the option with the smallest expected value (the probability of choosing the worst option). The horizontal axis is reversed with values of 0 to the right and values of 1 to the left so that the upper right of the figure has the more desirable property. Fig. 15.1 shows the results of the strategy

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combination assuming that all three people have the same weight for the attribute. Fig. 15.2 shows the results of the computer simulation assuming that all three people have different weights, and that the group weights are their average values. We have also included a randomly selected one for comparison. Figs. 15.1 and 15.2 show that there are various results depending on the combination of each decision-

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making strategy, but since the final decision is decided by the two decision makers with the highest number of votes, the result is basically the same as that of a single decision maker when the number ratio is 2 to 1. If the number of people is 2 to 1, the result is basically the same as that of a single decision maker. Both Figs. 15.1 and 15.2 show that the combination of noncompensatory decision strategies such as lexicographic strategy (LEX), lexicographic-semiorder (LEX-S), and elimination by aspect (EBA) strategies makes it easier to choose the best option and harder to choose the worst option. In addition, noncompensatory decision strategies such as DIS are not inferior to compensatory decision strategies such as ADD. In addition, noncompensatory decision strategies such as DIS are less likely to choose the best option and more likely to choose the worst option if there is a majority, even in a group of three. Next, let us examine the abovementioned computer simulation with a two stage decision-making strategy. For the sake of simplicity, we will consider three members of a group and assume that all members use the same decision strategy. Under these conditions, let us consider a two stage strategy in which the individual decision-making strategy is narrowed down to two options from the most efficient LEX and the decision is made by ADD. Figs. 15.3 and 15.4 show the rate of choosing the worst and best options, respectively, in terms of weighted additive expectation (Takemura, Tamari, & Nakamaru, in preparation). The upper panel of each figure shows the results when all three people are assumed to have the same weight for the attribute. The lower panel shows the results of computer simulations assuming that all three individuals have different weights and that the group weights are their average values. For comparison the results for LEX, DIS, and ADD only are

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also plotted. Both Figs. 15.3 and 15.4 show that the two stage decision strategy from LEX to ADD is not inferior to the compensatory decision strategy such as ADD, as it is easier to choose the best option and harder to choose the worst option in a three-person decision. DIS tends to be relatively more likely to choose the worst option and less likely to choose the best option. Next, in Figs. 15.5 and 15.6, we show similar results for the worst and best choices, respectively, for different alternatives (Takemura, Tamari, & Nakamaru, in preparation). The top row of each figure shows the results when all three people are assumed to have the same weight for the attribute, and the bottom row shows the results of the computer simulation when all three people are assumed to have different weights and the group weight is their average value. Examination of these figures shows that when the number of alternatives is small, a noncompensatory decision strategy such as LEX still has no low probability of choosing the worst alternative, but as the number of alternatives increases, it becomes harder to choose the worst alternative. In addition, Figs. 15.7 and 15.8 show similar results for the worst and best choices, respectively, for different alternatives (Takemura, Tamari, & Nakamaru, in preparation). The top row of each figure shows the results when all three people are assumed to have the same weight for the attribute, and the bottom row shows the results of the computer simulation when all three people are assumed to have different weights and the group weight is their average value. Examination of these figures shows that when the number of attributes is small, noncompensatory decision strategies such as DIS and LEX still have a low probability of choosing the worst option, but when the number of options increases, they are more likely to choose the worst option. The two stage decision-making strategy of LEX 1 ADD

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shows that even when the number of attributes increases, the probability of choosing the worst option is low and the best option is relatively easy to choose. Figs. 15.9 and 15.10 show similar results for the worst and best choices, respectively, for each level of dispersion of the attribute weights (Takemura, Tamari, & Nakamaru, in preparation). The left side of the figure shows the case of high dispersion, and the right side of the figure shows the case of low dispersion. Examining these figures, we can see that when the dispersion of the attribute weights is high, LEX has a relatively low probability of choosing the worst option and is more likely to choose the best option, but when the dispersion of the attribute weights is low, the results are somewhat worse. In contrast, the two stage decision-making strategy of LEX 1 ADD has a relatively low probability of choosing the worst option and a relatively high probability of choosing the best option, regardless of the level of the dispersion of the attribute weights. Finally, Figs. 15.11 and 15.12 show similar results for the worst and best choices, respectively, with and without the dominance of attributes (Takemura, Tamari, & Nakamaru, in preparation). The left side of the figure shows the case without dominance, and the right side of the figure shows the case with dominance. These figures show that when dominance is present, LEX has a relatively low probability of choosing the worst option and is more likely to choose the best option, but when dominance is removed, the result is somewhat worse. In comparison, the two stage decision-making strategy of LEX 1 ADD, regardless of dominance, has a relatively low probability of choosing the worst option and a relatively high probability of choosing the best option. DIS also tended to produce worse results when there was no dominance compared to when there was dominance. Dispersion: High

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Figure 15.9 Rate of choosing the worst option (the alternative with the minimum expected value) for each decision strategy in the different dispersion levels. Note: Upper row indicates the vales when the weight of attribute is equal. Lower indicates the values when the weight of attribute is different.

Situation dependence of group and individual decision making and bad decisions

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Figure 15.10 Rate of choosing the best option (the alternative with the maximum expected value) for each decision strategy in the different dispersion levels. Note: Upper row indicates the vales when the weight of attribute is equal. Lower indicates the values when the weight of attribute is different.

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Figure 15.11 Rate of choosing the worst option (the alternative with the minimum expected value) for each decision strategy in the different dominance levels. Note: Upper row indicates the vales when the weight of attribute is equal. Lower indicates the values when the weight of attribute is different.

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Figure 15.12 Rate of choosing the best option (the alternative with the maximum expected value) for each decision strategy in the different dominance levels. Note: Upper row indicates the vales when the weight of attribute is equal. Lower indicates the values when the weight of attribute is different.

15.2

Consequences from Condorcet’s Jury Theorem

In this chapter, we presented the results of computer simulations from a group of three people, but if we assume independence among the members, it can be suggested that the two stage decision-making strategy of narrowing down the choices to about two using a noncompensatory decision-making strategy such as LEX and then considering the remaining choices using the ADD strategy is relatively superior in avoiding the worst decision and in choosing the best decision even in a group of three people, as analyzed in the individual decision-making strategy. The results suggest that the two stage decision-making strategy is relatively superior in avoiding the worst decision and choosing the best decision. This finding can be further extended and used by extending Condorcet’s (1785) Jury Theorem. In this section, I will explain Condorcet’s Jury Theorem first. Condorcet’s Jury Theorem is a law that is based on a simple mathematical model of majority rule. Condorcet, an 18th-century French revolutionary, is a pioneering theoretical thinker on group decision-making and voting. Majority rule is used in elections and in voting, but to simplify it, majority rule is to adopt the option chosen by the largest number of people. Majority rule is often used when a large number of people decide to do something. Condorcet’s (1785) mathematical model is a judgment model that assumes that what people vote for is a “judgment” that is either true or false. It has positive consequences for democratic decision-making in that it proves the “Jury Theorem” [named by Black (1958)] that a group with a majority rule can make more correct decisions than a

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group of voters with average judgment or a single voter with the highest judgment. On the other hand, he is said to have created a positive consequence for democratic decision-making in that he proved the “Jury Theorem” [named by Black (1958)] that people can decide. On the other hand, he points out that the paradox of collective choice, like the impossibility theorem proved by Arrow (1951), arises based on a model of preference that states that what people vote for are “preferences” that are neither true nor false. Let us illustrate Condorcet’s (1785) Jury Theorem with the following threeperson decision. Let us assume that the three decision makers are Mary, Rachel, and Devlin, each of whom independently decides whether to accept or reject a certain decision problem. Each of the three decision makers is expected to give either a “correct” or an “incorrect” answer to the problem. In other words, each of these women has a parameter called the “correct answer rate.” It is assumed that the higher this value is, the more likely they are to always derive the correct answer; if Mary’s correct answer rate p is .8, it means that she has an 80% probability of getting the correct answer for the problem in question. For the sake of simplicity, let us assume that all three people have the same percentage p of correct answers. What the jury theorem says here is that “when three people independently judge and answer a decision problem, if a majority decision is made in which the majority of the opinions of each of the three people are taken as the opinion of all the people, the rate of correctness of the collective decision of the three people will increase if p is greater than 0.5, compared to answering the question by one person.” The first step is to determine the correct answer of three people. First of all, there are eight patterns of correct and incorrect answers for three people, since there are three powers of two. For example, Mary, Rachel, and Devlin each answer correctly. As long as either “all three are correct” or “two out of the three are correct” occurs, the answer will be correct when the majority vote is taken. In other words, there are four cases: Mary, Rachel, and Devlin are each correct, Mary and Rachel are correct, Mary and Devlin are correct, and Rachel and Devlin are correct. The probability that a majority of people will choose the correct answer means the probability that either “all three people will choose the correct answer (case 1)” or “two of the three people will choose the correct answer” (cases 2, 3, and 4). If p is .8, the third power of p is .512. If p is .8, the cube of p is .512. Then, what is the “probability that two out of three people choose the correct answer”? We can see that it is enough to multiply the probability of choosing the correct answer by p twice and the probability of choosing the wrong answer by (1 2 p) once. If p is .8, the result is .128. If p is .8, the probability is .128, and since we want to find the probability of “either” of these two situations occurring, we add these probabilities together to get p3 1 3p2(1 2 p). Here, since there are three ways in which two out of three people are correct as shown earlier, we multiply the probability of p2(1 2 p) by 3. If p is .8, the probability is .896. When the probability p for each person is .800; the total probability of correct answer is .896 when there are three people. So the percentage of correct answers is higher. When there is only one person, the probability is .600 and probability is .648 when there are three people; it is .7 when there are

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three people, and the probability is .784 when there are three people. If the probability of correct answers is .600 for each person, the total probability of correct answers is .648; if the probability of correct answers is .700, the probability of correct answers is .896; if the total probability of correct answers is .972; and so on. Here is a proof of the jury theorem in the case of three people. The proposition we want to prove is p3 1 3p2 ð1 2 pÞ 2 p . 0;

where :5 , p , 1:

Factorizing and transforming the abovementioned equation, we get p(2p 2 1) (1 2 p) . 0. Now, it is clear that in all the factors appearing here, it is always positive no matter how many numbers from .5 to 1 we put in p. And since it remains a positive number, no matter how many positive numbers we multiply it by, we know that it is always positive as a whole as well. This proves the jury theorem in the case of three people. This story can be generalized to the case where there are n members of a group. In other words, the jury theorem states that “when n people independently judge and answer a decision problem, if a majority decision is made in which the majority of the opinions of each of the n people are taken as the opinion of all the people, then if p is greater than .5, the rate of correctness of the collective decision of the n people will be higher than when only one person answers.” For example, let us consider the case where there are 5 members of a group, and the situation in which the majority of the answers are correct. The probability of getting all five correct is p5, the probability of getting four out of five correct is p4(1 2 p), and the probability of getting three out of five correct is p3(1 2 p)2. Since there are five possible combinations of four out of five in 5C4, and 10 possible combinations of three out of five in 5C3, adding them all up gives the following formula. In other words, p5 1 5p4(1 2 p) 1 10p3(1 2 p)2. Substituting .8 for p, we get .942, which is larger than the .896 when there were three people. Therefore the following is a general formula for the probability that group decision-making by majority rule is correct. ðn21 XÞ=2

nCk pn2k ð12pÞk

k50

where .5 , p , 1. The jury theorem shows that as the number of group members increases, the probability of choosing the correct answer by majority vote converges to 1. This property can be derived from the central limit theorem. Immediately from this, we can see that the following propositions about bad decision-making holds.

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Proposition 15.1: Jury thorem when the probability of individual corect answer is less than .05. When n people independently judge and answer a decision-making question, if a majority decision is made in which the majority of the opinions of each of the n people are taken as the opinion of all the people, the probability of correctness for the collective decision of the n people will be lower than the probability of individual correct answer p of the n people is the same and p is smaller than .5. This means that if the correct answer rate of the members is lower than .5, the more people there are, the worse the correct answer rate of the majority decision becomes, and the less efficient the group decision-making becomes. Proof: The proposition 15.1 will be easily proved by letting p be less than .05. ’ Similarly, let q be the probability of making a wrong decision. Proposition 15.2: Propositions of reducing the probability of wrong group decision-making. When n people make independent decisions to answer a decision problem, if a majority decision is made in which the majority of the opinions of each of the n people are taken as the opinion of all the people, the error rate (probability) of the collective decision of the n people will be lower than the individual error rate (probability) q when the error rate of the n people is the same and q is smaller than .5. Proof: The proposition 15.2 will be easily proved by the jury theorem ’ List and Goodin (2001) extended Condorcet’s Jury Theorem to the case of voting for k alternatives. They extend the jury theorem to the case of polynomial voting for k alternatives, where exactly one alternative (e.g., option i) is epistemically the “correct” outcome. According to their theorem, we have the following. Proposition 15.3: The jury theorem when the number of choices is three or more (List & Goodin, 2001) There are k alternatives, and each voter/juror has an independent probability p1, p2, pk to vote for choices 1, 2, . . ., k, respectively. Assuming that the probability pi of an individual voting for the “correct” outcome i is the same for the group and exceeds the probability pj(j 6¼ i) of voting for the other alternatives, the probability Pi of deciding on the “correct” outcome i of the group decision by majority vote exceeds the probability Pj(j 6¼ i) of voting for each of the other group decision alternatives (i.e., pi . pj!Pi . Pj). That is, the proposition states that if the probability pi of voting for the “right” outcome, i, is greater than the probability pj of voting for the “wrong” outcome, j ( 6¼ i), respectively, the probability Pj of deciding that the “right” option i is superior

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to any other option j in the population is higher. According to List and Goodin (2001), the proof is outlined as follows. Proof: (List & Goodin, 2001): This proposition 15.3 follows immediately from the probability function of the joint distribution of the random variables X1, X2, . . ., Xk. In other words, the proof follows if we prove that if for all j 6¼ i, the probability of the group members answering each option correctly is pi . pj, for all j 6¼ i, the probability of group decision-making holds the relation Pi . Pj. Suppose that j 6¼ i. It should be noted that, for all k-tuple of nonnegative integers, we have ANj if and only if ANi, where n0 i 5 nj, n0 j 5 ni, and, for all h 2 = {i, j}, nh 5 n0 h. By calculating Pi and Pj by probability distribution formula, we get n0 i . n0 j, for all j 6¼ I, and we get that if pi . pj for all j 6¼ i,Pi . Pj. ’ Proposition 15.4: Convergence theorem for the case where the number of alternatives is three or more (List & Goodin, 2001) Assuming that pi is the same for the group and exceeds the probability of voting for any of the other alternatives pj(j 6¼ i), the probability Pi of the group decision that alternative i is better than the other j converges to 1 as the number of voters/ jurors approaches infinity. Proof: (List & Goodin, 2001): What leads to this result: Proposition 15.4 is the law of large numbers. Consider a vector of random variables X 5 hX 1, X 2, . . ., X ki. Here, for each i, let X i 5 Xi/n. The joint distribution of X i is a polynomial X i with mean vector p 5 hpi, mean vector p 5 hp1, p2, . . ., pki, and the polynomial distribution of the variance
covariance matrix Σ 5 (sij)k 3 k. Here, for each i and each j, sij 5 pi(1 2 pi) for i 5 j, and sij 5 2pipj for i 6¼ j. By the central limit theorem, assuming that pi is the same for the group and exceeds the probability of voting for the other option pj(j 6¼ i), the probability Pi that option i is the winner over any option j in a group decision converges to 1 when the number of voters/jurors approaches infinity. When the number of voters/jurors approaches infinity, the probability that the “correct” option is the winner over any of the options converges to 1.’ By interpreting this theorem of List and Goodin (2001), the following proposition can be easily derived. Proposition 15.5: Collective decision-making for the worst option when the number of alternatives is three or more. There are k alternatives, and each voter and juror has an independent probability q1, q2, . . ., qk with choices 1, 2, . . ., k to vote for the worst alternative. Assuming that the probability qi of voting that the worst outcome determined by an individual is i is the same for the group and exceeds the probability of voting for the other alternatives qj(j 6¼ i), the probability Qi that the group decision on the worst

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alternative by majority vote is determined to be the worst outcome i is equal to the probability of voting for the worst alternative for each of the other group decisions exceeds the voting probability Qj(j 6¼ i). Proof: It is obvious that q and p, Q and P are just different expressions. It is clear that q and p, Q and P are just different expressions. ’ Proposition 15.6: Convergence of the probability of the worst option being chosen in a group decision when the number ofalterntivesis three or more. There are k alternatives, and each voter and juror has an independent probability q1, q2, . . ., qk with choices 1, 2, . . ., k. Assuming that qi is the same in the population and exceeds the probability of voting for the other option qj(j 6¼ i), the probability Qi of option i being chosen over the other option j in the population converges to 1 as the number of voters/jurors approaches infinity. Proof: It is obvious that q and p, Q and P are just different expressions. It is clear that q and p, Q and P are just different expressions. ’ Proposition 15.7: The probability that the option with the lowest individual probability of being the best when the number of options is three or more will be chosen in a group decision. There are k alternatives, and each voter/juror has an independent probability p1, p2, . . ., pk to vote for choices 1, 2, . . ., k, respectively. Assuming that the probability pi of an individual voting for the “correct” outcome i is the same for the group and is the lowest compared to the probability pj(j 6¼ i) of voting for the other options (for all j, pi , pj), the probability Pi of choosing option i in a group decision by majority voting is less than Pj(j 6¼ i) (Pi , Pj). This indicates that the probability of selection in the population of the option with the lowest individual voting probability is lower than the probability of any selection. Proof: It is clear that by reversing the inequality relation in Proposition 15.3. ’ Proposition 15.8: Convergence of the probability that thealternativewith the lowest individual probability of being the best when the number ofalternativesis three or more is chosen in a group decision. There are k alternatives, and each voter/juror has an independent probability p1, p2, . . ., pk to vote for choices 1, 2, . . ., k. Assuming that pi is the same for the group and lower than the probability of voting for the other option pj(j 6¼ i), the probability Pi that the group decision by majority vote will be to choose that option i converges to 0 as the number of voters/jurors approaches infinity. This indicates that in group decision-making, the option that had the lowest probability of individual voting will not be chosen as the number of group members

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increases and approaches infinity. It suggests that the option that had the lowest probability in individual decision-making will hardly be chosen in group choice as the number of group members increases. Proof: It is clear by reversing the inequality relation in Proposition 15.4. ’ Propositions 15.7 and 15.8 imply that if the probability of an individual choosing the best option exceeds the probability of choosing the other options under independence among individuals, even in the multiple-choice situations considered in the previous chapters, the probability of the group choosing the worst option is lower than for the other options, and as the group membership is increased, the probability converges to 1. This implies that the probability converges to 1. Furthermore, consider the probability pi that an individual judges option i to be the best and the probability pj that an individual judges option j to be the best and assume that if pi . pj, the probability qi that an individual judges option i to be the worst and the probability qj that an individual judges option j to be the worst is qi , qj. This assumption assumes that the best and worst judgments are symmetric, which is not such an unnatural assumption. Then the following proposition holds. Proposition 15.9: Probability that the worst alternative will be chosen in a group decision when the number of alternatives is three or more. There are k alternatives, and each voter/juror has an independent probability p1, p2, . . ., pk to vote for choices 1, 2, . . ., k. Consider the probability pi that an individual judges option i to be the best and the probability pj that an individual judges option j to be the best and assume that if pi . pj, the probability qi that an individual judges option i to be the worst and the probability qj that an individual judges option j to be the worst is always qi , qj. Assuming that the individual’s probability pi of voting for the “correct” outcome i is the same in the group and is the highest compared to the probability pj(j 6¼ i) of voting for the other options (for all j, pi . pj), the probability Qi that option i is the worst in the group decision by majority vote is less than Qj(j 6¼ i) (Qi , Qj). This indicates that the probability that the option with the highest individual voting probability will be the worst option in the group decision is lower than the probability of any of the options. Proof: By the assumption that pi . pj!qi . qj, we have Pi . Pj!Qi , Qj, and it is clear from this and Proposition 15.7. ’ Proposition 15.10: Convergence of the probability that the worst alternative is chosen in a group decision when the number of alternatives is three or more. There are k alternatives, and each voter/juror has an independent probability p1, p2, . . ., pk to vote for choices 1, 2, . . ., k. Consider the probability pi that an individual judges option i to be the best option and the probability pj that an individual

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judges option j to be the best option and assume that if pi . pj, the probability qi that an individual judges option i to be the worst option and the probability qj that an individual judges option j to be the worst option is always qi , qj. Assuming that pi is the same for the group and higher than the probability of voting for the other option pj(j 6¼ i), the probability qi that option i is the worst in a group decision by majority vote converges to 0 as the number of voters and jurors approaches infinity. This indicates that the option that had the highest probability of being voted as the individual’s best option will not be chosen as the option that is judged to be the worst in group decision-making as the number of group members increases and approaches infinity. It suggests that the option that had the highest probability of being the best individual decision will rarely be chosen as the option that is judged to be the worst in a group decision as the number of group members increases in majority vote on the worst option. Proof: By the assumption that pi . pj!qi . qj, we have Pi . Pj!Qi , Qj, and it is clear from this and Proposition 15.8. ’ Propositions 15.9 and 15.10 show that in the multiple-choice situations considered in the previous chapters, if the probability of an individual choosing the best option exceeds the probability of choosing the other options under independence among individuals, the probability of the group choosing the worst option is lower than for the other options, increasing the group membership. This implies that the probability converges to 0. This implies that even using a noncompensatory decision-making strategy such as LEX, which was used in the analysis of individual decision-making in this book, the worst decision can be avoided as the number of group members increases. I would like to note that these applications of Condorcet’s Jury Theorem are not just about the percentage of correct answers but can also be applied to the accuracy of decision-making, the percentage of choices for the best decision, and the percentage of choices for the worst option. This is because the jury theorem is merely an application of the central limit theorem of statistics to the problem of decisionmaking by a jury in the first place and can be considered more broadly. Again, interpreting the results of our computer simulations and experiments, we find that the strategy that was effective in the two stage decision-making strategy using the additive form from LEX is also effective in majority voting, both in terms of avoiding the worst option and adopting the best option, as long as the independence of the members is guaranteed. If the independence of the members is guaranteed, the tendency converges to probability 1 as the number of members increases. This means that the decision-making strategies recommended by individuals can be very effective in terms of avoiding the worst decisions under the assumptions of independence among individuals and majority rule. However, this finding seems to differ from the results of the experiment on group decision-making conducted in Chapter 11, Decision Strategies and Bad Group Decision-Making: A Group Meeting Experiment, in which decision-making was conducted in an interactive environment, with decision strategies defined in

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terms of group decision-making, rather than individuals making decisions independently in advance. This implies that the independence of decisions between groups is not guaranteed.

15.3

Group decision-making in the situations where independence among group members is not ensured

A number of theoretical studies extending Condorcet’s Jury Theorem have shown that, in general, when there is a correlation between judgments among individuals (e.g., when individuals are making judgments based on the same cues and evidence), as well as social influences such as sympathy and obedience, the correctness of majority decisions deteriorates (Berend & Sapir, 2007; Berg, 1993; Boland, 1989; Boland, Proschan, & Tong, 1989; Dietrich & List, 2004; Hastie & Kameda, 2005; Kao & Couzin, 2014; Ladha, 1992, 1995; Nakawake, 2017; Nitzan & Paroush, 1984). For example, Ladha (1992) pointed out that even if individuals make independent judgments in a jury situation, there will be a correlation between their individual judgments if they are based on common evidence. Thus even if individuals make judgments independently, if some factors, such as common judgment criteria or thought processes, have a common influence on decision makers, correlations can occur between individual judgments. These correlations increase the correlations between judgments and degrade the collective performance of collective intelligence (Dietrich, 2008; Dietrich & List, 2004; Ladha; 1992). Asch (1955) showed that people’s judgments are influenced by the judgments of others, even when there is an objective correct answer, such as in judging the length of a line. Such a phenomenon of modifying one’s own judgment by referring to the decision information of others is known as the information cascade, which produces irrational outcomes at the group level (Anderson & Holt, 1997; Banerjee, 1992; Bikhchandani, Hirshleifer, & Welch, 1992; Hung & Plott, 2001). Groupthink, which was discussed in the previous chapter, is another example of irrational decisionmaking (Janis, 1972, 1982), where people may not express their own opinions because they are concerned about what others think of them (Noelle-Neumann, 1974), and where debate can lead to more radical opinions. Sunstein and Hastie (2008, 2015) have extensively examined this phenomenon in group decisionmaking. Sunstein and Hastie (2008, 2015) provide an extensive examination of group decision-making for such phenomena. However, the fundamental reason for this inability to guarantee the independence of individual decisions due to social influences comes down to the fact that people communicate with each other. Let us consider the relationship between two people in a very simple case. In a two-person relationship, for example, there is a dynamic interdependence in which an action from A to B prescribes an action from B to A, and vice versa. For example, B’s action would be different if A made a recommendation about an option or not. In addition, A’s own action has the aspect of defining

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the next action of A. Furthermore, in a bilateral relationship, each person may behave strategically. For example, if A says to B, “What will B think if I tell him my opinion?” For example, A may think, “If I tell B what I think, what will B think?” Communication between two parties alone is complicated, but when it becomes more than a three-way relationship, the way of communication becomes even more complicated. In addition, C may observe the communication between A and B, and A and B may communicate strategically by anticipating the actions that result from C’s observation. Thus even just considering the communication relationship between two or three persons is very complicated, and it is very difficult to predict the behavior of each person. What if we assume that there are five people in a relationship, and the number of ordered pairs of any two-person relationship among the five people, excluding the relationship between themselves, is 20 (5C2・2! 5 20). Furthermore, if we consider a three-person relation such as A!B!C, it becomes a ternary relation in set theory, and there are 60 (5C3・3! 5 60) if we exclude the relation between the self, 120 (5C4・4! 5 120) if we consider a four-person relation, and 120 (5C5・ 5! 5 120) if we consider a five-person relation. In this way, there are only five people. Thus even if we consider a society of only five people, the interrelationships are very complex. To understand human behavior in society, it is necessary to understand that each individual communicates and acts in such complex relationships (Takemura, 2019). Through linguistic communication, people are influenced by each other to make decisions in social situations. The decision-making outcome of an individual’s social action will be determined by the function (mapping) from the adopted social action options (A) and the state of the situation (Θ) to the outcome (X), that is, f: A 3 Θ!X. The notation in terms of sets is A 3 Θ 5 {(ai, θk)|aiAA, θkAΘ}. This means that A 3 Θ determines the set, the elements of which are the paired sets (ai, θk) considering the order of any element ai of the set of social actions A and any element θk of the set of situations Θ. The simplest preference relation on outcomes is the relation on binary terms, such as which of the two alternatives is preferred. If we consider the preference relation of a decision maker on the elements of a set of outcomes X, we can consider an empirically observed relation such as which is preferred and represent the relation by the symbol h. We can define the preference structure by considering the set of all ordered pairs (xi, xj) such that ixj, (Takemura, 2014, 2019, 2020). From these, we can consider that the set of five sets A, the set of states Θ, the set of outcomes X, the map f: A 3 Θ!X, and the preference structure (X, R) of a social action together represent in a very simplified form a decision problem that depends on various states. As we will see in Chapter 6, Multiattribute DecisionMaking, Multiobjective Optimization, and the Additive Conjoint System, in decision theory, this set D 5 (A, Θ, X, f, (X, R)) can be expressed as the “decision problem” of an individual, and as an extended example of this decision problem, we can deal with interactions among individuals. Now, I would like to further extend the individual decision-making problem defined earlier to consider mutual action. In the case of interaction situations or social decision-making where

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multiple decision makers are considered, let the set of decision makers be I, and suppose that the choices Ai and the preference relations Ri differ according to iAI, then the decision problem is (A1, A2, . . ., An, Θ, X, f, (X,R1), (X,R2), . . ., (X,Rn)). Even considering such a simple structure, we believe that decision-making within a group is quite complex, and that it is extremely difficult in practice to guarantee independence among individuals. In this sense the effectiveness of group decisionmaking by majority rule, as shown in the jury theorem, is not very viable in the real world (Takemura, 2019). In recent years, group decision-making research has produced a number of concepts of “epistemic democracy” (e.g., List & Goodin, 2001) that justify majority rule from the perspective that majority rule produces superior performance, and collective intelligence is used as the theoretical basis for this. However, Nakawake (2017), through a review of existing research and theoretical considerations, argues that the superior performance of majority rule based on collective intelligence depends heavily on the distribution of individual abilities or correlations among judgments, and that if we take into account the distribution of individual abilities in reality and the creation of correlations among judgments in reality, majority rule is best. He pointed out that if we take into account the distribution of abilities and correlations among judgments in reality, majority rule is not robustly superior to the best member or the presumed best member. He criticized epistemic democracies that use collective intelligence as the rationale for their decisions, because based on this result, there is no rationale that majority rule based on collective intelligence is robustly superior to other decision rules. This argument can be applied to the interpretation of our experiments and computer simulations of decision-making strategies. In this chapter, I have not fully considered the concept of collective knowledge and epistemic democracy, but I would like to point out that there are practical limitations in the application of the jury theorem. I would also like to point out that when considering the problem of collective decision-making, it is necessary to consider the situational dependence of decision-making on the interaction among individuals, rather than assuming the independence of individuals.

15.4

Experimenton situation dependence of decisionmaking and bad decisions

Previous research on decision-making has shown that in verbal communication between individuals, the representation of a decision problem can change the decision outcome (Takemura, 2014, 2019). The phenomenon of changing decision outcomes depending on how the exact same decision problem is linguistically expressed has also been described in decision research as the framing effect (Tversky & Kahneman, 1981). On the other hand, although it is not a framing effect in the strict sense, a context-dependent effect is known, in which preference reversal occurs depending on how the problem is grasped and the information is presented.

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In this section, we report on an experiment conducted by our research group, in which the situation-dependent effect of linguistic expressions caused people to choose the option with the higher total price when making purchase decisions for the same product (Ideno et al., 2014; Takemura, 2014).

15.4.1 Outline of the experiment In the experiment, we set up a situation in which participants had to choose a store to go shopping based on flyers from two supermarkets. The task was to create an information matrix that mimicked an everyday flyer and set up a situation in which the decision-making strategies used by the participants in the experiment could be inferred. The assumed strategy was an additive decision-making strategy, in which the participants calculated the total price of each product in each store. To examine the process of attention more directly, we conducted an experiment using an eye movement measurement device. The reason why we used an eye tracker was because we were considering tracking the decision-making process (e.g., Payne, 1976; Payne, Bettman, Koehler, & Harvey, 2004).

15.4.2 Decision task To meet practical needs, we set up a situation in which the participants had to decide which store to purchase a product based on the flyers distributed in two supermarkets. The purpose of this study was to examine the effects of additional information on decision-making strategies. Therefore it is necessary to use a task that (1) enables the measurement of the decision-making process and (2) limits the decision-making strategies used to some extent. Therefore for (1), we applied the information monitoring method, which has been used to study the decision-making process, to create the task. Specifically, we presented participants with a 2-alternatives 3 3-attribute stimulus that resembled a supermarket flyer and asked them to choose which supermarket they would prefer to use, based on the assumption that they would purchase all the products listed in the flyer (i.e., eggs, rice, and cabbage). For (2), we assumed an additive decision-making strategy in which the values of all attributes are added for each option as a decision-making strategy used in the execution of the task. In addition, since it has been pointed out that a low price decreases the likelihood of liking a product, we constructed a condition in which the quality of the product is the same even if the selling price is low by presenting external reference prices and normal prices for all products. We chose three types of products, rice, eggs, and cabbage, because it is easy to add up the amounts of each product and make a decision in situations where there are two or fewer choices, and because adding up the amounts of products requires cognitive effort in situations where there are four or more choices. The reason for this is that it is expected that the use of the additive decision-making strategy will decrease. In addition, when the number of choices was reduced to three, it was possible to create a choice that was cheaper than the other choices for two products,

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but higher in total amount, when a comparison was made between the choices for each product. Fig. 15.5 shows a sample of the image stimuli created for this experiment. Fig. 15.13 shows an English translation, but the actual images presented are in Japanese. For each choice the product image, price, and prediscounted price for three attributes (i.e., egg, rice, and cabbage) were displayed, as well as the discount rate for some products. The product image and the price before discount were common among the choices, while the selling price and the discount rate were different among the choices. The discount rate is indicated in two places for each option, and there is a difference in the discount rate between the options. Specifically, in option 1 (i.e., supermarket A), the discount rate for attribute 1 is 40% and that for attribute 3 is 50% (half price), while in option 2 (i.e., supermarket B), the discount rate for attribute 1 is 20% and that for attribute 2 is 10%. The total amount for each option was 3460 yen for option 1 and 3430 yen for option 2. Therefore option 2 is 30 yen cheaper than option 1. This means that the discount rate for option 1 is higher than that for option 2, but the total price is higher. To increase the prominence of the discount rate, all items were marked in medium gray, and for items without a discount rate, the selling price was marked in dark gray. To confirm that the number of subjects using additive decision-making strategies decreases in a 2-choice 3 3-attribute information matrix, and as assumed when creating the task, we conducted a control experiment using stimuli in which the discount rate indicator was removed.

Figure 15.13 Task in the experiment. Reproduced with permission from: Ideno, T., Okubo, S., Tamari, Y., Iyobe, N., Murakami, H., & Takemura, K. (2014). Aitorakka- wo mochiita Kokoku Juyouji no Shohisa no Ishiketteikatei no Kentou: Chirashi no Waribiki Hyouji Kouka no Kentou [Eye-tracking study of consumer decision making process: An examination of the effect of discount rate for advertisement leaflets]. Transactions of Japan Society of Kansei Engineering, 13, 535
541 (in Japanese).

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15.4.3 Preliminary study A control experiment using a questionnaire method was conducted by creating a stimulus in which only the discount rate was removed from the supermarket flyer used in this experiment, and the other conditions were the same as in this experiment. We also conducted a control experiment using a questionnaire method. To examine whether the strategy of calculating the total amount of products to be purchased and making a purchase decision, which was assumed when the experimental stimuli were created, was affected by the number of products purchased, we also conducted a task of purchasing two products.

15.4.3.1 Method of preliminary experiment Experimental participants The experimental participants were 61 university students [mean age 20.5 years, standard deviation (SD) 5 1.00]. The questionnaire consisted of two questions. The purpose of task 1 was to measure the extent to which participants used the strategy of making decisions based on the total price of all products by creating a stimulus in which all discount rate indications were removed from the stimulus for this experiment (Fig. 15.13). Participants in the experiment were asked, “You have decided to go to the supermarket to buy eggs, rice, and cabbage. Based on the flyers of the two stores below, please choose which supermarket you would prefer to use.” The stimuli are shown in Fig. 15.13. As shown in Fig. 15.13, as in the main experiment, supermarket B is the choice with the lowest total amount of all products. For task 2, three questions were created using a combination of two of the three products used in task 1, and the participants were asked to select a supermarket store. For example, in the purchase condition for eggs and rice, the questionnaire asked, “You have decided to go to the supermarket to buy eggs and rice. Based on the flyers of the two stores below, please choose which supermarket you would like to use.” We created a response box with the names of the two supermarkets below the task sentence and the stimuli below it. For the purchase situation of eggs and rice and rice and cabbage, supermarket B was the choice with the lowest total amount, and for the purchase situation of eggs and cabbage, supermarket A was the choice with the lowest total amount. For both questions 1 and 2, one question item was presented on a sheet of A4 paper. The left and right positions of the stores were counterbalanced through the experimental participants. The order of presentation of the three questions in Q2 was randomized for each participant in the experiment.

Procedure The experiment was conducted as a group experiment in a classroom. After answering task 1, the participants answered task 2.

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Table 15.1 Result of choice task.

Task 1 Task 2

Egg, rice, cabbage Egg, rice Rice, cabbage Egg, cabbage

Alternative 1

Alternative 2

Supermarket A

Supermarket B

25 10 8 59

35 50 52 1

Source: Ideno, T., Okubo, S., Tamari, Y., Iyobe, N., Murakami, H., & Takemura, K. (2014). Aitorakka- wo mochiita Kokoku Juyouji no Shohisa no Ishiketteikatei no Kentou: Chirashi no Waribiki Hyouji Kouka no Kentou [Eyetracking study of consumer decision making process: An examination of the effect of discount rate for advertisement leaflets]. Transactions of Japan Society of Kansei Engineering, 13, 535actions of Japan So

15.4.3.2 Results and discussion The data of one person with missing data were deleted, and the data of 60 people were analyzed. The results of the selection of tasks 1 and 2 are shown in Table 15.1. 1. Task 1: In task 1, where three products were presented, the selection rate of Super B with the lowest total amount of the three products was 58%. As a result of a direct probability test, no significant difference was found and no bias was found in the selected ratio. 2. Task 2: In task 2, which is a two-product selection task, the probability of choosing the supermarket with the lowest total price was 83% in the condition of buying eggs and rice, 87% in the condition of buying rice and cabbage, and 98% for eggs and cabbage. The results of the direct probability test showed a significant difference in all conditions (p , .01). To examine the selection tendency for tasks 1 and 2, the selection patterns were determined based on the results of each subject’s supermarket selection. The most common choice pattern was to select the supermarket with the lowest total price regardless of the number of products, which accounted for 55% of the total. The second most common pattern was to select the supermarket with the highest price for three products and the supermarket with the lowest total price for two products, which accounted for 20% of the total.

From the results of the control experiment, it was observed that the decision strategy based on the total amount was used in the two-product choice condition, while the number of experimental participants who used the choice strategy based on the total amount decreased in the three-product condition.

15.4.4 Experiment 15.4.4.1 Method of the experiment Experimental participants Ten adult females (mean age 48.4 years, SD 5 5.14) participated in the experiment.

Eye-tracking equipment The EyeLink CL Illuminator TT-890 from SR Research was used for eye movement measurements. The programs for stimulus presentation and eye movement

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335

measurement were created using Experiment builder (SR Research). Fig. 15.14 shows the eye movement measurement system and the experimental situation. A game controller was used for response measurement.

Experimental procedure The experiment was conducted as an individual experiment. The participants were asked to participate in a task in which they had to decide which supermarket they wanted to buy eggs, rice, and cabbage from. We will measure their eye movements during this process. After that, we explained the eye movement measurement system, calibrated it, and conducted the experiment. The time required for the experiment was about 15 minutes. We counterbalanced the stimuli used in the experiment among the participants.

15.4.4.2 Results Although the total price of the three products was higher in supermarket A than in supermarket B, all the participants chose supermarket A because of its relatively high discount rate. The total price of the three products was higher in supermarket A than in supermarket B. A direct probability test was conducted to compare the selection results of this experiment with those of the control experiment task 1. Since the number of choices for supermarket B in this experiment was zero, a correction of 1.5 was made for each condition before conducting the test. The results showed a significant

Figure 15.14 Eye tracker in the experiment. Reproduced with permission from: Ideno, T., Okubo, S., Tamari, Y., Iyobe, N., Murakami, H., & Takemura, K. (2014). Aitorakka- wo mochiita Kokoku Juyouji no Shohisa no Ishiketteikatei no Kentou: Chirashi no Waribiki Hyouji Kouka no Kentou [Eye-tracking study of consumer decision making process: An examination of the effect of discount rate for advertisement leaflets]. Transactions of Japan Society of Kansei Engineering, 13, 535
541 (in Japanese).

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difference (p , .01), indicating a bias toward supermarket A in this experiment. This suggests that the discount rate was effective in this experiment.

Eye movement measurement results 1. Gaze pattern: We created a heat map from the eye movement data obtained by the eye movement measurement system (Fig. 15.14) to visually examine the gaze pattern. In the heat map, we used a scale from light gray to dark gray to indicate which part of the stimulus the subject was gazing at. The closer the color is to dark gray, the more the participants gazed at the corresponding part of the stimulus. Fig. 15.15 shows the heat maps of the two participants in the experiment. For example, in the left panel of Fig. 15.15, all the attributes of both choices were gazed at evenly, but the third attribute (i.e., cabbage) was gazed at relatively less than the other attributes. The right figure also shows that they paid attention to the discount rate in attribute 1 of option 1 more than the other attributes, although they paid attention to the information of all products.

Based on the eye movement data, the number of gazes was counted for each area of six attribute information (choice (2) 3 number of attributes (3)) on the presented stimulus. The number of gazes was counted for each of the six attributes (option (2) 3 number of attributes (3)). Table 15.2 shows the average number of gazes per area from stimulus presentation to decision-making. Table 15.2 shows the average number of gazes for each domain from stimulus presentation to decisionmaking. Table 15.2 shows that the number of gazes for option 1 was not necessarily higher than that for option 2. On the other hand, attributes 1 (i.e., egg) and 2 (i.e., rice) of both options were gazed at more frequently than attribute 3 (i.e., cabbage). To examine the difference in the mean number of gazes per area, we conducted an analysis of variance of two factors (choice (2) 3 attribute (3)). The results showed that there was no main effect of the choice factor (F(1,9) 5 0.60, n.s.) and no difference in the number of gazes among the choices. On the other hand, a significant main effect was found for the attribute factor (F(2,9) 5 5.14, p , .05). The

Figure 15.15 Heat map of eye gaze pattern. Reproduced with permission from: Ideno, T., Okubo, S., Tamari, Y., Iyobe, N., Murakami, H., & Takemura, K. (2014). Aitorakka- wo mochiita Kokoku Juyouji no Shohisa no Ishiketteikatei no Kentou: Chirashi no Waribiki Hyouji Kouka no Kentou [Eye-tracking study of consumer decision making process: An examination of the effect of discount rate for advertisement leaflets]. Transactions of Japan Society of Kansei Engineering, 13, 535
541 (in Japanese).

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Table 15.2 Average number of eye gaze in each area. Area of attention

Supermarket A

Supermarket B

Egg (attribute 1) Rice (attribute 2) Cabbage (attribute 3) Total

13.0 11.1 7.3 31.4

9.8 12.5 6.8 29.1

Source: Ideno, T., Okubo, S., Tamari, Y., Iyobe, N., Murakami, H., & Takemura, K. (2014). Aitorakka- wo mochiita Kokoku Juyouji no Shohisa no Ishiketteikatei no Kentou: Chirashi no Waribiki Hyouji Kouka no Kentou [Eyetracking study of consumer decision making process: An examination of the effect of discount rate for advertisement leaflets]. Transactions of Japan Society of Kansei Engineering, 13, 535
541 (in Japanese).

results of the subtests showed significant differences between attributes 2 and 3 (t (19) 5 2.89, p , .01) and between attributes 1 and 3 (t(19) 5 2.65, p , .05). There was no significant difference between attributes 2 and 3 (t(19) 5 0.24, n.s.), indicating that there were no differences in the number of times attributes 1 and 2 were gazed at and that the number of times attribute 3 was gazed at was less than attributes 1 and 2. In addition, there was no significant interaction between the choice factor and the between-attribute factor (F(2,18) 5 1.97, n.s.). 2. Examination of the decision-making process (variability): The purpose of this section was to examine the decision-making process. The variability was calculated by dividing the mean number of trials by the SD. The variability between alternatives (VA) was calculated by Eq. (15.1), and the variability between attributes (VD) was calculated by Eq. (15.2).

" #1=2 n
2 1 1X VA 5 Ai 2A A n i51

(15.1)

" #1=2 m
2 1 1X VD 5 Dj 2D D m j51

(15.2)

However, n is the number of choices, Ai is the number of information searches for choice Ai, m is the number of attributes, and Dj is the number of attribute searches for attribute Dj. In addition, A and D are defined as the average values of A and D, respectively. Variability reflects the bias in the amount of attention paid to each option or attribute, and the higher the value, the more attention is paid to a particular option or attribute. The results are shown in Table 15.3. Table 15.3 shows that there was a tendency for low variability among the choices and high variability among the attributes throughout the first half of the experiment. This suggests that in the two-choice, three-attribute condition of this experimental task, there was no bias in the number of gazes among the choices, while there was a bias in the number of gazes among the attributes. This tendency is consistent with the results of the gaze counts for each domain as shown in

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Table 15.3 Change of the variability in decision process.

Variability (VA) Variability (VD)

Early period

Late period

0.19 0.62

0.18 0.40

Source: Ideno, T., Okubo, S., Tamari, Y., Iyobe, N., Murakami, H., & Takemura, K. (2014). Aitorakka- wo mochiita Kokoku Juyouji no Shohisa no Ishiketteikatei no Kentou: Chirashi no Waribiki Hyouji Kouka no Kentou [Eyetracking study of consumer decision making process: An examination of the effect of discount rate for advertisement leaflets]. Transactions of Japan Society of Kansei Engineering, 13, 535
541 (in Japanese).

Table 15.2. In addition, the interattribute variability tended to be lower in the second half of the experiment than in the first half, so the interattribute variability was calculated for each participant in the experiment and a t-test was conducted. As a result, no significant difference was found (t(9) 5 1.50, n.s.). 3. Examination of the decision-making process (transition of gazing): The transition of gazing was examined using the index of Payne (1976). This index is calculated by subtracting the number of information searches in attributes from the number of information searches in alternatives and dividing by the sum of the number of information searches in alternatives and attributes. It takes values from 21 to 1. If the value is 21, it means that all the information searches were within attributes, and if the value is 11, it means that all the information searches were within options. The result was 20.21, indicating that more information search was done between alternatives than within alternatives.

15.4.4.3 Discussion In the selection results, all 10 experimental participants chose the option with the higher displayed discount rate and the higher total amount. This suggests that the display of the discount rate was effective. On the other hand, since all participants chose the same option, it was difficult to examine the relationship between the choice and the gaze. Therefore in the following, we will discuss the effect of the discount rate based on the number of gazes between the choices. From Table 15.2 the bias of gazing by attribute was examined. In attribute 1, where both discount rates were presented, the gazing frequency was higher for option 1 with a higher discount rate. In attribute 2 the number of gazes was higher for option 2, which presented the discount rate, and in attribute 3 the number of gazes was higher for option 1, which presented the discount rate. In attribute 3 the number of gazes tended to be higher for option 1, which presented the discount rate, than for option 2, which presented the discount rate. These results suggest that the participants’ attention to the discount rate affected the selection results. On the other hand, the results of the analysis of variance of the number of gazes showed that the amount of gazes for attribute 1 (egg) and attribute 2 (rice) was higher than that for attribute 3 (cabbage), indicating that there were fewer gazes for option 1 attribute 3 (i.e., half price), which had the highest discount rate. This suggests that the factors of presentation position and important attributes such as price affected the amount of gazing.

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The analysis of the variability of the number of gazes, which was conducted in (2) variability of the decision-making process, showed that the variability between attributes was high and that between options was low. This suggests that in the experimental condition of flyers with two options and three attributes, attention is equally directed to the options, while attention to the attributes tends to be biased. In Takemura and Takagi’s (1985) study the interattribute variability tended to be higher than the interchoice variability. In the study by Takemura and Takagi (1985), interattribute variability tended to be higher than interchoice variability throughout the first half of the decision-making process. The results of Takemura and Takagi’s (1985) study suggest that people tend to narrow down their choices in the latter half of the decision-making process. The results of Takemura and Takagi (1985) suggest that people tend to narrow down their choices in the latter half of the decision-making process. In the examination of the decision-making process (transition of gazing) (list item (3)), it was shown that gazing between alternatives was more frequent than gazing within alternatives. These results suggest that, under the conditions of this experiment, the participants may have checked the prices between alternatives for each attribute and selected the store with the highest number of attributes that was cheaper. This experimental study by Ideno et al. (2014) examined the influence of discount rate displays on decision-making using consumers’ store selection situations as the subject, using selection results and eye movement measurements as indicators. In addition, based on practical requirements, we created stimuli that mimic flyers used in everyday situations and used people who actually purchase groceries at supermarkets on a daily basis as participants in the experiment. The comparison of the choice results between this experiment and the control experiment showed the effect of the discount rate display, indicating the possibility of examining the decision-making process by using the set of choices and attributes used in this study. One limitation of the findings of this study is that the participants in the control experiment were university students, who differed from the participants in this experiment in terms of age-group and other factors, so there is a possibility that factors other than the discount display affected their decision-making strategies. Despite these problems, however, the results of this experiment showed experimentally that purchase choices can lead to higher irrational decisions depending on the way discount displays are used. Such a phenomenon can be called a framing effect in a broad sense, but it can be interpreted as basically caused by a change in attention.

15.5

Conclusion

In this chapter, computer simulations of group decision-making and the jury theorem were used to show that if the members of a group were independent of each other, they would be more likely to avoid the worst possible choice. As we have discussed in the past, we conducted an experimental study on whether individuals

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can detect irrational meeting processes and worst case choices in group decisionmaking and group meetings in the absence of interaction. The results showed that if we observe group meetings and group decision-making in the absence of interaction, it has been found that irrational meetings and worst choices can be detected. However, under group interaction, worst case decision avoidance is often more difficult to achieve. These considerations suggest that the reason why the worst possible choice is made in group decision-making is that the cognition, judgment, and decision of irrational meetings and decisions are distorted under the influence of interactions among group members. In this chapter, I have discussed the phenomenon of preference reversal due to situation-dependent decision-making, which is known as the framing effect, as a distortion of cognition, judgment, and decisionmaking under such interactions. Basically, he pointed out that attention shifts can occur depending on the way language is presented in intercommunication, and group decision-making can be more distorted by these situation-dependent effects. The last experimental study introduced by Ideno et al. (2014) examined the effect of discount rate displays on decision-making using consumers’ store selection situations as a measure of selection outcomes and eye movement measurements. In addition, based on practical requirements, we created stimuli that mimic flyers used in everyday situations and used people who actually purchase groceries at supermarkets on a daily basis as participants in the experiment. The comparison of the choice results between this experiment and the control experiment showed the effect of the discount rate display. In addition, we conducted a multiple-choice, multiple-attribute task with additional information to study the decision-making process. From Chapter 16, The Contingent Focus Model and Bad Decisions, onward, we will discuss attention and decision-making models that explain situation-dependent decision-making such as framing effects.

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458.

The contingent focus model and bad decisions

16

In the previous chapter, I mentioned the possibility that due to the situational dependence of decision-making, the jury theorem does not hold for group decisionmaking, and that avoidance of worst case decisions cannot be acquired through interaction within a group. I also pointed out that the situational dependence of decision-making is caused by shifts in attention, such as the framing effect. In this chapter, I will explain the contingent focus model (Fujii & Takemura, 2001a, 2001b; Takemura & Fujii, 2015; Takemura, 1994), which is a descriptive model of the phenomenon that gives rise to the situation-dependence of decision-making such as the framing effect, and discuss its relationship with making bad decisions. The contingent focus model explains preference reversal phenomenon that is depending on the shift of attention to the attribute.

16.1

Situation dependence of decision-making and bad decisions

In the previous chapter, Ideno et al. (2014), based on their experiment, illustrated that attentional shifts can cause undesirable decisions for decision makers, such as comparing the same product and buying the more expensive one. Such undesirable decision-making due to situational dependence in individual decision-making may also occur at the group level. It is thought that the jury theorem does not hold because communication between individuals causes a shift in attention, which increases the situation dependence of decision-making and does not guarantee the independence of group members. This shift in attention explains the framing effect and other situation-dependent effects in decision-making. In the contingent focus model (Fujii & Takemura, 2001a, 2001b; Takemura, 1994; Takemura & Fujii, 2015), we believe that a psychological characteristic called “focus of attention” is involved. The focus of attention means that people’s attention is drawn to certain attributes by verbal messages or image representations, and decisions are often made based on the evaluation of the attributes that attracted the attention. Why do people’s decision-making processes depend on situations and paths? One possible explanation is that the scope of human attention is limited, and decisions are guided by attention. Based on this idea, we developed a decision-making model called the “contingent focus model” to explain and predict decision-making (Fujii & Takemura, 2001a, 2001b; Takemura, 1994; Takemura & Fujii, 2015). Generalizing this model, as shown in Fig. 16.1, the amount of attention actually Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00017-X © 2021 Elsevier Inc. All rights reserved.

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Figure 16.1 Generalization of the contingent focus model.

changes depending on conditional factors, and the weights of the decision attributes change. Since decisions are made based on these changes, the decision-making process is expected to be situation-dependent. Path dependency can be explained by a mode of decision-making that does not incorporate information relevant to all alternatives due to this concentration of attention and limitation of attentional scope. According to the contingent focus model, bad decisions may be made by decision framing and hence focusing on unimportant attribute of the decision-making. In other word, bad decision would be brought by not paying attention to the important aspect of the decision problem. The contingent focal point model suggests that the choice adjustments by the way of calling people’s attention to other attributes. Based on such a perspective, Fujii, Takemura, and Kikkawa (2002) and Takemura and Fujii (2015) validated that decision-making is now not only meant for gambling tasks but is also associated with social dilemmas such as site visitors issues. People’s cooperation can be prompted to a degree, and some decisions to clear up social dilemmas can be taken by using advertising attention to particular attributes with a payoff matrix. The reality that decision-making can be changed by the way of attention implies that bad decisions would be made by using altering how statistics is introduced and what data are emphasized. Calling people’s attention to different attributes might cause confusion or limit self-belief in irrational decision-making. However, it is vital for the overall performance of pluralistic decision-making.

16.2

Framing effect as situation-dependent preference reversal

Several controversial problems related to decision-making under risk have not been solved by any theory on decision-making to date. One such problem is a phenomenon that deviates from procedure invariance (Tversky, Slovic, & Kahneman, 1990) that different decision outcomes occur through different decision procedures, such

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as a matching problem and a choice task. Another is a phenomenon called the framing effect, which deviates from description invariance (Tversky & Kahneman, 1986). Typical theories related to decision-making, expected utility theory, subjective expected utility theory, and even recently proposed nonlinear utility theory (Fishburn, 1988) have been unable to resolve these problems. There is, however, a phenomenon referred to as the framing effect that cannot be defined in its essence with the aid of the physique of utility theory. The framing effect refers to phenomena in which desire is reversed even for the identical selection making problem because of modifications in perspectives resulting from differences in the linguistic expressions used to describe the selection making problem, ensuing in different consequences of decision-making. Framing effect is considered an attribute or attention filter of decision problem. Therefore framing effect could be related to the making of bad decisions. This chapter reviews the findings of research of behavioral decision-making theory, consisting of the reasons underlying the incapability of utility principle to provide an explanation for the framing effect, the located depth of the framing effect, and the kinds of elements affecting the framing effect. Finally, this chapter briefly considers the bad decision-making from the perspective of the contingent focus model. Many researchers are now resolving the former problem theoretically using preference reversal (Holt, 1986; Karni & Safra, 1987; Segal, 1988; Tversky et al., 1990; Tversky, Sattath, & Slovic, 1988). Nevertheless, although many experimental studies of the matter have been completed, the framing effect has few models, except for an explanation by prospect theory (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992), which still includes distinct shortcomings. Takemura (1994) first proposed a contingent focus model to explain the framing effect, and Fujii and Takemura developed the model and the analysis (Fujii & Takemura, 2001a, 2001b; Takemura & Fujii, 2015). This chapter first shows that the framing effect cannot be explained with the framework of utility theories, especially expected utility theory, subjective expected utility theory, and recent nonlinear utility theory. Second, it introduces prospect theory
which explains the framing effect
and discusses some of its shortcomings. Third, it proposes and formulates the contingent focus model explaining the framing effect, proves its representation theorem, and examines estimation methods of the model parameter. Finally, this chapter presents consideration of the evaluation of this model in decision-making research along with prospects for future study. In decision-making tasks, although identical alternatives are formed in the same objective situation, a decision might be made differently, depending on the mode of psychological structure (framing). This is called the framing effect. For instance, when a decision must be made about whether one agrees to undergo a surgical operation or not, the patient’s decision might be different when a doctor tells a patient that there is 95% probability of living, from when a doctor informs the patient that there is 5% probability of dying. The presence of this effect suggests that entirely different decisions are made psychologically even when a person is confronted by mathematically identical decision-making problems. Therefore it indicates the limit of utility theories that postulate the uniqueness of a mathematical description.

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Tversky and Kahneman (1981) thought of a question under the following two frame conditions, which is a typical example of the framing effect, and let subjects make a choice under each condition. Positive frame condition: Imagine that the United States is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of programs are as follows. Which of the two programs would you favor? Total 200 people will be saved if program A is adopted. A one-third probability exists that all 600 people will be saved, and two-thirds probability that no people will be saved if program B is adopted. G

G

Negative frame condition: The question is identical except for the description of programs that were changed as follows: If program C is adopted, 400 people will die. If program D is adopted, there is one-third probability that nobody will die, and a twothirds probability that 600 people will die. G

G

Here, although the modes of description differ, it is clear that programs A and C are the same, and programs B and D are the same in extensively confirmed meaning. Namely, “be saved” equals “not die,” and “not be saved” equals “die.” Tversky and Kahneman (1981) reported that even if a profitable side was emphasized in description as positive frame condition, most subjects chose A(5C) which are risk-averse selections. If a losing side of a decision problem is emphasized in the description as a negative frame condition, most subjects chose D(5B) which are risk-taking selections. Tversky and Kahneman (1981, 1986) reported that the framing effect in decision-making is a robust phenomenon. They said that
just as visual illusion phenomenon in sensation
the framing effect engenders a paradoxical judgment in its process, even though the paradox might be recognized afterward. In fact, this framing effect influences physicians’ medical judgments (McNeil, Pauker, Sox, & Tversky, 1982; Perneger & Agoritsas, 2011; Wilson, Kaplan, & Schneiderman, 1987) and management decision-making (Cornelissen, Werner, 2014; Qualls & Puto, 1989; Tabesh, Tabesh, & Moghaddam, 2019). It means that we have little chance to improve paradoxical decisions if the framing effect is as robust a phenomenon as they insist. In contrast, cases for which the framing effect is not observed have been reported (Fagley & Miller, 1987; Mandel, 2013; Rybash & Rodin, 1989). In addition, Takemura (1992, 1993, 1994) elucidated that the framing effect is restrained by certain manipulations, such as giving longer time for decision-making process, or requesting justification of a decision before it is made. Results of these studies imply that the framing effect is not a robust phenomenon: it can be improved to a certain point by education or support for decision-making. Considering that few opportunities exist for us to conduct profound information processing in ordinary social lives (e.g., Langer, 1978), it is presumed that the framing effect occurs nearly always in decision-making in our social and political lives (Bullock & Vedlitz, 2017; Cornelissen & Werner, 2014; Levin, Schnittjer, & Thee,

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1988; Shan, Diao, & Wu, 2020; Thaler & Johnson, 1990). As Mandel (2013) explains, the framing effect itself may not be an irrational choice, but it can cause deviations in the transitivity of decision-making or lead to organizational risks due to excessive risk orientation of leaders (Osborn & Jackson, 1988), and it is quite possible that the framing effect can lead to bad decision-making.

16.3

Inadequacy of utility theory for explaining the framing effect

The most representative decision-making theory is the utility theory that tries to explain all decision-making phenomena using the concept of utility. The idea of the utility theory goes back to D. Bernoulli in the 18th century. Many variations are characterized using mathematical models (e.g., Fishburn, 1982, 1988). In this section I will discuss why the framing effect cannot be explained by utility theories, especially even by traditional expected utility theory (von Neumann & Morgenstern, 1944), subjective expected utility theory (Savage, 1954), and utility theory using Choquet integral calculus related to nonadditive probability measurement (Murofushi & Sugeno, 1990; Schmeidler, 1989), which is attracting attention recently because it can solve various paradoxes in decision-making such as the Allais’ paradox (Allais, 1953) or Ellsberg’s paradox (Ellsberg, 1961). Utility is a subjective value or a desire against a decision acquired by choosing an alternative; it is thought to be a real number value. In addition, utility is called a utility function because when a set of outcomes can be regarded as a variable, it becomes a function from the set of outcomes onto subjective value or desirability. Now, here is a simple example related to utility. Presuming a decision by which one should choose between devil fish and octopus at a Japanese Sushi restaurant, when one prefers octopus sushi to squid sushi or prefers them equally (octopus h squid), utility is the real number value for which the utility of fried rice (u(octopus) is higher than or equal to the utility of devil fish (u(squid)). That is, the following relation holds: uðoctopusÞ $ uðsquidÞ3octopushsquid Here, “octopus” can be said as “devil fish” especially in Western culture. If such phrasing can be admitted, the following relation must hold: uðdevil fishÞ $ uðoctopusÞ3devil fish h squid It can be said that preference reversal resulted from the framing effect if this relation does not hold. In fact, a preference reversal phenomenon of this type is considered to be observed often in our daily lives. Such a framing effect cannot be explained by expected utility theory or subjective expected utility theory that explains decision-making under risk. Expected

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utility theory is a theory to consider an expected value of utility based on the probability distribution under the natural situation; if the subjective probability is postulated in the probability under the natural situation, it is called subjective expected utility theory. von Neumann and Morgenstern (1944) and Savage (1954) elucidated that people’s preferences are the same as choosing the alternatives by which expected utility or subjective expected utility becomes the highest if a certain few axioms are accepted. However, the framing effect is not explainable using utility theories. The fundamental problem of the framing effect is characteristic in that it shows no deviation from a group of axioms in utility theory (e.g., Slovic & Tversky, 1974), such as Allais’ paradox (Allais, 1953) or Ellsberg’s paradox (Ellsberg, 1961), but a more severe deviation
a deviation from description invariance (Tversky & Kahneman, 1986). The framing effect is not explainable by expected utility theory using the Choquet integral, which is attracting attention recently because it can explain Allais’ paradox (Allais, 1953) and Ellsberg’s paradox (Ellsberg, 1961). To explain this, it can be said first that the decision-making problem is to be described as a set D in the following set in utility theory. D 5 ðX; Θ; A; f ; hÞ In that equation, X is a set of possible outcomes, and Θ is a state space. The possible value of xAX against alternative aAA is presumed to be subject to θAΘ. In the equation presented earlier, f represents a mapping that regulates which the outcome will be when the natural situation θ is decided after an alternative a is chosen, and (f :Θ!X) is a preference relation of mapping f in a set. As explained in the next chapter, the expected utility by Choquet (1955) integral related to nonadditive possibility (fuzzy measurement) π(θ), which was theorized by Murofushi and Sugeno (1990) and Schmeidler (1989), can be considered a set function. Therefore it is readily apparent that the expected utility value becomes the same if the input value is identical. Because the framing effect means the different preference in spite of the same values for θ and x, it is clear that expected utility theory by Choquet integral cannot explain the framing effect. This fact also holds in nonlinear utility theory (e.g., Fishburn, 1988) which is without the expected utility model by the Choquet integral.

16.4

Prospect theory explains the framing effect and its problem

Tversky and Kahneman (1981), using prospect theory, which they proposed (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992), explained why the framing effect occurs. They identified differences of respondents’ subjective values for gain and loss. The value function is a concave function in the gain area, so it is risk-averse, and it is risk-taking in the loss area because it is a convex

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function. Furthermore, the slope of the value function is steeper in the loss area than the gain area. According to a revised theory (cumulative prospect theory) by Tversky and Kahneman (1992), the prospect theory using the Choquet integral is placed under the category of recent nonlinear utility theory (Fishburn, 1988) with respect to its mathematical description. Whereas the detailed explanation of the cumulative prospect theory will executed into the next chapter, the special point of prospect theory is that the reference point corresponds to the origin of utility theory, and prospect theory assumes that the reference point shifts easily depending on the mode of framing in a decision-making problem. Prospect theory explains that by shifting the reference point, risk is avoided in a positive frame condition and risk is preferred in a negative frame condition of the same decision problem. In addition, another cause of the framing effect is explained by Tversky and Kahneman (1981): the weighting value of the probability that is assigned to a preference is nonlinear. Therefore the framing effect becomes more prominent as the value of gain or loss for a certain alternative increases, according to the relation. Accordingly, concepts of these prospect theories explain why description invariance—that decision-making problems that are identical in form have the same preference order—is not met. That the nature of the value function differs between the gain area and the loss area, or alternatively, that the probability affects preference outcome nonadditively, are adopted by many other theories such as nonlinear theories (e.g., Fishburn, 1988). Nevertheless, a necessary point in prospect theory is that the shift of the reference point engenders reference reversal. Then, what kind of formulation can theoretically explain the shift of the reference point? To date, no positive answer has been found. Prospect theory cannot tell how the reference point shifts but has a difficulty in predicting the preference or choice outcome. That is, a problem exists: although prospect theory postulates that a decision maker changes the coordinate system, it cannot elucidate how a decision maker changes the coordinate system.

16.5

Concept of the contingent focus model

The model suggested later is based on the idea that in the framing effect, fundamentally, the means used to examine the outcome value and uncertainty specifically are subject to a situation, not the idea that the reference point shifts according to framing, as prospect theory holds. That is to say, Fig. 16.2 shows that under a positive frame condition, certainty is more weighted than the possible outcome value (e.g., possible amount of money to be gained), which engenders risk aversion, and under a negative frame condition, the possible outcome value is more weighted than the elimination of uncertainty, which results in being risktaking. Described more metaphorically, the idea is that under positive frame condition, a decision maker regards certainty as the most important, while under a

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Figure 16.2 Basic framework of contingent focus model (Takemura & Fujii, 2015; Takemura, 1994).

negative frame condition, one underrates certainty, being narrow-sighted with the large scale of possible profit to be gained. This model is formulated extremely simply as presented later. Given a set of outcome alternatives is X 5 {X1, X2, X3, . . .} and a set of possibilities with values between [0, 1] is P 5 {P1, P2, P3, . . .}, consider alternative objects as Cartesian product set X 3 P. For instance, in the study of Tversky and Kahneman (1981), 200, the number of people to be saved, is thought to be X1, and one-third, the possibility to be saved is P2, and so on. Given that the value on the status quo is 0, consider a value of an alternative aj 5 (Xj, Pj) under positive frame condition, UP [FP (Xj), GP (Pj)], and a value on negative frame condition, UN [FN (Xj), GN (Pj)]. The total utility function can be expressed in the following function for simplicity. 



 UP FP Xj ; GP Pj 5 FP Xj GP Pj 



 UN FN Xj ; GN Pj 5 FN Xj GN Pj Therein, each function Fi, i 5 P, N is a function that subjectively converts the outcome value; Gi, i 5 P, N is a function that subjectively convert probability; Ui, i 5 P, N is a function to evaluate Fi and Gi comprehensively. Furthermore, if an assumption to be described later is adopted, then the preference relation between two alternatives is F (Xj)ai  G (Pj)βi, i 5 P, N. Moreover, given wi 5 αi/β i, it is equivalent to the relative value size of F (Xj)wi  G (Pj), where αi, β i, wi are parameters that are peculiar to each frame condition. In other words, Ui[Fi (Xj), Gi (Pj)], i 5 P, N is described by functions F and G, which are common to both frame conditions, and power index, αi, β i, wi, which are peculiar to each frame condition. Consequently, the framing effect is thought to occur because of the relative relation of how to examine αi and β i specifically. Here, interestingly, if power indexes of function F and G are deleted and simply weighted given Ui, the comprehensive evaluation function of this model is a nonlinear function. It is mathematically formulated identically to a contingent weighting model, which explains the paradox between a choice and a matching problem (Tversky et al., 1988).

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The
contingent focus model considers the values under positive frame conditions 
 UP ½FP xj ; GP ðpj Þ. The values under negative frame conditions, UN ½FN xj ; GN ðpj Þ, are considered more specifically as the following functions: 


αP
βP UPo FP xj ; GP pj 5 FP xj GP pj 


αN
βN UN FN xj ; GNe pj 5 FN xj G N pj In the previous equations, each of Fi , i 5 P; N is a function to convert the value of results subjectively; Gi , i 5 P; N are the functions to convert probability subjectively; and Ui , i 5 P; N are the functions to evaluate Fi and Gi comprehensively.

16.6

Formulation of contingent focus model

A process of formulation must be indicated to clarify what kind of postulation is behind this model. As defined earlier, given that a set of outcomes of an alternative is X 5 {X1, X2, X3, . . .}, and given a set of its possibility is P 5 {P1, P2, P3, . . .}, consider the alternative objectives as a Cartesian product set X 3 P. Here, the preference relation to meet weak order (preference relation to meet comparative possibility and transitionality) hP and hN is to be a preference relation under a positive frame condition and a preference relation under negative frame condition, respectively. In addition, under each frame condition, all the attribute values are postulated such that one attribute value is independent from the fixed value of the other attribute. That is to say, regarding arbitrary X1, X2 ∊X, P1, P2∊P, the following relations hold: ðx1 ; p1 Þhi ðx2 ; p1 Þ 3 ðx1 ; p2 Þhi ðx2 ; p2 Þ ðx1 ; p1 Þhi ðx1 ; p2 Þ 3 ðx2 ; p1 Þhi ðx2 ; p2 Þ where i 5 P; N. The previous postulation and weak order of preference relation hi , and a B postulate that the equal values of X 3 P have an order-dense countable subset that engenders the presence of functions Fi, Gi, Ui, indicating a relation being defined by X, P and Re 3 Re as shown next. Furthermore, these postulations are understood to be the necessary and sufficient condition for the presence of the following function (Krantz, Luce, Suppes, & Tversky, 1971). That is, regarding attribute X1, X2AX, P1, P2AP, ðX1 ; P1 Þhi ðX2 ; P2 Þ 3 Ui ½F1 ; ðX1 Þ; Gi ðP1 Þ ^ Ui ½Fi ðX2 Þ; Gi ðP2 Þ

(16.1)

In those representations, Ui, i 5 P, N is a monotonic increasing function of its each argument. Eq. (16.1) is a general form of a contingent focus model, which explains the framing effect.

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Therefore the following relation is postulated regarding X1, X2AX, P1, P2AP. ðX1 ; P1 Þ h PðX2 ; P1 Þ3ðX1 ; P1 ÞhN ðX2 ; P1 Þ; ðX1 ; P1 Þ h PðX1 ; P2 Þ3ðX1 ; P1 ÞhN ðX1 ; P2 Þ This postulation is the necessary and sufficient condition for the following relation of monotony. FP ðX2 Þ ^ FP ðX1 Þ3FN ðX2 Þ ^ FN ðX1 Þ; GP ðP2 Þ ^ GP ðP1 Þ3GN ðP2 Þ ^ GN ðP1 Þ

(16.2)

That is to say, because each pair of FP and FN, and GP and GN has uniqueness related to monotonic increasing transformation, irrespective of whether it is under a positive or a negative frame condition, each function related to the outcome and probability reserves order. Here, attention should be given to the fact that the functions UP [FP, (Xj), GP (Pj)] and UN [FN (Xj), GN (Pj)] do not necessarily have uniqueness related to monotonic increasing transformation; preference orders are not reserved, which explains the preference reversal by the framing. Then, to identify a general form of the model further, assuming that the indiffer0 0 ence curve is differentiable, and assuming that Fi and Gi , respectively, represent partial derivatives of Ui by Xj and Pj, then the following holds:  

 @ 0
U i Fi X j ; G i Pj F i Xj 5 @Xj  

 @ 0
Gi P j 5 Ui Fi Xj ; Gi Pj @Pj In addition, the rate RSi is defined as  0
Fi X j RSi Xj ; Pj 5 0
 G i Pj




(16.3)

In that equation, RSP (Xj, Pj)/RSN (Xj, Pj) 5 f (Xj, Pj), which is generally considered. By simplification, however, the rate between RSP and RSN is assumed to be equal at each point on the indifference curve. This assumption is the necessary condition for Eq. (16.2). Namely,
 RSP Xj ; Pj
 5K (16.4) RSN Xj ; Pj where K is a constant.

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Furthermore, function Ui must be identified. The contingent weighting model of Tversky et al. (1988), which explains the paradox of choice and matching, assumes Ui as a linear function. Actually, it is considered more appropriate in decisionmaking under risk that it be described as the product of an outcome value function and a probability value function, taking account of the studies of decision-making theories and the outcomes of psychological studies to date. At the very least, adopting the product is considered more appropriate than adopting the sum, the difference, or the quotient, of an outcome value function and a probability value function. Accordingly, the following formulation is assumed: ðX1 ; P1 Þhi ðX2 ; P2 Þ3Fi ðX1 Þ  Gi ðP1 Þ ^ Fi ðX2 Þ  Gi ðP2 Þ; i 5 P; N

(16.5)

Given that Fi (Xj), Gi (Pj) are positive numbers, by logarithms of both latera, Eq. (16.5) is equal to the following relation: ðX1 ; P1 Þhi ðX2 ; P2 Þ3Fi ðX1 Þ  Gi ðP1 Þ ^ Fi ðX2 Þ  Gi ðP2 Þ; i 5 P; N 3log Fi ðX1 Þ 1 log Gi ðP1 Þ ^ log Fi ðX2 Þ 1 log Gi ðP2 Þ; i 5 P; N

(16.6)

Then, given that Eq. (16.1) holds, it implies the representation theorem to an additive form (Krantz et al., 1971) to assume the following condition for the cancellation of Krantz et al. (1971) regarding arbitrary X1, X2, X3AX, P1, P2, P3AP is the necessary and sufficient condition for the presence of logarithmic linear model of Eq. (16.6). ðX1 ; P2 Þhi ðX2 ; P3 Þ and ðX2 ; P1 Þhi ðX3 ; P2 Þ3ðX1 ; P1 Þhi ðX3 ; P3 Þ; i 5 P; N Then, substituting the logarithmic linear model of Eq. (16.6) for Eq. (16.3), we obtain

 1=Fi xj dFi xj =dxj

 RSi xj ; pj 5 1=Gi pj dGi pj =dpj




Substituting this result into Eq. (16.4) yields the following:



 FN xj dFP xj =dxj GN pj dGP pj =dpj


 5K
 FP xj dFN xj =dxj GP pj dGN pj =dpj Because the left latus is a function consisting of only Xj and the right latus Pj, both latera are variable. The following relations are obtained:

 1 dFP Xj α dFN Xj

 5 dXj dXj FN Xj F P Xj

(16.7)

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 1 dGP Pj β  dGN Pj

 5 ; dPj dPj GN Pj GP P j

(16.8)

where α and β  are constants. Moreover, it is clear that Eqs. (16.7) and (16.8) are, respectively, Eqs. (16.9) and (16.10).

 d log FP Xj  d log FN Xj 5α dXj dxj

 d log GP Pj  d log GN Pj 5β dPj dPj

(16.9)

(16.10)

Consequently, by integrating both latera of Eqs. (16.9) and (16.10), the following relation is obtained:

 log FP Xj 5 α log FN Xj 1 γ

 log GP Pj 5 β  log GN Pj 1 δ Therein, α , β  , γ, and δ are constants. Accordingly, by assuming Eq. (16.4) regarding the rates of partial derivative of Ui by Fi and Gi, and Eq. (16.6) regarding the nature of Ui, it is understandable that the following functions F and G that are defined on X and P and the constants α and β exist, and that the following relation holds in relation to attributes X1, X2AX, P1, P2AP. ðX1 ; P1 Þhi ðX2 ; P2 Þ 3αi log F ðX1 Þ 1 β i log GðP1 Þ ^ αi log F ðX2 Þ 1 β i log GðP2 Þ; i 5 P; N 3wi log F ðX1 Þ 1 log GðP1 Þ ^ wi log F ðX2 Þ 1 log GðP2 Þ; i 5 P; N

(16.11)

where wi 5 αi/β i, i 5 P, N and F(X1), G(P1) are positive numbers. Here, Fig. 16.3 shows an indifference curve with log F(X1) on the horizontal axis and log G(P1) on the vertical axis. According to this chart, the inclination of each indifference curve is
wP under a positive frame condition, and
wN under a negative frame condition.

16.7

Representation theorem of contingent focus model

In this way, Eqs. (16.4) and (16.6) lead to Eq. (16.11), and what condition enables this equation? By representation theorem to additive form, it is known that whether

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Positive condition Negative condition

Log G(P)

log F(X)

Figure 16.3 Indifference curve of log G(P) and log F(X) (Takemura, 1994).

Eq. (16.6) holds or not can be confirmed according to preference relation of the order measure standard. By adding the assumption of Eq. (16.4), the validity of the model cannot necessarily be confirmed by preference relation of order measure standard. Now, this problem is considered later. The solution is, because Eq. (16.11) is the same value as the interlocking condition described by Tversky et al. (1988) indicated, whether the model holds or not can be confirmed by the preference relation of the order measure standard. The condition is that the following relation holds related to any X1, X2, X3, X4AX, P1, P2, P3, P4AP, ðX3 ; P1 ÞhP ðX4 ; P2 Þ4ðX4 ; P4 ÞhP ðX3 ; P3 Þ4ðX2 ; P2 ÞhN ðX1 ; P1 Þ 3ðX2 ; P4 ÞhN ðX1 ; P3 Þ

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Therein, it is necessary that even if attributes X, P and preference relations hP , hN are switched in this condition, the previous relation holds. wP log F ðX3 Þ 1 log GðP1 Þ ^ wP log F ðX4 Þ 1 log GðP2 Þ 3log GðP1 Þ 2 log GðP2 Þ ^ wP ½log F ðX4 Þ 2 log F ðX3 Þ wP log F ðX4 Þ 1 log GðP4 Þ ^ wP log F ðX3 Þ 1 log GðP3 Þ 3wP ½log F ðX4 Þ 2 log F ðX3 Þ ^ log GðP3 Þ 2 log GðP4 Þ wN log F ðX2 Þ 1 log GðP2 Þ ^ wN log F ðX1 Þ 1 log GðP1 Þ 3wN ½log F ðX2 Þ 2 log F ðX1 Þ ^ log GðP1 Þ 2 log GðP2 Þ Consequently, the following representations are obtained: wN ½log F ðX2 Þ 2 log F ðX1 Þ ^ log GðP3 Þ 2 log GðP4 Þ 3wN log F ðX2 Þ 1 log GðP4 Þ ^ wN log F ðX1 Þ 1 log GðP3 Þ Thereby, it is clarified that this interlocking condition holds if Eq. (16.11) holds. Second, we elucidate that Eq. (16.11) holds only when the interlocking condition holds under the condition that the logarithmic linear model of Eq. (16.6) holds. By applying the interlocking condition, under the condition the logarithmic linear model of Eq. (16.6) holds, the following relation is obtained: log Fi ðX2 Þ 2 log Fi ðX1 Þ ^ log Fi ðX4 Þ 2 log Fi ðX3 Þ as well as log Gi ðP1 Þ 2 log Gi ðP2 Þ ^ log Gi ðP3 Þ 2 log Gi ðP4 Þ The relation is obtained independently from the frame condition. In each attribute, it is indicated that preference orders of both conditions are the same in each attribute. Additionally, log FP and log FN, and log GP and log GN are both linear and convertible because they meet the conditions as interval measures. Consequently, the following relation holds: Fi ðx1 Þαi Gi ðp1 Þβ i ^ Fi ðx2 Þαi Gi ðp2 Þβi ; i 5 P; N 3αi log Fi ðx1 Þ 1 β i log Gi ðp1 Þ ^ αi log Fi ðx2 Þ 1 β i log Gi ðp2 Þ; i 5 P; N 3wi log Fi ðx1 Þ 1 log Gi ðp1 Þ ^ wi log Fi ðx2 Þ 1 log Gi ðp2 Þ; i 5 P; N 3Fi ðx1 Þwi Gi ðp1 Þ ^ Fi ðx2 Þwi Gðp2 Þ; i 5 P; N

(16.12)

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where, wi 5 αi =β i , i 5 P; N, and Fðxj Þ and Gðpj Þ take positive values. Accordingly, it is confirmed that it is the necessary and sufficient condition for Eq. (16.11) to hold that the interlocking condition holds under the condition that the logarithmic linear model holds. Then, because the fact that Eq. (16.6) holds is equal to the fact that Eq. (16.5) holds, the necessary and because the sufficient condition for Eq. (16.5) is to be a condition of an additive conjoint system (Krantz et al., 1971) that a condition which cancels the condition of Eq. (16.1) holds. Consequently, that the interlocking condition holds under the condition under which the condition of additive conjoint system holds implies that Eqs. (16.5) and (16.11) hold. That is the necessary and sufficient condition for a contingent focus model. Therefore the following theorem is obtained. As the necessary and sufficient condition for Eq. (16.13), the following contingent focus model is that the interlocking condition holds under the situation by which the condition of additive conjoint system holds. Namely, regarding arbitrary X1, X2AX, P1, P2 AP, ðx1 ; p1 Þhi ðx2 ; p2 Þ3Fi ðx1 Þαi Gi ðp1 Þβi ^ Fi ðx2 Þαi Gi ðp2 Þβi ; i 5 P; N 3αi log Fi ðx1 Þ 1 β i log Gi ðp1 Þ ^ αi log Fi ðx2 Þ 1 β i log Gi ðp2 Þ; i 5 P; N 3wi log Fi ðx1 Þ 1 log Gi ðp1 Þ ^ wi log Fi ðx2 Þ 1 log Gi ðp2 Þ; i 5 P; N 3Fi ðx1 Þwi Gi ðp1 Þ $ Fi ðx2 Þwi Gðp2 Þ; i 5 P; N

(16.13)

where wi 5 αi =β i , i 5 Po; Ne, and Fðxj Þ and Gðpj Þ take positive values. The representation theorem that indicates the necessary and sufficient conditions of the contingent focus model in the previous equations has been described by Takemura (1994). In this way, it is indicated that the contingent focus model holds under the conditions defined from the preference relation of the order-measure standard, the additive conjoint system condition, and the interlocking condition. The meaning is that, in confirming the validity of this model, not to require a decision maker necessarily for evaluation beyond the order measure, which is regarded as valid as a measurement.

16.8

Conclusion and future perspective

In this chapter, we have discussed the framing effect as situation-dependent decision-making, explained the phenomenon, and described the theoretical aspects of the contingent focus model that explains the framing effect. Although we cannot conclude that the framing effect immediately leads to irrational and bad decisions, it may well lead to irrational and bad decisions in verbal communication in group interaction.

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Gigerenzer’s group has been actively arguing in recent years that humans make decisions based primarily on unidimensional attributes. They have proposed the notions of fast and frugal heuristics and have developed a study of judgment and choice. First, Gigerenzer and Goldstein (1996) used computer simulations to show that choosing the most populous city between two alternatives using cognitive heuristics, in which the decision is based only on whether the respondent knows the city or not, is still rational. They also showed that “ease of attention,” a property unrelated to the problem of comparative judgment, could be an important factor in the decision. The series of studies that began with this was not a study of decisionmaking in the first place, but a counterexample to the traditional study of judgment bias, in which available heuristics that rely on memory produce irrational judgments. Brandst¨atter, Giggerenzer, and Hertwig (2006) proposed priority heuristics by extending the idea of fast and frugal heuristics to decision-making. It became clear that many decision-making phenomena can be fully defined based on the assumption that most of them are chosen without difficulty by a single motive alone assumed in the priority heuristic model. I do not believe that rational decision-making, as pointed out by Gigalenzia and others, always arises from simple heuristics, but it is a fully accepted idea that people make decisions by paying attention to fewer or single attributes. Also, the simplification of the decision problem and the use of simple heuristics as postulated in the priority heuristics and others are quite close to the assumptions of the contingent focus model. Unidimensional decision-making is a decision-making strategy represented by lexicographic (LEX) strategy, which has been found to be easy to avoid the worst decisions and lead to rational decisions, as found in previous computer simulation results. However, focusing on less important attributes in group interactions can lead to undesirable decisions. While such decisions may guide the process in a relatively rational way, they are exposed to several risks. For example, when expanding the scope of reconstruction assistance after a major earthquake in various areas, deciding on the target based on economic benefits alone, or on safety alone without considering economic factors, would be a less desirable decision. Similar problems exist in the Covid-19 problem. In fact, many people tend to evaluate and conclude even very important decisions by focusing on a limited set of attributes, and there is an inherent need to explore more important attributes, and in some cases, warnings should be issued to improve the situation (Takemura, 2014). Why do humans often make erroneous decisions based entirely on less important attributes? We believe it is because humans make choices by distorting their goal consciousness without considering data from different attributes. I believe that there is a psychological property called “focus of attention” that explains this phenomenon. The focus of interest is the possibility that verbal messages, image representations, etc. will draw people’s attention to unique attributes, and that decisions will be made regularly based on their evaluation of the attributes that drew their attention. Why does the way people make decisions depend on the situation or path? One purpose could be that the range of interests is limited and decisions are made by attention. Based on this idea, we devised the “contingent focus model”

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introduced in this chapter to explain and predict decisions that are irrational in some respects and not so irrational in others, considering actual measurement and parameter estimation methods. Generalizing this model, the amount of interest and attention changes virtually according to situational factors, and the weights of decision-making attributes change. As choices are made based on these changes, the decision-making system is expected to be situation-dependent. Path dependence can be explained by a mode of choice that does not incorporate data on all alternatives because of this focus of interest or range of interest problem.

References Allais, M. (1953). Le comportement de l’homme rationnel devant le risque: Critique des postulates et axiomes de l’ ecole Americaine. Econometrica, 21, 503
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17. (In Japanese). Fujii, S., & Takemura, K. (2001b). Risuku taido to chui: Jokyo izonteki shoten moderu ni yoru furemingu koka no keiryo bunseki [Risk attitude and attention [A psychometric meta-analysis of framing effect by Contingent Focus Model]. In: Paper presented at international meeting of the psychometric society 2001, Osaka, Japan. Fujii, S., Takemura, K., & Kikkawa, T. (2002). Kimekata to goi keisei: Shakaiteki jiremma niokeru rikoteki doki no yokusei ni mukete [Decision strategy and consensus formation: Towards inhibition of selfish motive in social dilemma]. Dobokugakkai rombunshu, 709, 13
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Ideno, T., Okubo, S., Tamari, Y., Iyobe, N., Murakami, H., & Takemura, K. (2014). Aitorakkawo mochiita Kokoku Juyouji no Shohisa no Ishiketteikatei no Kentou: Chirashi no Waribiki Hyouji Kouka no Kentou [Eye-tracking study of consumer decision making process: An examination of the effect of discount rate for advertisement leaflets]. Transactions of Japan Society of Kansei Engineering, 13, 535
541. (in Japanese). Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47, 263
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685. Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971). Foundations of measurement Volume 1: Additive and polynomial representations. New York: Academic Press. Langer, E. J. (1978). Rethinking the role of thought in social interaction. In J. H. Harvey, W. Ickes, & R. F. Kidd (Eds.), New directions in attribution research (Vol. 2, pp. 35
58). Hilsdale, NJ: Lawrence Erlbaum. Levin, I. P., Schnittjer, S. K., & Thee, S. L. (1988). Information framing effects in social and personal decisions. Journal of Experimental Social Psychology, 24, 520
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150) (in Japanese). Osborn, R. N., & Jackson, D. H. (1988). Leaders, riverboat gamblers, or purposeful unintended consequences in the management of complex dangerous technologies. Academy of Management Journal, 31, 924
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236. Shan, L., Diao, H., & Wu, L. (2020). Influence of the framing effect, anchoring effect, and knowledge on consumers’ attitude and purchase intention of organic food. Frontier in Psychology, 11, 2022. Available from https://doi.org/10.3389/fpsyg.2020.02022. Slovic, P., & Tversky, A. (1974). Who accepts Savage’s axiom? Behavioral Science, 19, 368
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Takemura, K. (1993). The effect of decision frame and decision justification on risky choice. Japanese Psychological Research, 35, 36
40. Takemura, K. (1994). Furemingu Koka no Rironteki Setsumei: Risukuka Deno Ishikettei no Jokyo Izonteki Shoten Moderu [Theoretical explanation of the framing effect: Contingent focus model for decision-making under risk]. Japanese Psychological Review, 37, 270
293. Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical descriptions of human choice behavior. Tokyo: Springer. Takemura, K., & Fujii, S. (2015). Ishikettei no shoho¯ [Prescription for decision making]. Tokyo: Asakura Shoten. (in Japanese). Thaler, R. H., & Johnson, E. J. (1990). Gambling with the house money and trying to break even: The effects of prior outcomes on risky choice. Management Science, 36, 643
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An experiment on, and psyschometric analysis of, the contingent focus model

17

In Chapter 16, The Contingent Focus Model and Bad Decisions, I explained a model for describing decision-making behavior that is situation-dependent and in some cases leads to irrational decisions or choosing the worst option. The first purpose of this contingent focus model is to explain the framing effect, but it does not necessarily explain only the framing effect but also the decision-making that varies depending on the factors of the situation. This chapter is somewhat technical in nature, but it describes quantitative analysis methods and psychological experiments, such as parameter estimation methods of the contingent focus model, which explain situation-dependent decision-making represented by the framing effect. In addition, I will explain the quantitative methods and psychological experiments that can explain why people make irrational decisions or choose the worst option in certain situations. I will also introduce the concept of risk attitude to explain decisions about risky alternatives as explained in Chapter 16, The Contingent Focus Model and Bad Decisions, and explain its relationship to the contingent focus model.

17.1

Risk attitudes and the contingent focus model

In Chapter 16, The Contingent Focus Model and Bad Decisions, I explained decision-making under risk in terms of the magnitude of the focal parameter of the power function. The meaning of this will be explained here. Basically, the contingent focus model assumes that the weights on the attributes of the additive model of multiattribute decision-making vary depending on the situation. In decisionmaking under risk the function of the value of the outcome and the evaluation of the probability is in the form of multiplication, but if we take the logarithm, the representation of the model becomes the log-linear form from the perspective of ordinal scale or ordinal utility (Takemura, 1994a; Takemura, & Fujii, 2015). In the system of expected utility theory, risk attitude can be defined as a preference for gambles in which the expected value is zero (called fair gambles). First, risk-averse means that the risk-free gamble with a fixed asset level (i.e., the expected value of L, E(x, L), can be obtained with certainty) is preferred to the gamble where the final asset level is determined by L [i.e., E(u, L) , u(E(x, L))]. To be risk-neutral is to judge that the final asset level is determined by the gamble L and that the riskless gamble [i.e., the expected value E(x, L) of L is obtained with certainty] is nondiscriminatory [i.e., E(u, L) 5 u(E(x, L)) holds]. In this case, we can say that the system Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00018-1 © 2021 Elsevier Inc. All rights reserved.

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is risk-oriented. In addition, risk orientation is when the final asset level is determined by a gamble L, which is preferred to a riskless gamble with a fixed asset level. In other words, a firm is said to be risk-oriented if E(u, L) . u(E(x, L)). The contingent focus model proposed in this chapter considers a simplified situation in which a gambling outcome X is received with probability P, and an outcome of zero value is received with probability 1
P (Takemura & Fujii, 2015). As shown earlier, the overall evaluation function for outcome X and probability P is: 

 U i Fi Xj ; G i Pj 5 Xj w i Pj Then, in the contingent focus model, the risk attitude is defined by whether wi is greater than or less than 1. Here, if wi is less than 1 (i.e., wi , 1), then: X j wi P j , X j P j Therefore it is risk-averse, and if wi is greater than 1 (i.e., if wi . 1), then: X j wi P j . X j P j If wi is equal to 1 (i.e., if wi 5 1), then it is risk-neutral. The overall evaluation function for outcome X and probability P is: 

 Ui F i X j ;Gi Pj 5 Xj αi Pj βi Then, in the contingent focus model, the risk attitude is defined by whether αi is greater or less than β i. If αi is smaller than β i (i.e., if αi , β i), then:
α Xj αi Pj β i , Xj Pj i If αi is smaller than β i (i.e., if αi . β i), then:
α Xj αi Pj β i . Xj Pj i If αi is equal to β i (i.e., if αi 5 β i), then it is risk-averse. If αi is equal to β i (i.e., if αi 5 β i), then it is risk-neutral. More generally, canbe
defined 
therisk
attitude   by the relationship between the magnitude of Ui Fi Xj ; Gi Pj and Ui Fi Xj Pj . However, such a definition only holds in the formulation where one gambling outcome X is one and the value of the other outcome is zero. Thus risk attitude can be measured by the parameter wi in a simplified contingent focus model. To illustrate these relationships the shapes of the focal parameters and the value function are shown in Fig. 17.1. Next, we consider risk attitudes in more complex situations. The situation is more complicated when we consider gambling (prospecting), which is a decision

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Figure 17.1 Focusing parameters and risk attitude. Reproduced with permission from Takemura K., Fujii S., (2015). Ishikettei no shoh¯o [Prescription for decision making] Asakura Shoten Tokyo (Takemura & Fujii, 2015).

under risk and has multiple outcomes. In this case, the consideration differs depending on whether one considers a system such as expected utility theory, a sum of products of a function of probability and a function of the value of the outcome, which is similar to expected utility theory, or a nonlinear expected utility theory based on the Schocke integral, which will be explained later. The overall evaluation function for outcome X and probability P is: 

 U i Fi Xj ; G i Pj 5 Xj w i Pj

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I thought of it as a simplification, but the model can be generalized slightly as follows: 


 U i Fi Xj ; G i Pj 5 Fi Xj Pj In addition, if the overall evaluation is the sum of the above terms, that is: Eðu; LÞ 5

n X


 Fi Xj Pj

j51

Let us consider the risk attitude when it can be expressed as If we do so, we can derive the following properties of the risk attitude (Takemura & Fujii, 2015).

17.1.1 Properties of risk attitudes under the assumption of a contingent focus model For multiple attributes decision the expected value is defined as follow: Eðu; LÞ 5

n X


 Fi Xj Pj

j51

The following property holds when the overall evaluation function is assumed to be such that (Takemura & Fujii, 2015).

17.1.1.1 Risk aversion If the decision maker is risk-averse, the value function Fi(Xj) will be concave (narrowly concave). A concave function (narrowly defined concave function) is a function of two arbitrarily different points x, y, and any t in the open interval (0, 1). Fi ðtx 1 ð1 2 tÞyÞ . tFi ðxÞ 1 ð1 2 tÞFi ðyÞ In addition, if the contingent focus model is assumed, the following relation holds: Eðu; LÞ 5

n X

X j wi P j ;

j51

where wi , 1, if and only if the decision maker is risk-averse.

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17.1.1.2 Risk neutrality If the decision maker is risk-neutral, then the value function Fi(Xj) is a linear function. The value function Fi(Xj) is a linear function if and only if the decision maker is risk-neutral. The linear function means that for any two different points x, y, and any t in the open interval (0, 1). Fi ðtx 1 ð1 2 tÞyÞ 5 tFi ðxÞ 1 ð1 2 tÞFi ðyÞ In this case, it is the case that In addition, the contingent focus model is: Eðu; LÞ 5

n X

X j wi P j

j51

In addition, if the contingent focus model is assumed, the following relation holds: Eðu; LÞ 5

n X

X j wi P j ;

j51

where wi 5 1, if and only if the decision maker is risk-neutral.

17.1.1.3 Risk-seeking If the decision maker is risk-averse, the value function Fi(Xj) will be convex (narrowly convex). A convex function (narrowly defined convex function) is a function of two arbitrarily different points x, y, and any t in the open interval (0, 1). Fi ðtx 1 ð1 2 tÞyÞ , tFi ðxÞ 1 ð1 2 tÞFi ðyÞ In this case, it is the case that In addition, if the contingent focus model is assumed, the following relation holds: Eðu; LÞ 5

n X

X j wi P j ;

j51

where wi . 1, if and only if the decision maker is risk-seeking.

17.1.2 Proof of the nature of the risk attitude Let us prove the properties shown previously. First, we prove a theorem about the risk aversion property. Consider a gamble that has outcome x with probability p and outcome y with probability (1
p). For a risk-averse decision maker, by definition of risk aversion: Fi ðpx 1 ð1 2 pÞyÞ . pFi ðxÞ 1 ð1 2 pÞFi ðyÞ

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This equation is also the definition of Fi being concave, so we know that Fi is concave if the decision is risk-averse. On the other hand, ifPFi is a concave function, then for all x1, . . ., xn A X and α1, . . ., αn A (0,1), where nj51 αj 5 1. Fi

n X

! αj xj $

j51

n X


 α j Fi x j

j51

The equality above the relationPholds for all x, x1 5 . . . 5 xn. Then, the probabilities p1, . . ., pn A (0,1), where ni51 pi 5 1, the following relation holds: Fi

n X j51

! p j xj .

n X


 p j Fi x j :

j51

The value function Fi is a concave function. Therefore if the value function Fi is a concave function, then the decision will be risk-averse. Also, in the simplified contingent focus model, if wi A (0,1), then for any two different points x, y, and any t in the open interval (0, 1), Fi ðtx 1 ð1 2 tÞyÞ 5 ðtx1 ð12tÞyÞwi . tFi ðxÞ 1 ð1 2 tÞFi ðyÞ 5 txwi ð1 2 tÞywi : Therefore the value function Fi becomes a concave function, which leads to riskaverse decision-making. This proves the theorem on risk aversion. The properties of risk neutrality and risk orientation can be proved in the same way.

17.2

Experiment of contingent focus model and measurement

This chapter explains the method of measurement, parameter estimation, and the application to some experiments on the contingent focus model. This chapter also explains some of the theoretical ideas of the quantification of the contingent focus model and the experiments using them. In particular, in the experiments, the contingent focus model as a model for explaining the phenomenon of deviating from the description invariance (Tversky & Kahneman, 1986), which is called the framing effect, and the experiments based on it is discussed. Lastly, this chapter explains the contingent focus model to explain the phenomenon that deviates from the description invariance (Tversky & Kahneman, 1986) and experiments based on the model, focusing on past research examples (Fujii & Takemura, 2001a, 2001b; Takemura, 1994a; Takemura, Hu, & Fujii, 2001).

17.2.1 A simple parameter estimation method for contingent focus model Thus in the contingent focus model, the reversal of preference due to the framing effect explained in Chapter 16, The Contingent Focus Model and Bad Decisions, is explained

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by the difference in the relative loadings between the outcome and the probability, and the difference between the positive and negative framing conditions is explained by the constant wi . In other words, the strength of the preference is represented by the functions F and G common to both framing conditions and the exponents αi, β i, and wi, specific to each framing condition. Here, if we know the ratio of wN to wP , w 5 wN =wP , we can predict the mutual preferences of the positive and negative framing conditions. The general utility theory, including nonlinear utility theory, implicitly assumes that wP 5 wN , that is, w 5 1. On the other hand, in the framing effect reported by Tversky and Kahneman (1981), wP , wN , which means that w . 1 is assumed. The contingent focus model does not consider that the reference point changes with framing, as in prospect theory, which will be explained later, but basically considers that the focus on the value and uncertainty of the outcome changes with the situation. In the contingent focus model described in Chapter 16, The Contingent Focus Model and Bad Decisions, the coordinate system of the decision maker is consistent from the standpoint of the observer and the focus on the decision maker’s attributes is consistent from the standpoint of the observer. This makes it easier to describe the decision from the observer’s point of view, which is useful in terms of prediction. Then, how can we estimate this parameter w with the data? A parameter estimation method based on random utility theory is possible, but a simple estimation method is presented next. In general, econometric models are often formulated in a simplified form of the original mathematical model to some extent, and the following are three simple methods for parameter estimation.

17.2.2 A simple estimation method in which the choice ratio and utility are considered to be ratio scale First, let us consider the case where we believe that the choice ratio and utility can be assumed to be ration scale. First, let CP ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ and CN ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ be the ratio of the number of people who choose ðX1 ; P1 Þ over ðX2 ; P2 Þ in the positive frame and negative frame conditions, respectively (but assume that the choices are sorted so that X1 is preferred to X2). These ratios are based on the experimental data and can be obtained from the experimental data. Now, we assume that the ratio of the degree of preference is proportional to the ratio of the rate of selection. That is, we assume that the following relationship holds for the representation system of the contingent focus model (Eq. 4.13) and Ci ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ, i5P,N F ðX1 ÞwiUGðP1 Þ Ci ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ Ci ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ 5 5 wi F ðX2 Þ UGðP2 Þ Ci ððX2 ; P2 Þ; ðX1 ; P1 ÞÞ 1 2 Ci ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ This means that w can be estimated from the data, that is:
 logDN ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ 1 log GðP2 Þ=GðP2 Þ
 w5 logDP ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ 1 log GðP2 Þ=GðP2 Þ

(17.1)

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where Di ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ 5 ðCi ððX1 ; P1 Þ; ðX2 ; P2 ÞÞÞ=ð1 2 Ci ððX1 ; P1 Þ; ðX2 ; P2 ÞÞÞ; i5P,N. It is clear that this assumption (17.1) satisfies Luce’s choice axiom (Luce, 1959). Because by expanding Eq. (17.1), we get: F ðX1 Þwi GðP1 Þ 5 Ci ððX1 ;P1 Þ;ðX2 ;P2 ÞÞ F ðX1 Þwi GðP1 Þ 1 F ðX2 Þwi GðP2 Þ This is because it satisfies Luce’s choice axiom. For simplicity, let us assume that G(Pj) 5 Pj and estimate w in the experimental results of Tversky and Kahneman (1981). In their study of the Asian disease problem, in the positive frame condition, 72% of the participants chose the norisk option and 28% chose the risky option, while in the negative frame condition, 22% of the experimental participants chose the no-risk option and 78% chose the risky option. Based on this result, we estimate w to be 15.33. In other words, in their experiment, the negative frame condition had a coefficient that was about 15 times higher than the positive frame condition, indicating a strong framing effect. Note that the value of w is a monotonically increasing function of the ratio of logDN ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ to logDP ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ, as is clear from the defining equation. We can see that w is not proportional to the difference in the selection rate between the positive and negative frame conditions. For example, if 60% of the participants in the experiment chose the risk-free option in the positive frame condition and 40% of the participants in the experiment chose the risk-free option in the negative frame condition, it is more likely that 80% of the participants in the experiment chose the risk-free option in the positive frame condition and 40% of the participants in the experiment chose the risk-free option in the negative frame condition. Although the difference between 40%
60% and 60%
80% is 20%, the framing effect seems to be stronger for the change from 40% to 60% because the majority of participants changed their preferences. In this sense, the estimated value of w well reflects the strength of the framing effect. Next, we discuss the parameters of psychological and situational factors that inhibit or promote the framing effect. As previous studies have shown, the selection rate varies depending on the experimental conditions (Takemura, 1992, 1993, 1994b). For example, in a study by Takemura (1993), he compared conditions that require justification of decision-making with conditions that do not require justification. In the justification condition, experimental participants were taught before making a decision to explain later how the outcome of the decision was correct, while in the nonjustification condition, no such instruction was given to experimental participants. As a result, in the justification condition, 46% of the experimental participants chose the risk-free option in the positive frame condition, while 19% of the experimental participants chose the risk-free option in the negative frame condition. In contrast, in the unjustified condition, 66% of the experimental participants chose the risk-free option in the positive frame condition, while 37% of the experimental participants chose the risk-free option in the negative frame condition. The estimated values of w were 2.00 for the justified condition and 3.71 for the unjustified condition.

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This implies that the value of w is a function of other psychological and situational factors in addition to the framing condition. Here, we assume that the value of w observed in a given condition is the product of the framing effect wc in the control condition and the effects of other psychological and situational factors, W(Ψ). In other words, we assume that: w 5 W ðΨ Þwc

(17.2)

However, let Ψ be a set of psychological or situational factors (the direct product set of some factors), and let W(Ψ) be a parameter of the set Ψ. If there are multiple possible factors, we can simplify and express W(Ψ) as follows: m
 W ðΨ Þ 5 gðΨ 1 ;Ψ 2 ;. . .;Ψ m Þ 5 L Wj Ψ j

(17.3)

j51

However, let Wi(Ψ i) be a parameter of a set of psychological or situational factors Ψ i. By substituting Eq. (17.3) into Eq. (17.2), we can estimate the value of Wi(Ψ i) from the data. For example, in a study by Takemura (1993), the framing condition was used as a factor within the experimental participants, and an experiment was conducted using a decision-justifying condition and a nonjustifying condition. In this experiment, if WE(Ψ E) is the psychological parameter inherent in the conditional manipulation that justifies the decision, then: WE ðΨ E Þ 5

w wc

Therefore WE(Ψ E) was estimated to be 0.54. Therefore the conditional manipulation of the decision justification is interpreted as reducing the strength of the framing effect by about half. In general, if Wi(Ψ i) . 1, the factor Ψ i promotes the framing effect, and if Wi(Ψ i) , 1, it suppresses the framing effect.

17.2.3 Estimating the strength of preferences that can be rated Thus it has become clear that the parameters of the contingent focus model can be estimated from actual data, but is it possible to predict the framing effect from the data obtained so far? One solution is to extrapolate the values of the parameter w obtained from the choice data to other choice behaviors, but another possible solution is as follows. One solution is to extrapolate the value of the parameter w obtained from the choice data to other choice behaviors, but another solution is to estimate and predict the parameter from the value of the direct rating of preference instead of the choice rate.

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For simplicity, if it is assumed that: 

 U i Fi Xj ; G i Pj 5 Xj α i Pj β i then the abovementioned equation becomes: 

 log Ui Fi Xj ; Gi Pj 5 αi logXj 1 β i logPj

(17.4)

and further multiplying both sides by 1/β i, the following equality is obtained: 

 1 log Ui Fi Xj ; Gi Pj 5 wi logXj 1 logPj (17.5) βi where wi 5 αi =β i ; i5P;N . However, if the probability, Pj, is zero, this logarithm goes to minus infinity, so, the estimation is done by adding one to the probability for convenience, as shown next. 


 (17.6) log Ui F i X j ;Gi Pj 5 αi log Xj 1 β i log 1 1 Pj Such a measure is often used for models that involve the logarithm of the probability. Furthermore, dividing both sides by β i, we get: 


 1 (17.7) log Ui F i X j ;Gi Pj 5 wi log Xj 1 log 1 1 Pj βi where wi 5 αi =β i ; i5P;N .

17.2.4 Estimation method assuming utility with error term The estimation method assuming with error term, so-called random utility model, will be explained as follow. First, as in Section 2.2, let CP ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ and CN ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ be the ratio of the number of people who choose ðX1 ; P1 Þ over ðX2 ; P2 Þ in the positive frame and the negative frame conditions, respectively (but with the choices rearranged so that X1 is preferred to X2). This is the ratio of the number of people who choose ðX1 ; P1 Þ over ðX2 ; P2 Þ in the frame condition. These ratios can be obtained from the experimental data. Now, assume that the difference in utility with respect to preferences is proportional to the log-odds ratio of the selection rate, that is, assuming the representation system of the contingent focus model defined in Chapter 16, The Contingent Focus Model and Bad Decisions, and assuming that the relationship in Eq. (17.1) holds with respect to Ci ððX 1 ;P1 Þ;ðX 2 ;P2 ÞÞ; i5P;N . Expanding Eq. (17.1), we have: " wi loge

" " # # # F ðX1 Þ GðP1 Þ Ci ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ 1 loge 5 loge F ðX2 Þ GðP2 Þ 1 2 Ci ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ

(17.8)

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Eq. (17.8) states that the logarithm of the odds ratio of the choice probability can be expressed as the sum of the logarithm of the ratio of the value of the outcome times the focal parameter times the logarithm of the ratio of the probability functions. This is equivalent to the so-called logistic regression model. Let us consider a decision intention problem with equal expected values, such as the Asian disease problem as presented by Tversky and Kahneman (1981). For simplicity, consider F(X) 5 X and G(P) 5 P. Since the expectation values are equal, X1P1 5 X2P2, Eq. (17.8) becomes: "

# " # " # " # X1 P1 X1 X2 wi loge 1 loge 5 wi loge 1 loge X2 P2 X2 X1 " # " # " # X1 X1 X1 5 wi loge 2 loge 5 ðwi 2 1Þloge X2 X2 X2

(17.9)

In addition, let us assume that X1 , X2 and P1 5 1,  P2 , 1. If wi in Eq. (17.9) is equal to 1, that is, wi 5 1, then ðwi 2 1Þ loge X 1 =X 2 5 0. In this case, Ci ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ 5 0:5, a risk-neutral selection tendency; in the case of wi . 1,  indicating  ðwi 2 1Þ loge X 1 =X 2 . 0, and Ci ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ , 0:5, indicating a risk-oriented selection tendency. In addition, when wi, 1, the choice is risk-oriented.  Furthermore, when wi , 1, ðwi 2 1Þloge X 1 =X 2 , 0, and Ci ððX1 ; P1 Þ; ðX2 ; P2 ÞÞ . 0:5, indicating a risk-averse tendency. In the contingent focus model the risk attitude is defined by whether wi is greater or less than 1. Thus when wi is greater than 1, it becomes a convex function (a function that is convex downward), indicating riskoriented decision-making. When wi is smaller than 1, the function becomes concave, indicating risk-averse decision-making. When wi is equal to 1, it becomes a linear utility function, indicating risk-neutral decision-making. Let us assume that w is distributed among individuals j, and that its expected value is stochastically affected by various experimental conditions, as assumed in the situation-dependence hypothesis of focusing. For example, in the conditions of Takemura’s (1993) study, wj is the focal parameter of individual j, Const is a constant term, Pos is a positive frame dummy, No_Just is a dummy variable for the no-justification condition, Just is a dummy variable for the justification condition, and If α, β, and χ are parameters and εj is an error term, then:   wi 5 exp Const 1 αPos 1 βNo Just 1 χJust 1 εj

(17.10)

If we assume for simplicity that the functions F and G for outcome X and probability P are F(X) 5 X and G(P) 5 P, respectively, then as explained earlier, in the contingent focus model, the risk attitude is defined by whether wj is greater or less than 1. When wj is greater than 1, the function becomes convex (downward convex function), indicating risk-oriented decision-making. When wj is less than 1, it

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becomes a concave function, indicating risk-averse decision-making. When wj is equal to 1, it becomes a linear utility function, indicating risk-neutral decision-making. This means that the risk attitude is determined by the positive or negative value of the exponential function in the right side of Eq. (17.10). As a result, the probability that an individual in the experiment will be risk-averse (P(risk-averse)) and risktake (P(risk-take)) can be calculated as:
 Pðrisk2averseÞ 5
P wj .1 5 PðV . 0Þ; Pðrisk2takeÞ 5 P wj , 1 5 PðV . 0Þ where V 5 Const 1 αPos 1 βNo Just 1 χJust 1 εj . If we assume that the shape of the distribution of the error term εj is logistic (e.g., McFadden, 1973), then each: Pðrisk 2 averseÞ 5

expðV Þ 1 ; and Pðrisk2takeÞ 5 ; expðV Þ 1 1 expðV Þ 1 1

where V 5 Const 1 αPos 1 βNo Just 1 χJust 1 εj . After defining the likelihood using the probabilities formulated based on the parametric assumptions about the distribution of the focal parameters as described previously, the parameters and constant terms can be estimated by the maximum likelihood estimation method.

17.3

Experiment of contingent focus model

Thus in the contingent focus model, several methods of estimating the parameters of the model can be considered based on its formulation. The most important hypothesis in the contingent focus model is the focusing hypothesis, which implies that the allocation of attention during decision-making affects risk attitude. However, this hypothesis had not yet been experimentally tested in a way that controls attentional factors. To test this hypothesis, three experimental studies were performed to manipulate attention during decision-making to examine whether the risk attitudes of the participants change in the direction. The first two experiments are by Fujii and Takemura (2001a), the quantitative analysis by Fujii and Takemura (2001a, 2001b), and the last experiments using the information monitoring acquisition are by Takemura et al. (2001).

17.3.1 Experiment of the contingent focus model and the focusing hypothesis 1: experiment of the reflection effect The most basic and important hypothesis of the contingent focus model is the “focusing hypothesis,” which states that the allocation of attention to outcomes and

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probabilities in decision-making influences risk attitudes. To test this hypothesis, Fujii and Takemura (2001a) conducted two experiments to determine whether participants’ risk attitudes would change as predicted by the focusing hypothesis by experimentally manipulating the attention used to establish perceptions in the decision-making process. In Experiment 3.1, 180 students and faculty members of Kyoto University were adopted as participants. A total of six experimental conditions were employed: a two-step frame condition (positive, negative) and a three-step emphasis condition (result-oriented, no-emphasis, risk-oriented). Then, 30 participants were randomly assigned to each condition. As shown in Fig. 17.2, in the outcome emphasis condition, the text indicating the result was enlarged and written in bold, and an auxiliary word was added to it. In addition, auxiliary words were added for further emphasis. Similarly, in the condition emphasizing risk, the text indicating the probability was enlarged and written in bold, and auxiliary words were added to emphasize it. As shown in Fig. 17.2, in the outcome emphasis condition, we increased the size of the letters for the result (10.5 fonts for nonemphasized letters and 18 fonts for emphasized letters), made them bold, and added an auxiliary word to emphasize them. Similarly, in the risk-weighted condition, we increased the size and thickness of the letters for probability and added a particle for emphasis. In the Outcome Emphasis condition, the amount of attention to the outcome is expected to be higher than in the Risk Emphasis condition. Therefore the focusing hypothesis of the contingent focus model predicts that the risk orientation tendency is stronger in the outcome stress condition than in the risk stress condition in both the negative and positive conditions. The experiment was conducted using an interview method with a questionnaire, in which the experimenter verbally informed the participants that he or she was requesting them to choose between two options, and then presented them with the questionnaire.

Figure 17.2 Manipulation of attentional focus and reflection effects. Reproduced with permission from Fujii, S., & Takemura, K. (2001a). Risuku Taido to Chuui: Joukyou Izonteki Shouten Moderu niyoru Keiryou Bunseki [Risk attitude and attention: Psychometric analysis of framing effect by contingent focus model]. The Japanese Journal of Behaviormetrics, 28, 9
17. (in Japanese).

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Table 17.1 Experimental results of the reflection problem. Experiment condition

Risk-emphasis conditions No-emphasis condition Outcome-emphasis conditions

Positive frame condition

Negative frame condition

Risky option % (N)

Riskless option % (N)

Risky option % (N)

Riskless option % (N)

90.0 (27)

10.0 (03)

50.0 (15)

50.0 (15)

83.3 (25) 63.3 (19)

16.7 (05) 36.7 (11)

56.7 (17) 30.0 (9)

43.3 (13) 70.0 (21)

Reproduced with permission from: Fujii, S., & Takemura, K. (2001a). Risuku Taido to Chuui: Joukyou Izonteki Shouten Moderu niyoru Keiryou Bunseki [Risk attitude and attention: Psychometric analysis of framing effect by contingent focus model]. The Japanese Journal of Behaviormetrics, 28, 9
17. (in Japanese).

The results of this experiment are shown in Table 17.1. There was no clear tendency to dislike or accept risk in the negative, risk-enhanced and unenhanced conditions. This result is not necessarily consistent with the predictions of prospect theory. On the other hand, the contingent focus model predicted that negative outcomes would receive more attention than positive outcomes. This result supports the basic hypothesis of the contingent focus model, not prospect theory. In addition, both positive and negative outcomes were found to be more likely to take risks in the outcome-focused condition than in the risk-focused condition. This result means that the tendency to accept risk is stronger in the outcome-oriented condition than in the risk-oriented condition, which is consistent with the prediction of the Focusing Hypothesis, the basic hypothesis of the contingent focus model. This indicates that the risk orientation tendency is stronger in the negative condition than in the positive condition. A hierarchical log-linear analysis of the entire sample showed that the interaction between risk attitude (risk avoidance and risk acceptance) and the positive/negative condition was significant (χ2(1) 5 25.81, p , .001). In addition, a two-factor log-linear analysis was conducted for the risk-enhancement, control, and result-enhancement conditions, and a significant interaction between risk attitude and the positive/negative conditions was found for all conditions (χ2(1) 5 12.21, p , .001; χ2(1) 5 5.22, p 5 .022; χ2(1) 5 10.28, p 5 .001, respectively). The abovementioned results are similar to a phenomenon called the reflection effect (Kahneman & Tversky, 1979), which is one of the empirical findings underlying prospect theory. However, the reflection effect implies risk avoidance when positive outcomes are evaluated and risk orientation when negative outcomes are evaluated. However, there is no clear risk-avoidance tendency in the risk-enhancement condition or the negative control condition. However, the negative conditions in the risk-enhancement and control conditions do not show a clear risk-acceptance tendency. In fact, the results shown here only indicate that the negative conditions are “relatively” more risk-oriented than the positive conditions. In other words, this result is not necessarily consistent with the prediction of prospect theory. On the other hand, the contingent focus model predicts that negative outcomes will attract relatively more attention than positive outcomes. Therefore this result

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supports the basic hypothesis of the contingent focus model, rather than prospect theory. Next, we focus on the difference in risk attitude between the positive and negative conditions. The results show that in both the positive and negative conditions, the result-oriented tendency is stronger in the result-oriented condition than in the risk-oriented condition. A hierarchical log-linear analysis of the entire sample showed that the interaction between risk attitude (risk avoidance and risk acceptance) and the emphasis condition (risk emphasis, control, and outcome emphasis) was significant (χ2(2) 5 11.00, p , .001). The log-linear analysis of the positive and negative conditions indicated that there was a significant difference in risk attitudes between the risk-enhanced and result-enhanced conditions (χ2(1) 5 6.26, p , .05; χ2(1) 5 4.67, p , .05, respectively). The log-linear analysis showed that the interaction between risk attitude, emphasis condition, and positive/negative condition was not significant (χ2(2) 5 0.85, n.s.). These results mean that the tendency to accept risk is stronger in the outcome emphasis condition than in the risk emphasis condition, which is consistent with the prediction based on the focusing hypothesis, the basic hypothesis of the contingent focus model, and the situation-dependent focasing hypothesis.

17.3.2 Experiment of the contingent focus model and the focusing hypothesis 2: Asian disease problem In this experiment, we used the Asian disease problem by Tversky & Kahneman (1981). As in Experiment 3.1, there were five conditions: two frame conditions (positive/negative) and three emphasis conditions (outcome emphasis/no-emphasis/ risk emphasis). A total of 30 participants were randomly assigned to each condition. For the emphasis condition the size and thickness of the letters and the presence or absence of particles were used to emphasize the result and the risk. The method of presenting the problem was the same as in Experiment 3.1. The results of this experiment are shown in Table 17.2. First, as predicted by both prospect theory and Table 17.2 Experimental results of disease problems in Asia. Experimental condition

Risk-emphasis conditions No-emphasis condition Outcome-emphasis conditions

Positive frame condition

Negative frame condition

Risky option % (N)

Risky option % (N)

Riskless option % (N)

Riskless option % (N)

70.0 (21)

30.0 (09)

40.0 (12)

60.0 (18)

60.0 (18) 43.3 (13)

40.0 (12) 56.7 (17)

56.7 (17) 20.0 (06)

43.3 (13) 80.0 (24)

Source: Fujii, S., & Takemura, K. (2001a). Risuku Taido to Chuui: Joukyou Izonteki Shouten Moderu niyoru Keiryou Bunseki [Risk attitude and attention: Psychometric analysis of framing effect by contingent focus model]. The Japanese Journal of Behaviormetrics, 28, 9
17. (in Japanese).

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the contingent focus model, the framing effect, that is, risk aversion in the positive frame condition and risk orientation in the negative frame condition, was confirmed. The log-linear analysis showed that the difference in risk attitude between the frame conditions was significant. In addition, a log-linear analysis of risk attitude and positive/negative frame conditions as factors for each emphasis condition showed that the difference in risk attitude between frames was significant in the outcome and risk emphasis conditions, although no significant difference was found in the no-emphasis condition. However, Table 17.2 shows that the risk-averse tendency is stronger in the no-emphasis condition regardless of the frame condition, and conversely, the risk-oriented tendency is stronger in the consequence-emphasis condition regardless of the frame condition. Although this result deviates from the prediction of prospect theory, the relative tendency for risk aversion to be stronger in the positive frame condition appears in both emphasis conditions, as was also seen in Experiment 3.1. Therefore this result is consistent with the predictions of the contingent focus model rather than prospect theory. First, as predicted by both prospect theory and the contingent focus model, a framing effect was observed, that is, a tendency to be risk-averse in the positive frame condition and risk-oriented in the negative frame condition. The loglinear analysis showed that the difference in risk attitude between the frame conditions was significant (χ2(1) 5 4.28, p , .05). In addition, a log-linear analysis of risk attitude and positive/negative frame conditions as factors was conducted for each emphasis condition. The difference in risk attitudes between the frames was significant in the results- and risk-weighted conditions [χ2(1) 5 3.84, p , .05; χ2(1) 5 5.54, p , .05, respectively]. However, Table 17.2 shows that the riskavoidance tendency is stronger in the no-emphasis condition regardless of the frame condition, while the risk-orientation tendency is stronger in the outcome emphasis condition regardless of the frame condition. This result deviates from the prediction of the prospect theory, but in both emphasis conditions, as seen in Experiment 3.1, there is a tendency for risk aversion to be relatively stronger in the positive frame condition. Therefore this result is more in line with the prediction of the contingent focus model rather than the prospect theory. Next, focusing on the difference in risk attitudes among the emphasis conditions, we found that, as in Experiment 1, regardless of the frame condition, the result-oriented tendency was stronger in the resultoriented condition than in the risk-oriented condition. A hierarchical log-linear analysis of the entire sample showed that risk attitude differed significantly depending on the emphasis conditions (risk emphasis, control, and outcome emphasis) (χ2(2) 5 8.14, p , .05). A log-linear analysis of the positive and negative frame conditions showed that there was a significant difference or a tendency for there to be a difference in risk attitude between the risk-weighted and outcome-weighted conditions (χ2(1) 5 4.40, p , .05; χ2(1) 5 2.90, p , .10). The log-linear analysis showed that the interaction between risk attitude, emphasis condition, and frame condition was not significant (χ2(2) 5 2.59, n.s.). As in Experiment 1, these results indicate that the tendency to accept risk is stronger in the outcome emphasis condition than in the risk emphasis condition, supporting the focusing hypothesis and the situational dependence of focusing hypothesis.

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17.3.3 Quantitative analysis of the experimental results For these two experiments, we conducted an econometric analysis to quantitatively understand the effect of this experimental manipulation on the focus parameters (Fujii & Takemura, 2001a). First, as mentioned earlier, assuming for simplicity that the functions F and G for the outcome X and the probability P are linear, respectively, the contingent focus model considers that the decision is made based on the size between the following U(X, P)’s definition. U ðX; PÞ 5 X a Pð12aÞ Here, since 1
a . 0, the preference relation by U(X, P) is equal to the following preference relation by U0 (X, P). U 0 ðX; PÞ 5 X a=ð12aÞ P: where risk attitude is risk-oriented when a/(1
a) exceeds 1, and risk-averse when a/(1
a) is below 1. In decision-making experiments such as Experiments 3.1 and 3.2 of this study, some participants usually respond in a risk-seeking manner, while others respond in a risk-averse manner. In prospect theory, such heterogeneity in risk attitudes among individuals is not accounted for, and the formulation is based on the average individual. However, the contingent focus model can explain the differences in risk attitudes among individuals by introducing a supplementary assumption that a/(1
a) is distributed among individuals. In order to faciliate understanding of the analysis in the experiment, the parameter estimation method of the psychometric analysis will be again explained with the experimental procedures. Let us assume that a/(1
a) is distributed among individuals, and that its expected value is affected by the experimental conditions, as assumed by the situation-dependent focusing hypothesis, that is:
 ai 5 exp Const 1 αPos 1 βNo Emp 1 χOut Emp 1 εj 1 2 ai where ai is the focal parameter of individual i; Const is a constant term, Pos is a positive frame dummy; No_Emp is a no-emphasis dummy; Out_Emp is an outcome-emphasis dummy; α, β, χ are parameters, and i is the error term. Since the risk attitude is defined by whether ai/(1
ai) is greater or less than 1, the risk attitude is determined by the positive or negative value of the function in exp on the right side of the abovementioned equation. As mentioned above, from the above the probability that an individual in Experiments 1 and 2 will be risk-averse, P(risk2averse), and the probability that he or she will be risk-oriented, P(risk2take), are as follows:

 Pðrisk2averseÞ 5 P wj . 1 5 PðV 1 εi . 0Þ; and Pðrisk2takeÞ 5 P wj , 1 5 PðV 1 εi . 0Þ;

where V 5 Const 1 αPos 1 βNo Emp 1 χOut Emp.

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If we assume that the shape of the distribution of the error term i is logistic (e.g., McFadden, 1973), then: Pðrisk2averseÞ 5

1 expðV Þ ; and Pðrisk2takeÞ 5 expðV Þ 1 1 expðV Þ 1 1

where V 5 Const 1 αPos 1 βNo Emp 1 χOut Emp, as mentioned in the previous section. After defining the likelihood using the probability formulated based on the parametric assumptions about the distribution of the focal parameters as described previously, we estimated the parameters in Experiments 3.1 and 3.2, using the maximum likelihood estimation method, and the constant term Const, which are shown in Table 17.3. The estimation results show that the parameters are significantly negative in both experiments, indicating that the focus on the outcome is stronger in the negative condition than in the positive condition. Similarly, the fact that the parameter is significantly positive indicates that the resultant emphasis also leads to a stronger focus on the resultant. Here, as mentioned earlier, the focusing hypothesis predicts that stronger outcome focusing leads to stronger risk acceptance tendencies. Therefore the estimated results of parameter of the contingent focus model in Table 17.3 can be considered to reflect the trend found by the log-linear analysis that the risk acceptance tendency is stronger in the negative condition as well as in the outcome focusing condition. The difference in the absolute values of the parameter estimates for the influence of the frame condition and the influence of the emphasis condition was slightly larger for the latter in both experiments. The difference between the absolute values of the parameter estimates for the influence of the frame condition and the influence of the emphasis condition was slightly larger for the latter in both experiments. The difference in the absolute values of the parameter estimates for the influence of the frame condition and the emphasis condition was slightly larger for the latter in both experiments. However, in both experiments, the absolute difference in the estimated values between the two conditions was 0.02 (t 5 0.032, P 5 .974) in Table 17.3 Estimation results of focal parameters (Fujii & Takemura, 2001a). Experiment 3.1 (n 5 180)

Const α (Pos) β (No_Emp) χ (Out_Emp)

Experiment 3.2 (n 5 180)

Coeff

T

P

Coeff

t

P


0.53
1.55 0.33 1.57


1.30
4.03 0.70 3.20

.193 .000 .185 .001

0.20
0.81
0.14 1.01

0.65
2.58
0.38 2.60

.516 .010 .707 .009

Source: Fujii, S., & Takemura, K. (2001a). Risuku Taido to Chuui: Joukyou Izonteki Shouten Moderu niyoru Keiryou Bunseki [Risk attitude and attention: Psychometric analysis of framing effect by contingent focus model]. The Japanese Journal of Behaviormetrics, 28, 9
17. (in Japanese).

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381

Experiment 3.1 and 0.20 (t 5 0.40, P 5 .689) in Experiment 3.2, both of which were not significant. In any case, these results imply that the emphasis manipulation in this experiment is at least as effective as the positive/negative framing effect found by Tversky and Kahneman (1981).

17.3.4 Testing the focusing hypothesis of the contingent focus model using the information monitoring acquisition method As explained earlier, the contingent focus model predicts that the decision maker’s attention is focused on the situational cues, and that the decision weight is determined by a monotonically increasing function of the degree of focusing, which in turn determines the risk attitude. Thus it explains how attention determines the context- and situation-dependence of decisions. In this experiment, we used the information monitoring acquisition method to control the order of information to be processed by the participants in the experiment to control the internal processing of the decision maker to some extent. The information monitoring method is a technique used to examine the decision-making process and is a psychological method to understand how decision makers acquire information to reach a decision. In this experimental study, we conducted an experiment using the information monitoring method in which the experimenter controls the information presented to the participants, which is somewhat different from the traditional information monitoring method, and tried to empirically examine the proposition that preference reversal occurs due to attentional focusing, which is a basic assumption of the contingent focus model. The most basic and important hypothesis among the set of hypotheses of the contingent focus model is the focusing hypothesis, which implies that the allocation of attention during decision-making influences risk attitude. To test this hypothesis, three experiments were conducted to experimentally manipulate attention during decision-making and to examine whether the risk attitudes of the participants in the experiments would change in the direction predicted by the focusing hypothesis.

17.3.4.1 Experiment 3.4.1: the Asian disease problem In Experiment 3.4.1 the Asian disease problem was used as the decision-making task. The participants in the experiment were 40 undergraduate and graduate students (32 males and 8 females) from the University of Tsukuba, ranging in age from 18 to 37. A total of 17 were science and engineering students, and 23 were social science students. As in the previous experiment, a total of four conditions were set: two frame conditions (positive and negative) and two emphasis conditions (outcome and risk). In the frame condition the same participants performed the same number of repetitions in a random order, while the emphasis condition was performed by different participants. The assignment of experimental participants for the emphasis condition was done randomly.

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After entering the experimental room the participants received an explanation of the experimental task from the experimenter while viewing the screen of the personal computer. As shown in Fig. 17.3, the probability and the number of people for each option A and B were hidden under the buttons on the first screen, and the information (probability and number of people) under the buttons appeared in a random order for 100 ms by pressing the start button. In the Outcome Emphasis condition, the probability was presented once, while the number of people was presented three times. Similarly, in the risk-weighted condition, the number of people was presented once while the probability was presented three times. Before the participants tackled the experimental task, they were given a preliminary exercise to help them understand the task better. In the preliminary exercise an explanatory screen was provided as shown in Fig. 17.3. After completing the preliminary exercise the participants worked on the experimental task. We assume that the amount of attention to the outcome will be higher in the outcome enhancement condition than in the risk enhancement condition due to this

Figure 17.3 Decision task using monitoring information acquisition. Reproduced with permission from: Takemura, K., Hu, K. & Fujii, S. (2001). Jouhou Monitaringu Hou wo Mochiita Jokyo Izonteki Shoten Moderu no Kentou [Examination of contingent focus model using a method of monitoring information acquisition]. Paper Presented at the Japan Society for Kansei Engineering, Tokyo, Japan.

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Table 17.4 Percentage of participants (%) and number (N) in the experiment who chose risky option in the Experiment 3.4.1. Positive frame

Risk emphasis Outcome emphasis Total

Negative frame

Total

%

(N)

%

(N)

%

(N)

31.6 66.7 50.0

(6) (14) (20)

44.4 68.2 57.5

(8) (15) (23)

37.8 67.4 53.8

(14) (29) (43)

Source: Takemura, K., Hu, K. & Fujii, S. (2001). Jouhou Monitaringu Hou wo Mochiita Jokyo Izonteki Shoten Moderu no Kentou [Examination of contingent focus model using a method of monitoring information acquisition]. Paper Presented at the Japan Society for Kansei Engineering, Tokyo, Japan.

experimental manipulation. The focusing hypothesis predicts that in both the negative and positive conditions, the risk-orientation tendency is stronger in the consequence-enhanced condition than in the risk-enhanced condition, and conversely, in both the negative and positive conditions, the risk-aversion tendency is stronger in the risk-enhanced condition than in the consequence-enhanced condition. The results for each condition are shown in Table 17.4. As Table 17.4 shows, there was no framing effect and a significant trend was found in both the negative and positive conditions, consistent with the focusing hypothesis that the outcome emphasis condition was more risk-oriented than the risk emphasis condition (χ2(1) 5 7.01, p , .001).

17.3.4.2 Experiment 3.4.2: a variant of the Asian disease problem The same experiment participants were asked to solve a variant of the Asian disease problem as follows. An island in the Pacific Ocean is home to 600 inhabitants. One day, a deadly epidemic begins to spread on the island, and all the inhabitants are infected in a short time. Two types of vaccines, A and B, are available to combat this epidemic. The number of people who will be saved and the probability of survival when vaccines A and B are used are as follows. Vaccine A: Number of people 300 Probability 100%. Vaccine B: 600 people, probability 50%. As before, there were four experimental conditions: two frame conditions (positive and negative) and two emphasis conditions (outcome and risk). The frame condition was performed by the same experimenter in a randomized order, and the emphasis condition was performed by a different participant in the experiment. In the outcome enhancement condition the amount of attention to the outcome was increased compared to the risk enhancement condition. The focusing hypothesis predicts that in both the negative and positive conditions, the risk-orientation tendency will be stronger in the consequence-enhanced condition than in the riskenhanced condition, and conversely, in both the negative and positive conditions, the risk-aversion tendency will be stronger in the risk-enhanced condition than in

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Table 17.5 Percentage of participants (%) and number (N) in the experiment who chose risky option in the Experiment 3.4.2. Positive frame

Risk emphasis Outcome emphasis Total

Negative frame

Total

%

(N)

%

(N)

%

(N)

31.3 79.2 60.0

(5) (19) (24)

35.0 75.0 55.0

(7) (15) (22)

33.3 77.3 57.5

(12) (34) (46)

Source: Takemura, K., Hu, K. & Fujii, S. (2001). Jouhou Monitaringu Hou wo Mochiita Jokyo Izonteki Shoten Moderu no Kentou [Examination of contingent focus model using a method of monitoring information acquisition]. Paper Presented at the Japan Society for Kansei Engineering, Tokyo, Japan.

the consequence-enhanced condition. The results for each condition are shown in Table 17.5. As can be seen from Table 17.5, there was no framing effect, and in both the negative and positive conditions, there was a significant trend consistent with the focusing hypothesis that the outcome emphasis condition was more risk-oriented than the risk emphasis condition (χ2(1) 5 7.02, p , .001).

17.3.4.3 Experiment 3.4.3: reflection effect problem The same participants, under the same four experimental conditions, were given the following decision task on the reflection effect. Suppose you have 20,000 yen available in addition to the money you have. You are in a situation where you have to choose between two options (options A and B). The amount of money and the probability of getting it when you take options A and B are as follows. Option A: 5000 yen with probability 100%. Option B: 20,000 yen with probability 50%. As mentioned earlier, in the Outcome Emphasis condition, the amount of attention to the outcome is expected to be higher than in the Risk Emphasis condition. The focusing hypothesis predicts that in both the negative and positive conditions, the outcome enhancement condition will have a stronger risk orientation tendency than the risk enhancement condition, and vice versa in both the negative and positive conditions, the risk enhancement condition will have a stronger risk avoidance tendency than the outcome enhancement condition. The results for each condition are shown in Table 17.6. As can be seen in Table 17.6, there was no framing effect and no trend consistent with the focusing hypothesis that the risk orientation tendency was stronger in the outcome emphasis condition than in the risk emphasis condition in either the positive or negative conditions (χ2(1) 5 0.19, n.s.). The focusing hypothesis was only tested in Experiment 3.4.3. In this study, we examined the effects of the two conditions on the tendency to be more risk-oriented than in the risk-enhanced condition.

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Table 17.6 Percentage of participants (%) and number (N) in the experiment who chose risky option in the Experiment 3.4.3. Positive frame

Risk emphasis Outcome emphasis Total

Negative frame

Total

%

(N)

%

(N)

%

(N)

52.6 57.1 55.0

(10) (12) (22)

50.0 55.0 52.5

(10) (11) (21)

51.3 56.1 53.8

(20) (23) (43)

Source: Takemura, K., Hu, K. & Fujii, S. (2001). Jouhou Monitaringu Hou wo Mochiita Jokyo Izonteki Shoten Moderu no Kentou [Examination of contingent focus model using a method of monitoring information acquisition]. Paper Presented at the Japan Society for Kansei Engineering, Tokyo, Japan.

17.3.5 Discussion of the experimental results In the first of the experimental studies presented here (Experiment 3.1), we conducted an experiment in which we tried to manipulate attention to consequences and risks by changing the size of letters to test the basic hypotheses of the contingent focus model, namely, the focusing hypothesis and the situation-dependent nature of focusing hypothesis. The results of the experiment showed that in both the reflection effect problem (experiment) and the Asian disease problem (experiment), regardless of the positive-negative frame condition, the tendency toward risk orientation was stronger in the case of outcome emphasis than in the case of risk emphasis. The results showed that the tendency toward risk orientation was stronger in the outcome than in the risk-emphasis case, regardless of the positive
negative frame conditions. The results of the econometric analysis of the focus parameter with some additional assumptions indicated that the focus parameter, which refers to the degree of focus on the outcome, was larger in the outcome emphasis condition. These results suggest that risk attitudes change depending on the relative focus on the outcome or risk, or the attention paid to them. In addition, to examine the basic hypothesis of the contingent focus model, we conducted an experiment in which we manipulated attention to consequences and risks by controlling the number of times information was presented using the information monitoring method in Experimental Study 3.4. The experimental results showed the existence of phenomena that can be explained by the focusing hypothesis of the contingent focus model. The first two experiments in Experimental Study 3.4 supported the focusing hypothesis, which is the basic hypothesis of the model. However, as shown in the third experiment (Experiment 3.4.3), there were some results that could not be fully explained by either prospect theory or the contingent focus model. Further research is needed on this point.

17.4

Conclusion and future perspectives

To test the basic hypotheses of the contingent focus model, that is, the focusing hypothesis and the situation-dependent nature of focus hypothesis, we conducted

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various experiments in which we tried to manipulate attention to consequences and risks. The results of the experiments showed that the reflection effect problem (Experiment. The results of the experiments showed that the reflection effect problem, Experiment 3.1) and the Asian disease problem (Experiment 3.2) were similar. The results of the experiments were positive in both the reflection effect problem (Experiment 3.1) and the Asian disease problem (Experiment 3.2). The results showed that, regardless of the positive-negative frame condition in each experiment, the tendency toward risk orientation was stronger in the case of outcome emphasis than in the case of risk emphasis. The results of the psychometric analysis of the focal parameter with some additional assumptions showed that the focal parameter, which refers to the degree of focus on the outcome, was larger in the outcome emphasis condition. These results suggest that risk attitudes change depending on the relative focus on the outcome or risk, or the attention paid to them. Prospect theory predicts that there will be differently shaped value functions for positive and negative outcomes, and that the former will lead to risk aversion and the latter to risk orientation. However, experiments with the reflection effect problem and Experiment. In the negative frame condition, there was no tendency toward risk orientation in the risk-emphasis condition and in the no-emphasis condition, where neither risk nor outcome was emphasized. In other words, the results deviated from the predictions of prospect theory. However, in both emphasis conditions, the negative frame condition was relatively more risk-oriented than the positive frame condition. This result was also obtained in Experiment 3.2 using the Asian disease problem. These results support the prediction of the contingent focus model that negative outcomes attract relatively more attention than positive outcomes. However, the results of the present experiment alone do not sufficiently test whether the amount of attention to the outcome and risk changes depending on the positive or negative frame condition. In this regard, it would be necessary to externally observe the amount of attention during decision-making by using an eye gaze recorder or other methods. In fact, Fujii and Takemura (2003) attempted to directly measure the focusing response using an eye movement measurement system and found a choice result opposite to the prediction of prospect theory due to changes in eye movements (Fujii & Takemura, 2003). We have also used an eye movement measurement device to monitor information acquisition to investigate the decision-making process (see Fig. 17.4). At each stage of the decision-making process, we analyzed the decision-making process by determining the number of times the subject captured the user’s attention, the average duration of attention, the number of options to which attention was directed, and the percentage of attention that was devoted to the final option selected (Takemura, 2014, 2019). The results suggested that people tend to make decisions based on fairly asymmetric information, rather than observing all available information equally (Takemura, 2014). This finding may be the focus of attention behind the situation-dependent focus model and the reason why people’s decision-making processes tend to be situation- and path-dependent (Fujii & Takemura, 2001a, 2001b, 2003; Takemura & Fujii, 2015).

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Figure 17.4 Contact type of eye movement measurement system (Tobii Glass Eye Tracker, product of Tobii). Note: A camera to record the visual range of the test subject is amounted on the left side of the glasses.

The quantitative analysis also showed that the emphasis manipulation performed in the present experiment was as effective as the frame manipulation known from previous studies. In addition, the quantitative analysis showed that the emphasis manipulation used in the present experiment had the same effect as the frame manipulation known from previous studies. The emphasis manipulation used in the present experiment has been frequently employed in the design of advertisements in the field of marketing, and its effect has been empirically known. This study can be said to provide theoretical and empirical evidence that such an emphasis operation affects decision-making. However, the effect of emphasizing risk was small, and there was no significant difference between the focal parameters of the risk-emphasis and no-emphasis cases. This may allow us to formulate a new hypothesis that the emphasis manipulations that have a significant impact on decision-making are limited to those on the outcome. However, further theoretical investigation and additional experiments will be necessary to investigate this point in detail. Although the contingent focus model does not necessarily predict irrational decisions or decisions to make the worst choice, in some cases, it may explain how attentional focusing can lead to unimportant attributes that lead to bad decisions. The contingent focus model is characterized not only by its psychological theoretical basis but also by its ability to describe behavioral decision-making econometrically. In particular, if we make additional assumptions about the distribution of heterogeneity among individuals, we can perform a quantitative analysis of the

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situation-dependence of decision-making. Thus the contingent focus model is expected to provide various insights into decision-making in actual environments. We also generalized the contingent focus model described in Chapter 16, The Contingent Focus Model and Bad Decisions, and this chapter and set up a function that holds the following multiattribute preference relation as a representation of the multiattribute utility function (Takemura, 2011, 2014) where αxk is a parameter that focuses on the kth attribute of choice x. Assuming that U is positive and taking the logarithm of both sides, we can clearly see that the relative size of the focus points has a linear effect on the log utility such that: x * y 3 U ðxÞ $ U ðyÞ where U ðxÞ 5 Lk51 uðxk Þαxk ; U ðyÞ 5 Lk51 uðyk Þαxk . In the future, we would like to conduct more experiments to test the basic hypothesis of the model, and at the same time, we would like to obtain applied knowledge on such decision-making. In the contingent focus model, it is believed that preferences change when people pay attention to other attributes. From this perspective, Fujii, Takemura, and Kikkawa (2002) and Takemura and Fujii (2015) showed that not only in gambling tasks but also in decision-making related to social dilemmas such as traffic problems, using a payoff matrix to encourage people to pay attention to certain attributes can encourage people to cooperate to some extent, and that social dilemma We showed that it is possible to make decisions to solve social dilemmas. The fact that attention can change decision-making means that it may be possible to avoid “bad decisions” by changing the way information is presented and which information is emphasized. Focusing attention on other attributes may lead to confusion and irrational decision-making. q

q

References Fujii, S., & Takemura, K. (2001a). Risuku Taido to Chuui: Joukyou Izonteki Shouten Moderu niyoru Keiryou Bunseki [Risk attitude and attention: Psychometric analysis of framing effect by contingent focus model]. The Japanese Journal of Behaviormetrics, 28, 9
17. (in Japanese). Fujii, S., & Takemura, K. (2001b). Psychometric meta-analysis of framing effect by contingent focus model. In: Paper presented at the 29th international meeting of the psychometric society (IMPS 2001), Osaka, Japan, 164
167. Fujii, S., & Takemura, K. (2003). Attention, frames condition and decision making under risk: An empirical test of the contingent focus model using an eye gaze recorder. In: Paper presented at the society for judgment and decision making, Vancouver, Canada. Fujii, S., Takemura, K., & Kikkawa, T. (2002). Decision Strategy and Consensus formation: Towards Inhibition of Selfish Motive in Social Dilemma. Proceedings of Japan Society of Civil Engineers, 709, 13
26. Kahneman, D., & Tversky, A. (1979). On the interpretation of intuitive probability: A reply to Jonathan Cohen. Cognition, 7, 409
411.

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Luce, R. D. (1959). On the possible psychophysical laws. Psychological Review, 66, 81
95. McFadden, D. (1973). Conditional logit analysis of qualitative choice behavior. In P. Zarambka (Ed.), Frontiers in econometrics (pp. 105
142). New York: Academic Press. Takemura, K. (1992). Effect of decision time on framing of decision: A case of risky choice behavior. Psychologia, 35, 180
185. Takemura, K. (1993). The effect of decision frame and decision justification on risky choice. Japanese Psychological Research, 35, 36
40. Takemura, K. (1994a). Furemingu Koka no Rironteki Setsumei: Risukuka Deno Ishikettei no Jokyo Izonteki Shoten Moderu [Theoretical explanation of the framing effect: Contingent focus model for decision-making under risk]. Japanese Psychological Review, 37, 270
293. (in Japanese). Takemura, K. (1994b). The influence of elaboration on the framing of decision. The Journal of Psychology, 128, 33
39. Takemura, K. (2011). Tazokusei ishikettei no shinri moderu to “yoi ishikettei” [Psychological model of multi-attribute decision making and good decision]. Opereshonzu risachi, 56, 583-59. (in Japanese). ¯ ¯ Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical descriptions of human choice behavior. Tokyo: Springer. Takemura, K. (2019). Foundations of economic psychology: A behavioral and mathematical approach. New York: Springer. Takemura, K., & Fujii, S. (2015). Ishikettei no shoho¯ [Prescription for decision making]. Tokyo: Asakura Shoten. (in Japanese). Takemura, K., Hu, K. & Fujii, S. (2001). Jouhou Monitaringu Hou wo Mochiita Jokyo Izonteki Shoten Moderu no Kentou [Examination of contingent focus model using a method of monitoring information acquisition]. In: Paper presented at the Japan Society for Kansei Engineering, Tokyo, Japan. Tversky, A., & Kahneman, D. (1986). Rational choice and the framing of decisions. The Journal of Business, 59(4), S251
S278. Tversky, A., & Kahneman, D. (1981). The framing of decisions and the psychology of choice. Science (New York, N.Y.), 211, 453
458.

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The contingent focus model and its relation to other theories

18

In Chapter 16, The Contingent Focus Model and Bad Decisions, and Chapter 17, An Experiment on, and i Analysis of, the Contingent Focus Model, I explained the contingent focus model as a theory to explain situational dependence and described the phenomenon that attention is focused on specific attributes by this model. We have discussed the possibility that this focusing of attention may lead to irrational decision-making or choosing the worst option. In this chapter, I will explain the relationship between this contingent focus model and related utility and prospect theories. In particular, I will explain expected utility theory, which is the most commonly used one in decision theory. After explaining what kind of axiomatic system it is, I will introduce the Allais paradox (1953), which contradicts the axiomatic system of the model, and state how Allais’ paradox can be explained by the contingent focus model and nonlinear expected utility theory. In addition, I explain the framing effect that cannot be explained by the nonlinear expected utility theory and explain the prospect theory that explains this phenomenon. Finally, I will explain the relationship and differences between the contingent focus model and prospect theory and discuss the problems and future prospects of the contingent focus model.

18.1

Expected utility theory

In their major work on game theory and economic behavior, von Neumann and Morgenstern (1944, 1947) proved that the expected value of utility based on objective probability represents a preference relation if the decision satisfies some axioms described later and axiomatized the expected utility theory. In this chapter, I will discuss the axioms of expected utility theory. Their expected utility theory does not necessarily assume a logarithmic utility function as in the expected utility theory of Bernoulli (D) but formulates the utility function in a more abstract form. In the expected utility theory of von Neumann and Morgenstern, expected utility is expressed as follows (Takemura, 2014, 2019; Tamura, Nakamura, & Fujita, 1997). First, let the set of alternatives be A 5 {al, am, . . .}, let pi be the probability that outcome xi is obtained when the decision maker chooses option alAA, let qi be the probability that outcome xi is obtained when amAA, and let X 5 {x1, x2, . . .}. Let X 5 {x1, x2}Pbe theP set of all possible outcomes. Then, for all i, let pi ^ 0, qi ^ 0, . . ., and i pi 5 i qi 5 ? 5 1 is satisfied. When the utility function on X is u: PX!R, the expected utility when the choices are al, am, . . . is P Eal 5 i pi uðxi Þ; Eam 5 i qi uðxi Þ; . . ., respectively. In this expected utility theory, Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00019-3 © 2021 Elsevier Inc. All rights reserved.

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it is assumed that the decision maker will adopt the option with the maximum expected utility from the set of options A. Furthermore, it is known that this utility function does not lose its essential meaning even after positive linear transformation, and it has the property of radix utility (interval measure). To theoretically examine decision-making under risk, let us first take up the definition of probability, define gambling and lottery, and then consider expected utility theory. First, consider a set X of outcomes. A subset E (ECX) of this set X is an element of 2X in the power set of X (EA2X). Here, the power set of X is the set of all subsets of X, denoted by 2X. Note that the elements of the power set are themselves a set. For example, when X 5 {x1, x2, x3}, 2X is a set of eight elements as follows (except that ϕ is the empty set):   2X 5 ϕ;fx1 g; fx2 g; fx3 g; fx1 ;x2 g; fx1 ;x3 g; fx2 ;x3 g; fx1 ;x2 ;x3 g : Now consider a finite additive probability measure p on 2X. A finite additive probability measure is a “probability,” such as p({x1}) 5 0.4. p is a finite additive probability measure on 2X such that for all Ei, EjA2X, 1. p(X) 5 1 2. p(Ei) $ 0 3. Ei - Ej 5 ϕ.p(Ei , Ej) 5 p(Ei) 1 p(Ej)

is a set function such that (1) the overall probability of the result set X is 1, (2) the probability of any subset Ei of X is greater than or equal to 0, and (3) if the product set of any subsets of X, Ei - Ej, is empty (i.e., there is no intersection of Ei and Ej), then the probability of the union set of Ei and Ej (i.e., the set of Ei and Ej) is the property that the probability of the sum of Ei and Ej (i.e., the combined set of Ei and Ej) is equal to p(Ei) 1 p(Ej). Next, consider a convex set PX of finite additive probability measures on 2X (called probability measures for simplicity), where PX is a convex set if 0 # λ # 1 and any p, q are elements of PX(p, qAPX), then λp 1 (1 2 λ)q is also an element of PX((λp 1 (1 2 λ)q)APX). In other words, we say that any mixture of the probabilities of any two outcomes is an element of PX. When EiAPX is a finite set, the probability measure that p(Ei) 5 1 is said to be simple. This simple probability measure can be interpreted as gambling or lottery. Therefore the fact that PX is a convex set can be interpreted to mean that composite lotteries and composite gambles, which combine lotteries and gambles with a certain probability λ and (1 2 λ), are also elements of PX. First, since PX can be interpreted as a set of alternatives, we consider the binary relation on PX, and for all p, qAPX pgq3Φðp; qÞ . 0 We can assume a real-valued function Φ on PX 3 PX satisfying where g is a strong preference relation [i.e., ’ p,qAPX, phq 4 :(qhp), and h is a weak order preference relation].

The contingent focus model and its relation to other theories

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Based on this real-valued function Φ, we explain the axiomatized expected utility theory from the following linear utility model. A linear utility model is a linear functional U on PX such that Φ(p,q) 5 U(p) 2 U(q) for all p, qAPX. A linear functional can be defined as follows: if PX is a linear space on R, then the map U: PX!R has the following two properties (linearity), that is, 1. ’ p; qAPX ; U ðp 1 qÞ 5 U ðpÞ 1 U ðqÞ 2. ’ aAR; ’ pAPX ; U ðapÞ 5 aU ðpÞ

We say that U is a linear functional in PX if for any p, qAPX and any λ(0 , λ , 1), U is linear. This is to become U ðλp 1 ð1 2 λÞqÞ 5 λU ðpÞ 1 ð1 2 λÞU ðqÞ: From the definition of the linearity of U, we know that since Φ is unique even when multiplied by a positive constant (i.e., because it is a proportional measure), U is unique over the range of positive linear transformations (i.e., because it is an interval measure). This is because, if U0 5 αU 1 β(α . 0), then αΦ(p, q) 5 U0 (p) 2 U0 (q). A linear utility model based on the utility U(pi) of a simple probability measure pi that produces m Poutcomes xjAX of a gamble αiAA, which makes U linear, each with probability pij ð m j51  be thought of as finding the expected value of U(xj), P pij 5 1Þ
can because U ðpi Þ 5 m p U x , and U(pi) find the expected value of U(xj). In this ij j j51 sense the linear utility model U can be thought of as an expected utility model, and the expected utility theory uses the linear utility model U to find the expected utility. There are a number of necessary and sufficient conditions for expected utility theory to hold, and von Neumann and others have proposed axiomatic systems that show the necessary and sufficient conditions, but the axiomatic system of Jensen (1967) is often cited in general, so it is presented later. The following axiomatic system is assumed to hold for all p, qAPX and all 0 , λ , 1, as defined earlier [the representation of the axiomatic system is based on Tamura et al. (1997) and Gilboa (2009)]. Axiom A1: (weak order axiom) * is on PX. In other words, this means that for a preference relation * 1. Transitivity ’ p; q; rAPX ; p*q and q*r.p*r 2. Completeness ’ p; qAPX ; p*q3q*p

Axiom A2: (independence axiom) ’ p; q; rAPX ; λAð0; 1Þ; p*q, then λp 1 ð1 2 λÞr*λq 1 ð1 2 λÞr Axiom A3: (continuity axiom) If pgq and qgr, then there exists some α, βA(0, 1) such that αp 1 ð1 2 αÞrgq and qgβp 1 ð1 2 β Þr, where pgq is p*q and not (q*p).

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A theorem: of expected utility theory (Jensen, 1967) If and only if axioms A1, A2, and A3 hold, then there exists a linear functional U on PX such that for all p, qAPX p*q3U ðpÞ $ U ðqÞ; where U ðpÞ 5

m X j51

m X

 pj U xj and U ðqÞ 5 qj U x j : j51

Also, U is unique up to a positive linear transformations (U is an interval scale). The independence axiom of axiom A2 is a necessary and sufficient condition for U to be linear, and the continuity axiom of axiom A3 is a necessary axiom for U to be a map of PX to a set of real numbers. The theorem of expected utility theory suggests that if the decision maker satisfies the previous three axioms, the preference relation can be represented by an expected utility model, and the basic model to explain decision-making under risk can be soldiered from a few axioms.

18.2

A counterexample to expected utility theory: Allais paradox

Does such a utility theory reflect the decisions of real people? Expected utility theory is a theory that is widely used in traditional economics. There is a counterexample to expected utility theory, called the Allais paradox, which is based on thought experiments and psychological experiments, not on the actual practical use of expected utility theory (Takemura, 2014, 2020). Allais’s paradox is a deviation from the independence axiom of expected utility theory, which was presented earlier. These phenomena indicate that expected utility theory does not adequately reflect realworld decision-making (Slovic & Tversky, 1974; Takemura, 2014, 2020). Allais (1953) cites a counterexample of expected utility theory (Takemura, 1996, 2014). Let us consider the following decision problems. First, Problem 1 is a choice between alternatives A and B, as shown in Fig. 18.1. Choosing option A is a sure way to get $1 million. Choice B is a “lottery” with a 10% chance of winning $5 million, an 89% chance of winning $1 million, and a 1% chance of winning $0 (no prize). Then, in Problem 2, we consider two lotteries, that is, choice C, which gives an 11% chance of winning $1 million, and choice D, which gives a 10% chance of winning $5 million. In this case, most people would prefer D to C. However, this result is clearly inconsistent with expected utility theory. This is because, first of all, the areas enclosed by the dashed squares in the figure are common to each problem and, therefore, do not need to be taken into account in the preference, according to the axiom of independence of expected utility theory. This is because the areas not enclosed by dashed squares are the same as A in Problem 1 and C in Problem 2, and B in Problem 1 and D in Problem 2 (see Fig. 18.1). The Allais

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Figure 18.1 Representation of Allais paradox. Modified from: Takemura, K. (1996). Ishikettei to sono shien [Decision making and decision support]. In S. Ichikawa (Ed.), Ninchi shinrigaku 4 shiko [Cognitive psychology 4: Thought] (pp. 81
105). Tokyo: University of Tokyo Press (in Japanese).

paradox has been found to be demonstrated by many subjects in psychological experiments (Slovic & Tversky, 1974; Tversky & Kahneman, 1992), and psychologically it is known as the certainty effect, which is the preference of a certain gain over an uncertain gain. In psychology, it is thought to be caused by the certainty effect, which is the preference of certain gains over uncertain gains. Allais paradox can be explained by a deviation from the independence axiom in expected utility theory. In the case of decision-making under risk, the independence axiom states that for any probability distributions p, t, and r, if pgt, the preference relation between the convex combination of probability distributions p and r (λp 1 (1 2 λ)r) and the convex combination of t and r (λt 1 (1 2 λ)r) are the same. That is, for all probability distributions p, t, rAPX and for all probabilities 0 , λ , 1, pgt.λp 1 ð1 2 λÞrgλt 1 ð1 2 λÞr The independence axiom does not hold although the existences of a certain probability distribution p, t, rAPX and a certain probability 0 , α , 1, and pgt, αq 1 (1 2 α)rgαt 1 (1 2 α)r are true (Tamura et al., 1997).

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In the case of the Allais paradox, in Problem 1, choosing option A will ensure that you get $1 million, while option B will choose a “lottery” with a 10% chance of getting $5 million, an 89% chance of getting $1 million, and a 1% chance of getting $0 (no prize). Option A can be broken down into a 10% chance of winning $1 million, an 89% chance of winning $1 million, and a 1% chance of winning $1 million, so the common denominator between A and B is that there is at least an 89% chance of winning $1 million. Now, if we denote option A by p, option B by q, and the probability of getting nothing with a 10 in 11 chance of getting $5 million by a 1 in 11 lot t, then p 5 0:11p 1 0:89p;

q 5 0:11t 1 0:89p

Therefore by the independence axiom, if pgt, then pgq. In addition, in Problem 2, there are two lots: choice C, which gives an 11% chance of getting $1 million, and choice D, which gives a 10% chance of getting $5 million, but what both C and D have in common is that there is at least an 89% chance of getting nothing. Expressing option C as r, option D as s, and the lot that will surely get nothing as t0 , we get r 5 0:11p 1 0:89t0 ;

18.3

s 5 0:11t 1 0:89t0

Nonadditive probability and nonlinear utility theory

As explained so far, the Allais paradox is interpreted as arising from the fact that the independence axiom does not hold empirically. Psychologically, the Allais paradox can be explained by the certainty effect, which favors certainty (Takemura, 1996, 2014). There are various theoretical frameworks to explain such paradoxes (Camerer, Lowenstein, & Rabin, 2004; Takemura, 2000, 2014, 2019; Tamura et al., 1997). The explanation is based on the nonlinear utility theory, which relaxes the independence axiom and others. This theoretical system is a generalization of expected utility theory (Starmer, 2000; Tamura et al., 1997). In the field of economics, this theoretical system is called nonlinear utility theory (Edwards, 1992; Fishburn, 1988) or generalized expected utility theory (Quiggin, 1993) and is mathematically very similar to the theoretical system of fuzzy integrals based on fuzzy measure theory in the field of engineering (Sugeno & Murofushi, 1993). In the system of nonlinear utility theory, we consider a nonadditive probability weighting function that transforms probabilities such that additivity does not hold given probability information in decision-making under risk, as in the case of the Allais paradox. Nonadditive probability is sometimes referred to as capacity, since it was originally used in the field of physics, but in the field of fuzzy engineering it is called a fuzzy measure. Although the names are different, the mathematical definitions are the same. A nonadditive probability is a set function π: 2Θ![0,1] from a set consisting of subsets of a nonempty set Θ to a closed interval [0,1] satisfying the following conditions. In other words, the condition of boundedness [π(ϕ) 5 0, π(Θ) 5

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397

1] and the condition of monotonicity [if subsets E and F of Θ satisfy the relation π(E) # π(F) if EDF]. Nonadditive probability does not necessarily satisfy the additivity condition, hence its name. In expected utility theory the expected utility maximization criterion can be viewed in terms of the Lebesgue integral for stochastic measures, but there are several other integral representations of expected utility for nonadditive probabilities as defined earlier. In the field of fuzzy measure theory in engineering, there are several integral representations from the viewpoint of integration called fuzzy integrals (Sugeno & Murofushi, 1993). Among these the expected utility based on the Choquet (1955) integral has been vigorously studied by researchers of nonlinear utility theory and fuzzy theory. The expected utility theory by this integral was axiomatized by Schmeidler (1989) and has become one of the most representative nonlinear utility theories, which can explain the Allais paradox. The expected utility by the Choquet integral can be shown as follows (Camerer, 1995; Takemura, 2014). First, a state of nature siAΘ has u(f(s1)) $ u(f(s2)) $ ? $ u(f(sn)) $ 0, depending on the utility u(f(si)) for the outcome f(si) due to the alternative f. The expected utility EUc by the Choquet integral over a finite set of nonadditive probabilities π is EUc 5

n X

   i i21 uðf ðsi ÞÞ π , sj 2 π , sj j51

i51

j51

(18.1)

If π is an additive measure and the states of nature sj are contrary to each other, then the previous expected utility is consistent with that of subjective expected utility theory (Camerer, 1995). This integral theory of expected utility is very similar to the rank-dependent utility theory, and both models agree when the objective probabilities are defined and the description is in the form of distorting them with nonadditive probabilities. The reason it is called rank-dependent is that it ranks the goodness of the results and integrates based on that. In addition, the model of Choquet-expected utility function on a set of alternatives, F, can be displayed in a general form as follows (Tamura et al., 1997): ð n X ðui 2 ui11 Þπf ðui Þ; EUc 5 ðCÞ uððf ðsÞÞdπ 5 θ





i51

where F 5 f jf :Θ ! X ; πf is a monotonic function
  and πf ðtÞ 5 π sAΘ:uðf ðsÞ $ t :

(18.2)

Another representation of EUc that is equivalent to above representation is as follows: 1N ð

EUc 5 0




1-π




sAΘ: uðfsÞ # τ



ð0 dτ-N


  π sAΘ:uðfsÞ # τ dτ:

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In other words, decision-making under uncertainty is structured in such a way that a certain outcome x∊X is known when a certain choice f is chosen and a state s∊Θ occurs. If we know the choice f and the state s, then we have x 5 f(s), and the choice can be interpreted as the result x in state s. There are various kinds of uncertainty: we may know the mapping from Θ to X, or we may not know it, or we may not know what the elements of Θ are, or we may be in a state of ignorance where we do not even know what the elements of X are. Now, let us denote the relation in the binary relation of * which is a subset of F 3 F. We can think of the set of alternatives as a mapping from the set of states to the set of outcomes, but if we think of the outcomes as having uncertainty defined by the objective probability, then we can think of PX as a convex set of finite additive probability measures on 2X, and the set of alternatives as Fp, so that for f ∊ Fp, we have f (Θ) 5 {f(s)∊PX: s∊Θ}. Since f(s) and g(s) are probability measures, the fact that PX is a convex set implies that its convex combination is also a probability measure. Also, since λf 1 (1 2 λ)g∊Fp, we know that Fp itself is also a convex set (Tamura et al., 1997). Schmeidler (1989) constructed an axiom system by changing the independence condition of Anscombe and Aumann’s (1963) axioms on subjective expected utility theory to the following comonotonic independence condition (Gilboa, 2009). To be comonotonic means that there is no s and t such that f(s) . f(t) and g(s) , g(t). And comonotonic independence means that, for any pair of comonotonic f, g, h∊Fp and α∊(0,1), there is no f *g3αf 1 ð1 2 αÞh*αg 1 ð1 2 αÞh: This axiom says that independence holds only when the alternatives are comonotonic. This axiom says that independence holds if and only if the alternatives are comonotonic. Schmeidler has derived a representation theorem for expected utility by the Choquet integral. Schmeidler derives a representation theorem for expected utility by the Choquet integral by putting the following axioms A1
A5 concerning the expected utility model by the Choquet integral (Gilboa, 2009; Schmeidler, 1989; Tamura et al., 1997). Here, for the sake of clarity, I will again enumerate the necessary and sufficient conditions for the representation theorem of expected utility theory by the Choquet integral. A1 Weak order: Preference relations * are complete and transitive. A2 Continuity: For any f, g, h ∊Fp, if fgggh, then there exist α, β∊(0, 1) such that αf 1 ð1 2 αÞhgggβf 1 ð1 2 β Þh: A3 Comonotonic independence: In any pair, for comonotonic f, g, h∊Fp and α∊ (0, 1), f *g3αf 1 ð1 2 αÞh*αg 1 ð1 2 αÞh: A4 Monotonicity: For any f, g∊Fp, if f(s)*g(s), then f*g for any s∊Θ. A5 Nontriviality: There exist f, g∊Fp such that fgg.

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Representation theorem of nonlinear expected utility models by Choquet integral (Schmeidler, 1989) The preference relations * satisfy A1, A2, A3, A4, and A5 if and only if there exists a linear functional U and a nonadditive probability measure π on 2Θ such that for any f, g∊Fp, ð f *g3ðCÞ

Θ

ð U ðf ðsÞÞdπðsÞ $ ðC Þ U ðgðsÞÞdπðsÞ; Θ

Ð

where (C) is the Choquet integral, and furthermore, U is unique up to a positive linear transformations. In other words, π is the nonadditive probability and U is the utility function, which means that the Choquet-integrated utility can explain the preference relation under uncertainty. In addition, this utility is an interval measure, which means that a positive linear transformation does not change the description of the preference relation.

18.4

Why nonlinear utility theory cannot explain the framing effect

I have already written in Chapter 16, The Contingent Focus Model and Bad Decisions, that nonlinear utility theory cannot explain the framing effect, but let me explain this further in another way. Utility is a real-valued function that represents preference relations for alternatives, both in traditional utility theory and in nonlinear utility theory. Here is a simple example of utility. Consider a consumer’s decision to choose between brands A and B of a product. In this case, utility is a real-valued value such that the utility of brand B [u(brand B)] is higher or equal to the utility of brand A [u(brand A)] than the utility of brand B [u(brand B)] if and only if the consumer prefers brand A to brand B (brand A*B). In other words, the relationship is as follows: uðbrand AÞ ^ uðbrand BÞ3brand A*brand B Now, if we call the name of brand A to P and the name of brand B to Q, but they both refer to the same brand, then uðPÞ ^ uðQÞ3P*Q This relationship must be established. Also, if we change the name of the brand and call the name of brand A to S and the name of brand B to T, but we are still referring to the same brand, then uðSÞ ^ uðT Þ3S*T

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If this relationship does not hold, we can say that a preference reversal due to the framing effect has occurred. If this relationship does not hold, we can say that a preference reversal due to the framing effect has occurred. In fact, this kind of preference reversal is often observed in daily life (Takemura, 2014; Tversky & Kahneman, 1981, 1986). Such framing effects cannot be explained by expected utility theory or subjective expected utility theory, which explain decision-making under risk. Expected utility theory is a theory that considers the expected value of utility based on the probability distribution of the state of nature, and the theory that assumes subjective probability in the probability of the state of nature is called subjective expected utility theory. Moreover, this framing effect cannot be explained by nonlinear utility theory either. The essential problem of the framing effect is not a deviation from a set of axioms of utility theory (e.g., Slovic & Tversky, 1974), as in Allais’ paradox (Allais, 1953) or Ellsberg’s paradox (Ellsberg, 1961), but rather a more serious deviation. It is characterized by a more serious deviation from descriptive universality (Tversky & Kahneman, 1986). Of course, just like the theoretical structure of ordinary utility theory, the expected utility in the Choquet integral depends on the outcome, the state of nature, the mapping from the state of nature to the outcome, and the preference relation, so it is obvious that if the values of these inputs are exactly the same, the value of the expected utility will also be the same. Since framing effect refers to the fact that preferences are different regardless of the same value, framing effect obviously cannot be explained by the expected utility theory based on the Choquet integral. This is also true for nonlinear utility theories other than the Choquet integral expected utility model (e.g., Edwards, 1992; Fishburn, 1988; Quiggin, 1993; Tamura et al., 1997).

18.5

Framing effects and prospect theory

Prospect theory, proposed by Kahneman and Tversky (1979) and Tversky and Kahneman (1992), is a theory that synthesizes previous findings in behavioral decision theory and nonlinear utility theory (or generalized expected utility theory). Prospect theory is a theory that synthesizes previous findings in behavioral decision theory and nonlinear utility theory (or generalized expected utility theory). Prospect theory was initially proposed as a descriptive theory that deals with decisionmaking under risk (Kahneman & Tversky, 1979), but it was later developed into cumulative prospect theory (Tversky & Kahneman, 1992), a theory that can also explain decision-making under uncertainty (Tversky & Kahneman, 1992). “Prospect” in prospect theory is the combination of various outcomes and corresponding probabilities of adopting a certain option, which is the same as “gambling” in decision-making under risk. In decision-making under risk, we choose a desirable prospect among several prospects. That is, consider a set of outcomes X 5 {x1, . . ., xj, . . ., xm}, and the probability distributions on X, p1 5 [p11, p12, . . .,

The contingent focus model and its relation to other theories

401

p1m], p2 5 [p21, p22, . . ., p2m], . . ., pl 5 [pl1, pl2, . . ., plm], can be replaced by the question of which prospect to choose. In this case, one prospect is (x1, p11; . . .; xj, p1j; . . .; xm, pmj). Prospect theory assumes that this prospect is evaluated in a different way than expected utility theory. In prospect theory the decision-making process is divided into an editing phase, in which the problem is recognized and the decision framework is determined, and an evaluation phase, in which the alternatives are evaluated according to the problem recognition (Kahneman & Tversky, 1979). The former phase is situationdependent and can be altered by slight differences in linguistic expression, whereas in the latter phase, once the problem is identified, situation-independent evaluations and decisions are made. According to prospect theory, the framing effect occurs when the same decision problem is perceived differently in different linguistic expressions in the editing stage. When the framing effect occurs, the prospect theory assumes that each prospect is reconstructed in the editing stage, and the prospect with the highest evaluation value is selected in the evaluation stage based on these reconstructions. In the evaluation stage, they are evaluated by a kind of utility function, which they call value function, and a weighting function for probability. It is important to note that the reference point, the origin of the value function, is determined at the editing stage. The method of evaluation in this evaluation stage is basically the same as that of expected utility theory by the Choquet integral in nonlinear utility theory. As shown in Fig. 18.2, the value function is a concave function in the gain domain, making it risk-averse, and a convex function in the loss domain, making it risk-oriented. Furthermore, the slope of the value function is generally larger in the loss domain than in the gain domain. This implies that losses have a larger impact than gains. Prospect theory differs greatly from ordinary nonlinear utility theory in that it assumes that the origin of utility theory is a reference point, and that the reference

Figure 18.2 Value function in prospect theory. Source: Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47, 263
292.

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Escaping from Bad Decisions

point can easily be shifted depending on how the decision problem is edited. In prospect theory the evaluation of the outcome is based on the amount of deviation from the reference point, which is the psychological origin, and the decision maker evaluates the outcome as either a gain or a loss. Prospect theory also assumes that decision makers are risk-averse when they evaluate gains and risk-oriented when they evaluate losses. By shifting the reference point, the same decision problem becomes riskaverse when the decision maker grasps the options in the gain domain, and riskoriented when the decision maker grasps the options in the loss domain. Thus the framing effect can explain the reversal of preferences that makes people risk-averse or risk-seeking in the same decision problem shown in Fig. 18.3. Next, I would like to explain the cumulative prospect theory, which explains decision-making under uncertainty. First, let X be a set of outcomes, Θ be a set of states of nature, and let f: Θ!X be a prospect (choice) under uncertainty. In other words, if for some state of nature sAΘ, there exists a function such that f(s) 5 x if and only if xAX is an outcome. For simplicity, however, we assume that the outcome xAX is a monetary value. For example, f is a lottery such that if tomorrow’s weather is “rainy” (s1), you will receive 10,000 yen (x1), and if it is “not rainy” (s2), you will receive 50,000 yen (x2). To consider cumulative prospect theory, we rank the outcomes in order of increasing desirability as a preparation. For example, according to the outcome, the outcomes are ranked as follows: 10,000, 50,000 yen, and so on. This method of obtaining the overall evaluation value by ranking the desirability of the outcomes is basically the same as that used to obtain the nonlinear expected utility by the Choquet (1955) integral, as explained earlier. In fact, the cumulative prospect theory also uses the Choquet integral. Also, if {si} is a subset of Θ, and if si occurs, the result will be xi, then the prospect f can be represented as a sequence of pairs of (xi, si). For example, in the example of rolling the previous dice, the prospect f 5 (10,000 yen, rain; 50,000 yen,

Figure 18.3 Probability weighting function in prospect theory. Source: Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47, 263
292.

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403

nonrain). Again, the states of nature corresponding to the outcome are arranged in ascending order of desirability of the outcome. Cumulative prospect theory assumes that the value function is different in the gain and loss domains, so we treat f1 as a prospect with a positive outcome and f2 as a prospect with a negative outcome. That is, if f(s) . 0, then f1(s) 5 f(s); if f(s) # 0, then f1(s) 5 0; if f(s) , 0, then f2(s) 5 f(s); if f(s) $ 0, then f2(s) 5 0. In the earlier example of the dice rolls, f1(s1) 5 10,000 yen, f1(s2) 5 50,000 yen, f2(s1) 5 0 yen, f2(s2) 5 0 yen, and so on. As in expected utility theory, if prospect f is preferred or indifferent to prospect g, we can consider

a function such that V(f) $ V(g), where, V ðf Þ 5 V f 1 1 V ðf 2 Þ; V ðgÞ 5 V g1 Þ 1 V ðg2 Þ, and assume that the overall utility can be obtained by summing the functions of the prospect in the gain domain and the prospect in the loss domain. In cumulative prospect theory a narrowly defined monotonically increasing function v: X!R is considered the value function and is assumed to be standardized to satisfy v(x0) 5 v(0) 5 0. For example, as a concrete example, we may assume a function such as v(x) 5 2x0.8, but value functions are often discussed in general terms, as in the explanation of utility functions. The overall evaluated value of a prospect, V(f), is explained by the sum of V(f1) and V(f2) as shown earlier, and furthermore, V(f1) and V(f2) are defined as follows:
 V ðf Þ 5 V f 1 1 V ðf 2 Þ; n 0 X
 X 2 π1 vðx Þ; V ð f Þ 5 π2 V f1 5 i i i vðxi Þ; i50

i52m

and in this case, f1 5 (x0, a0; x1, a1; . . .; xn, an), f2 5 (x2m, a2m; x2m11, a2m11; . . .; x0, a0). 1 2 2 In addition, π1 0 ; . . .; πn are the weights in the gain region, and π2m ; . . .; π0 are the weights in the loss region. The weights are determined based on the desirability ranking of the results. It is important to note that the weights are determined based on the desirability ranking of the results. In the cumulative prospect theory, weights are defined as follows: 1 2 2 π1 n 5 W ðAn Þ; π2m 5 W ðA2m Þ 1 1 π1 i 5 W ðAi , ? , An Þ 2 W ðAi11 , ? , An Þ; 0 # i # n 2 1; 2 2 π2 i 5 W ðA2m , ? , Ai Þ 2 W ðA2m , ? , Ai21 Þ; 1 2 m # i # 0

The decision weight’s π1 i are related to the gain region where the outcome is positive and are the difference between the nonadditive probability of an event having an outcome at least as desirable as xi and the nonadditive probability of an event having an outcome less desirable than xi. π2 The decision weights relate to negative outcomes and are the difference between the nonadditive probability of an event having an outcome at least as desirable as xi and the nonadditive probability of an

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Escaping from Bad Decisions

event having a less desirable outcome than xi. If each W is additive, then W is a probability measure, πi, and is simply the probability of Ai. 2 To simplify the representation, let us denote it as πi 5 π1 i if i $ 0 and πi 5 πi if i , 0. V ðf Þ 5

n X

πi vðxi Þ

i52m

Next, I will explain the cumulative prospect theory under risk. If the prospect f 5 (xi, Ai) is given by the probability distribution p(Ai) 5 pi, then it becomes a decision problem under risk, and the prospect can be represented as f 5 (xi, pi). In the case of this decision problem under risk, the decision weighting is as follows: 1 2 2 π1 n 5 W ðpn Þ; π2m 5 W ðp2m Þ 1 1 π1 i 5 W ðpi , ? , pn Þ 2 W ðpi11 , ? , pn Þ; 0 # i # n 2 1; 2 2 π2 i 5 W ðp2m , ? , pi Þ 2 W ðp2m , ? , pi21 Þ; 1 2 m # i # 0

However, W1 and W2 are monotonically increasing functions in the narrow sense and are standardized as W1(0) 5 W2 (0) 5 0 and W1(1) 5 W2(1) 5 1. As in cumulative prospect theory under uncertainty, if i $ 0, then πi 5 π1 i , and if i , 0, then πi 5 π2 , then i V ðf Þ 5

n X

πi vðxi Þ

i52m

18.6

Relationship between the contingent focus model and nonlinear expected utility theory and prospect theory

As explained in Chapter 17, An Experiment on, and Psyschometric Analysis of, the Contingent Focus Model, the relationship between the contingent focus model and risk attitude becomes more complicated when there are multiple prospects. The way of explanation changes depending on whether we adopt a form based on expected utility theory, a variant of expected utility theory such as Handa (1977), or even a nonlinear expected utility theory based on the Choquet integral, etc. However, the simplest way to express it would be to take the form of expected utility theory or a variant of expected utility theory such as Handa’s (1977). The Choquet integral representation of the contingent focus model is also possible, but in the following, I will try to explain the Allais paradox in its simplest form.

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First, adopting the expected utility theoretic form, the contingent focus model is consistent with the expected utility model when the relative focalization parameter w is equal to one. Allais’s paradox can be explained when the focalization parameter corresponding to the probability is not equal to one. Allais’s paradox can be explained by taking a variant of expected utility theory, such as Handa (1977), in which the expected utility (CFU) of the model can be obtained as follows: First, in Problem 1, we have CFU ðAÞ 5 F ð$1millionÞGð1:00Þ: CFU ðBÞ 5 F ð$0ÞGð0:01Þ 1 F ð$5millionÞGð0:10Þ 1 F ð$1millionÞGð0:89Þ: and for simplicity, F(x) 5 x, G(p) 5 pβ. If we assume that β . 1, then CFU(A) . CFU(B). Then, in Problem 2, we have CFU ðCÞ 5 F ð$1millionÞ Gð0:11Þ 1 F ð$0ÞGð0:89Þ; CFU ðDÞ 5 F ð$5millionÞGð0:10Þ 1 F ð$0ÞGð0:90Þ; and for simplicity, F(x) 5 x, G(p) 5 pβ. If we assume that β . 1, then CFU(D) . CFU(C). This explains the reversal of preferences shown in the Allais’s paradox. Similarly, the Choquet integral expected utility model based on nonadditive probability can also explain the Allais’s paradox, as shown earlier. Expected utility maximization by the Choquet integral satisfies the first-order stochastic dominance criterion of rationality. This property can be explained as follows. For random variables X and Y that take values in the interval [a, b], if the corresponding cumulative distribution functions are FX(x) and FY(x), respectively, then X is said to have first-order stochastic dominance over Y if FX(x) # FY(x) holds for any x∊[a, b]. Or, for the cumulative distribution function, FX is said to have first-order probability superiority over FY. Choosing an option that does not have a first-order probability advantage is considered unreasonable. The contingent focus model does not necessarily satisfy first-order stochastic dominance, which is different from the model based on the Choquet integral. The fact that the expected utility model based on the Choquet integral satisfies the first-order stochastic dominance is clear from the Choquet integral scheme in Eqs. (18.1) and (18.2). On the other hand, it is easy to understand why the contingent focus model does not satisfy the first-order stochastic dominance if we consider the following case. That is, if the series of outcomes are x1gx2g?gxn, and for simplicity, suppose G(p) 5 pα (but 1 , α) and F(x) 5 x, as assumed in the contingent focus model, then CFU 5 Gðp1 Þx1 1 Gðp2 Þx2 1 ? 1 Gðpn Þxn

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However, when the value of x1 is gradually decreased to become closer to x2, the following relation holds: G(p1 1 p2) . G(p1) 1 G(p2). Therefore, the following relation holds: CFU 5 Gðp1 1 p2 Þx2 1 ? 1 Gðpn Þxn . Gðp1 Þx2 1 Gðp2 Þx2 1 ? 1 Gðpn Þxn In this case the first-order stochastic dominance is not satisfied, whereas it is only satisfied when G(p) 5 p (Fishburn, 1978). From the standpoint of rationality, it is undesirable that the contingent focus model does not satisfy first-order stochastic dominance as per research findings at the level of description (Levy, 2008). The question of whether the contingent focus model using a variant of expected utility theory such as Handa’s (1977) is inappropriate as a descriptive model has become an open question, and there is room for further study. If the decision maker’s preferences satisfy first-order stochastic dominance in most cases, it may be better to apply a form of nonlinear expected utility theory with Choquet integrals to the contingent focus model. Next, prospect theory (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992), together with the contingent focus model, explains the framing effect, but (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992), together with the contingent focus model, explain the framing effect, but only the positive frame corresponding to the value function in the gain domain and the negative frame corresponding to the value function in the loss domain are discussed. However, in actual decision-making situations, various frames are considered to exist. However, there may be some phenomena that are difficult to categorize into either positive or negative frames. For example, judgments and decisions about which is more beautiful, which is bigger, which is more generous, etc. are difficult to classify, and it is unclear how they can be translated into prospect theory, which corresponds to models of decision frames. In addition, it has not been sufficiently clarified how the constituent concepts of decision frames function and guide decision-making. In other words, the model of decision frames deals with the mental constructs of decision problems and points out that these mental constructs have important effects on decision-making. However, it does not sufficiently mention how the decision maker psychologically constructs the situation, what the nature and function of the decision frame or psychological wallet are, and how it leads to judgment and decision-making. As is clear from the explanation of the framing effect in prospect theory, the existence of reference points occupies an extremely important position in prospect theory. Since the risk attitude on which a decision depends is the relative relationship between the outcome and the reference point, and it is no exaggeration to say that a decision depends on the reference point. This implies that it is essential to specify the location of the reference point if we aim to describe individual decisions more objectively and quantitatively based on prospect theory. However, Tversky and Kahneman (1981) only make the following qualitative observation in this regard: “The mental construct

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(frame) used by the decision maker depends on the form of the choice problem or on the norms, habits, or personal characteristics of the decision maker” (p. 453). Fischhoff (1983) tried to theoretically identify the location of the reference point from the selection results under the assumption that prospect theory is correct. However, many subjects did not succeed in identifying the location of the reference point. In addition, we found that in many subjects, the posterior reported value of the reference point did not correspond to the reference point inferred from the selection result. Furthermore, although prospect theory assumes a single reference point, it does not necessarily mean that there is only one reference point for decisionmaking. As Takemura (1998) argues, it is more than possible for a decision maker to have more than one reference point. In fact, in a protocol analysis of subjects with the Asian disease problem, it was confirmed that over 40% of the decision makers (5 out of 12) made decisions based on multiple reference points in at least one of the two decision problems (Maule, 1989). Thus although prospect theory can theoretically explain the framing effect, it is difficult to use it from the perspective of behavioral measurement for two reasons: the problem of identifying reference points (Fischhoff, 1983) and the problem of the possibility of multiple reference points (Maule, 1989; Takemura, 1998). It is difficult to use the method from the viewpoint of behavioral measurement for two reasons. The contingent focus model was proposed to theoretically explain the framing effect after rejecting the concept of reference point, which is fraught with such problems. In this model the framing effect does not necessarily appear because the reference point changes as claimed by prospect theory, but because the focus on the value and uncertainty of the outcome changes depending on the situation. In the positive frame condition, people become risk-averse because they give more relative weight to certainty than to the value of possible outcomes, and in the negative frame condition, they become risk-oriented because they give more relative weight to the value of possible outcomes than to the reduction of uncertainty. In the contingent focus model, we believe that the coordinate system of the decision maker is consistent from the standpoint of the observer, and that the focus on the attributes of the decision maker changes. However, we do not necessarily reject the position of prospect theory. However, we do not necessarily disagree with the position of prospect theory, because the perspective of the change in reference point is easily understood from the standpoint of the decision maker and is not necessarily inconsistent with the contingent focus model. As a future research topic on this issue, it is pointed out that it is necessary to theoretically clarify the relationship between the system of prospect theory, including the shift of reference point, and the system of the contingent focus model.

18.7

Conclusion and future perspectives

Although this book focuses on the framing effects of decision-making under risk, the contingent focus model can also explain other framing effects. The contingent

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focus model can also explain other framing effects, not only positive and negative framing conditions. Furthermore, the problem of psychological purse phenomenon (Kojima, 1994), which is similar to the framing effect, can be applied in principle. The contingent focus model is similar to that of Tversky, Sattath, and Slovic (1988), which explains the phenomenon of preference reversal between choice and matching tasks. This means that it will probably be possible to explain the phenomenon of deviation from descriptive universality such as the framing effect and the phenomenon of deviation from procedural universality explained by the model of Tversky et al. from a unified perspective by basically the same mathematical formulation. In addition, the phenomenon of preference reversal such as the comparative focus effect (e.g., Chiba & Takemura, 1994; Dhar & Simonson, 1992) can also be explained by the contingent focus model, and in fact, data analysis by applying the model is in progress. Future work on these problems includes extending the model to multiple attributes, analyzing various experimental and survey data, including the problem of individual differences, and examining decision-making behavior from the characteristics of the resulting parameters. As introduced in Chapter 16, The Contingent Focus Model and Bad Decisions, Gigerenzer and Goldstein (1996) also showed that “ease of attention” is an important factor in comparative judgment and extended this idea of fast and frugal heuristics to decision-making, and by developing the concept of heuristics they showed that many decision phenomena can be fully defined based on the assumption that they are chosen effortlessly with only a single attribute (Brandst¨atter, Gigerenzer, & Hertwig, 2006). Although this model is different from utility theory, it has the potential to explain situational dependence. In addition, research of Krajbich, Armel, and Rangel (2010) and Krajbich and Rangel’s (2011) on decision-making models from a neuroscientific point of view tries to explain situational dependence using the theory of stochastic processes, which has similarities with the contingent focus model. The situational dependence of decision-making suggests that the neuroscientific basis for relatively simple decisions plays a major role even in higher order decisions in the real world such as product choice. Finally, a discussion of the position of the model presented in this chapter in decision-making research is presented. Although the contingent focus model adopts a mathematical representation, it clearly differs from the traditional view of utility theory. However, if the subjective transformation function of the probability of this model is restricted to satisfy the coherence criterion (Shigemasu, 1985), it can be considered to be a subjective model like the “flexible Bayesian approach” of Shigemasu and Yokoyama (1994), which allows for the situational dependence of utility (Shigemasu & Yokoyama, 1994), which allows for situational dependence of utility. Payne, Bettman, and Johnson (1992) divided research frameworks for explaining the situation dependence of decision-making into perceptual research, as represented by Tversky and Kahneman (1981, 1986), and computational research, as represented by Payne, Bettman, and Johnson (1993). Although the model proposed in this study may rather fall within the framework of perceptual research, it can be considered to be slightly closer to computational research in that it eliminates concepts that are difficult to incorporate into computational research, such as the concept of reference points,

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from the representation system, and makes it easier to predict and evaluate the model. In this way, we can think of it as being slightly closer to computational research. In addition, the problem of situational dependence, and in particular the framing effect, is a deviation from descriptive universality, and in fact there are actually serious epistemological problems in situational focus models and other theories. Descriptive universals are strictly assumed in any mathematical scientific model, and deviations from them can lead to difficult epistemological problems. The framing effect, which is a typical phenomenon of situation-dependent decision-making, may be a common phenomenon for psychological researchers and practitioners because similar phenomena have been known for a long time, but it raises the question of “what is meaning?” Frege, G., the founder of predicate logic, said that “dawn star” has the same “meaning (Bedeutung)” as “evening star” because it refers to “Venus,” but the “significance (Sinn)” is different. In other words, the “dawn star” has a different name and a different atmosphere from the “evening star,” but since it refers to the exact same “Venus,” it can be regarded as the exact same. From the point of view of this kind of extrapolative logic, it is extremely unreasonable that preference judgments of the same thing can be changed by linguistic expressions. However, it is also psychologically true that different names have different meanings and lead to different psychological effects on choice. Thus the problem of framing effects involves philosophical issues such as what is meaning and the difference between significance and meaning. The contingent focus model discussed in this book is a heuristic model for the purpose of explaining and predicting phenomena, and its discussion leaves the issue of semantics unanswered. In the future, theoretical elucidation of the framing effect will require a theorization that resolves the problems suggested by Frege and clarifies the semantics. In this respect the fundamental problem suggested by Frege has not been sufficiently solved in the current proposal of the “contingent focus model,” and I believe that there are major problems to be overcome in the future.

References Allais, M. (1953). Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l’ecole Americaine [Rational man’s behavior in the presence of risk: Critique of the postulates and axioms of the American school]. Econometrica, 21, 503
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Chiba, T., & Takemura, K. (1994). Hikaku handan kadai ni okeru senkou no hitaishousei [Preference asymmetry in comparative judgment tasks]. Proceedings of the 35th annual meeting of the Japanese Society of Social Psychology (pp. 102
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116. Fishburn, P. C. (1978). On Handa’s “new theory of cardinal utility” and the maximisation of expected return. Journal of Political Economy, 86, 321
324. Fishburn, P. C. (1988). Nonlinear preference and utility theory. Baltimore, MD: The Johns Hopkins University Press. Gigerenzer, G., & Goldstein, D. G. (1996). Reasoning the fast and frugal way: Models of bounded rationality. Psychological Review, 103, 650
669. Gilboa, I. (2009). Theory of decision under uncertainty. Cambridge, NY: Cambridge University Press. (translated by Kawagoe, T. (2014). Decision Theory under Uncertainty. Keiso Shobo.). Handa, J. (1977). Risk, probabilities, and a new theory of cardinal utility. Journal of Political Economy, 85, 97
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Shigemasu, K. (1985). Beizu toukei nyumon [An introduction to Bayesian statistics]. Tokyo: The University of Tokyo Press, in Japanese. Shigemasu, K., & Yokoyama, A. (1994). Flexible Bayesian approach for psychological modeling of decision making. Japanese Psychological Research, 36, 20
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382. Sugeno, M., & Murofushi, T. (1993). Koza faji 3: Faji sokudo [Course fuzzy 3: Fuzzy measure]. Tokyo: Nikkan Kogyo Shimbun. Takemura, K. (1996). Ishikettei to sono shien [Decision making and decision support]. In S. Ichikawa (Ed.), Ninchi shinrigaku 4 shiko [Cognitive psychology 4: Thought] (pp. 81
105). Tokyo: University of Tokyo Press. (in Japanese). Takemura, K. (1998). Jokyo izonteki ishikettei no teiseiteki moderu: Shinteki monosashi riron niyoru setsumei [Qualitative model of contingent decision-making: An explanation of using the mental ruler theory]. Ninchi Kagaku, 5(4), 17
34. (in Japanese). Takemura, K. (2000). Vagueness in human judgment and decision making. In Z. Q. Liu, & S. Miyamoto (Eds.), Soft computing for human centered machines (pp. 249
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The mental ruler model: Qualitative and mathematical representations of contingent judgment

19.1

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Contingent judgment

Judgment can be defined as the assignment of an object to an element of a set of categories. In the usual case, it is the positioning of an object at a level within an attribute. For example, one judgment is to assign an apple to the category of being very tasty. People make judgments under a variety of circumstances in complex real-world settings (Klein, Orasanu, Calderwood, & Zsambok, 1993). For example, a consumer may make a purchase decision almost impulsively under one set of circumstances, but the same person may make a very cautious decision under another set of circumstances. Is it possible to explain these decision-making phenomena in a unified way? Utility theory is a representative theoretical system that explains decisionmaking phenomena. Utility theory uses mathematical methods and has been most frequently introduced in consumer activity research in economics. Utility theory can explain most decision-making phenomena, but it cannot fully explain contingent or situation-dependent decisions. In this chapter, we critically introduce the decision frame model (Tversky & Kahneman, 1981) and the psychological purse model (Kojima, 1959, 1994), which explain situation-dependent and contingent decision-making. The “mental ruler” model is then proposed. The mental ruler model involves the assumption that people readily create unidimensional mental rulers by subjectively constructing situations, and that decisions are made in support of mental rulers created on the basis of subjective situations. The author is not at all arguing that decision-making is always unidimensional. Rather, even though the problem is multidimensional, unidimensional decisions may be made quite often in naturalistic situations. Of course, there are cases where multidimensional judgments and decisions are made, as envisioned in various decision theories. In the mental ruler model, unlike recent utility and prospect theories, utility or value and subjective probability are not treated as different functions, but as basically the same valuation function. In addition, unlike other theories, it predicts that judgments become unstable beyond the end point of the mental ruler, and it also predicts other characteristics. The mental ruler model, therefore, explains the phenomenon of judgment in certain attributes. Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00020-X © 2021 Elsevier Inc. All rights reserved.

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In this chapter, I will first describe the phenomenon of situation-dependent judgments and decision-making and metaphorically describe the qualitative nature of the mental ruler model. Second, as a starting point for a more precise formulation of the mental ruler model, we explain the model partially using set theory, with a mathematical description of the evaluation function. Third, the results of experiments on contingent decision-making reported so far are discussed and interpreted using the mental ruler model. Finally, I will report a discussion and future perspectives on how the mental ruler model described in this chapter can be used to make irrational or bad decisions.

19.2

Contingent judgment and the problems in its modeling

19.2.1 Contingent judgment Contingent judgment, which depends on circumstances, is considered the most typical judgment phenomenon. “Contingency (situation-dependent)” can be seen very often and widely, at least as seen in the phenomena described later (Takemura, 1995). Contingencies such as (1)
(7) later are not mutually exclusive but rather can occur together. Here, contingencies are defined broadly to support the general discussion. 1. Time contingency: A phenomenon in which different mental processes are observed or different judgments or decisions are made, depending on the time at which the judgment or decision was made. In judgments and decisions, chronological changes in mental processes usually occur within a time period of a few days or shorter. In the longer term, developmental changes are present. 2. Contingency of place: A phenomenon in which different mental processes are observed, or different judgments or decisions are made, depending on where the judgment or decision is made. 3. Contingency of human relations: A phenomenon in which different mental processes are observed and different judgments and decisions are made depending on the human relations in the situation in which the judgment or decision is made. The two cases of human relations are the cases of different persons and different status of them. 4. Procedural contingency: A phenomenon in which different mental processes are observed or different judgments or decisions are made depending on the judgment or decisionmaking procedure. This phenomenon includes response mode effects, which break procedural invariance (Tversky, Slovic, & Kahneman, 1990) and produce different outcomes depending on the decision-making procedure, such as matching or choice tasks. 5. Contingency on description: A phenomenon in which different mental processes are observed or different judgments or decisions are made depending on the form of description of the information required for judgment or decision-making. This phenomenon includes framing effects that violate description invariance (Tversky & Kahneman, 1986). 6. Contingency to other external environments: A phenomenon in which different mental processes are observed or different judgments or decisions are made due to other external environmental factors when judgments or decisions are made.

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7. Contingency of internal states: A phenomenon in which different mental processes are observed or different judgments or decisions are made depending on a person’s internal state when making judgments or decisions. For example, it includes emotional states.

19.2.2 Why is it difficult to explain contingent judgment by utility theory? To address this question, let us consider the problem of “descriptive contingency” as an example. This problem was also explained in Chapter 18, The Situated Focus Model and its Relation to Other Theories. For example, suppose that a telephone with a standard price of $198 is sold at an electronics store for $148.50. Even though both descriptions convey exactly the same discount information, the difference of psychological impact exists between the point-of-purchase (POP) and that says “$49.50 off the standard price” and the one that says “25% off the standard price. In fact, Kojima (1986) argues that the effect of POP advertising can be different depending on whether it is written as “$49.50 off the standard price” or “25% off the standard price. In fact, the author reported that products that consumers consider to be top-level brands sell better when the discount rate is displayed rather than the discount amount. On the other hand, for second-tier and lower tier brands, they found that products sold better when the discount amount was displayed rather than the discount rate. Such phenomena reflect the fact that mathematically identical decision problems lead to psychologically different decisions, which cannot be explained by utility theory because it implicitly assumes the uniqueness of mathematical statements. Many utility theories and mathematical models generalize explanations by ignoring differences in descriptive forms (Takemura, 1994, 2014). Besides such framing effects, it is difficult to explain contingent judgments and decisions with a system of utility theory. For example, time contingency also shows that judgments and decision-making phenomena are quite different between points in time, but ordinary utility theories do not assume that preferences are reversed between points in time and cannot rationally explain the phenomenon of preference reversal between points in time. Some theories attempt to explain the contingency of decision-making within the framework of utility theory (Fishburn, 1988; Takemura, 1994; Tversky & Kahneman, 1992; Tversky & Simonson, 1993; Tversky, Sattath, & Slovic, 1988). These models can explain only a part of contingent decision-making (e.g., preference reversal between selection and matching, framing effects under risk, and contextual effects of alternative positioning), and currently no theory can explain decision contingency in a unified way. To resolve this question, we consider a problem of “contingency on description” as an example. In fact, Kojima (1986) reported that if an article is considered a toplevel brand by consumers, it sells better when the discount percentage is indicated than the discount amount is indicated. In contrast, if an article is considered a second-level or lower level brand, it sells more when the discount amount is indicated than when the discount percentage is indicated.

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Phenomena of this kind reflect that a mathematically identical decision problem might elicit different decisions psychologically, which cannot be explained by utility theory because it tacitly assumes mathematical descriptive uniqueness. Most utility theory and mathematical models disregard differences in descriptive forms to generalize explanations (Takemura, 1994, 1996). Recently, new models have been produced to try to explain contingency of decision-making under the framework of utility theory (Fishburn, 1988; Takemura, 1994; Tversky & Kahneman, 1992; Tversky & Simonson, 1993; Tversky et al., 1988). These models can explain only part of the contingent decision-making (e.g., preference reversal of choice and matching, framing effect under risk, context effect by alternative positioning), but no theory exists now that can explain the contingency of decision-making from a unified perspective.

19.2.3 Existing models explaining contingency of judgment Let us next consider how to address contingent judgment, which is difficult to systematize mathematically. A possible approach is the capture of complicated judgmental phenomena by describing a contingency of the judgment either qualitatively or metaphorically. Approaches of this kind are sometimes effective in marketing, etc. because they help to conceptualize an ongoing problem. The decision frame model, psychological purse model, and range
frequency model are the representative methods of the approach.

19.2.3.1 Decision frame model Tversky and Kahneman (1981) proposed the concept as a psychological framework to recognize decision-making problems. They demonstrated that the decisionmaking process includes an editing stage to recognize the problem and an evaluation stage to evaluate the alternatives according to recognition of the problem. They also showed that a different decision can be made for the same problem depending on how the decision frame is produced in the former stage. Although they gave little explanation of the nature or the function of the decision frame, they explained contingency using an intuitively easily understandable word, “frame,” and proved by experimentation that consumers make a different choice on a purchase if they are given a different frame.

19.2.3.2 Psychological purse model More than 20 years before, research done by Tversky and Kahneman (1981), Kojima (1959) indicated that consumers are affected strongly by the contingent recognition of a problem when they decide on a purchase or regarding the satisfaction after the purchase. They elucidated the contingent recognition of a problem by a constructive concept called the “psychological purse.” According to this model, consumers act as if they have plural and different purses and pay from different psychological purses according to the variety of the article, the kind of service, or

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the situation in which they purchase it. Even if they pay the same amount for the same article, if the purse they pay from is different, then they feel a different degree of satisfaction or mental pain pertaining to the expense (Kojima, 1959, 1994). Kojima, Akamatsu, & Hama, 1983 conducted factor analytical research based on questionnaires and clarified the psychological purses from which money is taken to buy various merchandise.

19.2.3.3 Rage
frequency model Range
frequency theory (Parducci, 1965, 1995) explains the contextual effects in judgments. It states that the actual judgment reflects a compromise between these two principles. Mathematically, the subjective judgment Sik of stimulus i in context k can be thought of as a compromise between the two principles of range R and frequency F, with the weighting parameter w being a value between 0 and 1. Sik 5 wRik 1 ð1 2 wÞFik There is a range principle that states that equal segments of a judgment scale are assigned to equal segments of the contextual range. Thus the range of a stimulus corresponds to a continuous categorical evaluation, which is a subrange of equal intervals. It is also important to remember that the judgment of any given stimulus is determined according to the two end points of the contextual range. The principle of frequency describes the effect of changing the distribution of contextual values. This theory explains the contextual effects of judgments. A study that applies range
frequency theory to the problem of judgment and decision-making can be considered to be the model of decision by sampling (Bhui & Gershman, 2018; Stewart, Chater, & Brown, 2006).

19.2.4 Problems of the previous contingent judgment models In the frame model, only the positive frame corresponding to the value function in the gain domain and the negative frame corresponding to the value function in the loss domain of prospect theory (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992) were discussed. However, in actual decision-making situations, more types of frames are likely to be present. While it is easy to understand that there are two broad categories of positive and negative frames, there must be some phenomena that cannot be classified into either frame. For example, judgments and decisions such as “which is more beautiful?,” “which is bigger?,” and “which is more generous?” cannot easily be classified. It is not clear whether they can be interpreted in prospect theory corresponding to decision frames; as in the work of Hsee (1998) in Section 19.5.2, judgments about “how generous a person is” cannot be explained only in terms of positive and negative frames. The psychological purse model is to be highly praised because it proves what kind of psychological purse exists through factor analytic studies and other

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methods. However, when strictly evaluated, this model is only at the stage of situational classification. Also, the psychological purse model is naturally a model of consumer buying behavior, and while it may be applicable to corporate and accounting activities other than buying behavior, it cannot explain people’s other everyday decision-making problems. In addition, neither the decision frame model nor the psychological purse model fully illustrates how structural concepts work and how decisions are elicited. Both the models deal with the internal structure of the decision problem and show that the internal structure has a strong influence on decision-making, but they do not fully explain how the decision maker psychologically constructs the situation, what the nature and function of the decision frame and psychological purse are, and how judgments and decisions are drawn from them. The range
frequency model quantitatively explains the situational dependence of judgment. It also explains the process of judgment generation, assuming that judgments are determined by a compromise between the range and the frequency principles. However, the author explains contingent judgments by focusing attention, as postulated in the contingent focus model, rather than that they are determined by the range and the frequency principles.

19.3

Qualitative description of “mental ruler”

19.3.1 Basic hypothesis of the model and basic property of mental ruler Here I present the “mental ruler” model to solve the aforementioned problems and to develop basic ideas of a decision frame model (Tversky & Kahneman, 1981) and psychological purse model (Kojima, 1959, 1994). The basic hypothesis of this model postulates that people make judgment as if they have a ruler. In everyday life, it is often said metaphorically that every person uses a ruler with a different value to make judgments. Although a metaphor of this kind is valid only in our daily conversations, if we consider this metaphor thoroughly and scientifically, it is more useful than we might think to explain contingent decision-making. Objects of the mental ruler can be divided into gain and loss areas just as the decision frame model, but phenomena that cannot be classified into gain and loss areas can be included, such as the judgment on personal impressions such as those related to generosity or calmness, or a judgment related to probability. Let us first consider the basic meaning of “ruler.” A ruler is used to measure “length.” The reason why people use a ruler is, of course, that merely looking at an object is not good in judgment on length because it causes unevenness or distortion. Psychologically, people cannot judge with confidence without using a ruler. We use a ruler as a standard for judgment. A physical ruler enables us to judge length with certainty and relief. What do we do if we have no physical ruler? I assume that people construct a ruler internally in their mind in a sense for such a situation. This can be regarded as a creative process in recognition of decision-making problem.

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Then consider characteristics of the mental ruler further and capture and discuss the characteristics of decision-making metaphorically.

19.3.1.1 Basic property 1: the ruler has graduation The author assumes that people make a decision based on the graduation of the mental ruler, which can be fine or rough, just as units of millimeter or centimeter on the graduation of a physical ruler. For example, let us consider a judgment of price. With fine graduation, consumers must be sensitive to a difference by even 1 cent. On the contrary, with rough graduation, they can be insensitive to a difference by several units of $100. Such a difference of sensibility about prices can be described using the fineness or roughness of the graduation of the mental ruler. As described later, we can imagine the roughness of the graduation of the ruler which might change for the same person depending on the situation.

19.3.1.2 Basic property 2: the ruler length is bounded (boundedness) This property seems quite basic, but the metaphor denotes a great deal. For example, for judgment related to price, we cannot easily judge if the price of an object exceeds the length of the mental ruler greatly in both directions, that is, when the price is extremely high or extremely low. Consumers might joint several rulers when the ruler is too short, but the elicited judgment probably varies widely.

19.3.1.3 Basic property 3: the ruler is one-dimensional A physical ruler measures a one-dimensional property called length. Even though people make a judgment founded on multidimensional information, it is quite possible that they finalize the judgment one dimensionally. In Japan, many people think that education based on the standardized value of test scores is not good, but simultaneously they tend to be concerned about the standardized value of test scores very much. People like to check rankings of various kinds, such as a “best seller” ranking at a shop. These tendencies seem to indicate an important facet of human nature: one-dimensional judgment.

19.3.2 Basic function of mental ruler Based on the basic properties of the mental ruler described earlier, some theoretical predictions about its basic functions are presented next.

19.3.2.1 Basic function 1: people construct an appropriate mental ruler depending on the situation People construct a mental ruler with appropriate graduation and of appropriate size, depending on the situation. People do this so naturally that they usually do not perceive it themselves. This phenomenon, however, can often be perceived if we

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compare purchasing situations. For example, in Japan, if a person thinks of purchasing a new car, a consumer constructs a mental ruler with graduation of 10,000-yen (approximately 120 yen/$) unit when negotiating with a car dealer about the price or optional equipment because a brand-new car very often costs more than 1 million yen. In such a situation a price differential of several 100 yen is treated as an error and is seldom examined. The same consumer, however, goes to a supermarket after the car dealer and can be satisfied with the price of a package of 10 eggs that is lower than usual by 20 yen or be disappointed by a price that is higher than usual by 30 yen and might not buy the eggs. A person is concerned about a price of 10-yen units to make a judgment or a decision in this situation. Similarly, we can presume that people specifically examine the ongoing situation and construct the situation subjectively and construct a mental ruler upon the situation.

19.3.2.2 Basic function 2: reference points or end points of the ruler are applied differently depending on the situation For example, in judging on price, a reference point changes according to the object group that is compared. Either a price that is lower than that at another shop or than a prior price makes the reference point of the ruler move to a different position; a judgment of the price or the decision on the purchase might be changed. The ruler end points are also assumed to change according to the situation such as a comparison of groups of objects.

19.3.2.3 Basic function 3: graduation of the ruler becomes particularly finer around the reference point and the end points (nonlinearity of the ruler) This property does not apply to a physical ruler. For instance, a consumer who is trying to buy an article for the budget of $100 becomes more sensitive to the difference between $95 and $100 than that between $50 and $55. It becomes extremely difficult to evaluate if the comparing prices exceed the end points. For instance, if the budget is $100, the consumer becomes insensitive to the difference between $150 and $155, and the evaluation becomes unstable.

19.3.2.4 Basic function 4: more knowledge or more involvement creates finer graduation of the ruler If a consumer has much knowledge related to an article or if a consumer is involved in an article very much, the graduation of the ruler becomes finer, then the consumer becomes sensitive to small differences, which engenders the classification of similar articles very precisely. Therefore it happens that the consumer tends to buy the article at a higher price if and only if its quality is only a little better than that of the others.

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19.3.2.5 Basic function 5: even if information is given multidimensionally, a one-dimensional judgment is elicited using the mental ruler Decision makers might construct another ruler to cope with the information overload in the recognition of decision-making problem. For instance, by reading fashion magazines or through repeated shopping experiences, consumers construct a ruler such as “good taste” based on the complicated information about clothes to make a purchase decision. The mental ruler in this case is also fundamentally onedimensional.

19.3.2.6 Basic function 6: it is difficult to compare different mental rulers It is presumably difficult for consumers to compare and evaluate various mental rulers themselves they have constructed mentally, depending on the situation. Such contradictory judgments or decisions among situations such as examples of a car purchase and an egg purchase cannot be perceived by the consumers themselves, which is true because people usually specifically examine the situation, construct the situation subjectively, and construct a mental ruler on the situation. It, therefore, becomes difficult to construct more than two rulers for one situation from the cognitive load perspective. People sometimes use a different ruler for the same value from an economic rationality perspective or use the same ruler for situations in which they should use different rulers.

19.3.3 Compatibility of stimulus-response structures as a mental ruler construction principle Finally, I discuss the mental ruler construction principle. I presume that the compatibility of stimulus
response structures plays an important role in constructing the mental ruler. The compatibility of stimulus
response structures denotes compatibility between structural characteristics of the input mode and response mode (Selart, 1997). The efficiency of the information process in a judgment or a decision increases if they match or correspond well. I assume that a consumer constructs a mental ruler as an input mode corresponding to a given response mode. For instance, the purchase choice situation “to buy or not to buy” has a two-valued response mode; the consumer constructs a two-valued mental ruler, “good or bad.” On the other hand, if a consumer is asked to evaluate an article by ranking or by points, the consumer constructs a mental ruler of multiple values. A consumer has difficulty in judgment if the stimulus
response structure does not correspond well. For instance, if a mental ruler has already been constructed, then a consumer cannot judge precisely if the ruler only has rough graduation, and vice versa.

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From this compatibility of a stimulus
response structure perspective, too, the reason why the mental ruler is one-dimensional might be explained. The environment’s structure requires a one-dimensional response mode of the judgment or the decision. Therefore the mental ruler becomes one-dimensional. In addition, one can also assume that we often use linguistic terms of dual values such as “good or not good” to evaluate merchandise and so forth, which is true because judgments are constructed in dual-value response modes such as “to buy or not to buy.”

19.4

Mental ruler explanation using set theory and its mathematical description

For simplification an explanation is presented here by set theory for the mental ruler and its partial mathematical description. Later, I elucidate the qualitative and metaphorical description I indicated before by adding the structure. Therefore it is not the perfectly retrieved qualitative and metaphorical description. Nevertheless, to create a psychometric model or to conduct various quantitative experiments, we will need to undertake formulation to some degree. To that end the following is attempted.

19.4.1 Definition of the situation Let X0 denote the whole situation to be discussed. Actually, X0 is generally regarded as a finite set. Let S0 (S0 CX0 ), which is a subset of X0 , denote the focused situation. For instance, presume that X0 denotes the purchasing situation in a supermarket, and that S can be a situation in which one must decide whether to buy some cola or not, or whether to buy a set of five notebooks or not, etc. The problem here is the focused situation that is determined cognitively by the decision maker. In fact, although it is more natural to presume that a situation S0 denotes a subset of X0 for the Cartesian product (S0 CX0 3 X0 3 ? 3 X0 ) because situations are often a set of relation in a situation, presume a state S a subset of X0 for simplicity. An important point here is that S0 is subject to how the decision maker pays attention: S0 will have different elements if the same person specifically examines another side of the same situation, according to one’s mood. Nevertheless, the hypothesis here is that S0 is a commonly subjective situation that can be recognized by other people, too. S0 is a set of events that exist over an individual’s subject and can be denoted extensively. For example, whether an article of $10 sells for $2 off or for 20% off is the same situation, as long as the meaning of the event is stated denotatively.

19.4.2 Definition of subjective situation Next, we discuss the subjective situation. Let the limited set X denote the whole subjective situation, whereas S represents the subjective situation surrounding the decision maker. Therefore X0 , the set of the whole situation, corresponds to X, and S0 , the subjective situation, corresponds to S. One element in a situation, however,

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can have more than two elements in a subjective situation because the compatibility of X0 and X, and S0 and S are a many-to-one mapping (univalent correspondence) from the subjective to the objective situations. For instance, although both descriptions-“$2 off” and “20% off” for an article of $10 represent the same choice as long as they denote an event extensionally, they can be different elements in a subjective situation. Furthermore, even in the same situation S’, there are multiple subjective situations S1, S2, . . ., Sn which differ depending on how they are mentally constructed. Therefore, the mapping f to the situation S’ is considered to vary depending on the mental configuration of the decision problem, and can exist like f1, f2, . . ., fn. The set of these functions F ( f1, f2, . . ., fnAF) is considered to be constrained according to the cognitive ability of human beings (e.g., Holyoak & Thagard, 1995). Finally, the mapping from the subjective to the objective situation, f, is not onto mapping generally. Therefore elements of the subjective situation do not necessarily cover the elements of a situation but can be omitted partially, which can be considered because of the cognitive constraints of the decision maker’s attention, memory capacity, or searching ability. I presume that the mapping has the direction to promote the stimulus
response compatibility stated earlier, or to create the dominance structure (Montgomery, 1983, 1993) in a decision-making problem.

19.4.3 Structure of mental ruler I hereby define the mental ruler. This ruler approximately differs with positive and negative areas, just like the value function in the prospect theory. The greater number, the better it is in one case and the worse it is in another. Nevertheless, as stated earlier, the objects of the mental ruler model also include rather neutral ones such as probability judgment, not only the gain and loss areas. For simplification, however, this matter is only discussed in the positive area. Moreover, the author first discusses the mental ruler model for a case in which the evaluation object as an element of subjective situation S can be described objectively using an additive measurement such as price, length, or size. Then I describe the mental ruler as a set function from the subsets of the subjective situation S to one-dimensional real number space R. First consider a case in which an element x is of the subjective situation; S can be described objectively as an additive function to price, length, proportion, probability, and so forth, as m(x)AR. Consider a function m from S to one-dimensional real number space R, m: S!R. For instance, let m(x) denote the discount rate m for an article x. Moreover, consider the mental ruler using the function v from onedimensional real number space R, which is mapped by m, to one-dimensional real number space R, which describes the evaluation value v: R!R. Here, v has the following property. m ð x Þ 5 0 ! v ð mð x Þ Þ 5 0

(19.1)

x 5 arg max mðxÞ ! vðmðx ÞÞ 5 k;

(19.2)

xAS

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where k is a positive constant. mðxÞ $ mðyÞ ! vðmðxÞÞ $ vðmðyÞÞ

(19.3)

Eqs. (19.1) and (19.2) denote the boundedness of the mental ruler. For example, the evaluation for the relative income of $0 is 0, where the evaluation for the evaluation object that has the most value in the subjective situation is a real number k. Here, x  denotes x which maximizes m(x). For instance, when the upper limit of a relative income is considered to be $10,000, the alternative which gives the $10,000 is x  . Alternatively, considering the evaluation for a price using the mental ruler, if the upper limit of the budget is $100, then the article equivalent to the $100 is equivalent to x  . Eq. (19.3) describes the monotonicity of the mental ruler. It suggests that evaluation using the mental ruler does not exceed k in the subjective situation S. Moreover, if the mental ruler is unique with regard to the positively proportional transformation (the similarity transformation), by an adequate scale transformation, then v ðmðx ÞÞ 5 1;

(19.4)

where x 5 arg max mðxÞ: xAS

As stated earlier, x denotes x which maximizes m(x), where x always denotes the same quantity in the following discussion. Additionally, for simplification, the evaluation function of the mental ruler is presumed to hold always for Eq. (19.4) in the discussion later.

19.4.4 Subadditivity of the mental ruler and its mathematical description Although the mental ruler has monotonicity of Eq. (19.3), it has no additivity such as the following: vðmðxÞ 1 mðyÞÞ 5 vðmðxÞÞ 1 vðmðyÞÞ

(19.5)

The mental ruler is considered to hold the subadditivity of following two kinds (Tversky & Fox, 1995; Tversky & Wakker, 1995): 1. Lower subadditivity vðmðxÞÞ $ vðmðxÞ 1 mðyÞÞ 2 vðmðyÞÞ;

(19.6)

where mðxÞ 1 mðyÞ $ 1 2 ε; ε $ 0: Eq. (19.6) describes that the evaluation function becomes concave downward when m (x) is low. This property is the same as that of the weighting function for lower probability in the prospect theory; it is also the same as that of diminishing marginal utility in the utility theory.

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2. Upper subadditivity vðmðxÞÞ 2 vðmðxÞ 2 mðxÞÞ $ vðmðxÞ 1 mðyÞÞ 2 vðmðyÞÞ;

(19.7)

where mðxÞ $ ε0 ; ε0 $ 0.

This property denotes an event for which the evaluation function of the mental ruler becomes convex downward when m(x) is high. This is the same as the property of the certainty effect indicating that the weighting of probability 1 is much greater than the probability less than 1, as explained using the prospect theory. The mental ruler model, however, forecasts that this property holds not only with the weighting probability but also with the values of the outcomes. This forecast is completely contrary to the property of the diminishing marginal utility in the utility theory or in the prospect theory. In the utility or the prospect theory, a function that is concave downward is always assumed, although the mental ruler model includes the assumption that a function exists that is convex downward around the upper bound. For example, when negotiating on a discount for the price, the sensibility rises around the target. Let m(x ) denote the targeted gain for the negotiation, and the function becomes convex downward around the targeted price, although it becomes concave downward around the zero gain, where m(x) 5 0. The function which holds the property of Eqs. (19.6) and (19.7) is an S-shaped function. An S-shaped mathematical description that has such a property is  γ   m ðxÞ vðmðxÞÞ 5 exp 2 2loge : (19.8) mðxÞ Prelec (1995) originally used this function as a weighting function for probability. Here, m(x)/m(x ) takes interval [0, 1]; its price interval is also [0, 1]. Then the fixed point becomes 1/e A0.36 irrespective of the value of γ (Wu & Gonzalez, 1996). Another such function that is consitent with the properties of the mental rular model is:
γ mðxÞ=mðxÞ vðmðxÞÞ 5

(19.9) γ
γ λ mðxÞ=mðxÞ 1 12mðxÞ=mðxÞ Here, if λ 5 1, it is the same as probability weighting function of Karmakar (1978), if λ 5 1/γ, it is the same as the probability weighting function of Tversky and Kahneman (1992). Wu and Gonzalez (1996) conducted a psychological experiment to investigate the weighting function to probability, applied functions of many kinds, and proved that the function by Tversky and Kahneman (1992) showed high applicability, as did the function of Prelec (1995). They also proved that although the weighting function is concave downward around the probability 0.40, it becomes convex downward if it exceeds about 0.40. Although the weighting function they obtained is expressed only against the probability, it can be assumed that

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the expertise of the same kind is obtainable for the value such as money, from the mental ruler perspective. Additionally, it is already proved that the evaluation function of the number of surviving lives is S-shaped, as shown in the evaluation experiment later. Moreover, the following function has been proposed neither in the research on the existing probability weighting function nor in the research on the prospect theory but is now being proposed in Takemura (1998) and is assumed to be an evaluation function which satisfies upper and lower subadditivity.  vðmðxÞÞ 5 w1

mðxÞ mðxÞ

α



1 w2

m ðxÞ 1 2 12 mðxÞ

β ! ;

(19.10)

where w1 $ 0; w2 $ 0; w1 1 w2 5 1 In this evaluation function, let w1 denote the strength in relative focus against the upper bound (strength of attention), w2 the strength in relative focus against the upper bound, α and β index of power function against the upper and the upper bound, respectively. This evaluation function is assumed to be applicable not only to the weighting function to probability, but also to psychophysical and perceptual judgment such as length or size, or economic values such as money.

19.4.5 Threshold as graduation of the mental ruler The author showed in Section 19.3 that the mental ruler has graduation. The description as a measure satisfying the monotonicity and subadditivity earlier, however, is insufficient in describing the concept of the graduation appropriately. Therefore the threshold is assumed to exist when a judgment or a decision is made using the mental ruler; it becomes higher or lower according to the subjective situation. For instance, if a shopper is devoting attention to the $100 unit, then compared to when one is devoting attention to the 1-cent unit, the threshold is assumed to be high. Alternatively, the threshold is assumed to differ with the situations when a Japanese person is shopping using yen in Japan, using dollars in the United States, or using yuan in China, even though these units can be exchanged proportionally. The threshold is also assumed to be low around the end points of the ruler, and high around the middle of the ruler. Preference becomes indifferent within the threshold. The indifference can be denoted as binary relation I on S when a strict preference relation R on set S (i.e., a relation that can indicate which is preferred) is assumed. For any x, yAS, if x and y are indifferent. We can define the indifference relation xIy such that: xIy2:½xRy4:½yRx:

(19.11)

Consequently, in a judgment or in a decision-making, there must be a relation when which is preferred cannot be described. Therefore when preference relation R in

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a set S is considered, a real-valued function where indifference occurs related to a certain difference and which has a threshold can be assumed as follows. For all x, yAS, xRy2vðxÞ . vðyÞ 1 δðx; yÞ

(19.12)

where v is assumed to be an evaluation function of the mental ruler, and δ a positive value function of the threshold, which is subject to the objects x and y. Additionally, both v and δ are assumed to be dependent on the subjective situation S. For simplification, presume that the threshold is constant in the situation S, then Eq. (19.12) becomes as follows. For all x, yAS, xRy2vðxÞ . vðyÞ 1 δ

(19.13)

where δ is a positive constant. The necessary and sufficient condition for Eq. (19.13) is, according to the theorem by Scott and Suppes (1958), that the preference structure (S, R) is the semiorder if and only if following three properties hold. That is, for all w, x, y, and z, ð1Þ :½xRx holds; ð2Þ wRx and yRz ! ½yRz or yRz; ð3Þ wRx and xRy ! ½wRz or zRy:

(19.14)

Eq. (19.14) is the necessary and sufficient condition for Eq. (19.13). Therefore assume that the threshold is constant in the subjective situation, then the preference structure is to be semiorder, and vice versa. Then, how does this threshold correspond to the graduation of the mental ruler? Here large δ means the rough graduation of the ruler, and the small δ means the fine graduation. Actually, δ is, therefore, a function of the subjective situation S, which becomes small when the knowledge or the involvement level is higher.

19.4.6 Restructure of the subjective situation and the mental ruler I have explained that the mental ruler takes the value within the limited interval [0, k] or [0, 1] as a function of additive measure m(x) of the element x in subjective situation S. In natural decision-making situations, however, the subjective situation changes at every moment. The actual problem in complex real-world settings is that the subjective situation becomes larger. Many situations exist in which one must extend the subjective situation in the past. For instance, such a situation when a person who seldom goes shopping must go to buy daily goods for the week for the family because of a sudden illness of one’s spouse, when one is going to purchase a car or real estate for one’s first time, or when an inexperienced teacher must evaluate candidate students for admission. How do people construct the mental ruler in these cases? In utility theory, the nonlinear utility theory, or the prospect theory in the past, the evaluation function

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was denoted on the universal set. Therefore it was assumed that the evaluation function is already made up. In the mental ruler model, however, it is assumed that people cannot use the mental ruler appropriately in a new situation. For instance, let T (T*S) denote a larger set that includes a set S. In constructing the mental ruler in this situation, the judgment is considered difficult to make. The evaluation function of the mental ruler might have an error term (or a disturbance term) in such area, or the value of the disturbance term in the past is assumed to become much greater. A phenomenon of this kind is considered to hold even in such cases as the evaluation function is described by Eqs. (19.8)
(19.10). For example, Eq. (19.10) becomes Eqs. (19.15)
(19.17), according to the area of the value of m(x). If m ðxAT Þ A ½0; mðx Þ;
α

β then v ðmðxÞÞ 5 w1 mðxÞ=mðx Þ 1 w2 12 12mðxÞ=mðx Þ 1 eðmðxÞÞ; (19.15) where w1 $ 0, w2 $ 0, w1 1 w2 5 1, e(m(x))AR, ε $ e(m(x)) $ 0, and ε is a positive constant. If m ðxAT Þ 2 = ½0; mðx Þ; and also mðxÞ $ 0; then v ðmðxÞÞ 5 1 1 e ðmðxÞÞ;

(19.16)

where e(m(x))AR, δ $ e(m(x)) . ε, and ε is a positive constant. If m ðxAT Þ 2 = ½0; mðx Þ; and also mðxÞ , 0; then v ðmðxÞÞ 5 2 e ð 2 mðxÞÞ;

(19.17)

where e(m(x))AR, ζ , e(m(x)) # η, and ζ and η are positive constants. Although a concrete representation of the function e(m(x)) indicates that the disturbance term is unknown, its dispersion changes according to the value of m(x), it is a probabilistic variable average value of which is a monotonic increasing function of m(x). The dispersion of e(m(x)) is thought to become greater rapidly outside the interval [0, m(x )]. Moreover, threshold δ is considered to become rapidly greater outside the interval [0, m(x )] in the case of preference declaration. Therefore the graduation of the ruler becomes rougher. We next consider how the mental ruler would be when a set of the subjective situations such as T, which does not include S, is constructed. It is almost impossible to construct a stable mental ruler if a set of the subjective situations and the existing set S are both independent and have no common property. If they have a common or a similar property, the existing subjective situation can be corresponded through an inference involved by analogy (e.g., Holyoak & Thagard, 1995), and the mental ruler is constructed on the set of the situations. In this case the attribute not corresponding to the one in the existing subjective situation is disregarded. In addition, when the compatibility by analogy is insufficient, the disturbance term of the evaluation function becomes greater, and the threshold becomes high.

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19.4.7 Mental ruler as a set function The mental ruler is now discussed as a set function, as expanding the idea in the past considering the mental ruler using the evaluation function (v:R!R) against the additive function m(x)AR of element x in the subjective situation S. Presuming that the evaluation function V of the mental ruler is a set function from the set of all subsets in the subjective situation S, 2s, to a one-dimensional real number space R, (V:2s!R), then V has the following properties: V ðϕÞ 5 0

(19.18)

V ðSÞ 5 K;

(19.19)

where K is a positive constant S+A; S+B; A+B ! V ðAÞ $ V ðBÞ

(19.20)

Eqs. (19.18) and (19.19) indicate the boundedness of the mental ruler as a set function. Eq. (19.20) shows the monotony of the mental ruler. For example, let S denote a set of patients in a certain area who need medical care ({x1, x2, . . ., xnAS}), let A ({x1, x2, . . ., xmAA}, where m , n) and B ({x1, x2, . . ., xmAB}where 1 , m) denote a set of patients in S whose lives will be saved by a certain remedy. The desirability here has monotonicity of V which is indicated in Eq. (19.20). Here, V(φ) 5 0 means that nobody is saved; V(S) 5 K means that all the patients are saved. An appropriate scale transformation elicits Eq. (19.21) if the mental ruler is unique with regard to the similarity transformation. V ð SÞ 5 1

(19.21)

The mental ruler as a set function here is mathematically the same as the fuzzy measure in fuzzy theory, the capacity in the integral theory, or the nonadditive probability in nonlinear utility theory, but it differs from them in its interpretation. The fuzzy measure, the capacity, and the nonadditive probability are generally interpreted as a weighting function to the subjective index for uncertainty or risk, whereas the mental ruler can be interpreted not only as a subjective index for uncertainty or risk, but also as the evaluation function of judgment or decision. The subjective situation is constructed optionally. Even if the situation S0 is the same, there can be events for which the subjective situation S1 is included in S2 and S1 is smaller than the S2. In these events, according to Eqs. (19.18)
(19.21), the values of the mental ruler for the subset A are described as Eq. (19.22). Here, V1 against S1 becomes equal to or greater than V2 against S2. ADS1 DS2 ! V1ðAÞ $ V2 ðAÞ

(19.22)

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This formulation reflects that taking the broader comparison area in decisionmaking reduces the relative value of the object and lowers the evaluation. For example, let (A) denote a set of articles for which a $5
$6 discount is possible, (S2) a set of articles that can be purchased at less than $500, and (S1) a set of articles that can be purchased at less than $50. When one evaluates (A), the value of the mental ruler for (S1) is assumed to be higher than the value for (S2). Although the mental ruler has the monotonicity indicated by Eq. (19.20), generally it has no additivity, as in the next formula: A - B 5 φ ! V ðA , BÞ 5 V ðAÞ 1 V ðBÞ:

(19.23)

The mental ruler V is, as well as the mental ruler v, assumed to have the subadditivities of the following two kinds (Tversky & Fox, 1995; Tversky & Wakker, 1995): Lower Subadditivity V ðAÞ $ V ðA , BÞ 2 V ðBÞ;

(19.24)

where A and B are independent and V (A , B) takes a lower value than around the upper bound value (K－ε, ε $ 0). This property indicates that the impact of a set A against the null set is bigger than the impact of a set A against a set B. For example, let S denote a set of patients in a certain area who need medical care ({x1, x2, . . ., xnAS}), let A ({x1, x2, . . ., xjAA}, where j , n) and B ({x1, . . ., xk, . . ., xpAB} where j , k , p , n) denote a set of patients in S whose lives will be saved by a certain remedy. The evaluation of the desirability here is assumed to be in the following relation by the lower subadditivity of V indicated in Eq. (19.24): V(A) $ V(A , B) 2 V(B). More concretely, for example, the lower subadditivity is satisfied by the event when there are 100 patients ({x1, . . ., x100}) and the impact that the number of lives to be saved becomes 1 ({x1}) from none (ϕ) is bigger than the impact that the number becomes 51 ({x1, . . .x51}) from 50 ({x2, . . .x51}). Upper Subadditivity V ðSÞ 2 V ðS 2 AÞ $ V ðA , BÞ 2 V ðBÞ;

(19.25)

where A and B are independent and V (B) takes higher value than around the upper bound value (ε0 , ε0 ^ 0). This property indicates that the impact when a set A is taken away from the set of the subjective situation, S, is bigger than the impact when a set A is taken away from its subset A , B. The uncertainty effect explained using the prospect theory, that the impact of certain event is much greater than the impact of uncertain event, has the same property. The mental ruler model, however, presumes that the same property holds not only on the probability weight, but on the values of the outcomes. This presumption means the complete contrary to the property of the diminishing the marginal utility n in the utility theory or the prospect theory, just as in the case of property v of the mental ruler. For instance, let S denote a set of patients in a certain area who need medical care ({x1, x2, xnAS}), let A ({x1, x2, . . ., xjAA},

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where j , n) and B ({xk, . . ., xpAB}where j , k , p , n) denote a set of patients in S whose lives will be saved by a certain remedy. The evaluation of the desirability here is assumed to be in the following relation by the upper subadditivity of V indicated in Eq. (19.25): V(S) 2 V(S 2 A) $ V(A , B) 2 V(B). More concretely, for example, the upper subadditivity is satisfied by the event when there are 100 patients ({x1, . . ., x100}) and the impact that the number of lives to be saved becomes 100 ({x1, . . ., x100}) from 99 ({x2, . . ., x100}) is bigger than the impact that the number becomes 51 ({x1, . . ., x51}) from 50 ({x2, . . ., x51}).

19.5

Explanation of experimental findings

Later, some experimental outcomes that were reached in the past are qualitatively explained using the mental ruler model just proposed.

19.5.1 Interpretation of experimental results by Tversky and Kahneman An experiment conducted by Tversky and Kahneman (1981) about purchase decision-making using the mental ruler confirmed that the decision frame changes the decision [Eq. (9.10)]. They separated 181 college students into two groups. Then two versions of questions were presented to the different groups. Version 1: Imagine that you are about to purchase a jacket for $125 and a calculator for $15. The calculator salesperson informs you that the calculator you wish to buy is on sale for $10 at the other branch of the store, located 20-minutes drive away. Would you make the trip to the other store? Version 2: Imagine that you are about to purchase a jacket for $15, and a calculator for $125. The calculator salesperson informs you that the calculator you wish to buy is on sale for $120 at the other branch of the store, located 20-minutes drive away. Would you make the trip to the other store?

The outcome was that 68% of the respondents were willing to make an extra trip to save $5 on a $15 calculator; only 29% were willing to exert the same effort when the price of the calculator was $125. This is contradictory to the utility theory because both versions presented the same choice between a total amount of $140 for a jacket and a calculator in a nearby shop and $135 for the same articles in a distant shop. Regarding the total amount, both versions are expected to be chosen indifferently. This experimental outcome is contradictory to the utility theory under the hypothesis that the choice rate is a monotonic increasing function of the utility. Tversky and Kahneman (1981) interpreted this outcome using their decision frame concept that the subjects used different decision frames for each item, not for the total amount. Their interpretation seems to be fundamentally correct, but they did not explicate why the different frames for the two articles had occurred.

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The mental ruler model is used to interpret the process of obtaining this outcome. First, the situation of this problem can be presented as follows: Version 1: S0 1 5 {($125 jacket, $15 calculator, no extra trip), ($125 jacket, $10 calculator, an extra 20-minutes trip)} Version 2: S0 2 5 { ($15 jacket, $125 calculator, no extra trip), ($15 jacket, $120 calculator, an extra 20-minutes trip)}

Next, in the subjective situations, common information are canceled and deleted, and especially, the unmentioned information “no extra trip” is not examined: Version 1: S1 5 {($15 calculator), ($10 calculator, an extra 20-minutes trip)} Version 2: S0 2 5 {($125 calculator), ($120 calculator, an extra 20-minutes trip)}

A comparison can be made here because only the calculator is described, for different prices, in both versions. Subjects are assumed to construct an evaluation function of the mental ruler, v, which is shown in Eqs. (19.8)
(19.10), and consider the extra trip to evaluate the discount. Here, the evaluation function of the discount amount of price F can be described by v1 and v2, the functions of the mental rulers, which have different m(x ): Version 1: F ($5 discounted from $15)＝v1 ($5) Version 2: F ($5 discounted from $125)＝v2 ($5)

Nevertheless, if the evaluation function F is applied to the evaluation function v in Eqs. (19.8)
(19.10), m(x ) becomes $15 for v1 in Version 1 and $125 for v2 in Version 2, whereas m(x) is $5 for both v1 and v2. According to the property of the evaluation function v in the positive area, which is included in Eqs. (19.8)
(19.10), v1 ($5) . v2 ($5) is elicited for both the evaluation formulas. Therefore F ($5 discounted from $15) . F ($5 discounted from $125).

19.5.2 Interpretation of the experiment by Hsee Hsee (1998) conducted an experiment to confirm the “less is better effect” (Study 1). Subjects are 83 college students separated into two groups, and each group received one of the two versions of the next questionnaire. Version 1: Imagine that you are about to study abroad and have received a good-bye gift from a friend. It is a wool coat from a nearby department store. The store carries various wool coats. The worst costs $50 and the best costs $500. The one your friend bought you costs $55. Version 2: Imagine that you are about to study abroad and have received a good-bye gift from a friend. It is a wool scarf from a nearby department store. The store carries various wool scarves. The worst costs $5 and the best costs $50. The one your friend bought you costs $45.

In both conditions, participants were asked how generous they thought the friend was. Answers were given on a 0
6 point scale where 0 indicated “not generous at

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all,” and 6 indicated “extremely generous.” The result was, although the $55 coat was certainly more expensive than the $45 scarf, those receiving the scarf considered their gift giver to be significantly more generous than those receiving the coat (mean rating values equal 5.63 and 5.00, respectively). An interpretation of this experiment is shown as follows: Version 1: {$55 wool coat, worst $50, best $500} Version 2: {$45 wool coat, worst $5, best $50}

Subjects are assumed to construct a mental ruler using the given information. In Version 1 the ruler is assumed to be constructed between $50 and $500, and in Version 2, it is between $5 and $50. Presuming that the subjects take the highest price as a comparative object, the evaluation function F can be illustrated using the following functions of the mental ruler, v1, v2, which have different m(x ): Version 1: F ($55 wool coat) 5 v1 ($55) Version 2: F ($45 wool scarf) 5 v2 ($45)

Nevertheless, if the evaluation function F is applied to the evaluation function v in Eqs. (19.8)
(19.10), m(x) becomes $55 for v1 in Version 1 and $45 for v2 in Version 2, whereas m(x ) is $500 for v1 and $50 for v2. Additionally, if a psychological reference point is applied to the lowest price and the highest price, m(x) becomes $5 for v1 in Version 1 ($55
$50), and $40 for v2 in Version 2 ($45
$5), whereas m(x ) is $450 for v1 ($500
$50), and $45 for v2 ($50
$5). Irrespective of the reference point, the following is elicited according to the property of the evaluation function v in the positive area denoted by Eqs. (19.8)
(19.10) for both the evaluation formulas. By the above assumptions, v1 ð$55Þ , v2 ð$45Þ: Therefore F($55 wool coat) is lesser than F($45 wool scarf). Hsee (1998) conducted another experiment in which it is asked how much subjects are willing to pay for a serving of ice cream, presenting two versions: 8 oz of ice cream in a 10-oz cup, and 7 oz of ice cream in a 5-oz cup (Study 2). The experiment indicated less-is-better effect in separate evaluation (the between-subject design). The average price for 8-oz ice cream is $1.66, although it was $2.26 for 7-oz ice cream. This result implies that if the subjective situation is set very widely, the decision will be unstable because the subjective situation is a support on which people construct the mental ruler to make a decision. In the mental ruler model, m(x) is 8 oz and m(x ) is 10 oz in the case of a 10-oz cup, whereas m(x) is 7 oz and m(x ) is 5 oz in the case of a 5-oz cup. Using Eqs. (19.8)
(19.10), and (19.16), it is elicited that the 7 oz of ice cream in a 5-oz cup is evaluated as preferred to the 8 oz of ice cream in a 10-oz cup. Hsee (1998) found that a clear preference reversal occurs in joint evaluations: in within-subject evaluation, the subjects presented higher price for 8-oz ice cream than 7-oz ice cream. This can be interpreted as follows, using the mental ruler model: in the joint evaluation the focus is set on “7 or 8 oz” to construct the mental

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ruler in the subjective situation because both versions are presented simultaneously. In each version the evaluation function of the mental ruler has m(x) of 7 and 8 oz, respectively, and m(x ) of 8 oz, under which a decision is made. As Hsee (1998) reported that experimental results of this kind are difficult to explain using decision-making theories used in the past such as those describing contingency. For example, the decision frame model and the prospect theory are insufficient to expound the phenomenon, because both versions are regarded as gain frames. To apply a decision frame model and the prospect theory to the evaluation such as generosity shown in Study 1 earlier is also difficult. Moreover, the psychological purse model cannot explain phenomena of this kind, either. These models or theories can only presume after the fact that there might have existed a different purse or a different frame. Furthermore, as Hsee (1998) described, the prominence hypothesis presented by Tversky et al. (1988)

that the conspicuous attribute got weight

is also insufficient. Hsee (1998) presented an evaluability hypothesis: that the mutually evaluable attributes such as cup size and amount of ice cream are combined, thereby producing an effect on judgment. The salient presumption is that the cup size has no great effect on the judgment in joint evaluation as the comparison of the amount of ice cream is easier than that of the cup size. This explanation is not contradictory to the explanation by the mental ruler model stated earlier. The evaluability hypothesis by Hsee (1998), however, did not explain how the subjective situation is constructed or how evaluation is made on it, or what kind of judgment or decision emerges. It only states what kind of attribute tends to relate mutually to produce an effect on the judgment, which is meaningful for understanding the structure of the subjective situation in the mental ruler model.

19.5.3 Interpretation of the evaluation experiment on the value of saved lives Takemura (1998) conducted an experiment where 17 each of male and female college students answered to the following questionnaire, which is slightly transformed from the questionnaire of the Asian disease problem by Tversky and Kahneman (1981): Question: Imagine that a certain local area in Japan is preparing for the outbreak of an unusual disease, which is expected to kill 100 people. It is considered important that as many people as possible recover from the disease and do not die. Answer the status of preference for the following cases according to your subjective value, on a 0
100 point ruler where 0 indicates “nobody recovers and all people die,” and 100 indicates “all people recovers and nobody dies.”

The subjects evaluated the preference on each case in which the number of saved lives is 1, 2, 3, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 97, 98, and 99.

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100 90 80 70

Value

60 50 40 30 20 10 0 0

20

40 60 80 Number of saved lives

100

120

Figure 19.1 Interpretation of the evaluation experiment on the value of saved lives. Source: Takemura, K. (1998). Jokyo izonteki ishikettei no teiseiteki moderu: Shinteki monosashi riron niyoru setsumei [Qualitative model of contingent decision-making: An explanation of using the mental ruler theory]. Ninchi Kagaku, 5(4), 17
34. (in Japanese).

Both positive and negative sides of the situation in a sentence were presented as follows, to suppress the elements of the framing effect. 1. One person is saved; 99 persons die (points). 2. Two persons are saved; 98 persons die (points).

The average evaluation values in each case are presented in Fig. 19.1. The result implies, as indicated in Fig. 19.1, that the S-shaped evaluation function is presumed using the mental ruler model. Especially, the property of the evaluation function obtained from this result is implied to be similar to the property of the evaluation function denoted as Eq. (19.10).

19.5.4 Interpretation of the perceptual judgment experiment Study 1 by Miwa and Takemura (1998) was an experiment investigating the perceptual judgment on line length, circle area size, and rectangular area size using the

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magnitude estimation method. The subjects were seven college and graduate students who were presented comparative stimuli of 15 kinds in a random order and asked to judge four times per stimulus. The response time before each judgment was measured. No significant difference was found among the response time for line length, or the circle or rectangular area sizes, although there was a tendency by which area sizes were judged slightly more quickly than length. This result reflects that no significant difference exists between the response time for a line, which is a physically one-dimensional object, and for a circle or a rectangular, which is physically two-dimensional. Study 2 was an experiment investigating the perceptual judgment on the area size, the length and the width of a rectangular in each different session, using the magnitude estimation method. The subjects were eight college and graduate students who were presented comparative stimulus of 12 kinds in random order and asked to judge 10 times per stimulus. The dispersion of the responded value for each area, length, or depth was measured. Results show that the dispersion of area judgments (the difference of the upper bound and the upper bound of the assumed value) was much smaller than the product of the dispersions of length and width. The result implies that the subjects did not evaluate the length and the width of a rectangle consciously and then duplicate them to judge the area size of the rectangular, but they perceptually judge on area. These results imply that the subjects did not judge the sides or diameter of the subject serially first and then integrated the information into an area but instead constructed a one-dimensional mental ruler directly according to the dimensions of values such as length or size. These results, however, fail to eliminate the possibility that the subjects unconsciously considered the data of length for each dimension of the subject by the parallel distributed processing and integrated the data afterward to judge the area. They do not eliminate the possibility, either, that the judgment of length or area size is a response after processing physical property of an object that is of a lower dimension than the length. Although fully admitting these possibilities, the author considers that the explanation using the mental ruler is effective as a macroscale and metaphorical interpretation, which is not contradictory to these possibilities.

19.5.5 Interpretation of price judgment experiment The mental ruler model assumes that people evaluate objects using an inverse Sshaped function, and that this property holds not only for weighted probabilities but also for outcome values. This property is completely opposite to the property of diminishing marginal utility in utility theory and prospect theory. While utility theory and prospect theory assume a function that is always concave downward, the mental ruler model assumes the opposite, that there is a function that is convex downward near the upper limit. In real-world purchasing situations, such as supermarkets and department stores, price marketing policies often involve reducing or manipulating the prices of products to encourage consumer purchasing behavior. Kojima (1986) studied the contents of advertisements in many supermarkets and department stores in Japan and

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reported that most of the prices offered to consumers were odd prices such as 98 yen or 14,980 yen. In addition, price marketing policies using odd prices tend to be prevalent in the United States and Europe (Foxall & Goldsmith, 1994). According to the mental ruler model, odd prices are evaluated as considerably cheaper for consumers based on their sense of neighborhood at the end point of the mental ruler (implying an inverse S-shaped evaluation function). However, this odd price effect may also be explained by the loss function of prospect theory. To determine if the properties of the inverse S-shaped valuation function are observed, we need to ask consumers to rate values from zero point (which usually means “free”) to the maximum point (which usually means standard price or maximum price). Fortunately, in Japan, due to the sales policy of the cell phone companies, despite the standard price, the product is sold for free (0 yen). Therefore it is natural to ask consumers to evaluate the value of the product from 0 yen to some upper limit price. Roy and I conducted a questionnaire on the discount rates of various consumer goods among 203 adult male and female subjects living in Tsukuba, Japan. The subjects were asked to rate the discount rate at 0, 1, 2, 3, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 95, 97, 98, 99, and 100 (Takemura & Loi, 1999). To examine the robustness of the properties of the mental ruler to different framing of the same problem description, we prepared four different framing conditions, including positive and negative, percentile and absolute value descriptions. Respondents were asked to numerically rate their satisfaction with a cell phone price cut at various levels from 0% to 100% discount, ranging from 0 (not satisfied at all) to 100 (absolutely satisfied). A Japanese brand cell phone (initial price: 8800 yen) was used as the product in the survey. Each subject was assigned to one of the four frame conditions; the linguistic descriptions of the four frames were at the level of, for example, a 10% discount. Frame 1: 10% discount off the original price. Frame 2: You can purchase the product at a discount of 880 yen from the original price. Frame 3: You can purchase it at 90% of the original price. Frame 4: Can be purchased at a discounted price of 7920 yen.

The average evaluation values for each case are shown in Fig. 19.2. As shown in these figures, the results are consistent with an inverse S-shaped evaluation function for all four frame conditions. Note that regardless of the type of framing, the obtained evaluation function was inverse S-shaped. This result supports the mental ruler model. We believe that the mental ruler model can also be applied to explain the so-called zero-risk effect, in which protective behavior that leaves no losses is evaluated more highly than protective behavior that leaves losses, even if the amount of loss reduction is exactly the same. The zero-risk effect has been observed in many social situations and is believed to hold in many areas where society tries to reduce risk (Nakayachi, 1998a). For example, this effect appears in the evaluation of policies for protection from radiation, waste disposal, air and water pollution, etc. (Nakayachi, 1998a). The zero-risk effect may be explained by prospect theory; Tversky and Kahneman (1981) called this effect the “pseudo-certainty effect.” According to their empirical research, people prefer pseudocertainty options that appear to eliminate risk by framing the decision problem. Tversky

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Figure 19.2 (A)
(D) Show mean rating values for a mobile phone in four frame versions of price reduction description. (A) Mean rating values in Frame 1 (Frame 1: For example, 10% discount from original price). (B) Mean rating values in Frame 2 (Frame 2: For example, discount of 880 yen from original price). (C) Mean rating values in Frame 3 (Frame 3: For example, you may purchase the item at 90% of the original price). (D) Mean rating values in Frame 4 (Frame 4: For example, you may purchase the item at 7920 yen after the discount).

and Kahneman (1981) also state that protective behavior that reduces the probability of harm from 1% to 0% is valued more highly than behavior that reduces the probability of the same harm from 2% to 1%. Nakayachi (1998a) also presents empirical findings of the zero-risk effect on decreasing probability in the medical problem of neonatal death and in the problem of regulating used cars. The zero-risk effect on decreasing probability can be explained both by prospect theory and by the mental ruler model. However, the zero-risk effect on outcomes, such as the number of deaths, may not be fully explained by prospect theory. According to prospect theory, zero-risk effects on outcomes are predicted only in the negative framing condition, where the decision problem is represented by negative aspects, and not in the positive framing condition, where the decision problem is represented by positive aspects. In contrast the mental ruler model predicts that the zero-risk effect occurs in both framing conditions. Nakayachi (1998b) conducted a study to examine the effect of framing on the zerorisk effect on willingness to pay (WTP) for protective behavior for the medical problem of newborn death. Undergraduate students were asked to rate their WTP for three protective actions to reduce the number of deaths to 800, 400, and 0. The results showed that the difference in WTP for actions to reduce the number of deaths to 800 and 400 was greater than the difference in WTP for actions to reduce the number of deaths to 0. This effect was obtained not only in the negative framing condition, but also in the positive framing condition. The finding in the positive framing condition cannot be explained by prospect theory, but it can be explained by the mental ruler model.

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19.5.6 Interpretation of probability weighting function Takemura (1998, 2001) proposed the mental ruler theory that the evaluation function in consumer price judgment is characterized by a concave downward near the lower limit and convex downward near the upper limit of the judgable stimulus and performed formulation, including Fechner’s and Stevens’ laws as special examples. This model was also used to estimate the probability weighting function and is a psychological evaluation function that does not particularly distinguish the probability and the result. Basically, the evaluation function of the mental ruler is the following function: Comprehensive evaluation 5 weighting to the left end point x evaluation function based on the left end point (downward concave function) 1 weighting to the right end point x evaluation function based on the right end point (downward convex function). Therefore the evaluation function of the mental ruler is the linear sum of the concave and convex functions, and it is generally considered to have an inverted S shape as a result. The property of the evaluation function of this mental ruler is completely opposite to the property of diminishing marginal utility in the utility theory and the prospect theory in the vicinity of the maximum value of the evaluation area. The utility and prospect theories always assume a downward concave function, but the mental ruler model predicts a downward convex function near the upper limit. For example, in the negotiation of price discount and others, if one is acting with a goal, the sensitivity would increase when the targeted price is near (see Fig. 19.3). According to this formulation, let the intensity of sensation be S, weight (0 # k # 1) be k, the stimulus be xAX, the psychophysical function u be the concave function X![0, 1], and the psychophysical function v be the convex function X![0, 1]. 0 1 x A S 5 ku@ possible maximum value of x 2 possible minimum value of x 0 1 x A 1 ð1 2 kÞv@ possible maximum value of x 2 possible minimum value of x are indicated. For example,  α x S 5 k possible maximum value of x2possible minimum value of x  β x 1 ð1 2 kÞ possible maximum value of x2possible minimum value of x where S is the intensity of sensation, k is a weight (0 # k # 1), xAX is the stimulus and a sensitivity parameter with 0 # α # 1 and 0 # β # 1. Murakami, Tamari, Ideno, Ohkubo, and Takemura (2014) conducted an experiment of the probability weighting function. A total of 44 university students (22 males, mean age: 21.0 years) participated in the experiment. One of the 44 participants was excluded from the analysis because the experiment was interrupted due to a malfunction of the experimental equipment.

Figure 19.3 (A) The inverted S-shaped evaluation function of mental ruler model. (B) The evaluation function of mental ruler model in which the reference point is located on the left end of the ruler. (C) The evaluation function of mental ruler model in which the reference point is located on the right end of the ruler.

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The experimental task was to present two lotteries with explicit probability and outcome information, and have the participants choose the preferred lottery. The experiment consisted of two blocks, in which participants participated in two conditions: a gain condition and a loss condition. The gain condition was a condition in which participants received a certain amount of money for choosing a lottery ticket, and the loss condition was a condition in which participants lost a certain amount of money depending on the lottery ticket they chose. In this experiment, the lottery was represented by a bar graph. The two lotteries presented on the screen were defined as risky lottery and riskless lottery by their relative relationship. A risky lottery is a lottery in which the probability of a certain outcome is lower than that of the paired lottery (a riskless lottery), but the amount of outcome that can be produced by choosing the lottery is higher. On the other hand, a riskless lottery is a lottery in which the probability of a certain outcome is higher than a risky lottery, but the amount of outcomes that occur is smaller. For the lotteries, we created six sets of lotteries in which one set (henceforth called ladder) consists of eight pairs of lotteries (henceforth called rung), referring to Wu and Gonzalez (1996). In this study, we combined the lottery patterns by Wu and Gonzalez (1996) and replaced them with Japanese yen, and three ladders were used for analysis. For each ladder a pair of standard lotteries was set. This standard pair of lots was designated as Rung 1. Then, the other Rungs 2
8 were constructed by adding to each of the standard pair of lotteries a lottery, result of which was equal to the result of the hard lottery in the standard pair of lotteries. The closer the lottery was to Rung 8, the greater the probability of the lottery being added. For example, in Ladder 3, Rung 1 is a lottery where 40,000 yen is generated in 5% of the lots (risky lottery) and 10,000 yen is generated in 20% of the lots (solid lottery). Then, Rung 2 was created by adding the same lottery (lottery that generates 10,000 yen at 5%) as the riskless lottery (lottery that generates 10,000 yen at 20%) in Rung 1 to each of the risky lottery and riskless lottery in Rung 1. Thus the risky lottery in Rung 2 is the lottery that produces 40,000 yen or 10,000 yen at 5%. On the other hand, a solid lottery would be one where 10,000 yen is generated at 25%. In Ladder 3, from Rung 3 onward, the outcome of the lottery (10,000 yen) is not changed, but the probability of the outcome is increased to 10%, 15%, 35%, 50%, 65%, and 80% and added to Rung 1, the standard pair of lotteries. In the first trial the gazing point was presented for 500 Ms, and then the choice screen with the two lotteries was presented, and the choice screen was presented until the preferred lottery was selected. When the participant selected the lottery, a blank screen was shown for 500 ms, and then the next trial was started. All pairs of lotteries were shown to each participant five times. The order of presentation of each pair of lots was random. Therefore the number of trials in each block was 240, and the total number of trials in the experiment was 480. The order of the trials, such as which condition was presented first, and the placement of the lotteries on the left and right sides were counterbalanced. At the beginning of each block, the participants were instructed whether the block they were about to perform was in the gain or loss condition. In addition, there was one break in each block.

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To estimate the free parameters of the stochastic load function, we used the estimation method by Wu and Gonzalez (1996). The model of the stochastic load function to be estimated is the model proposed by Tversky and Kahneman (1992) and the mental ruler model of Takemura (1998) and Takemura (2001). Many models of probability weighting functions have been proposed (Chechile & Barch, 2013; Gonzalez & Wu, 1999; Prelec, 1998). However, in a previous study using the same experiment and estimation method as Wu and Gonzalez (1996), which was referred to in the experiment and estimation method of this study (Takemura, 2004), the model of Tversky and Kahneman (1992) and the mental ruler model (Takemura, 1998, 2001) were found to fit better than other models of the probability weighting function, so these models were adopted. The probability weighting function π(p) proposed by Tversky and Kahneman (1992) is shown in the next equation: π ð pÞ 5

pγ ðpγ 1 ð12pÞγ Þ1=γ

where p is the probability and γ is a free parameter; γ takes values in the closed interval [0.27,1], and when γ 5 1, π(p) 5 p. In the mental ruler model the following equation was used to apply:
 πðpÞ 5 wpk 1 ð1 2 wÞ 1 2 ð12pÞk where w and k are free parameters. However, both w and k take values in the open interval (0,1). As with the conventional probability weighting function, the mental monosyllabic model has an inverse S-shape. As a property of each parameter, w is a parameter that determines the ratio of concave and convex functions that are linearly coupled, and the closer the value of w is to 0, the more the ratio of convex functions represented. And the closer the value of k is to zero, the greater the change in the probability load value near the probability end point and near the reference point. In Wu and Gonzalez (1996), to estimate the parameters of the probability weighting function, the probability that a risky lottery is selected over a riskless lottery is fitted by a logistic function of the difference between the utilities of the risky lottery and the riskless lottery. The free parameters of the probability weighting function were estimated by the least squares method, using the measured values as the percentage of risky lots selected in each rung of the ladder. This estimation equation is shown in the following equations: Pr ðRgSÞ 5 SSEðγ Þ 5

1 1 1 expðU ðSÞ 2 U ðRÞÞ

8 X

ð%Ri 2 Pr ðRi gSi ; γ ÞÞ

i51

In the previous equation, R is the risky lottery, S is the riskless lottery, U(S) is the utility of the riskless lottery, and U(R) is the utility of the risky lottery. However, the

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utilities of both lotteries were calculated using the cumulative prospect theory. For example, the utility of a lottery, outcomes of which are x and y and probabilities of which are p and q, respectively, is represented as U(p,x;q,y) 5 π(p)v(x) 1 [π(p 1 q) 2 π(p)]v(x). In the next equation, SSE(γ) is the sum of squares of the errors, and %Ri is the selection rate of risky lotteries in each rung. Pr(RigSi; γ) is the probability of choosing the riskless lottery over the risky lottery calculated from the parameter γ of Tversky and Kahneman’s (1992) model. We estimated the parameter γ that minimizes the objective function SSE(γ) shown in the next equation. The purpose of this study was to examine whether the characteristics of the probability weighting function, as indicated by previous research findings, are observed even when gambling information is presented graphically. Therefore we did not estimate the value function, but only the free parameters of the probability weighting function. The value function was set to the Beki function (v(x) 5 xβ), which is often used in previous studies, and in the loss condition, v(x) 5 xβ using the parameter λ, which represents the impact of loss on gain (Tversky & Kahneman, 1992). The parameters β and λ were set to β 5 0.88 and λ 5 2.25, respectively, from the estimation results of Tversky and Kahneman (1992). The experiment by Wu and Gonzalez (1996) was done only for the gain condition, so we compare the results of the selectivity for the gain condition. In their experiment the selection rate of risky lots in the 0%
10% probability range was 30%
50%, although there were differences among ladders. In addition, the selection rate of risky lots in the probability range of 10%
80% was 50%
90%, and the selection rate in the probability range of 90%
100% was 20%
40%. We estimated the free parameters of the Tversky and Kahneman (1992) model and the mental monosyllabic model (Takemura, 1998, 2001) using the estimation method of Wu and Gonzalez (1996) from the selection rates of risky lots for each rung in each ladder obtained from the lottery-selection task. We estimated the parameters. We also calculated the Akaike Information Criterion (AIC) (Akaike, 1974) as a measure of fit to the data. AIC is defined as AIC 5 2 3 (log likelihood) 1 2 3 number of parameters. The log likelihood represents the likelihood of the data given the parameters of the model, and since the log likelihood is multiplied by 22, the lower the value of AIC, the better the model explains the data. The second term represents the penalty for increasing the number of parameters. The result shows that the parameters of the Tversky and Kahneman (1992) model and the mental ruler model (Takemura, 1998, 2001) are significant at the 0.1% level for the gain/loss condition and all ladders. The parameter γ of the Tversky and Kahneman (1992) model and the parameter k of the mental rulerc model (Takemura, 1998, 2001) were both approximately equal to 1 for all ladders. In the estimation results of Wu and Gonzalez (1996), which were used as reference in the experiments and estimation methods of this study, the estimated values of the free parameters of the probability weighting function were about 0.6
0.9. This result suggests that the distortion of the evaluation to probability in this experiment is almost nonexistent and close to linear. The parameter w of the mental monosymbol model (Takemura, 1998, 2001) was approximately 0.5
0.7, indicating that the transition from a concave function to

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a convex function occurred with high probability. The result shows that the AIC values were lower in the mental ruler model (Takemura, 1998, 2001) than in the Tversky and Kahneman (1992) model for all ladders in the gain and loss conditions. This indicates that the mental rulerc model (Takemura, 1998, 2001) is a better fit to the results of this experiment than the conventional probability weighting function model of Tversky and Kahneman (1992). This result suggests that the mental ruler model can be applied to probability weighting function.

19.6

Conclusion and future perspectives

In this chapter, I briefly explained the difficulty of fully explaining contingent judgment in the mathematical systems underlying utility theory. Then, I introduced the decision frame model of contingent judgment (Tversky & Kahneman, 1981) and the psychological purse model (Kojima, 1959, 1994) and range
frequency theory (Parducci, 1965, 1995). Finally, this chapter introduced the “ruler of the mind” model to qualitatively explain contingent judgment. The basic hypotheses of the mental ruler were examined along with its basic functions and basic structural theories. The concept of this model is that people make judgments and decisions using a mental ruler constructed for subjective situations, which is constructed as a support so that a one-dimensional mental ruler can easily be created. The most significant feature of this model is that unlike recent utility theory and prospect theory, it treats utility, value, and subjective probability as basically the same evaluation function. As the evaluation function for these attributes, the mental ruler is proposed, and this evaluation function is suggested to be unidimensional in many decision-making situations. In addition, unlike conventional theories, it describes the instability of judgment in the region beyond the length of the mental ruler. We have presented a mathematical model to formulate the argument more rigorously. In this chapter, I specifically explained the unidimensionality of evaluation in judgment and decision-making. However, there are limitations to this argument. People may evaluate multidimensional attributes and evaluate information in a multidimensional manner. For example, there are often cases where people make judgments and decisions while consciously considering multidimensional information, as envisioned in multiattribute attitude theory and multiattribute decision theory. In the future, it will be necessary to clarify the situations in which unidimensional evaluations assumed by the mental ruler model are likely to be made and those in which evaluations that take multidimensional information into account are likely to be made. In addition, the models presented in this chapter are basically qualitative in nature. Any ambiguities need to be formulated precisely in future research. Also, predictions and interpretations of the model can be elicited through empirical testing. A variety of studies are possible, such as the prediction of perceptual judgments by the evaluation function proposed in this chapter, prediction of evaluation functions in the field of social judgments and decision-making, reinterpretation of possibility weight functions, prediction of risk assessment, and prediction of

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consumer activities. Future work should include empirical testing of these predictions to more accurately validate the model and its meaning. The mental ruler model can also explain irrational decision-making and the decision to choose the worst option in specific social situations. For example, a decision may be made based on an attribute that is easy to understand and evaluate, instead of evaluating the attribute that should be emphasized. In the case of the Covid-19 epidemic, public health policy tended to be based only on the statistics of the Covid-19 epidemic, but it goes without saying that public health policy should be based on the statistics of other diseases and health care. However, it goes without saying that public health policy should take into account other diseases and healthcare statistics. In addition, the pursuit of zero risk by focusing on the ruler end point in evaluation may lead to irrational decisions if it becomes excessive.

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How attention arises in and influences decision-making

20

In the view of the contingent focus model, decision-making will change with attention. This idea has been confirmed to some extent in our psychological experiments. For example, in risk-based decision-making, if an experimental operation that draws attention to probability information is performed, the weight on the probability attribute increases, and risk-averse decision-making that selects a safer option with lower risk is made. Experimental operations that are facilitated and focus on information about outcomes such as money and survivors increase the weight of outcome attributes and lead to risk-oriented decisions to adopt higher risk options. This experimental manipulation has also made it possible to some extent to form a risk attitude that is the opposite of the risk attitude assumed by Kahneman and Tversky’s prospect theory. We also found that even in game situations such as the prisoner’s dilemma task, conducting experimental operations that focus on the opponent’s gain promotes cooperative decisionmaking. Thus to some extent, it has become clear that decision-making can be changed by focusing on specific attributes. Then, how do people pay attention to everyday social situations? In social psychology and behavioral determinism so far, there has been a theory that attributes and events that are highly prominent and attributes and events that people are likely to recall are likely to be noticed. Since such a theory has a tautological impression, we adopt the principle that Mach, E. and Marr, D. implicitly assumed in perception to explain the phenomenon of attention more objectively. I tried to explain how attention to social and decision-making events depends on time series or spatial changes in the event. I explain that attention is not only an objective indicator of the event but also changes in the time series, considering the hypothesis that it is also affected by speed, change acceleration, etc. Thus this chapter points out that velocity (first derivative) and acceleration (second derivative) in the object’s space
time are related to the generation of attention. Furthermore, this chapter introduces the mental box model, a model of the nature of category focusing, as a microscopic process behind the contingent focus model and mental ruler model. The first and second derivatives of time in the object’s space
time may increase the sensitivity of the object. From these considerations, I will point out the possibility that so-called heuristics and biases, rather than actual objective statistical indices, may occur, sometimes resulting in irrational and worst-case decisions.

20.1

Function of attention

As William James said, attention has a clear nature and vivid. Berlyne (1969, 1970) wrote that attention has an intensive and a selective aspect. There are three types of Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00021-1 © 2021 Elsevier Inc. All rights reserved.

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the intensive aspect. The first type is attentiveness, which is degree of influence by information to the living body. The second type is the degree of concentration which is degree of focusing to a source among many sources. The third type is the arousal that is activation level of the cerebral cortex, suggested by the alpha attenuation of brain waves. Similarly, in terms of selectivity, three types are distinguished. The first type is the selective attention in which the behavior is defined only by a specific stimulus. The second type is the abstraction, which is paying attention only to certain attribute. The third type is the exploratory behavior, for example, seeking behavior and gazing behavior. Attention is a dynamic activity, and its state changes greatly with the passage of time and stimuli. If the state of attention changes significantly, the perceived content should always flow. In this chapter, I will explore the relationship among attention, information search, and decision-making. Kahneman (1973) proposed that selective attention is differential allocation of the processing capacity of the various channels that process information. According to Kahneman, the attention is considered to be effort or capacity corresponding to information input for the cognition. The idea that there is a limit to the amount of information that can be understood in a certain period of time when a person looks at an object and makes a judgment, that is, pays attention, is called a limit capacity model. There is the idea of attention resources. It is difficult to do some things together. This is because when people pay attention, they are using a fixed amount of resources, and they run out of resources to do a lot of things. In other words, one can only pay attention to the amount of attention resources available. Therefore there is a limit to the amount of information that can be processed. For example, the size of a cake in one hole is fixed. If you eat the cake, it will be gone. The size of the whole cake is the limit capacity, the cake is a resource of caution, and eating it is like being careful. If you eat one hole of cake, you will lose it, and you will lose your attention resources if you pay attention to the limit capacity. However, on the contrary, there is also the idea of an infinite capacity model in which there is no limit to the amount of information that can be obtained in a certain period of time. In this case, all the information will be processed at the same time. It means that there are an infinite number of cakes. We have found from some experiments that attention can guide decision-making as shown in Chapters 17
19. After obtaining such findings, independent of us, Shimojo, Simion, Shimojo, and Scheier (2003) have proposed the Gaze Cascade Hypothesis, which suggests that attention leads to preference. This is the hypothesis that active gaze forms preferences and has gained experimental support in facial preference experiments. This hypothesis is also consistent with the assumptions of the contingent focus model shown in the Chapter 16, The Contingent Focus Model and Bad Decisions. Although it is thought that such attention has some effect on decision-making, it is possible that attention alone to the alternative does not always guide decision-making but also attention to selection action itself guides decisionmaking. We are conducting some experimental studies, making working hypotheses that the act of making choices, not just attention, may influence preferences and the next decision (Ideno et al., 2011a,b; Takemura, Ideno, Hayashi, et al., 2012). We first create a task to experimentally control the selection behavior, asking you to

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Figure 20.1 Go and no-go decision task used in the preference construction experiment (Takemura, Ideno, & Hatori, 2012; Takemura, Ideno, Hayashi, et al., 2012).

Figure 20.2 Decision task in the preference construction experiment (Takemura, Ideno, & Hatori, 2012; Takemura, Ideno, Hayashi, et al., 2012).

press the “space key” as soon as possible when a ▲ (or ▼) is presented in the chocolate image as shown in Fig. 20.1. Then, we controlled the number of selections according to the type of chocolate. Then, we considered whether people would actually choose chocolate, which is often selected. For this study, two chocolates (Fig. 20.2) were presented to the participants after the experiment, and the dependent variable of the experiment was whether to bring back one of the chocolates. We also measured eye movements with an eye movement
measuring device. We examined the possibility of preference construction by choice behavior while controlling the exposure experience of options (Ideno et al., 2011a,b; Takemura, Ideno, & Hatori, 2012; Takemura, Ideno, Hayashi, et al., 2012). Although there was a tendency that the choice probability of the high-frequency choice products tended to be higher than that of the low-frequency ones, no clear evidence had obtained. Therefore we conducted the experiments using meaningless figure that is designed to control, as much as possible, the influence of the prepreference bias to examine the influence on preference construction of choice behavior itself (Ideno & Takemura, 2018). Specifically, we investigate whether choice behavior based on visual judgment, such as size judgment, has an influence on subsequent preference relations as shown in Fig. 20.3. Each experiment consists of three phases: (1) the perceptual judgment task, (2) the preference judgment task (two options choice), and (3) the favorableness evaluation. The perceptual judgment task performed was

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Figure 20.3 Decision task in the preference construction experiment (Ideno & Takemura, 2018).

a choice task unrelated to a preference statement. This task was created for the purpose of manipulating the number of choices of a specific stimulus. In Phase 2 the preference relations were measured according to the choice task of the two options. In Phase 3 the favorableness evaluation of objects was used for choice. Regarding the preference task, the results indicate that the number of choices of the multichoice target of the perceptual judgment task was significantly larger than that of the nonchoice target (65.8% vs 34.2%), as indicated by the direct probability test (p 5 .037). This finding suggests that preference is formed by a choice that is not related to preference.

20.2

Psychological model of attention

Thus our experimental study focused on the causal relationship of choice leading to preference. We focused on the aspect of preference through choice, as opposed to the implicit understanding of choice through preference, and conducted relevant laboratory experiments and analyzed the results. Although no clear difference was found in the experiment using chocolate and mineral water bottle, it was suggested that attention to the act of choice facilitated the formation of preferences. Considering that the preference judgment for the chocolate and the mineral water bottle is a kind of decision-making that is repeated on a daily basis, it is possible that preference criteria are formed in advance. By conducting the experiment using meaningless figures, we found that the causal relationship of choice leads to preference. Thus previous studies suggest that attention is an important factor in facilitating decision-making, but the mechanism by which attention is generated and decisions are made is not fully understood. This is also suggested by the experimental results that it is not always easy to predict the actual selection from the gaze pattern obtained by the eye movement
measuring device. We point out one possibility as to why attention is paid to this social event. The basic hypothesis is that the rate of attention to social events depends not only on the statistics of social events, but also on the indicators of changes in space
time

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(Takemura, Hatori, & Fujii, 2009; Takemura, Ideno, & Hatori, 2012). In addition, it is hypothesized that the index related to change is determined by velocity and acceleration. In this presentation, we will discuss this hypothesis, the mathematical model derived from that hypothesis, and the quantitative analysis related to it. We also discuss the method of empirical analysis of the model. People’s judgments about changes in social phenomena, for instance, crime and suicide, and in economic phenomena, such as business conditions, often differ from actual statistics. A tendency for judgments of various risk events has been found to differ from actual statistics (Slovic, 1987, 2010), and the same can be said for risk perception of Covid-19. Scientific journals such as Science Advances and Science have recently begun publishing research on the psychological and behavioral responses to Covid-19 (Holman, Thomson, Garfin, & Silver, 2020; Metcalf, Morris, & Park, 2020). Takemura et al. (2009) analyzed the statistical data of the social events. For example, they gave an example of a relationship between changes in the unemployment rate in Japan and the number of Google searches for the unemployment in Japan. The relationship between the two is not clear from this alone, but a logistic regression analysis corresponding to this hypothesis shows that social attention to unemployment increases as the actual unemployment rate increases, but not only that unemployment. It was found that the higher the rate change acceleration, the higher the rate of Google search. This tendency has been confirmed in the focus on influenza, stock prices, and social risks, and even in the perceptual judgment task using an eye movement
measuring device in the laboratory, people are affected by stimuli with a large acceleration of stimulus change (Takemura et al., 2009; Takemura, Ideno, & Hatori, 2012; Takemura, Ideno, Hayashi, et al., 2012; Hatori, Takemura, & Fujii, 2010).

20.3

Mathematical model of attention rate to social events

There are many social events, but for the sake of simplicity, it is assumed that there are two social events. The discussion is basically the same for three or more events, but it is possible to divide it into two events, one event and another. In addition, the attention rate for social events is not only changing from moment to moment but is also influenced by the history of changes so far. Now, let us take the attention rate of a certain social event 1 at a certain point in time t. The attention rate has a contradictory relationship with the attention rate to other event 2 (may be other than event 1). Attention rate is used to detect changes to a certain event. Thinking simply, a cognitive model of two phenomena would be Pi(t) 5 p (Ui(t) . Uj(t)). We are developing a mathematical model of this kind of cognitive model, considering correspondence with mathematical models of infectious disease and comparison with other cognitive models, and developing a behavior modification model using time and social factors. We also think that this psychophysical use

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is determined by the quantitative index of social events at that time, velocity, acceleration and personal tendency, and some stochastic fluctuation error term. That is,
 Pi ðtÞ 5 p Ui ðtÞ . Uj ðtÞ

(20.1)

where Pi(t) is the psychophysical quantity corresponding to the detection of change for the social event i at the time point t. According to our hypothesis, the following model is constructed: Ui ðtÞ 5 αxi ðtÞ 1 βvi ðtÞ 1 γai ðtÞ 1 di 1 εi Uj ðtÞ 5 αxj ðtÞ 1 βvj ðtÞ 1 γaj ðtÞ 1 dj 1 εj

(20.2)

where xi(t) represents the physical quantity related to event i at time t, vi(t) represents the rate of change of the physical quantity related to event i at time t, and ai(t) represents the acceleration of change of the physical quantity related to event i at time t, α, β, and γ represent the parameters of each variable. In addition, di represents the judgment tendency of an individual, and εi represents the error term of judgment. Eq. (20.1) expresses the hypothesis that the rate of attention to a social event is equal to the probability that the psychophysical quantity (U1) involved in detecting a change in that event is greater than the psychophysical quantity (U2) involved in detecting a change in the opposite event. To create a metric model, we assume a double exponential distribution (Gumbel distribution) that is independent of each other as the error term distribution of this model. Then, when the formula expansion, including the integral calculation, is performed,
 Pi ð t Þ 5 p U i ð t Þ . U j ð t Þ   exp αxi ðtÞ 1 βvi ðtÞ 1 γai ðtÞ 1 d i     5 exp αxi ðtÞ 1 βvi ðtÞ 1 γai ðtÞ 1 di 1 exp αxj ðtÞ 1 βvj ðtÞ 1 γaj ðtÞ 1 dj (20.3) Eq. (20.3) is equivalent to Eq. (20.4). loge





P i ðt Þ 5 α xi ðtÞ 2 xj ðtÞ 1 β vi ðtÞ 2 vj ðtÞ 1 γ ai ðtÞ 2 aj ðtÞ 1 di 2 dj P j ðt Þ (20.4)

This means that the logarithmic odds of attention rate are linear functions of quantitative index difference, velocity difference, acceleration difference, and personal tendency for change. The parameters α, β, γ, and di 2 dj of this model can easily be estimated by logistic regression analysis using the maximum likelihood method. At the conference presentation, we will report an experiment in which the velocity and acceleration of social events are tested, the attention rate is measured with an eye camera, and these parameters are estimated.

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20.4

455

Propositions and considerations derived from the model

Proposition 20.1: When the model shown in Eq. (20.1) is established and the error terms ε1 and ε2 of the random utility of Eq. (20.1) follow the following independent double exponential distribution [Gumbel distribution (Eq. 20.2)], Eqs. (20.3) and (20.4) hold. Proposition 20.2: Under the condition that the logarithmic comparative judgment (Fechner’s law) is established for the exponentials of quantitative judgment, velocity, and acceleration, the model shown in Eq. (20.1) is established, and the error term of random utility in Eq. (20.1) is established. When ε1 and ε2 follow the following double exponential distribution independent of each other [Gumbel distribution (Eq. 20.2)], the following Eq. (20.5) holds. Ui ðtÞ 5 αloge xi ðtÞ 1 βloge vi ðtÞ 1 γloge ai ðtÞ 1 dloge εi

(20.5)

Proposition 20.3: When the error terms ε1 and ε2 follow the previous double exponential distribution, the model of Eq. (20.1) is equivalent to the axiom of choice of Luce (1959a). Also, the parameters of the error term are unique for positive linear transformations. Here, the Luce choice axiom is that when considering the subset S of the choice set T and considering the subset Q of S, the probability that Q is selected from T is the probability that S is selected from T multiplies the probabilities that Q is selected from S (however, the selection probabilities are neither 0 nor 1).  α   P i ðt Þ v i ð t Þ β ai ð t Þ γ di 2dj xi ðtÞ 5e P j ðt Þ xj ðt Þ vj ðt Þ aj ð t Þ

(20.6)

Proposition 20.4: The fact that the distribution of the difference in the error terms of the model in Eq. (20.1) follows the logistic distribution Df(x) means that the model in Eq. (20.1) is equivalent to Eqs. (20.3) and (20.4). It is a necessary and sufficient condition. In addition, it is necessary and sufficient that Eq. (20.1) is equivalent to Eq. (20.5) under the condition that the distribution of the difference follows the logistic distribution and that Eq. (20.1) holds the Fechner law. Df ðxÞ 5 α . 0 This means that Eq. (20.1) is equivalent to Eqs. (20.3) and (20.4) only when the difference between the error terms has a logistic distribution and is equivalent to

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Eq. (20.5) under the condition of Proposition 20.2. It shows that when the error term of the random utility model is an independent double exponential distribution (Gumbel distribution), the distribution of the difference between the error terms is a logistic distribution, but the opposite is not always true. Yellott (1977) shows an example in which the distribution of the difference in error terms becomes a logistic distribution in other distributions.

20.5

Application to the psychometric model for attention rate to Covid-19 problem

20.5.1 Purpose of the study Looking broadly at society, along with the epidemic of the new coronavirus, communication regarding the risks of the new coronavirus is being carried out by governments, local governments, and various organizations. In this chapter, we will discuss how people have been paying attention to this infectious disease, based on our research so far, and give a psychological consideration on the social attention of the new coronavirus infection. I would like to give an opinion on the ideal way of risk communication. It has been pointed out that judgments about changes in social events such as crime and suicide and changes in economic events such as the economy are often different from actual social statistics, and various risk events are also judged differently from actual statistics. It has been reported to be easy (Takemura, Tamari, & Ideno, 2020). The same can be said about the risk perception of the new Corona. In recent years, research on the psychological and behavioral reactions of the new corona has begun to be published in scientific journals such as “Science Advances” and “Science.” Our study has also proposed a model that points out one possibility as to why and how attention is paid to social events such as coronavirus infection (Takemura et al., 2020). The basic hypothesis is that the rate of attention to social events is determined not only by the statistics of social events, but also by indicators of changes in space
time (velocity, acceleration, etc.). In addition, indicators related to change include velocity and acceleration. The point of this cognitive model is that the attention rate of social events such as severe acute respiratory syndrome depends not only on objective data but also on its history and change patterns. For example, if the number of infected people suddenly increases, it can be predicted that people will receive social attention even if the actual number is not so large. What can be said from the data analysis of social attention to the new coronavirus infection? Based on the previous model, we analyzed data on social attention to the new coronavirus infection. For the number of positive cases by the polymerase chain reaction (PCR) tests for the new coronavirus (single day), refer to the data

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published by the Ministry of Health, Labor and Welfare (https://www.mhlw.go.jp/ stf/covid-19/open-data.html). Using the period of the published data was from January 16, 2020 to July 31, 2020. As for the number of articles, the number of articles for each day was obtained from the Asahi Shimbun article database “Kikuzo.” The search date was August 1, 2020, and as a result of various attempts, the search keyword was set to “Corona,” and the search target period was set from January 9, 2020 to July 31, 2020. The search volume was taken from Google Trends (https:// trends.google.com/). As a result of the analysis, it was shown that the actual number of searches was influenced by the number of positive people, the number of articles, and their speed and acceleration. In addition, the analysis results suggested that the actual number of positives affected the search volume rather than the number of articles. This suggests that people are paying attention to the number of positives and their increase or decrease, which is different from previous analysis of pandemic influenza and other social events. We have shown the changes in the number of positives reported so far and the results of Google Trends until recently (Figs. 20.4 and 20.5), but the number of searches is not so large despite the further increase in the number of positives since the summer it turns out that it has not increased, suggesting that people’s interest has weakened to some extent.

20.5.2 Analysis and results The correlation coefficient was calculated to examine the relationship between the number of searches, the number of positives, and the number of articles (Table 20.1). At that time, regarding the number of positive persons and the number of articles, the difference from the next day and the difference from the day after the next day were calculated and set as speed v and acceleration a, respectively.

Figure 20.4 Number of Covid-19 infections. Source: Graph by Nippon TV from Japanese Government data (https://www.news24.jp/ archives/corona_map/index3.html).

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Figure 20.5 Google Searches for “Covid-19 in Japanese.” Source: Created on Google Trends (https://trends.google.co.jp/trends/?geo 5 JP). Table 20.1 Correlation (no delay model).

msrch mposi vposi aposi marti varti aarti

msrch

mposi

vposi

aposi

marti

varti

aarti

1.00 0.69 0.04 20.02 0.51 0.00 20.01

1.00 0.23 0.00 0.39 0.00 20.05

1 0.70 0.23 0.45 0.15

1.00 0.08 0.44 0.41

1.00 0.32 0.05

1 0.74

1.00

Here, as shown in Eq. (20.4), the logarithmic odds of the attention rate are linear functions of the difference between the quantitative indicators of the two events, the difference in velocity, the difference in acceleration, and the difference in personal tendency. Also, assuming that the physical index of event 2 is zero, and the reference system is stationary with respect to event 2; it is assumed that the logarithmic odds of the attention rate are proportional to Ui(t) 5 αxi(t) 1 βvi(t) 1 γ ai(t) 1 di 1 εi. Assuming this, linear regression analysis is performed to examine the effect of the number of positives and the number of articles on the search volume. To consider the effect of delay, we examined the cases where there was no delay and the cases where there was a delay of 1, 2, or 3 days. In addition, the data were smoothed and analyzed by a simple moving average of each variable. The period for calculating the moving average was 7, 14, and 28 days. The independent variables were positive persons and the number of articles or their simple moving average m, velocity v, and acceleration a, and the dependent variables were the search amount or its simple moving average m. Model 1 is the case where the independent variable is only the variable related to the number of infections, Model 2 is the case where the number of newspaper articles is only the function variable, and Model 3

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is the case where both are included. To take into consideration for the search amount delay, the simple moving average is used. The consistent trends shown in Tables 20.2
20.5 were as follows. In Model 1 the results showed significant standard regression coefficients for the number of infections. In Model 2, significant standard regression coefficients were found in the number of newspaper articles. In Model 3, significant standard regression coefficients were found in the number of infections, the velocity rate of infections, and the number of newspaper articles. The model that fits best was the condition shown in Table 20.5, in which the moving averages of all variables were set to 7 days and used for the analysis. Under this condition the regression coefficients of the speed of the number of infections and the velocity and acceleration of the number of newspaper articles were significant. In addition, when the analysis was performed using the logarithmic odds of the number of searches for the dependent variable, the condition with the highest explanation rate was the condition in which the search amount was used as the former analysis, where the moving average of all variables was set to 7 days. The standard regression coefficients that were significant in Model 3 were 0.41 for mp, 20.21 for ap, 0.39 for mn, and 0.21 for vn.

20.5.3 Discussion First, as can be seen from Table 20.1, there is not a strong correlation between the number of searches, the number of articles, their speeds, and accelerations related to the new corona. In addition, as a result of the regression analysis shown in Tables 20.2
20.5, it was shown that the actual number of searches was influenced by the number of positive persons, the number of articles, and their speed and acceleration. The results of the regression analysis suggested that the number of infections affected the search volume rather than the number of articles. In Model 1, it was shown that the number of infections and their acceleration affect the attention rate. In today’s information environment, the number of new infections is presented daily on information sites. Therefore it is suggested that the number of infections and the influence of the change may have been remarkable. In this study, velocity and acceleration were used as indicators of changes in information, but the degree of influence of velocity was consistently greater than the degree of influence of acceleration, suggesting that attention is affected by changes from the previous day. On the other hand, the fact that the effect of acceleration was not so strong may be that negative acceleration also increased the attention rate. However, the results of this study are different from the analysis of the search behavior for radiological materials when the Great East Japan Earthquake of March 11, 2011 was followed by a series of equipment failures, meltdowns, and releases of radioactive materials at the Fukushima Daiichi Nuclear Power Plant, resulting in the largest nuclear disaster since the Chernobyl nuclear accident in 1986. The results are different from those of the study by Takemura, Ideno, and Hatori (2012)

Table 20.2 Regression coefficient no delay model. Model 1

Const mposi vposi aposi marti varti aarti R2 Adjusted R2 

p , .05. p , .01.  p , .001. 

Model 2

β

t

P

21.70 0.94 21.25 0.47

13.81 12.68 23.61 1.97

.000 .000 .000 .050

 

β

t

P

9.07

2.99

.003





0.54 20.47 0.20 0.46 0.45

Model 3

9.27 23.64 2.41 0.31 0.30

.000 .000 .017

  

β

t

P

8.31 0.77 21.25 0.49 0.34 20.17 0.06

3.45 10.67 23.47 2.07 6.79 21.41 0.80 0.58 0.56

.001 .000 .001 .040 .000 .160 .425

    

Table 20.3 Regression coefficient (1-day delay model). Model 1

Const mposi vposi aposi marti varti aarti R2 Adjusted R2 

p , .05. p , .01.  p , .001. 

Model 2

β

t

P

21.83 0.95 20.77 0.27

13.87 12.65 22.05 1.05

.000 .000 .042 .297

 

β

t

P

10.73

3.47

.001





0.51 20.37 0.15 0.46 0.46

Model 3

8.55 22.82 1.74 0.28 0.27

.000 .005 .083

 

β

t

P

10.15 0.79 21.00 0.40 0.30 20.09 0.02

4.12 10.57 22.44 1.52 5.80 20.75 0.27 0.55 0.54

.000 .000 .016 .130 .000 .453 .788

   

Table 20.4 Regression coefficient (2-day delay model). Model 1

Const mposi vposi aposi marti varti aarti R2 Adjusted R2 

p , .05. p , .001.



Model 2

β

t

P

22.03 0.97 20.77 0.43

13.90 12.52 22.03 1.60

.000 .000 .044 .112

 

β

t

P

12.49

3.95

.000





0.47 20.33 0.16 0.46 0.45

Model 3

7.80 22.44 1.80 0.25 0.24

0.000 0.016 0.073

 

.

β

t

P

12.28 0.83 21.00 0.46 0.25 20.03 0.02

4.84 10.36 22.37 1.61 4.71 20.26 0.21 0.53 0.51

.000 .000 .019 .109 .000 .795 .833

   

Table 20.5 Regression coefficient (3-day delay model). Model 1

Const mposi vposi aposi marti varti aarti R2 Adjusted R2 

p , .05. p , .01.  p , .001. 

Model 2

β

t

P

18.67 0.41 20.16 0.10

11.20 5.46 20.44 0.42

.000 .000 .659 .678

 

β

t

P

14.23

4.40

.000

0.44 20.37 0.18 0.45 0.44

Model 3

7.09 22.65 2.03 0.21 0.20

.000 .009 .044



  

β

t

P

14.41 0.85 21.02 0.48 0.20 20.06 0.04

5.50 10.00 22.27 1.63 3.73 20.44 0.48 0.49 0.48

.000 .000 .024 .106 .000 .660 .629

   

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and Takemura, Ideno, Hayashi, et al. (2012) that analyzed the relationship among the intensity of radioactivity in Fukushima and Tokyo from March 11, 2011 onward to September 2011, the number of articles about nuclear power plants in the Asahi Shimbun, and inquiry-type Internet searches (via Google search engine) about nuclear power plants. The results of the correlation analysis showed that the number of Internet search queries about nuclear power plants in Fukushima and Tokyo was strongly related to the intensity of radiation in Fukushima. The number of articles about nuclear power plants in the Asahi Shimbun was significantly but weakly correlated with the number of query-based Internet searches. The results of the correlation and partial correlation analyses suggest that social interest in nuclear power plants is more strongly influenced by the intensity of radiation in Fukushima than by nuclear power plant articles in newspapers. We also analyzed the effects of the intensity of radioactivity, the speed of change in radioactivity (first derivative), and the acceleration of change in radioactivity (second derivative) on the number of searches for nuclear power plants in Fukushima and Tokyo. The results of the multiple regression analysis showed that the acceleration of the change in radioactivity in Fukushima had the strongest impact on the number of Internet searches for Fukushima and Tokyo. In the case of Covid-19 the actual number of infected people in Japan is reported daily through newspapers and TV, and this is the reason why the number of searches for radioactive materials during the meltdown is influenced by the number of positive people. This may have been different from the results of the search behavior for radiological materials.

20.6

Control of attention by psychological experiment

20.6.1 Experiment in which the speed and acceleration of change of the target were controlled 20.6.1.1 Purpose of the study Previous research on attention to social events have calculated and fitted the change speed (first derivative) and acceleration (second derivative) of the target, but they did not control the change speed or change acceleration of the target. In this study, to estimate the parameters of the abovementioned change detection model, we conducted an experiment in which we manipulated the quantitative indices, speed, and acceleration of figures (black dots and bars) moving on the personal computer (PC) screen and measured the rate of attention to the figures using an eye camera (Hatori et al., 2010).

20.6.1.2 Method of the study Participants: The participants in the experiment were 59 students [15 males, 44 females, mean age 21.6 years, standard deviation (SD) 0.95 years] enrolled at Waseda University.

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The experimental stimuli: Two types of stimuli were presented: a circular stimulus (Fig. 20.6) in which two black dots move in a circular path of the same radius on the left and right sides of the screen, and a bar stimulus (Fig. 20.7) in which two bars are stretched. For simplicity, we assumed constant acceleration. The stimuli were presented in such a way that their quantitative index (xi(t)), velocity (vi(t)), and acceleration (ai(t)) were different between the left and right sides. Here, the quantitative index is the position of the black dot on the circle (from 0 to 360 degrees) in the case of the circle stimulus, and the length of the stick in the case of the stick stimulus. We divided the range of each attribute value of quantitative index, velocity, and acceleration of the experimental stimuli into three large ranges (“large,” “medium,” and “small”). Then, considering the dominance structure of the difference between the left and right values of each attribute, we divided the range into three patterns: (1) a pattern in which only one attribute is dominant (e.g., the left stimulus is higher than the right one only for acceleration, while the other attributes are at the same level), (2) a pattern in which there is a trade-off between one attribute pair (e.g., the left stimulus is higher than the right one for acceleration, while the right stimulus is at the same level for the other attributes), and (3) a trade-off between two attribute pairs (e.g., the left stimulus is at a higher level than the right stimulus for acceleration and velocity, but the left stimulus is at a lower level than the right stimulus for the quantitative index). The values of each attribute of the experimental stimuli were set by random number generation within the corresponding range. Each participant was asked to watch two different patterns of each stimulus, totaling four movies. We asked each participant to watch the videos of the experimental stimuli on a PC screen and measured their gaze using an eye camera (eye movement
measurement device). For the point stimuli, we coded the gaze data by assuming that the participants were paying attention to the black dot on the circular orbit if they were looking at the square with the diameter of the circular orbit as one side. On the other hand, for the bar stimuli, we divided the PC screen into three parts and coded

Figure 20.6 Circular stimulus in the experiment (Hatori et al., 2010).

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Figure 20.7 Bar stimulus in the experiment (Hatori et al., 2010).

the data on the assumption that if the subject was looking at the left part of the screen, his attention was directed to the left bar stimulus, and if he was looking at the right part of the screen, his attention was directed to the right bar stimulus.

20.6.1.3 Experimental results We estimated the parameters (α, β, γ) of quantitative indices, velocity, and acceleration from the obtained measurement data by maximum likelihood estimation method. First, for the circular stimulus, only the acceleration parameter was significant (t(3087) 5 5.61, p , .001), as shown in Table 20.1. The likelihood ratio of the model was 0.582, which is a good value, and the model is considered to fit the measurement data well. For the rod stimulus, only the acceleration parameter was significant (t(1812) 5 4.89, p , .001). The likelihood ratio of the model fit was 0.285, which is relatively good. The results showed that the acceleration parameter was significant for both the circle and rod stimuli, indicating that people tended to pay more attention to stimuli with higher acceleration. This result suggests that people tend to pay attention not only to the statistics of social events, but also to the events with high acceleration.

20.6.1.4 Discussion In this study, we proposed a quantitative model for change detection in social events and conducted a quantitative analysis of the model through an experiment using an eye movement
measurement device. As a result, it was shown that the acceleration of the target event may have an effect on the change detection. In addition, Takemura, Hatori, and Fujii, (in preparation) showed that acceleration has a significant effect on change detection and decision tendency in experiments using more familiar social events, such as stock price fluctuations and changes in crime

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rates, as well as the results of the previous experiments. The results show that acceleration has a significant effect.

20.6.2 Experiments on stimulus variability and attention 20.6.2.1 Purpose of the study The products to which we direct our attention are different when we see a group of products arranged in a disorderly manner or when we see a group of products organized by color or size. It is assumed that the subsequent decision-making depends on the attention we pay when we acquire information, so it is important to develop a method to examine what attributes we pay attention to. Therefore the purpose of this study was to propose an experimental method for manipulating attention. In this study, we aimed to propose an experimental method for manipulating attention. Based on previous research on the manipulation of attention, an important concept is the saliency of an object (Braun & Julesz, 1998; Desimone & Duncan, 1995; Itti & Koch, 2001). Prominence refers to the relative ease with which a stimulus can be detected in space
time. In decision-making research, many studies have attempted to explain the phenomenon of preference reversal using the concept of saliency, but they often explain that the more salient attributes are given more weight, and there has been little research on what factors induce attention. In contrast, Takemura et al. (2009), Takemura, Ideno, and Hatori (2012), and Takemura, Ideno, Hayashi, et al. (2012) hypothesized that attention to an event is determined by the change of that event in space and time and developed a mathematical model that employs velocity and acceleration as indicators of change. Takemura, Ideno, and Hatori (2012) and Takemura, Ideno, Hayashi, et al. (2012) showed that the attention to radiation levels after the Great East Japan Earthquake was derived from the velocity and acceleration calculated from the changes in radiation levels. Takemura et al. (2009) examined the factors that lead to attention based on changes between time points. In this chapter, Murakami, Ideno, Tamari, and Takemura (2014) extend the concept of Takemura et al. They conducted a psychological experiment using a decision-making task and examined the effectiveness of the proposed method by measuring the eye movements of the decision makers.

20.6.2.2 Proposal of attention manipulation method Decision-making under risk refers to a situation in which the consequences of the adopted option and the probability of its occurrence are known (Takemura, 2014, 2019, 2020). In addition, in decision-making research under risk, lottery selection tasks are often used to study their nature (Takemura, 2014, 2020). Therefore we adopt the lottery selection task in our experimental system, following the previous studies. The experimental system consists of two stages. The first stage is to manipulate attention by the coefficient of variation (CV) (attention manipulation stage), and the

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second stage is to test whether attention has been manipulated by the CV (test stage). Eye movement data are obtained by measuring the gaze of the experimental participants during the selection process using an eye movement
measurement device. In this study, we employed the CV as a measure of the magnitude of the difference to examine whether the variability of events in a given problem space induces attention. The CV can be obtained by dividing the SD (σ) by the arithmetic mean (x), as shown in the following equation: CV 5

σ x

The proposed method assumes a decision-making situation in which two or more alternatives and the attributes of each alternative are explicitly stated. The CV is set for each attribute. By extending Takemura et al. (2009), it is thought that attention is directed to the part where the difference in information about the event at the same time is large. Therefore it is assumed that attention is induced to the attribute with high CV and not to the attribute with low CV. In the following example, a high CV is defined as a CV of 0.8 or higher, while a low CV is defined as a CV of 0.25 or lower.

20.6.2.3 Method of the experiment In this section, we report an application of the experimental system. To examine the effect of the CV on attention, we created four groups based on the combination of two alternative attributes and two high and low coefficients of variation and compared the eye movement data among the groups. To investigate the effectiveness of the proposed method, we examined whether the attentional tendencies of the four groups in the attention manipulation phase continued in the test phase. To test the effectiveness of the proposed method, the participants were asked to perform a choice task in which they manipulated their attention by the CV, followed by a choice task in which they tested the effectiveness of the proposed method. Eye movements during the choice task were acquired by an eye movement
measurement device. To examine the effect of the CV on attention, four groups (LL, HH, LH, and HL) were created by setting high and low coefficients of variation for the attributes of the choices (outcome and probability). There were 104 participants in the experiment (mean age 21 years, SD 2.9), 63 of whom were female. The experimental participants were randomly assigned to the following groups: 26 in the LL group, 27 in the HH group, 25 in the LH group, and 26 in the HL group. As an example of the manipulation of attention by the CV and the application of the experimental system, stimuli with high and low coefficients of variation for each attribute (outcome and probability) of the lottery selection task were presented to the experimental participants. For the lottery selection task in the attention manipulation stage, two lotteries were placed on the left and right sides of the

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screen. Two patterns of attributes were prepared: one with the result at the top and the probability at the bottom, and the other with the attributes positioned upside down. The participants belonging to the four groups were presented with the images of the lottery selection task 10 times, according to the combination of the two attributes and the high and low coefficients of variation. After the 10 lottery choices in the attentional manipulation phase, the participants were presented with the choice task of the lottery and the certain outcome twice in the test phase. In the lottery selection task, two alternatives were presented on the left and right sides of the test task, and the outcome and probability were switched. In the test task, two choices were presented on the left and right sides of the screen. The stimuli in the attentional control phase and the test phase were randomized in terms of the order of presentation. The results and the CV of the probability are shown below the stimuli of each group. For example, the CV of the LL group (upper left) is 0.22 for the outcome and 0 for the probability. For example, the CV of the LL group on the upper left is 0.22 for the result and 0 for the probability. The HH and LH groups are patterns in which the top and bottom of the result and probability are switched. In the test phase, we prepared two tasks, one with a high CV of the result and the other with a low CV, as an experiment. The purpose of this is to examine the effectiveness of the proposed method. According to the assumption of the proposed method, we can expect that the tasks with high CV of the results will induce attention to the results, and the tasks with low CV of the results will not induce attention to the results. If the manipulation of attention by the proposed method is not effective, it is expected that all four groups (LL, HH, LH, and HL) will show a tendency of attention such that no attention is induced to the outcome in test task 1 and attention is induced to the outcome in test task 2, with no difference in the tendency of attention among the four groups. It is predicted that there is no difference in the tendency of attention among the four groups. On the other hand, if the manipulation of attention by the proposed method is effective, the tendency of attention in the attention manipulation phase will be inherited in the test phase, and the tendency of attention in each of the four groups is expected to be different. The first task of the test phase has a low CV in the outcome and a medium CV in the probability. This task is called test task 1. For the second task the CV of the outcome is set to high and the CV of the probability is set to medium. This task is called test task 2.

20.6.2.4 Results The eye movement data obtained by the eye movement
measurement device were checked, and the data of one person whose eye movements were not recorded were excluded from the analysis. As a result, a total of 103 subjects (26 in the LL group, 27 in the HH group, 25 in the LH group, and 25 in the HL group) were included in the analysis. In this study, gaze pauses of 100 ms or longer were considered as gazing. Based on the raw data of eye movements, we counted how many times (gaze frequency) and how many seconds (gaze duration) the subjects gazed at the area surrounded by squares of outcome and probability information on the presented

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stimuli and calculated the results and their respective ratios (gaze frequency ratio and gaze duration ratio) for analysis and discussion. The ratio of gazing times is a numerical value obtained by dividing the total number of times a person gazed at the consequence category by the total number of times a person gazed at the consequence and probability categories before making a decision, and the ratio of gazing times is a numerical value obtained by dividing the total time a person gazed at the consequence category by the total time a person gazed at the consequence and probability categories before making a decision. The gaze time ratio is the total time spent gazing at the consequence category divided by the total time spent gazing at the consequence and probability categories up to the decision. The percentage of gazing times and the percentage of gazing durations in the manipulation phase of attention were calculated from the average of the eye movement data of the 10 choices of each participant in the experiment. The eye movements to be analyzed are from the time the stimulus is presented to the time the participant makes a decision. To examine the influence of the CV on attention, we examined the number of gazes, the duration of gazes, and their proportions in the attention manipulation stage. First, the overall tendency to gaze is described. Both the number of gazes and the duration of gazes were greater than the probability of gazing in all groups. Next, we describe the tendency of gazing for each group. The number of gazes and the duration of gazes of the probability were arranged in the order of the four groups from the most to the least, and the order of the number of gazes and the duration of gazes was LH, HH, LL, and HL group. In other words, when the CV of probability was high (LH and HH groups), the number of gazes and gazing time were higher than when the CV of probability was low (LL and HL groups), as predicted by the proposed method. In addition, a two-factor, two-level analysis of variance was conducted using the angle-transformed values of the percentage of gazing times and the percentage of gazing times as the dependent variables and the attributes of the choices and the high and low coefficients of variation as the independent variables. As a result, the main effect was significant between high and low coefficients of variation of probability for both the percentage of gazing times and the percentage of gazing times (F(1,99) 5 13.093, p , .001, and F(1,99) 5 12.010, p , .001). The effect of the CV on attention was statistically significant for probability, and the effect of the CV on gaze was observed for probability.

20.6.2.5 Discussion The purpose of this study was to conduct a psychological experiment using a decision-making task and to examine the effectiveness of the proposed method based on the eye movements of the decision makers in the experiment. The results of the application of the experimental system showed that the effect of the CV on attention depended on the attributes of the alternatives, and that attention was induced when the difference was small for the outcome of the alternatives, and when the difference was large for the probability. In this study, a decision-making task under risk was used, in which decision-making phenomena can be expressed

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numerically with a simple structure. The proposed method used a simple index of manipulation called the CV, and the effectiveness of the proposed method was also suggested by the application examples. This suggests that there is a possibility that attention can be controlled from the variability of task stimuli, and that situationdependent decision-making may occur accordingly.

20.7

Model of category focusing and construction of mental ruler

20.7.1 Prospect theory and the mental box model Kahneman and Tversky (1979) point out that human decision-making phenomena have qualitative characteristics similar to those of the human visual system. For example, they use the concept of reference point and the frame metaphor used in perceptual psychology to explain biases in judgment and decision-making. In prospect theory, there is a single reference point, and the value function in the gain domain is concave downward and the value function in the loss domain is convex downward. Typical examples of such approaches are “decision framing” (Tversky & Kahneman, 1981), “mental accounting” (Thaler, 1980, 1999), and “psychological purse” model (Kojima, 1959, 1994). However, these models (with the exception of the range
frequency model discussed later) account for preference reversal in choice and judgment, framing effects at risk, and contextual effects in monetary transactions and are context-dependent for category judgment. For example, people generally tend to focus on “something very beautiful” (or “something very ugly”) or “something very expensive” (or “something very cheap”), which belong to these categories. This can be interpreted as focusing on the endpoint of Luce (1959b) solved the functional equation in his paper “On Possible Psychophysical Laws,” and when stimulus and response are on an interval scale, the only psychophysical laws are Fechner’s logarithmic function or Stevens’ power function. However, the “possible psychophysical laws” have been proved only mathematically, and the preconditions may not be fulfilled. Takemura (1998, 2001) reconsidered the theory of perceptual judgments and proposed the “mental ruler theory” as an approximate law common to judgments and decisions. In the mental ruler model, unlike the prospect theory, an inverse S-shaped or S-shaped value function is expected to appear. Such a value function is actually observed in Fan and Takemura (2005). Such a value function is derived when there are two reference points, but in actual human judgment, there may be more than two reference points. In such a case the value function is expected to be wavy. Thus far in this book, situation-dependent judgments and decisions have been explained using the contingent focus model and the mental ruler model, but the basis of these processes is the hypothesis of category focus, which will be used as the basis for the explanation in this chapter.

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20.7.2 Category-focusing hypothesis and the mental box model 20.7.2.1 Range
frequency theory As explained in Chapter 19, The Mental Ruler Model: Qualitative and Mathematical Representations of Contingent Judgment, Parducci et al. proposed the range
frequency theory as a theoretical model to explain the situational dependence of category judgments (Parducci, 1965; Parducci & Perrett, 1971; Parducci & Wedell, 1986). Frequency theory explains the situational dependence of categorical judgments by two principles: the range principle and the frequency principle. The former principle states that the judge constructs a psychological range with the extremes (maximum and minimum) of the presented stimuli as its endpoints and divides the psychological range into categories. The latter principle is based on the fact that the decision maker has to decide between each category (e.g., “very large,” “a little large,” “normal,” “a little small,” “very small”). The latter principle represents allocating the presented stimuli equally to each category so that the judge uses each category (e.g., “very large,” “a little large,” “normal,” “a little small,” “very small”) with the same frequency. According to this theory, category judgments are expected to depend on the frequency of stimulus presentation. In other words, when the stimulus distribution is unimodal like a normal distribution, the mental range of the category near the center is expected to be narrower and, therefore, more sensitive to differences in the stimuli near the center. On the other hand, in the case of a bimodal distribution, where the stimulus distribution is higher at both ends, the mental range of the categories near the ends is expected to be narrower. However, the range
frequency theory assumes that people systematically allocate repeatedly presented stimuli to categories based on their distributions. However, in reality, there may be situations in which people make category judgments under conditions in which it is not always easy to make systematic judgments, such as when stimuli are presented singly or when the stimulus distribution is uncertain. Therefore to explain the situation-dependence of category judgments in various situations in a unified manner, it is difficult to say that the frequency principle described earlier is sufficient, and a theoretical framework to explain such situation-dependence from a more comprehensive perspective is necessary.

20.7.2.2 Category-focusing hypothesis Based on the previous, this study focuses on “attention” to the object of judgment as a more comprehensive explanatory concept than “frequency” of the object of judgment. Based on the hypothesis that the situation-dependence of human judgments and choices is caused by the dependence of attention to the judgment object on the situation and context (Takemura, 1994; Fujii & Takemura, 2001), we propose the category-focusing hypothesis as a basic mental process hypothesis to explain the relationship between the situation-dependence of category judgments and attention (Fujii & Takemura, 2002; Takemura & Fujii, 2001; Takemura, Fujii, & Karasawa, 2004).

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Aenon:Low

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Figure 20.8 Category-focusing hypothesis in the mental box model. Source: Modified from Hatori, T., Takemura, K., Fujii, S., & Ideno, T. (2011). Kategorii Handan niokeru Shoutenka Kasetsu no Kentou: Kokoro no Hako Moderu niyoru Setsumei [A test of the focusing hypothesis for category judgment: An explanation using the mental-box model]. The Japanese Journal of Psychology, 82, 132
140 (in Japanese).

The category-focusing hypothesis considers that when attention is focused on the category in question, the subjective proportion of members in that category decreases compared to the proportion of members in other unfocused categories (Fujii & Takemura, 2002; Takemura & Fujii, 2001; Takemura et al., 2004). This hypothesis can be expressed using a metaphorical conceptual model of a “mental box.” In other words, it is thought that people subjectively construct a “mental box” corresponding to each category according to the situation when they perform category evaluation. Then, using these mental boxes, we can think that we perform category evaluation as if we were classifying the object of judgment into each box. The category-focusing hypothesis predicts that when attention is focused on a mental box (category), the volume of that box decreases, and we are more sensitive to even small differences in the objects of judgment (Fig. 20.8). The category-focusing hypothesis can be explained using a mathematical model as follows. That is, if the amount of attention (focal parameter) to category Ci is ki, and the subjective proportion of members belonging to category Ci is p(Ci), the category-focusing hypothesis is pðCi Þ ~1=f ðki Þ

(20.7)

where f represents a monotonically increasing function and ~ represents a directly proportional relationship. The subjective composition ratio p(Ci) is the ratio of the number of elements in category Ci, Card(Ci), to the total number of elements and assuming that there is no overlap between categories. CardðCi Þ
 pð C i Þ 5 P j Card Cj

(20.8)

Eq. (20.7) shows that the subjective proportion of a category is inversely proportional to the monotonically increasing function of the amount of attention to that category.

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The predictions of the range
frequency theory described earlier can be derived consistently from the category-focusing hypothesis by including the assumption that the frequency of stimulus presentation is proportional to the frequency of category focusing (frequency of attention) (Takemura & Fujii, 2001; Takemura et al., 2004). In other words, the expectation that the mental range of the category near the center will become narrower in the case of a unimodal stimulus distribution can be explained consistently from the simple assumption of the category-focusing hypothesis if we consider that focusing on the category near the center to which highfrequency stimuli belong occurs. The case of bimodal distribution is also consistent with this hypothesis. Thus by assuming that there is a proportional relationship between the frequency of stimulus presentation and the frequency of attention, we can consistently derive the predictions of the range
frequency theory from the category-focus hypothesis. However, the focusing of attention in the category-focusing hypothesis is thought to depend not only on its “frequency” but also on the “persistence” and “intensity” of attention. Therefore it can be said that the category-focusing hypothesis presents a more comprehensive theoretical framework than the range
frequency theory.

20.7.2.3 Explanation of situation-dependent judgment phenomena by the category-focusing hypothesis According to the earlier category-focusing hypothesis, the evaluative function in situation-dependent judgment and the psychophysical function that relates sensory intensity to external stimuli are explained as functions that change according to the degree of focus on the category (Takemura & Fujii, 2001). In other words, according to this hypothesis, when we focus on the category to which an object belongs, we would expect the volume of that category to become smaller, and we would become more sensitive to differences between objects. This is the evaluation function near the object. It can be rephrased as indicating that the slope of the psychophysical function will increase. Describing the earlier mathematically, we have the following equation: dϕðxÞ ~f ðki Þ; xACi dx

(20.9)

where ϕ(x) represents the evaluation function (psychophysical function) for stimulus x belonging to category Ci, which is assumed here to be a differentiable continuous function. Eq. (20.3) shows that the derivative of the evaluation function for a stimulus (the slope of the function) is directly proportional to the monotonically increasing function of the amount of attention. From this hypothesis, we can theoretically explain the form of the evaluation function assumed in prospect theory and signal detection theory (Takemura & Fujii, 2001). First, the probability weighting function of Kahneman and Tversky’s (1979) prospect theory and the value function of Takemura’s (1998) psychological difference theory assume an inverse S-shaped evaluation function. This can be explained

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by the category-focusing hypothesis and the property that attention tends to be focused on the endpoint of a category (Takemura, 1998). That is, assuming that the category evaluation scale consists of five levels, from “I like it very much” to “I do not like it at all,” for example, as shown in Fig. 20.9. Attention is focused on the endpoint of the category, and Eq. (20.9) is obtained. Thus it is expected that the slope of the value function will increase near the endpoint. As a result, an inverse S-shaped value function is expected to be formed. In prospect theory the value function will be concave in the gain region near the reference point and convex in the loss region. According to the hypothesis of category focusing, the shape of such a value function would be near the reference point. Theoretically, this can be interpreted as being formed by the concentration of attention. On the other hand, in signal detection theory, an S-shaped evaluation function (e.g., logistic curve) is assumed, which can be explained as being caused by the concentration of attention on categories near the midpoint (threshold) shown in Fig. 20.10. Thus the categoryfocusing hypothesis consistently explains the value function and probability weighting function in prospect theory, and the value function in psychophysical difference theory and signal detection theory from the unified perspective of focusing attention on categories. In addition, social judgment phenomena pointed out in group psychology and social psychology can also be understood from a simpler and more unified perspective by using hypotheses that focus attention on categories (Takemura & Fujii, 2001). For example, Marques, Yzerbyt, and Leyens (1988) found that inferior or deviant members of the inner group were rated extremely low and were psychologically isolated from the inner group. It was pointed out that there is an ingroup and an outgroup bias, the so-called black sheep effect, in which outgroup members Value f (x)

x Not good

Very good

Figure 20.9 Inversed S-shaped value function and mental box. Source: Modified from Hatori, T., Takemura, K., Fujii, S., & Ideno, T. (2011). Kategorii Handan niokeru Shoutenka Kasetsu no Kentou: Kokoro no Hako Moderu niyoru Setsumei [A test of the focusing hypothesis for category judgment: An explanation using the mental-box model]. The Japanese Journal of Psychology, 82, 132
140 (in Japanese).

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Value

f (x)

x Not good

Very good

Figure 20.10 S-shaped value function and mental box. Source: Modified from Hatori, T., Takemura, K., Fujii, S., & Ideno, T. (2011). Kategorii Handan niokeru Shoutenka Kasetsu no Kentou: Kokoro no Hako Moderu niyoru Setsumei [A test of the focusing hypothesis for category judgment: An explanation using the mental-box model]. The Japanese Journal of Psychology, 82, 132
140 (in Japanese).

receive higher ratings even when they perform equally good tasks. Since group members’ attention to task performance is highly focused, it can be explained by the category focus transformation hypothesis if we consider that they have increased sensitivity to good or bad task performance, as in the case where attention is focused around a reference point. In addition, Sherif and Hovland’s (1961) study of social judgment found that individuals whose ego is involved in the attitude object become discriminating and less receptive to differences in attitude judgment between themselves and others. Published, this can also be consistently explained by the category-focusing hypothesis when we consider that there is a focusing on attitude categories. The category-focusing hypothesis predicts that when attention is focused on a category, the proportion of members belonging to that category will be lower than the proportion of members belonging to other unfocused categories. Metaphorically speaking, if we pay more attention to the heart box (category), the volume of that box will be smaller (see Fig. 20.8). Using another metaphor, we can think of the members of the focused category as being bloated and out of the box.

20.7.2.4 Composition of the mental ruler model from the mental box model and its relationship to the range and frequency model A mental ruler (a measure of psychological judgment) can be thought of as a collection of categories. In a simple example, a scale such as the Case 5 method can be thought of as a set of linguistic categories such as “very high” and “very low.” From the category-focus hypothesis and the assumption that we tend to focus on the endpoints of the categories, we can predict that the inverse S-shaped evaluation

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function assumed in psychological difference theory will appear. In other words, when we focus on the endpoint, the volume of the category becomes narrower, and as a result, the slope of the value function near the endpoint becomes steeper. Also, by focusing on the category near the midpoint, we can predict that an S-shaped valuation function will appear. In other words, focusing on the area near the midpoint narrows the volume of the category, and as a result, the slope of the value function near the midpoint becomes steeper. Thus an S-shaped value function is constructed as shown in Fig. 20.10. Wedell and Pettibone (1999) explained the contextual effect of the value function in terms of stimulus distribution, unlike the mental ruler model. He succeeded in explaining the decision-making phenomenon by modifying and using Parducci’s (1965) range
frequency theory, a theory of perceptual judgment. This range
frequency was originally a theory of categorical judgment and was developed by critically developing Helson’s theory of adaptive degree. The range
frequency theory states that perceptual judgments are made by a compromise (mathematical, weight averaging) of the range principle and the frequency principle. The range principle predicts that judgments are determined by the relative position (ratio) of the physical value of the stimulus within the stimulus range. The frequency principle also predicts that each category used in the judgment will be used with equal frequency. Therefore the frequency principle predicts that the judgment value will vary depending on the context of stimulus presentation (Wedell & Pettibone, 1999). Assuming that the frequency principle works for perceptual judgments, if the stimulus distribution is a one-peak-type distribution like a normal distribution, the evaluation function will be an S-shaped curve like a logistic function, and the stimulus distribution will be physical. If it is a bimodal-type distribution where the low and high points of the target stimulus are the vertices, the evaluation function will be an inverse S-shaped curve (Fig. 20.9). In this range
frequency theory, there is no psychological explanation why the stimulus distribution and the value function are related. The mental box model explains that the higher the stimulus frequency, the higher the attention and the smaller the volume of the category. The mental box model is able to qualitatively predict psychophysical functions and contextual effects from very simple qualitative properties. This hypothesis is simpler than the two principles assumed in range
frequency mathematical theory. It is also capable of predicting the evaluation function when there are multiple reference points.

20.7.3 Empirical study of mental box model 20.7.3.1 Purpose of the experiment In this way the category-focused hypothesis can provide a consistent explanation for the shape of the value function and various phenomena of social judgment assumed in existing theories, and although it has various theoretical spreads, it is empirical. The validity has not been fully verified directly. The purpose of this

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study is to examine the validity of this hypothesis by conducting experiments that manipulate the degree of attention focusing on categories. Regarding the effect of focusing on categories, the availability heuristics hypothesis (Tversky & Kahneman, 1974) exists as a hypothesis that competes with the category-focusing hypothesis (Fujii & Takemura, 2002). This hypothesis shows that the familiarity, salience, and imaginability of a case or event influence various judgments such as the estimation of the frequency of occurrence of the event. According to this hypothesis, requesting cognitive information processing for a category in advance makes it easier to recall that category and its corresponding events, and, thus, increases the availability of that category. As a result, it is expected that the response rate of the category will improve in the category evaluation task. For example, according to this hypothesis, those who think about “deliciousness” in advance are more likely to recall “deliciousness” and past experiences related to it than those who do not, and as a result, the subject. It is possible that the tendency to judge the case as “delicious” will increase. From the earlier, if the size of the category tends to decrease by experimentally manipulating the attention focusing on the category, the result is deduced from the availability heuristics hypothesis in the category evaluation task of this study. While disproving this expectation, it seems to support the category-focused hypothesis. We conducted the following experiment (Hatori, Takemura, Fujii, & Ideno, 2011).

20.7.3.2 Method Participants: Total 40 students from Waseda University were targeted (16 males, 24 females, average age 20.33 years, age SD 1.42 years). Experimental procedure: In this experiment a total of five themes were selected: “deliciousness,” “height,” “rich,” “blue,” and “moral correctness.” Request the collaborators to answer the written tasks using the questionnaire and then request the answers to the category-rating tasks using the PC or the questionnaire, as explained later for each theme. As the experimental conditions, the experimental collaborators were randomly divided into two groups of 20 each, and the conditions for the degree of attention focusing on each theme category were controlled by requesting answers to different descriptive tasks. Here, the experimental collaborators who promoted the focus of attention on the categories related to the subject are called the experimental group, and the other collaborators are called the control group. Through all five themes the experimental group performed only the descriptive tasks for the experimental group, and the control group performed only the descriptive tasks for the control group. In addition, the task order of the five themes was randomly set for each collaborator. All experiments were conducted in the same classroom on the Waseda University campus in a one-to-one individual experiment format between the experimenter and the collaborators. In addition, time control was not performed for both the description task and the category-rating task, and the experiment was completed when the collaborators completed the task. The previous five themes were set in consideration of the evaluation tasks for as many different categories as possible. For “deliciousness,” taste judgment for food,

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and for “height,” perceptual judgments on physical quantities, socioeconomic value judgments on “rich,” and visual judgments on “blue” are required. In addition, it was decided to include higher order social value judgments rather than “moral correctness” in the experimental tasks on a trial basis. At the beginning the category-focusing hypothesis was explained using the category by the five-case method as a general example, but in the following experiment, the judgment task using the two-case method is imposed. The reason for using the two-case method in this study is that by keeping the number of categories to a minimum, it is easier to perform an experimental operation of attention focusing on one category, and the alternative judgment is more focused. This is because it was thought that the effect of the earlier could be confirmed more clearly. To obtain more general knowledge about the category-focusing effect, it is important to set various number of categories and examine the effect. It is considered that it does not affect the essential relationship between the mental range of categories and the amount of attention in the hypothesis, and it is considered that empirical examination of this hypothesis is possible in this experimental task as well. Task 1 “Deliciousness”: First, in the description task, the degree of attention focusing on “deliciousness” was experimentally manipulated. Specifically, for the experimental group, “What do you think it means that food is ‘delicious’ in the first place? After thinking slowly, your thoughts are as follows, 3, 4 lines-Please describe in the range of about a dozen lines.”, and asked them to describe “delicious,” which encouraged the focus of attention on the “deliciousness” of food. On the other hand, for the control group, we arbitrarily chose the subject of “stairs” as something that is not considered to be related to the “deliciousness” of food and asked the participants “What is stairs in the first place. Would you like to think slowly and then describe your thoughts in the range of 3 or 4 lines-a dozen or so lines?”. We asked them to describe the stairs. The average time required for the description task was 248.05 seconds (SD 120.12 seconds) for the experimental group and 268.55 seconds (SD 103.08 seconds) for the control group. Immediately after completing the description task, move on to the category-rating task, present a total of 32 food photos one by one on the computer screen, and show the food photos that you think are “really delicious” and the food photos that are not. This selection answer is the dependent variable of this experimental task, and we compared and examined the experimental group and the control group. Task 2 “Height”: In the same way as earlier, in the description task, the focus of attention on “height” was experimentally manipulated. Teach the experimental group, “What do you think are the advantages and disadvantages of ‘tall people’ in the first place?” And describe the advantages and disadvantages of “tall people.” On the other hand, for the control group, the subject of “long-distance relationship” was arbitrarily selected as something that is not considered to be related to “height.” The participants in the control group were asked to describe the advantages and disadvantages of “longdistance romantic relationships.” The average time required for the description task was 310.40 seconds (SD 133.15 seconds) for the experimental group and 246.55 seconds (SD 104.21 seconds) for the control group. After completing the description task, immediately move on to the category-rating task and randomly present one height

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from the range of 160
190 cm on the computer screen at 1-cm intervals and think that it is “really tall.” I had them classify what was not. At that time, we did not specify the distinction between males and females and asked the participants to intuitively judge “whether or not they were really tall.” In this task the average number of selections per person was 0.48 out of 31 (SD) for those who answered “really tall” to a height shorter than the height that was not judged to be “really tall.” It is considered that the participants made consistent judgments in general. Task 3 “Rich”: First, in the description task, to experimentally manipulate the focus of attention on “rich.” The participants in the experimental condition were asked as follows: “What do you think ‘rich’ mean in the first place?”. They were also asked to describe “rich.” For the control group, we arbitrarily chose the subject of “chair” and instructed as follows: “What do you think ‘chair’ is in the first place?”. The participants in the control group were asked to describe “chair.” The average time required for the description task was 263.55 seconds (SD 120.80 seconds) for the experimental group and 273.80 seconds (SD 105.55 seconds) for the control group. After completing the description task, immediately move on to the category evaluation task and randomly present one annual income from the range of 3 million yen to 45 million yen on the computer screen in 500,000 yen intervals on the computer screen. The participants were asked to classify the annual income that seems to be “really rich” and the annual income that is not. Similar to the issue of “height,” the average number of times per capita selection of cases where “really rich” is answered for an annual income to be lower than the annual income that was not judged to be “really rich” was only 1.15 out of 85 (SD 1.09), and it is considered that the participants generally made consistent judgments. Task 4 “Blue”: First, in the description task, to experimentally manipulate the focusing of attention to “blue,” the participants in the experimental group were asked as follows: “Please list as many things as possible that you think are very ‘blue’.” They were also asked to describe what kind of ‘blue’ things are. On the other hand, for the control group, arbitrarily select the subject “round thing.” The participants in the control group were instructed as follows: “Please list as many things that you think are very ‘round’, and What about ‘round’ things?”. They were asked to describe if there was something like that. The average time required for the description task was 240.90 seconds (SD 162.62 seconds) for the experimental group and 292.60 seconds (SD 147.68 seconds) for the control group. After completing the description task, immediately move to the category-rating task, present a gradation bar on one questionnaire, and select the range of colors that you think is “blue” by drawing two straight lines vertically. The size of the gradation bar was 246 cm in width and 27 cm in height and showed colors from red [RGB (255,0,0), left end] to green [RGB (0,255,0), right end]. Task 5 “Morality correctness”: First of all, in the description task, to experimentally manipulate the focus of attention on “moral correctness,” the participants in the experimental group were asked as follows: “What do you think ‘morally correct’ is in the first place?”. They were also asked to describe “moral correctness.” For the control group, we arbitrarily selected the theme of “concrete” and instructed as follows: “What do

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you think ‘concrete’ is in the first place?”. They were also asked to describe “concrete.” The average time required for the description task was 255.50 seconds (SD 107.80 seconds) for the experimental group and 240.20 seconds (SD 93.87 seconds) for the control group. After completing the description task, immediately move on to the category-rating task, present a total of 34 types of action 7 to the collaborators one by one on the computer screen, and think that they are “morally correct in any situation.” We asked them to classify behaviors and nonbehaviors.

20.7.3.3 Results Task 1 “Deliciousness”: In general, it was confirmed that the experimental group tended to select the presented dish as “really delicious” less frequently than the control group. A t-test was performed on the difference in the average number of selections between groups, and a significant difference was found (t(38) 5 22.09, p , .05). Next, for each of the experimental and the control groups, the correlation between the number of selections and the amount of description (number of characters) in the description task was investigated. As a result, a significant positive correlation (r 5 0.54, p , .05) was found in the experimental group, and the larger the amount of description, the larger the number of selections. On the other hand, the correlation in the control group was not significant (r 5 20.23, n.s.). Task 2 “Height”: In general, it was confirmed that the experimental group tended to select the presented height as “really tall” less frequently than the control group. Significant differences were found in the differences in the average number of selections between groups (t(38) 5 22.1, p , .05). In addition, when the average of the thresholds that changed from the evaluation of “not tall” to the evaluation of “high” was calculated, it was 173.26 cm (SD 5.96 cm) for the experimental group and 169.25 cm (SD 5.02) for the control group. A significant difference was also found between the experimental and the control groups for this statistic (t(38) 5 2.22, p , .05). As in task 1, when the correlation coefficient between the number of selections and the amount of description was calculated, a significant correlation was found in both the experimental group (r 5 0.17, n.s.) and the control group (r 5 0.15, n.s.). Task 3 “Rich”: In general, it was confirmed that the experimental group tended to select the presented annual income as “really rich” less frequently than the control group. Significant differences were found in the differences in the average number of selections between groups (t(38) 5 23.56, p , .005). In addition, the average of the thresholds that changed from the evaluation of “not rich” to the evaluation of “rich” was calculated. It was a yen (SD 40.433 million yen). This statistic was also significantly different between the experimental and control groups (t(38) 5 3.74, p , .001). The correlation between the number of selections and the amount of description was not significant in either the experimental group (r 5 0.05, n.s.) or the control group (r 5 20.28, n.s.). Task 4 “Blue”: The average value of the selection range judged to be “blue” in the gradation bar was larger in the experimental group than in the control group. The median selection range was almost the same between the two groups. No

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significant difference was found in the difference in mean selection between groups (t(38) 5 1.04, n.s.). The correlation between the number of selections and the amount of description was not significant in either the experimental group (r 5 20.03, n.s.) or the control group (r 5 20.28, n.s.). Task 5 “Morality correctness”: The average number of times the presented behavior was selected as “morally correct in any situation” between the experimental group and the control group was about the same level. In addition, the median number of selections was higher in the experimental group than in the control group. No significant difference was found in the difference in the average number of selections between groups (t(38) 5 20.22, n.s.). The correlation between the number of selections and the amount of description was not significant in the experimental group (r 5 0.08, n.s.), but a significant negative correlation was found in the control group (r 5 20.59, p , .01), the larger the amount of description, the smaller the number of selections.

20.7.3.4 Discussions In this study, to verify the validity of the category-focusing hypothesis, we conducted an experiment of the category scoring task in which the degree of attention focusing on the category was manipulated. As a result, out of the five experimental tasks, the hypothesis was supported for the experimental tasks of “delicious food,” “height,” and “rich.” That is, the number of responses matched the theoretical prediction of the category-focusing hypothesis and selected the presentation stimulus to belong to the category under the conditions that promoted the focusing of attention to these categories, compared to the conditions that did not. The result was significantly reduced. Furthermore, for “height” and “rich,” the height threshold judged to be “really tall” and the annual income threshold judged to be “really rich” are for these categories. There was a tendency for it to increase significantly under conditions that encouraged focus of attention. These results suggest that, as this hypothesis predicts, focusing on a category reduces the subjective composition ratio (capacity of the heart box) of that category. As mentioned earlier, regarding the effect of focusing on categories, the opposite effect to the category-focusing hypothesis is expected from the availability heuristics hypothesis, but the previous experimental data are at least the categories targeted in this study. In the evaluation task, it can be said that it disproved the working hypothesis deduced from the availability heuristics hypothesis and supported the category-focusing hypothesis. However, for the experimental tasks of “blue” and “moral correctness,” the effect of attention focusing on the categories was not significant. The reason why such a result was obtained is not always clear from this experiment, but one possibility is as follows. First, regarding the “blue” task, it is possible that it was difficult to focus attention on the visual concept of “blue” itself under the experimental conditions of enumerating blue objects linguistically. In this regard, further studies will be required, such as devising experimental conditions that manipulate attention focusing on visual categories. On the other hand, regarding “moral correctness,” the collaborators have a firm belief in advance about the moral correctness of the

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behavior presented in the experiment, and it has already been sufficiently focused. It is possible that this is the cause of the results. If this possibility were valid, it is possible that it was difficult to sufficiently promote categorical focusing in this experimental operation. In addition, when the relationship between the category rating and the amount of description in the description task was examined, no significant relationship could be confirmed between the two, except for the tasks of “deliciousness” and “moral correctness.” It was. In addition, in the “deliciousness” task, the larger the amount of description in the experimental group, the larger the number of responses, and in the “moral correctness” task, the larger the amount of description in the control group, the smaller the number of responses. There was a tendency. Assuming that the amount of description in the description task is proportional to the amount of attention to the category, it is expected from this hypothesis that the larger the amount of description related to the category, the smaller the number of selected answers. At least from the results of this experiment, such an effect could not be confirmed. However, it is not always clear whether or not the amount of attention to the category and the amount of description in the description task are in a positive proportional relationship. For this point, for example, an eye gaze recorder is used. It will be necessary to further study by methods such as observing the amount of attention during experimental operations externally, such as measuring how much attention is paid to typical stimuli belonging to this category. As mentioned at the beginning, the category-focused hypothesis can explain the mechanism of the perceptual phenomenon in group psychology, the psychophysical function in psychophysics, or the value function in prospect theory and psychophysical difference theory. It is considered to be a basic behavioral hypothesis with a wide range of theoretical spreads. In the future, based on the results of this study, we will repeat additional experiments to test the hypothesis, and whether this hypothesis can provide theoretical and empirical grounds for such perceptual phenomena and decision-making models. It is important to consider. It is also a future task to quantitatively analyze the effect of category focusing. For that purpose, it is necessary to create a metric model composed of measurable variables based on the conceptual model proposed in this study, and to estimate the goodness of fit and focus parameters of the model. Furthermore, it is also an important task to compare with other related hypotheses such as range
frequency theory. Finally, the category-focusing hypothesis shows the mental mechanism that when attention is paid to a category, the mental range of that category is narrowed, but what kind of mental mechanism is behind such a mental process? It is not clear from this study whether or not is working.

20.8

Conclusion and future perspective

In this chapter, we have discussed the problem of attention, which is the basis of the mental ruler model and the contingent focus model. First of all, we proposed a

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mathematical model of attention that shows that the velocity (first derivative) and acceleration (second derivative) of an object in space and time affect not only the physical quantity of the object, but also its effect, and showed its validity to some extent in surveys and experiments. Thus it was suggested that attention is affected by things like speed and acceleration with respect to changes in the object, and that this can explain to some extent the availability heuristics and biases that have been mentioned. This suggests that these features of human attention may lead to irrational and poor decision-making in some situations. As an example of our investigation, we proposed a model that points to one possible reason why so much attention is being paid to the transmission of a new coronavirus. The basic hypothesis is that the rate of attention to a social event is determined not only by the statistics of the social event, but also by indicators of change in time and space. Indices related to change include velocity and acceleration. In this presentation, I describe this hypothesis, the mathematical model derived from it, and the related quantitative analysis and analyze the relationship between social attention to the new coronavirus infection and the actual number of infected people and the number of newspaper articles. Based on the results of these studies, I would like to consider the social psychological phenomenon of the new coronavirus problem. As suggested in this study, people’s social attention suggested by information search about the new coronavirus has an impact not only on whether the number of infected people is actually high or low, but also on the infection rate and acceleration. It was found that the number of cases received. This shows that people are influenced by factors other than objective indicators, such as the way information is presented and sequencing patterns. In this chapter, I further pointed out that a model of judgment and decisionmaking with two or more multiple points of reference, that is, a generalized mental ruler model, may be valid, and that there is an attention-focusing hypothesis behind this as well as a situation-dependent focusing model. In addition, in this chapter, I proposed the category-focusing hypothesis behind such a theory and presented a model of the mental box. I showed that from the category-focusing hypothesis, the mental ruler model can be constructed. In this chapter, I presented the model of the mental box as a new model of category judgment. In this model, we hypothesize that when attention is focused on a category, the psychological scope of that category becomes narrower (category-focusing hypothesis). To explain this hypothesis using the metaphor of the “mental box” model, the more attention is directed to a box of the mind (i.e., a category set), the smaller the size of that box (i.e., the cardinal number of the category set) becomes. This hypothesis was tested in an experiment in which the degree of attentional focus on a given linguistic category was manipulated. The results showed a category concentration effect in three experimental tasks (“food,” “height,” and “income”), supporting the hypothesis. Based on these results, the validity of the hypothesis was examined. Thus the slope of the value function becomes steeper when attention is too focused on the subject, suggesting a sensitive response. This suggests that excessive concentration of attention may be an opportunity to reach irrational decisions in some respects.

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We have proposed a model indicating one possible explanation of how people pay attention to events and how attention influences decision-making. The fundamental hypothesis is that attention rates of social phenomena are determined by indicators of change in time and space as well as statistical values, and the generated attention influences the category focusing and making decision. We believe that these factors need to be fully considered in risk communication of new coronavirus infections. The fact that great attention is now being paid to Covid-19 and that people are becoming anxious and fearful is related to the rapid occurrence of this infection. However, people are overreacting, especially in the early stages, and it is questionable whether the response is balanced with other health problems. The research introduced in this chapters must be further explored, and there are methodological limitations, but analysis suggests that attention toward social events such as Covid-19, as seen from information searches, is affected by the presentation of the information and its sequence pattern, not only by objective indicators. This tells me that these factors must be duly considered in relation to risk communication for Covid-19 as well. Governments and the media broadcast detail the numbers of infected and dead from Covid-19 but hardly provide any information comparing its risks to other risks such as other diseases or accidents. Providing comparison to other diseases or accidents is a principle of normal risk information, but in this case, it is rarely followed. This creates a bias in people’s risk perception and may be encouraging prejudice and discrimination and, hence, may make bad decisions. People’s perceptions of risk and decision-making do not always correspond to objective probabilities (Slovic, 1987, 2010). New risks especially tend to cause extreme responses (Committee of Infrastructure Planning and Management, Japan Society of Civil Engineers, 2021). With the current problem of Covid-19 also, comparing to other diseases or accidents, its risk is overestimated in people’s judgment, and there may well be a bias in their decision-making than usual (Committee of Infrastructure Planning and Management, Japan Society of Civil Engineers, 2021).

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Fan, L., & Takemura, K. (2005). Fitting a psychometric function to price Judgments: An analysis of consumers’ judgments for discounted price, Perceptual and Motor Skills, 101 (1), 223
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140, in Japanese. Holman, E. A., Thomson, R. R., Garfin, D. R., & Silver, R. C. (2020). The unfolding COVID-19 pandemic: A probability-based, nationally representative study of mental health in the United States. Science Advances, 6, eabd5390. Available from https://doi. org/10.1126/sciadv.abd5390. Ideno, T., & Takemura, K. (2018). Senko no keisei katei ni kansuru jikkenteki kento [An experimental study of preference construction process]. In K. Takemura (Ed.), Senko¯ keisei to ishikettei [Preference construction and decision making] (pp. 99
122). Tokyo: Keiso Shobo, in Japanese. Ideno, T., Hayashi, M., Sakagami, T., Fujii, S., Okubo, S., Tamari, Y., . . . Takemura, K. (2011a). Chikaku handan kadai wo moch¯ıta senk¯o keisei katei no kent¯o [An experimental study of preference construction using a perceptual judgment task]. In Proceedings of the 75th annual convention of the Japanese Psychological Association (p. 88) (in Japanese). Ideno, T., Hayashi, M., Sakagami, T., Fujii, S., Okubo, S., Tamari, Y., . . . Takemura, K. (2011b). Sentaku kodo ni yoru senko keisei katei no kisoteki kenkyu [A basic study of preference formation process by choice]. In Paper presented at the 15th conference of experimental social science (in Japanese). Itti, L., & Koch, C. (2001). Computational modelling of visual attention. Nature Reviews. Neuroscience, 2, 194
203. Kahneman, D. (1973). Attention and effort. Englewood Cliffs: Prentice-Hall. Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica: Journal of the Econometric Society, 47, 263
292. Kojima, S. (1959). Shohisha shinri no kenkyu [Consumer psychology]. Tokyo: Nihon Seisansei Honbu, in Japanese. Kojima, S. (1994). Psychological approach to consumer buying decisions: Analysis of the psychological purse and psychology of price. Japanese Psychological Research, 36, 10
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Marques, J. M., Yzerbyt, V. Y., & Leyens, J. P. (1988). The “black sheep effect”: Extremity of judgments towards ingroup members as a function of group identification. European Journal of Social Psychology, 18, 1
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369. Murakami, H., Ideno, T., Tamari, Y., & Takemura, K. (2014). Ishi Kettei Kadai niokeru Hendou Keisuu wo Mochiita Chuui no Yuudouhou no Teian: Gankyuu Undou Sokutei niyoru Kentou [Method of inducing attention using coefficient of variation in decision making task: Proposal and an empirical test by eye movement measurement]. Transactions of Japan Society of Kansei Engineering, 13, 527
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1322. Slovic, P. (1987). Perception of risk. Science (New York, N.Y.), 236, 280
285. Slovic, P. (Ed.), (2010). The feeling of risk: New perspectives on risk perception. New York: Routledge. Takemura, K. (1994). Furemingu Koka no Rironteki Setsumei: Risukuka Deno Ishikettei no Jokyo Izonteki Shoten Moderu [Theoretical explanation of the framing effect: Contingent focus model for decision-making under risk]. Japanese Psychological Review, 37, 270
291, in Japanese. Takemura, K. (1998). Jokyo izonteki ishikettei no teiseiteki moderu: Shinteki monosashi riron niyoru setsumei [Qualitative model of contingent decision-making: An explanation of using the mental ruler theory]. Ninchi Kagaku, 5(4), 17
34, in Japanese. Takemura, K. (2001). Contingent decision making in the social world. In C. M. Allwood, & M. Selart (Eds.), Decision making: Social and creative dimensions (pp. 153
173). Dordrecht: Kluwer Academic Publishers. Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical descriptions of human choice behavior. Tokyo: Springer. Takemura, K. (2019). Foundations of economic psychology: A behavioral and mathematical approach. New York: Springer. Takemura, K. (2020). Behavioral decision theory. Oxford research encyclopedia of politics. Oxford: Oxford University Press. Available from https://doi.org/10.1093/acrefore/ 9780190228637.013.958. Takemura, K. & Fujii, S. (2001). Shakaiteki Handan no Kategorii Shoutenka Kasetu: Mentaru Bokkusu Moderu niyoru Setsumei [Focusing hypothesis of social judgment: An explanation by mental box model]. In Proceedings of the 42th annual meeting of the Japanese Society of Social Psychology (pp. 83
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Takemura, K., Hatori, T., & Fujii, S. (2009). Shakaiteki joshou no henka kenshutsu to chumokuritsu ni kansuru suuri moderu to keiryou bunseki [Mathematical model and psychometric analysis of change detection and attention rate for social event]. In Proceedings of the 50th annual meeting of the Japanese Society of Social Psychology (pp. 172
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144.

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Epistemology of bad decision

To consider bad decision-making, this chapter first tries to capture this phenomenon from the perspective of rational choice in traditional economics (Takemura, 2020). From this perspective, although it is very formal, we can see that to say that the worst option (alternative) exists, at least acyclicity must be established. Even for the best alternative, acyclicity is essential. Furthermore, we know that mathematical treatment is easier when completeness and transitivity are established. However, it was pointed out that even such acyclicity may not be satisfied by human decisionmaking, and in particular, deviations from this acyclicity may occur frequently in multiattribute decision-making. It was also suggested that when considering multiattribute decision-making, it is difficult to generate weakly ordered satisfying preference relations of completeness and transitivity that are easy to handle mathematically, as is the case with acyclicity. Furthermore, by traslating the impossibility theorem by Arrow (1951) into a multiattribute decision-making problem, it was found that assuming Pareto property, independence from irrelevant alternatives, multi-attribute property, and unconstrainedness of the domain of the decision problem contradict with the weak order property. It was also suggested that loosening the weak ordering assumption to associate ordering and acyclicity does not cause inconsistency but still tends to result in decision-making by a small number of attributes (Takemura, 2014, 2018). These considerations are only based on an axiomatic approach and only state the logical relationship. In reality, decision-making data contain errors, and it is quite possible that something may be impossible in principle but possible in approximation. Therefore in addition to axiomatic analysis, this chapter also includes mathematical analysis using quantitative models that assume approximation, computer simulation, and analysis of experimental results. In addition, by examining axioms related to choice, it was found that there can be decisions with bad consequences even if they are rational, suggesting that the problem of rationality deduced from the manifest preference principle and the problem of bad decisions or so-called irrational choices are independent. For example, he pointed out that a decision that satisfies perfect rationality can be considered to be a completely bad decision, and conversely, a decision that is not completely rational and even does not satisfy formal rationality in a weaker sense cannot be considered to be a bad decision. Furthermore, it was suggested that many psychological and social sciences do not seem to include the assumption of human rationality on the surface but, in fact, Escaping from Bad Decisions. DOI: https://doi.org/10.1016/B978-0-12-816032-9.00022-3 © 2021 Elsevier Inc. All rights reserved.

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implicitly assume the manifest preference principle and the rationality of choice perspective. However, it was suggested that in theory, the formal rationality perspective, as assumed in chi-square economics in the tradition, has only a weak epistemological foundation. In this light, we can see that we must take a prescriptive approach to people’s decision-making while holding the epistemological position that the pursuit of human rationality or irrationality based on traditional choice behavior is impossible in principle. In addition, the results of computer simulation studies and psychological experiments in this chapter suggest that simple decision-making based on emotions and heuristic decision-making without much deliberation, which have been considered irrational decision-making, are not necessarily irrational in a broad sense and also are not necessarily bad decisions. On the other hand, even if we try to integrate information after careful consideration of all options, it can still be a bad decision.

21.2

Individual decision and group decision strategies

In this chapter, we consider the problem of individual decision-making from the perspective of multidimensional multiattribute decision-making and ask how we can avoid the worst decisions from the viewpoint of individual criteria, and how we can make relatively good decisions within a feasible range with less cognitive effort. Through mathematical analysis, computer simulations, psychological experiments, and surveys, we have examined the following questions. First of all, from the perspective of nonlinear optimization as a multiobjective problem-solving, we found that it is generally difficult to solve problems only from the perspective of Pareto optimality. Therefore we have developed a scalarized function that considers only the linear weighting of attribute values. In other words, if a certain condition (Kuhn
Tucker condition) is satisfied in a multiattribute function, the optimization of the scalarization function becomes a Pareto solution to the original problem. The best and worst decisions were considered operationally based on the weighted additive decision strategy (WAD) or the so-called additive decision strategy (ADD). The results of computer simulations showed that even when the number of attributes, the number of alternatives, and the conditions of dispersion of attribute weight and dominance were mutated, the lexicographic decision strategy (LEX), which narrows down the alternatives to those with the best values for a single attribute, was not effective. It was found that narrowing down the number of alternatives to about two and then using an ADD such as WAD was relatively close to the original WAD decision with low cognitive cost. It was also suggested that this two stage decision strategy is superior in terms of avoiding the worst decision. It was also found that LEX is also relatively good in terms of avoiding the worst option when the major goal is to minimize cognitive effort. In fact, the results of having the experimental participants execute these decision-making strategies and make decisions that showed that the suggested LEX to WAD strategy was effective in avoiding the worst option estimated from the

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conjoint analysis and also resulted in a relatively best option. Interestingly, however, when the WAD strategy was used, the participants in the experiment were confused, perhaps due to the information load, and were not as good at avoiding the worst option, and were not necessarily as likely to choose the best option. In addition, the two stage decision-making strategy from LEX to WAD has been frequently observed in previous studies of decision-making processes, suggesting that the low cognitive load heuristics that people usually use do not have such bad consequences. From this the recommended decision-making strategy was to make decisions lexicographically, considering the most important values, and then narrowing down to examine the remaining two or three options. In addition, in terms of preventing cognitive effort, it was found that only LEX could be used. These findings are consistent with the approach of Gigerenzer et al. (Gigerenzer, Gaissmaier, Kurz-Milcke, Schwartz, & Woloshin, 2007; Gigerenzer, Hertwig, & Pachur, 2011; Gigerenzer, Todd, & The ABC Research Group, 1999), who suggest that heuristics do not necessarily lead to bad decisions but rather are ecologically rational. However, his approach did not take the perspective of avoiding the worst possible option, and the findings presented in this chapter may be considered a complement to the findings of their approach. In addition, economist Altman (2017) argues that assuming individuals of limited rationality using the heuristics of Gigerenzer et al. (1999, 2007, 2011) does not necessarily lead to inefficient and irrational outcomes when considering the macroeconomics of society as a whole, and there is some common ground with the findings of this chapter. However, a strategy such as disjunctive (DIS), in which the search for information is terminated and a decision is made if the criterion is exceeded in any of the attributes, is not a good result even for heuristics. In group decision-making, it was found that it is harder to choose the worst option or get the best option than in WAD when group members consult in advance, decide on a common value, or try to make decisions in a collective LEX way, rather than thinking independently enough. However, the worst results were not obtained. However, the worst result was found for DIS, which suggests that following the norms and atmosphere in the group probably leads to the worst group decision-making. On the other hand, when the individuals in the group are independent and make decisions by majority rule, the two stage decision-making strategies of LEX and LEX to WAD were found to be able to avoid choosing the worst option and to easily choose the best option. However, for DIS, the results were not so good even in the majority voting condition. Furthermore, extending this problem to the case with a large number of members, it was found that when the members are independent, the jury theorem makes it easier to avoid the worst option and choose the best option as the number of members increases. Given this, for individuals, simple heuristics such as LEX will not pose much of a problem if we can determine what is the most important value. This means that we can avoid making the worst decisions. In addition to these conditions, the independence of the individual and the accuracy of the information presented were also suggested to be major factors in groups.

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Although it is desirable that these conditions are fulfilled in both individuals and groups, they do not seem to be fulfilled in actual society. The key to avoiding bad decisions would be to know what the important values are, to be able to make truly independent decisions, and to be able to recognize the situation accurately in the first place. Jean-Jacques Rousseau, the 18th-century thinker who is said to have conceived the idea of democracy, wrote in his book “The Social Contract” that if the people are well informed and debate and do not interact with each other beforehand, they will bring about the general will and the debate will always be good, but if this condition is not met, the debate will be bad. However, if these conditions are not met, the debate will become a struggle among countless subgroups, and the majority will overwhelm the others, and there will be no general will. What he pointed out seems to be consistent with the findings of this book. Hannah Arendt, a 20th-century thinker, also suggested that in politics, the ability of each individual to think and use his or her imagination without fear of isolation is effective in preventing totalitarianism. In addition to the above, I would like to point out that in the nineteenth century, Japanese thought was very different from that of other countries. Furthermore, Yukichi Fukuzawa, a Japanese thinker and educator of the 19th century, suggested that the independence of a country and the politics of a country can be established only when the people achieve self-respect and independence. In this connection, there are research studies that show that the tendency not to fear isolation in a group leads to the avoidance of bad decision-making. Hayashi, Ideno, and Takemura (2017) used a social survey to examine the relationship between the ability to detect inappropriate agendas in meetings and the tendency to fear isolation. The study predicted that people who strongly fear isolation from others would have a lower ability to detect inappropriate discussions, and this was tested by an online survey of Japanese participants (N 5 824). The results showed that fear of isolation was negatively and significantly correlated with the ability to detect inappropriate agenda items that were not in line with the purpose of the meeting, as measured by self-report (r(789) 5 20.46, P , .001). In addition, isolation phobia was also negatively correlated with the ability to detect less relevant suggestions for the causes of potential problems and their solutions (r(789) 5 20.46, P , .001). These results indicate that fear of isolation reduces the ability to detect inappropriate arguments. There is no need to erase the tendency to fear isolation from people, since it does not necessarily seem to be a cause of bad things in social life, and it can be a lubricant for relationships. And such attempts can even be dangerous. However, I believe that pressuring each individual to make independent judgments in social or group decision-making, or stoking the fear of social isolation, even if it is justified as a nudge, hinders the avoidance of bad decisions. Deliberative democracy theory is one of the traditional normative theories in political science, and deliberation to know the will of the people is attracting attention in this trend. In a direct democracy such as the United States presidential election, where the leader is in direct contact with the voters, there are concerns about the manipulation of the masses through the media by the leader and some of the

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interested parties surrounding him, and the growth of “public opinion” without deliberation. The importance of such deliberation has been pointed out. The importance of deliberation is also suggested by the German thinker Ju¨rgen Habermas, who explained the importance of discourse in deliberative politics. Deliberation may be important, but looking at the recent flare-ups and conflicts on social networking sites, I am not convinced that deliberation necessarily leads to the avoidance of bad decision-making. At the very least, I think it is important to think about decision-making issues independently of others before deliberating.

21.3

Situational dependence of individual decisionmaking and its psychological laws

In this book, we discussed the psychological laws of human beings as the causes of inability to grasp accurate information and bias in individual decision-making. Such causes have been repeatedly found by researchers such as Kahneman, Slovic, and Tversky (1982) and Gilovich, Griffin, and Kahneman (2002). In this book, we examine this issue based on theoretical hypotheses focusing on the mechanisms of attention in decision-making. First of all, this paper examines a contingent focus model in which the weights of attributes change according to the change in attention to the situation. We showed that such a change in the weights of attributes can explain the change from risk-averse decision-making to risk-oriented decision-making and preference reversal phenomena such as framing effects. This model has a feature that it can explain situation-dependent decision-making without assuming the shift of reference points in the value function as in prospect theory. Prospect theory can be said to be an internal model based on the decision maker’s reference system, and the contingent focus model can be said to be a model that describes changes in the decision maker’s attention from the standpoint of an observer. Both models can be said to have an alternative relationship and may be used in a complementary manner. The contingent focus model describes how people’s attention to attributes in a decision problem changes, which leads to changes in decision-making and, in some cases, irrational and bad decisions. Prospect theory may explain that the distortion of the probability weighting function and the value function leads to bad decisions. However, it seems to be difficult to explain why the probability weighting function and value function are distorted from prospect theory. The contingent focus model was a model to explain the weights of attributes in multiattribute decision-making, but this chapter also introduces the mental ruler model, which assumes a psychophysical function in the attributes rather than changes in the weights of the attributes, and shows some empirical studies. The mental ruler model is consistent with the LEX model. Even if the mental ruler model holds, it does not necessarily mean that the decision is irrational or bad. If the decision is made on the evaluation axis that is important to the decision maker,

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the decision will not be so bad, as the results of the computer simulation show. However, if a decision is made based on an unimportant attribute due to the nature of saliency, it may result in irrational or bad decision-making. In this chapter, I have introduced the category focusing hypothesis and mental box model behind the contingent focus model and mental ruler model. This model predicts that the slope of the psychophysical function of the category in which attention is focused will increase and become more sensitive to stimuli. For example, when Covid-19 is receiving social attention, people will be sensitive to the increase or decrease in the number of infected people. If the probability density function of an event is single peaked like a normal distribution function, the psychophysical function will be S-shaped like a logistic function, and if it is double peaked like two probability density functions overlap, the psychophysical function will be inverse S-shaped like a probability weighting function. In this way, I am trying to explain the shape of the psychophysical function in terms of attention and the environment that causes attention. Furthermore, I introduced a model in which the external factors that cause this attention are affected by the first derivative (velocity) and second derivative (acceleration) with respect to time in space-time of the stimulus object. For example, a new infection, disease, or novel risk event is predicted to be influential if the acceleration when it arises is large, as well as its real number. It was pointed out that this possibility may have led to an excessive social reaction to the Covid-19 problem. Altman (2020) has made a similar observation regarding Covid-19. According to him, blockading the economy was the main measure adopted to combat Covid-19 this time, but this measure was a simple solution to a complex problem and a relatively easy choice in times of crisis. However, he questions the adoption of such heuristics. According to him, most of the debate, in the United Kingdom, was a two-way approach: either blockade the economy or keep it open with little or no regulation. Such a dualistic and narrow approach, he said, implies the application of inappropriate mental models and analytical frameworks. He argues that this approach is not supported even by a preliminary review of the evidence regarding the desired outcome of minimizing the number of deaths. To use the example of Japan, neither the government’s expert panel nor the Prime Minister’s Office, nor the mass media, nor the Japan Medical Association has at all encouraged measures with a view to minimizing the number of deaths, including Covid-19 deaths, and measures have been taken to concentrate on avoiding Covid-19 deaths. In the case of Japan the total number of deaths from January 2020 to April 2021, when Covid-19 occurred, was 9255 (as of April 5, 2021). The population of Japan is approximately 125.48 million, and the simple death rate is less than 0.0001. On the other hand, 15,900 people died in the Great East Japan Earthquake that occurred on March 11, 2011, and 22,200 people died if missing persons and those related to the disaster are included. In addition, the number of suicides in FY2020 was 29,919, far more than the deaths caused by Covid-19. In addition, if the LEX strategy is to minimize the overall death toll, including other diseases, I can agree that it is reasonable to a certain extent, although it is a simple

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heuristic, but the policy is not considered from the perspective of minimizing the overall death toll, and the comparative information with other risks is not provided. However, most experts, politicians, and the media do not provide the public with comparative information on other risks. The Science Council of Japan, a government body that brings together domestic scientists to make scientific recommendations for Japanese policy, has done nothing to warn the public of this problem. This phenomenon suggests that many people, including experts, were thinking in terms of a single mental ruler: the number of Covid-19 deaths or infections. One reason could be the rapid increase in the number of infections and deaths around the world since the beginning of 2020, but media sensitization and sympathetic pressure from the influence process among citizens are also possible.

21.4

Nudges, boosts, and metacognition

In this chapter, while relating bad decision-making to Aristotle’s problem of akrasia, I have focused on the pluralism of decision-making and provided guidelines on how to avoid bad decision-making. As mentioned in the introduction, the approach of this book is to preach transparent prescriptive decision-making through heuristics of bad decision-making based on mathematical scientific thinking. Nudge’s ideas are that the transparency of the decision problem and the subjectivity of the decision maker are not ensured, and there seems to be a limit to the extent to which they can be ethically justified (Rizzo & Whitman, 2019). In particular, the paternalistic policy in the current Covid-19 global epidemic is a typical nudge (Thaler & Sunstein, 2008) approach and an extreme nudge, as Altman (2020) explains. It seems that such policies were often questionable in terms of conveying objective information to decision makers and allowing them to make impartial decisions. In addition, it seems that objective and impartial information is critically important in group situations. The position of this book is close to that of boost (Gu¨ne-Yanoff & Hertwig, 2016; Hertwig & Grune-Yanoff, 2017). However, it differs in that its approach places more emphasis on mathematical models, does not necessarily consider fast and frugal heuristics to have ecological rationality or validity, and aims at avoiding the worst decisions rather than pursuing the best decisions. It is also different in that it aims at avoiding the worst decisions rather than pursuing the best decisions. Even a simple two stage strategy such as the LEX to WAD (or ADD) recommended in this book can be a bad decision if it focuses on unimportant attributes. As the Little Prince written by Antoine de Saint-Exupe´ry’s novel learned that the important things are invisible, the important things may not even be known to the decision maker herself. If we know what is important, heuristics can help us avoid making the worst decisions, but how do we know what is important? How can we know what is important? This question seems to be surprisingly difficult. On the one hand, it may be better to think carefully with a reflective attitude, but on the other hand, the reflective attitude itself may distort the decision-making

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Escaping from Bad Decisions

process. For example, it has been reported that when the reasons for an attitude or choice are inaccessible in introspection, but one tries to analyze the reasons, the result can be that the person changes his or her mind (Hodges & Wilson, 1993). In addition, self-reported attitudes and choices based on reasons after analyzing—the reasons may not only be inconsistent with previous attitudes and choices, but also may not be the best (Wilson & Schooler, 1991). Philosopher Bortolotti points out that decisions based on intuition are not necessarily irrational, and that deliberation and reflection may lead to irrational decisions (Bortolotti, 2014). So, if intuition is good, it can also lead to irrational decisions, as many psychological studies have found (Bortolotti, 2014; Kahneman et al., 1982). As explained in Chapter 1, Introduction: Escaping From Bad Decisions, according to the philosopher Frankfurt (1971), what seems to be particularly characteristic of humans is that we are able to form what he calls “second-order desires” or “desires of the second order.” As suggested by psychologist Stanovich (2010), the concept of second-order desires can be used to further consider irrationality in decision-making. In other words, an irrational decision is one that seems bad from the perspective of second-order needs but can be considered rational from the perspective of first-order needs. This is what we call irrational decision-making, and it can be even worse. From the point of view of cognitive psychology, a bad decision can be explained by metacognition and its mechanism. The metacognitive mechanism model of decision-making, proposed by Takemura (1985, 1996), aims to provide a unified explanation of the consequences of task complexity, involvement, emotion, and various other factors on the decision of choice technique using the mechanism of metacognition. Metacognition refers to “cognition of cognition,” and here it refers to the decision maker’s own cognition about the decision-making process, such as “what is important to me,” “I no longer feel comfortable with the decision,” and “I want to avoid bad decisions.” The role of this metacognition consists of monitoring the decision-making procedure and allocating processing assets to control the decision-making process. First, monitoring is characterized by looking at the psychological procedure of recognizing the decision problem and imposing a choice strategy. It is a result of monitoring that one feels pressured or challenged by the decision-making process and the decision problem. This monitoring is most likely taking place while you are aware of the decision problem. However, this monitoring ceases to take place when the decisionmaking is habitual or when time is limited. Metacognitive processes are not necessarily conscious processes based on reflection; they may be intuitive. However, they do include cognition about the decision-making process, which we believe can lead to the recognition of the importance of attributes in decision-making.

21.5

Metacognitive model of decision-making process

The metacognitive mechanism model adopts an approach to making choices based primarily on the records obtained from this monitoring, which is governed by using

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Figure 21.1 Metacognitive model of decision-making process under information overload. Reproduced with permission from: Takemura, K. (1996). Ishikettei no shinri—sono katei no tankyu [Psychology of decision-making: Investigation of its process]. Tokyo: Fukumura Shuppan (in Japanese).

the properties of processing aid allocation. Processing assets are the sources of cognitive processing that support expectation, attention, and effort. Although the goal of selection technique decisions is to allocate processing assets efficiently, it is difficult to reliably achieve an efficient allocation of sources when the decision strategy is employed. It is expected that the system implementing the selection technique will be monitored through trial and error, and that the technique will be modified and adjusted until the best decision strategy for efficient allocation of processing resources is obtained. Figs. 21.1 and 21.2 suggest that monitoring continues from the beginning of the decision-making process, the mental construction of worries, through evaluation, resolution of decision strategies, implementation, and even after selection (Takemura, 1996, 2014). These processing resources are thought to be carefully related to the characteristics of the choice task (task complexity), the context (e.g., time constraints), and the psychological state of the decision maker, such as competence and involvement (Takemura, 1996, 2014). For example, complex decision problems with a large number of preferences and attributes and an overabundance of data require a huge amount of processing assets to evaluate the choice problem and various mental activities. As a result, the processing resources allocated at each stage of the decision-making procedure may decrease (Fig. 21.1). On the other hand, if the level of involvement is high, cognitive elaboration is more likely to take place, and the processing resources allocated at each stage of the decision-making process will be larger (Fig. 21.2). Similarly, the characteristics and context of the choice task, as well as the competence and psychological effort of the decision maker, are likely to be closely related to monitoring. For example, complex decision problems with a huge number of alternatives, attributes, and an overabundance of facts are likely to reduce the

498

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Figure 21.2 Metacognitive model of decision-making process under cognitive elaboration. Reproduced with permission from: Takemura, K. (1996). Ishikettei no shinri—sono katei no tankyu [Psychology of decision-making: Investigation of its process]. Tokyo: Fukumura Shuppan (in Japanese).

monitoring function at each stage of the decision process (Fig. 21.1). On the other hand, when the level of involvement is high, cognitive elaboration will eventually take place, which may improve the monitoring function at each stage of the decision-making strategy (Fig. 21.1). Fig. 21.1 shows the metacognitive mechanisms and the processes assumed for decision-making in the case of a complex decision problem with numerous picks and attributes and information overload. First, when the task is complex and information-overloaded, the processing assets to be allocated are likely to be reduced, the monitoring function is likely to be diminished, and so-called framing effects (Tversky & Kahneman, 1981) tend to occur in the mental construction of decision problems. Forms of psychological probability, evaluation of outcomes, and integration of records in the determination of choice strategies are expected to be simple noncompensatory type. Fig. 21.2 illustrates the metacognitive mechanisms of the kingdom that lead to cognitive elaboration and the ways in which they are assumed in decision-making. First, overinvolvement is expected to lead to cognitive elaboration, amplifying the allocated processing resources and increasing the monitoring function. As a result, the so-called framing effect (Tversky & Kahneman, 1981) will be controlled in the intellectual construction of decision problems. The psychological probability, evaluation, and data integration methods in the selection of choice strategies may be compensatory, and the process may be complex and involve repeated examination of information. Furthermore, this metacognitive mechanism model explains the annoyance of the influence of emotions and involvement on the decision-making process, which used to be the remaining time (Takemura, 1996). In other words, illusory emotions may limit the monitoring function of the metacognitive mechanism, limiting the

Escaping from bad decisions and future perspective

499

processing resources that can be allocated and, consequently, determining the easiest way to choose and shortening the time to choose. Negative emotions increase the monitoring function of metacognitive mechanisms but reduce the processing resources that can be allocated. Therefore factual integration of simple structures will not be employed, and decision-making will take longer than usual. Terrible emotions expand only the monitoring function, so interaction effects due to the fact of involvement appear. High-quality emotions limit the monitoring function, so the interaction effect due to the fact of involvement does not appear. This metacognitive mechanism model is qualitative and not suitable for quantitative prediction. However, it may be useful for interpreting and explaining the consequences of many factors on the choice of selection strategy in a unified manner. Takemura and Selart (2007) presented a metacognitive model of the decisionmaking process (Takemura, 1985, 1996) and showed empirical results using metacognitive mechanisms. In this empirical study, we examined the effects of informationseeking constraints on both information-seeking patterns and perceived internal states in the decision-making process. The following three information-seeking constraints were established: (1) the upper limit search (UL) condition, in which the same information cannot be examined more than once; (2) the lower limit search (LL) condition, in which all information must be examined more than once; and (3) the nonlimit search (NL) condition, in which any number of information can be examined. Participants were university students who were randomly assigned to one of the three conditions. The results showed that participants in the UL condition used noncompensatory simplifying decision-making strategies more frequently and checked information more slowly than participants in the LL and NL conditions. From the assumption of metacognitive processes, the experimental participants changed their decisionmaking strategies according to these conditions, but due to the homeostatic nature of keeping the internal state of the decision maker constant, there was no difference in terms of internal states such as the degree of confusion or hesitation, even in situations where the information load was considered to be high. Thus due to the functioning of metacognitive processes, people are making adaptive decisions to some extent. When people were allowed to make decisions freely, they were able to narrow down their choices by using LEX and WAD to a few choices. The fact that people are making relatively good decisions suggests that metacognition is working properly to detect important attributes. However, people’s decision-making may go in an undesirable direction if they are placed in an environment that inhibits their metacognitive abilities in situations such as information overload. Future research should explore how metacognitive abilities, including the detection of important attributes of decision makers, can be maintained and developed.

21.6

Conclusion

The title of this book, “Escaping From Bad Decisions,” was inspired by Fromm’s (1941) book, entitled “Escape from Freedom”. Fromm’s book is a reflection on

500

Escaping from Bad Decisions

Germany’s slide into Nazism, what led the people to that state of affairs, and what led them to that state of affairs. According to Fromm, freedom was given to all citizens at that time, which led to the creation of such a situation, and freedom essentially requires accepting the loneliness and responsibility of being given it. A society made up of those who seek and obtain freedom with such preparedness is a desirable form of society. However, he explained that the masses, who were given freedom at that time, were not ready to accept loneliness and responsibility voluntarily and lived their lives only to pursue their own happiness, which led the nation itself to such a situation. This book is about freedom, about freedom and loneliness, but it does not say that we should accept duty or responsibility for being free, but it discusses human consciousness and unconsciousness from historical events. It is rather the opposite of the theory that we should accept obligations and responsibilities to be free. Obligations and responsibilities are related to social common sense and expectations, but the thoughts, feelings, desires, and intentions that we think and feel are based on social common sense and expectations from the people around us. The question is whether they really originate from ourselves. Authoritarianism, destructiveness, and mechanical uniformity are described as mechanisms of escape from freedom. Running away from freedom can also lead to bad decision-making in the sense that this book describes. Morally, I agree that we should accept the obligations and responsibilities that come with being free, but in the first place, society has developed in such a way as to think of joint-stock companies and to spread out individual responsibilities and risks so as not to place too much obligation and responsibility on the individual. As Fromm explains, escape from freedom is inevitable. At the time of the Covid-19 epidemic, the majority of the mass media, politicians, and experts in Japan demanded the declaration of a state of emergency that would restrict the basic human rights of the people. Under the fear of infectious diseases, people easily gave up their freedom and welcomed coercion and surveillance by authority. Rationality, as in proximity to the word Ratio, seems to imply a balance of weights among multiple attributes. We think that such a situation of unbalanced weights in multiattribute decision-making may lead to irrational decision-making or bad decision-making. According to Fromm (1964), it is not necessarily true that authoritarianism (sadism and masochism) that renounces freedom is “evil,” but he declares that violence arising from self-defense, frustration, revenge, distrust, despair, and hatred is not “truly evil,” because they too can contribute to the increase of life (the power of creation), albeit in an inflected form. Fromm’s true evil is that which stifles and diminishes such raw power, that is, the power of creation. The title of this book is “Escaping From Bad Decisions,” but in contrast to Fromm’s writings, is it not true that escaping from bad decisions can itself have bad consequences? In the first place, good decision-making and bad decisionmaking are not attached to the decision-making options themselves but are interpreted by the decision maker. According to the mental box model presented in this book, the more we focus on the category “not bad,” the less we focus on the “not bad” category. It is predicted that the more we search for what is not bad or good,

Escaping from bad decisions and future perspective

501

the less good we will find. In this sense, I have written this book about avoiding bad decisions, but the more we become conscious of avoiding the worst, the more we can expect the worst to happen. Avoiding the worst is very important in life, and in this book, I have proposed strategies for decision-making and suggestions for group decision-making. However, paradoxically, I would like to conclude this book by saying that decision-making that focuses entirely on avoiding bad decisions can also be dangerous. I would like to conclude this chapter by saying that, paradoxically, there is also a danger in decision-making that is based entirely on avoiding bad decisions.

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42). Cheltenham: Edward Elgar. Altman, M. (2020). Smart thinking, lockdown and COVID-19: Implications for public policy. Journal of Behavioral Economics for Policy, 4(S), 23
33. Bortolotti, L. (2014). Irrationality. Cambridge: Polity Press. Frankfurt, H. (1971). Freedom of the will and the concept of a person. Journal of Philosophy, 68, 5
20. Fromm, E. (1941). Escape from freedom. New York: Henry Holt and Company, LLC. Fromm, E. (1964). The heart of man, its genius for good and evil. New York: Harper & Row. Gigerenzer, G., Gaissmaier, W., Kurz-Milcke, E., Schwartz, L. M., & Woloshin, S. (2007). Helping doctors and patients to make sense of health statistics. Psychological Science in the Public Interest, 8, 53
96. Gigerenzer, G., Hertwig, R., & Pachur, T. (Eds.), (2011). Heuristics: The foundations of adaptive behavior. Oxford: Oxford University Press. Gigerenzer, G., Todd, P. M., & The ABC Research Group. (1999). Simple heuristics that make us smart. Oxford: Oxford University Press. Gilovich, T., Griffin, D., & Kahneman, D. (Eds.), (2002). Heuristics and biases: The psychology of intuitive judgment. Cambridge: Cambridge University Press. Gu¨ne-Yanoff, T., & Hertwig, R. (2016). Nudge versus boost: How coherent are policy and theory? Minds and Machines, 26, 149
183. Hayashi, M., Ideno, T., & Takemura, K. (2017). Tandoku Koudou heno Chuucho to Shakai mondai ni tsuiteno Sikouryoku no Kankei [The relationship between fearing isolation and detecting inappropriate discussion in social problems]. In Paper presented at workshop on irrational group decision, the 64th annual conference of Japanese Group Dynamics Association, University of Tokyo, JP (in Japanese). Hertwig, R., & Grune-Yanoff, T. (2017). Nudging and boosting: Steering or empowering good decisions. Perspectives on Psychological Science, 12, 973
986. Hodges, S. D., & Wilson, T. D. (1993). Effects of analyzing reasons on attitude change: The moderating roles of attitude accessibility. Social Cognition, 11, 353
366. Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and biases. Cambridge: Cambridge University Press.

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Rizzo, M. J., & Whitman, G. (2019). Escaping paternalism: Rationality, behavioral economics, and public policy. Cambridge: Cambridge University Press. Stanovich, K. E. (2010). Decision making and rationality in the modern world. Oxford: Oxford University Press. Takemura, K. (1985). Ishi Kettei Sutoratejii Jikkou Ni Okeru Meta Ninchi Katei Moderu [Metacognition process model in the implementation of decision-making strategy]. Doshisha Psychological Review, 32, 16
22. (in Japanese). Takemura, K. (1996). Ishikettei no shinri—sono katei no tankyu [Psychology of decisionmaking: Investigation of its process]. Tokyo: Fukumura Shuppan. (in Japanese). Takemura, K. (2014). Behavioral decision theory: Psychological and mathematical descriptions of human choice behavior. Tokyo: Springer. Takemura, K. (2018). Avoiding bad decisions: From the perspective of behavioral economics. In Keynote paper presented at the international congress of applied psychology, Montreal, Canada. Takemura, K. (2020). Behavioral decision theory. Oxford research encyclopedia of politics. Oxford: Oxford University Press, 10.1093/acrefore/9780190228637.013.958. Takemura, K., & Selart, M. (2007). Decision making with information search constraints: A process tracing study. Behaviormetrika, 34, 111
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458. Wilson, T. D., & Schooler, J. W. (1991). Thinking too much: Introspection can reduce the quality of preference and decisions. Journal of Personality and Social Psychology, 60, 181
192.

Author Index

Note: Page numbers followed by “f” and “t” refer to figures and tables, respectively. A Abe, S., 289 Agoritsas, T., 346 Akaike, H., 443 Akamatsu, J., 416
417 Allais, M., 347
348, 394
395, 400 Altman, M., 491, 494
495 Anderson, L. R., 328 Anscombe, F. J., 398 Aristotle, 1
2, 9, 11, 92
94 Armel, C., 408 Arrow, K. J., 91
92, 96, 99, 110, 320
321, 489 Asch, S. E., 328 Aumann, R. J., 398 B Banerjee, A. V., 328 Barch, D. H., 442 Beach, L. R., 118 Becker, G. S., 2, 82 Bell, D. E., 6 Berend, D., 328 Berg, S., 328 Berlin, I., 92 Berlyne, D. E., 449
450 Berning, C. K., 179 Bettman, J. R., 92
93, 113
115, 117
121, 135
138, 141, 176
177, 179, 312, 331, 408
409 Bhui, R., 417 Bikhchandani, S., 328 Birnbaum, M. H., 63 Black, D., 320
321 Boland, P. J., 328 Bortolotti, L., 495
496 Bossert, W., 31

Bovens, L., 7
8 Brandst¨atter, E., 114
115, 176
177, 358, 408 Braun, J., 467 Brekke, N., 7
8 Brown, G. D. A., 417 Buchanan, J. M., 100
101 Bullock, J. B., 346
347 C Calderwood, R., 413 Camerer, C. F., 396
397 Carmone, F. J., 66 Cato, S., 31, 42
44, 100
101 Cattin, P., 66 Chater, N., 417 Chechile, R. A., 442 Chiba, T., 407
408 Choquet, G., 348, 397, 402 Condorcet, M. J. A., 320
321 Coombs, C. H., 57
58 Cornelissen, J. P., 252, 346 Couzin, I. D., 328 Crowder, G., 11
12, 92 D Dawes, R. M., 57
58 Desimone, R., 467 Dhar, R., 407
408 Diao, H., 346
347 Dietrich, F., 328 Duncan, J., 467 E Edwards, W., 396, 400 Ehrgott, M., 102 Ellsberg, D., 347
348, 400

504

F Fagley, N. S., 346 Fechner, G., 62 Feldman, M. A., 24
25 Fischhoff, B., 407 Fishburn, P. C., 344
345, 347
349, 396, 400, 406, 415
416 Fox, C. R., 424
425, 430 Foxall, G. R., 436
437 Frankfurt, H. G., 5, 247
248, 267, 269
270, 285, 496 Frege, G., 409 Freud, S., 80 Fromm, E., 499
500 Fujii, S., 108f, 137
138, 343
345, 350f, 364, 365f, 366, 368, 374
375, 379, 380t, 386, 388, 452
453, 466
467, 472
478 Fujita, S., 391
392 G Gaissmaier, W., 8
9, 491 Garfin, D. R., 453 Gershman, S. J., 417 Gigerenzer, G., 8
9, 114
115, 176
177, 358, 408, 491 Gilboa, I., 393, 398 Gilovich, T., 493 Goldsmith, R. E., 436
437 Goldstein, D., 7
8, 358 Goldstein, D. G., 408 Gonzalez, R., 425
426, 441
443 Goodin, R. E., 323
324, 330 Green, P. E., 66 Griffin, D., 493 Gu¨ne-Yanoff, T., 8
9, 495 H Hahn, M., 179 Hama, Y., 416
417 Handa, J., 404
406 Haraguchi, R., 113, 179 Hastie, R., 328 Hatori, T., 450
453, 464, 465f, 466
467, 466f, 477
478 Hausman, D., 82
83 Hayashi, M., 492 Hertwig, R., 8
9, 114
115, 176
177, 358, 408, 491, 495 Hirshleifer, D., 328

Author Index

Hodges, S. D., 495
496 Hoffrage, U., 142 Holman, E. A., 453 Holt, C. A., 328, 345 Holyoak, K. J., 422
423, 428 Hovland, C. I., 475
476 Hsee, C. K., 417, 432
434 Hu, K., 368 Hung, A. A., 328 I Ichikawa, A., 106
109 Ideno, T., 12
13, 113, 179, 220, 247
248, 269, 285, 289, 300, 331, 339
340, 343, 439, 450
452, 452f, 456, 467, 477
478, 492 Indow, T., 49, 62
63 Isobe, A., 220 Itti, L., 467 Iverson, G., 64
65 J Jackson, D. H., 346
347 Jacoby, J., 179 Jain, A. K., 66, 179 Janis, I. L., 226, 248
249, 268
270, 285, 308, 328 Jedidi, K., 142 Jensen, N. E., 393
394 Johnson, E. J., 7
8, 92
93, 113, 141, 179, 312, 346
347, 408
409 Judd, C. M., 64 Julesz, B., 467 K Kahneman, D., 62, 330, 344
350, 368
370, 373, 376
378, 380
381, 394
395, 400
401, 406
409, 413
418, 425
426, 431, 434, 437
438, 442
444, 450, 471, 474
475, 477
478, 493, 495
496, 498 Kameda, T., 328 Kao, A. B., 328 Kaplan, R. M., 346 Karasawa, K., 472 Karmakar, U. S., 425 Karni, E., 345 Kikkawa, T., 207
208, 344, 388 Klein, G. A., 413 Koch, C., 467

Author Index

Kohli, R., 142 Kohn, C. A., 179 Kojima, S., 407
408, 413, 415
418, 436
437, 444, 471 Krajbich, I., 408 Krantz, D. H., 21, 56
57, 105
109, 137
138, 351, 353, 357 Kurz-Milcke, E., 8
9, 491 L Ladha, K. K., 328 Lagakos, S. W., 179 Langer, E. J., 346
347 Lawson, R., 179 Lee, Y. G., 179 Levin, I. P., 346
347 Levy, H., 406 Leyens, J. P., 475
476 List, C., 323
324, 328, 330 Loi, K., 437 Louviere, J. J., 66 Lowenstein, G., 396 Luce, R. D., 21, 56, 62
65, 105
106, 137
138, 351, 370, 455, 471 Lurie, N. H., 179 M Mach, E., 449 Mackay, D., 7
8 Malhotra, N. K., 179 Mandel, D. R., 346
347 Mar, D., 449 Marques, J. M., 475
476 Martignon, L., 142 Masatlioglu, Y., 69, 82
84, 88
89 Matsui, H., 113
115 Maule, A. J., 407 McClelland, G. H., 64 McFadden, D., 374, 380 McNeil, B. J., 346 Metcalf, C. J. E., 453 Miettinen, K., 102
104 Mikami, R., 31 Milgram, S., 18 Miller, P. M., 346 Mitani, N., 225 Mitchell, T. R., 118 Miwa, T., 435
436 Miyajima, M., 269

505

Moghaddam, K., 346 Montgomery, H., 422
423 Morgenstern, O., 49, 347
348, 391 Morris, D. H., 453 Murakami, H., 439, 467 Murofushi, T., 347
348, 396
397 N Nakajima, D., 69 Nakamaru, M., 312
318 Nakamura, K., 88 Nakamura, Y., 391
392 Nakanishi, J., 208 Nakawake, Y., 328, 330 Nakayachi, K., 208, 437
438 Nakayama, H., 102
104 Nerlove, S., 66 Nitzan, S., 328 Noelle-Neumann, E., 328 O Oguni, E., 285 Ohkubo, S., 12
13, 94f, 220, 289, 439 Okuma, M., 269 Orasanu, J., 413 Osborn, R. N., 346
347 Ozbay, E. Y., 69 P Pachur, T., 8
9, 491 Parducci, A., 417, 444, 472, 477 Park, S. W., 453 Paroush, J., 328 Pauker, S. G., 346 Payne, J. W., 92
93, 113
115, 117
121, 132f, 136
138, 141, 143
144, 155
167, 161f, 162f, 163f, 164f, 165f, 177
181, 203
204, 312, 331, 338, 408
409 Perneger, T. V., 346 Perrett, L. F., 472 Pettibone, J. C., 477 Plott, C. R., 328 Prelec, D., 425
426, 442 Proschan, F., 328 Puto, C. P., 346 Q Qualls, W. J., 346 Quiggin, J., 396, 400

506

R Rabin, M., 396 Raiffa, H., 6 Rangel, A., 408 Richter, M. K., 2, 81 Rizzo, M. J., 13
14, 495 Roberts, F. S., 56 Robinson, A., 7
8 Rodin, P. A., 346 Romney, A. K., 66 Rybash, J. M., 346 S Safra, Z., 345 Saito, H., 285 Sakagami, T., 269, 285 Sapir, L., 328 Sasaki, K., 31 Sattath, S., 345, 407
408, 415 Savage, L. J., 347
348 Sayeki, Y., 49, 57
59, 65 Scheier, C., 450
451 Schmeidler, D., 347
348, 397
399 Schneiderman, L. J., 346 Schnittjer, S. K., 346
347 Schooler, J. W., 495
496 Schwartz, B., 12
13, 181 Schwartz, L. M., 8
9, 491 Scott, D., 87, 427 Segal, U., 345 Selart, M., 421, 499 Sen, A. K., 21, 24
27, 33
34, 36
37, 41, 43, 69
70, 100
101 Serrano, R., 24
25 Shan, L., 346
347 Shepard, R. N., 66 Sherif, M., 475
476 Shigemasu, K., 408 Shimojo, E., 450
451 Shimojo, S., 450
451 Silver, R. C., 453 Simion, C., 450
451 Simon, H. A., 32
33, 80, 114
116, 136 Simonson, I., 407
408, 415
416 Slovic, P., 344
345, 347
348, 394
395, 400, 407
408, 414
415, 453, 485, 493 Sox, H. C., 346

Author Index

Speller, D. E., 179 Stanovich, K. E., 5, 496 Starmer, C., 396 Stewart, N., 417 Sugeno, M., 347
348, 396
397 Sunstein, C. R., 7
8, 328, 495 Suppes, P., 21, 56, 87, 105, 137
138, 351, 427 Suzumura, K., 2, 31, 80
81 T Tabesh, P., 346 Takagi, O., 339 Takahashi, M., 225 Takahashi, N., 12
13, 220, 289, 300 Takemura, K., 9, 11
13, 17
18, 21
22, 31, 33, 63, 70, 72, 74, 77
80, 88, 91
93, 94f, 95
97, 99
100, 108f, 113
115, 117
121, 124, 135
138, 179, 181
182, 184
185, 203
204, 220, 225
227, 269, 285, 289, 312
318, 329
331, 339, 343
346, 350f, 357
358, 363
364, 365f, 366, 368, 370
371, 373
375, 379, 380t, 386, 388, 391
392, 394
397, 400, 407
408, 414
416, 426, 434
437, 439, 442
444, 450
453, 452f, 456, 466
468, 471
478, 489, 492, 496
499 Tamari, Y., 12
13, 113, 179, 220, 289, 312
318, 439, 456, 467 Tamura, H., 391
393, 395
398, 400 Tanino, T., 102
104 Thagard, P., 422
423, 428 Thaler, R. H., 7
8, 346
347, 471, 495 Thee, S. L., 346
347 Thomson, R. R., 453 Thorngate, W., 179, 203
204 Todd, P. M., 8
9, 491 Tong, Y. L., 328 Tsuzuki, T., 113
115 Tukey, J. W., 65, 105
106 Tversky, A., 6, 21, 56
58, 62, 85
88, 85f, 86t, 95, 105, 114, 137
138, 330, 344
351, 353, 355
356, 368
370, 373, 376
378, 380
381, 394
395, 400
401, 406
409, 413
418, 424
426, 430
431, 434, 437
438, 442
444, 471, 474
475, 477
478, 493, 498

Author Index

507

V Varian, H. R., 74, 77
78 Vedlitz, A., 346
347 von Neumann, J., 49, 347
348, 391

Wittink, D. R., 66 Woloshin, S., 8
9, 491 Wu, G., 425
426, 441
443 Wu, L., 346
347

W Wakker, P., 424
425, 430 Weber, M., 32 Wedell, D. H., 472, 477 Welch, I., 328 Werner, M. D., 252, 346 Whitman, G., 13
14, 495 Wilson, D. K., 346 Wilson, T. D., 7
8, 495
496

Y Yamamoto, M., 2
3 Yellott, J. I., 455
456 Yokoyama, A., 408 Yzerbyt, V. Y., 475
476 Z Zimbardo, P., 18 Zsambok, C. E., 413

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Subject Index

Note: Page numbers followed by “f” and “t” refer to figures and tables, respectively. A Absolute scale, 59 Abstraction, 449
450 Acceleration, 449 Accuracy, 141, 179 Acyclic preference, 25 Acyclicity, 20
21, 69 empirical investigation of, 84
86 Additive conjoint structure, 109 axiomatic properties of, 106
110 best decision with single attribute and utility function, 104
105 multiattribute decision-making and, 105
106 and quasi best decision, 104
110 Additive conjoint systems, 104, 106
109 Additive decision strategy (ADD), 179
181, 311
312, 490 Additive decision-making, 104 Additive difference (DIF), 143 Additive difference model, 87 Additive difference strategy (DIF), 143 Additive fuzzy utility difference structure model, 88 Additive methods, 13, 115 Additive strategy, 110, 117, 179 in multiattribute decision-making, 141
143 Additive utility function, 113 Agenda, 228 Aggregation, 17
18 Agreement rate, 235 Air suicide attacks. See Aircraft suicide attacks Aircraft suicide attacks, 4 Akaike information criterion (AIC), 237
238 Akrasia, 1
3 Allais paradox, 347
348, 394
396, 405

Alternatives, 88, 99
100 Ambiguity, 6 Analysis of variance (ANOVA), 252, 264
266 interaction between control and experimental groups, 266 Antisymmetry, 20, 52, 55 Archimedean property, 107 Arousal, 449
450 Asian disease problem, 377
378, 381
383 variant of, 383
384 Attention, 449 control of attention by psychological experiment, 464
471 function, 449
452 mathematical model of attention rate to social events, 453
454 model of category focusing and construction of mental ruler, 471
483 proposal of attention manipulation method, 467
468 propositions and considerations derived from model, 455
456 psychological model of, 452
453 psychometric model application for attention rate to Covid-19 problem, 456
464 Attentional focus, 381, 484 Attentiveness, 449
450 Axiom, 391, 393, 396, 398, 400 Axiomatic measurement theory, 49, 57 properties of additive conjoint structure, 106
110 B Bad choice, 229, 234
236 Bad decision-making, 207
208, 225 in group decision-making, 269
271

510

Bad decisions, 1, 17
18, 21
23, 31
32, 141, 155, 179
188, 247, 343. See also Worst decisions classical problem of bad decision-making and akrasia, 1
3 epistemology, 489
490 experiment on situation dependence of, 330
339 idea of worst and best decisions, 9
11 individual decision and group decision strategies, 490
493 metacognitive model of decision-making process, 496
499 nudges, boosts, and metacognition, 495
496 nudging and boosting, 7
9 pluralism in decision-making, 11
12 prescriptive approach of decision-making, 5
7 prescriptive pluralistic decision-making, 12
13 second-order desires and, 3
5 situational dependence of individual decision-making and psychological laws, 493
495 tabulations of, 235
237 Bad group decision-making, detection of, 285
287 Bad option in majority-based choice, 237 Beef liver task, 218 Behavioral decision theory, 400 Behavioral economics, 7 Behavioral observations, 49
50 Best choices, 318 rate, 171
176 first-stage strategy, 198
199 second-stage strategy, 199
200 for strategy, 198
200 Best decisions, 17
18, 93
94 best decision-making, 93
94 idea of, 9
11 with single attribute and utility function, 104
105 Best options, 21
23. See also Worst options choice rate, 200
203 conditions for guaranteeing preference relations, 24
26 existence condition of, 25 greatest element rationalizability and, 33

Subject Index

necessary and sufficient conditions for existence, 27 relation, 25
26 Biases, 449 Binary relation, 19, 51 Black sheep effect, 475
476 Body attack. See Kamikaze Special Attack Team Boosting, 7
9, 495
496 Budget constraint, 77 Bureaucracy, 32 C Cancellation, 229
230 Capacity, 396
397 Cardinal utility, 69 Category-focusing hypothesis, 374
377, 472
474 and mental box model, 472
477 range
frequency theory, 472 situation-dependent judgment phenomena, 474
476 Certainty effect, 394
396 Chebyshev scalarization function, 103 Choice accuracy, 179 function, 26
28, 81 rate of worst option, 150
155 ratio, 369
371 task, 468 Choquet integral, 397
398, 405 calculus, 347
348 expected utility model, 348, 398
399 Coefficient of variation (CV), 467
468 Cognitive dissonance, 5 Cognitive dissonance theory, 5 Cognitive effort, 122
132, 145
149 Cognitive processes in group decisionmaking, 247
249 Collective decision-making, 324 Collective knowledge, 330 Comonotonic independence, 398 Comparative judgments, 19 Compatibility of stimulus
response structures as mental ruler construction principle, 421
422 Compensatory decision strategies, 117, 207, 311
312

Subject Index

Complete complementary goods, 74
75 Complete irrationality, 69 Complete rationality, 69 Completeness, 20, 24, 52, 54, 69, 95 Computer simulation, 113
114, 144
145, 311
312 first stage strategies and relative accuracy, 122 purpose and methods, 119
121, 133
134 relationship between relative accuracy and cognitive effort, 122
125 results, 122
132, 134
135, 145
176 strategies and cognitive effort in first stage, 122 studies of multiattribute decision-making process and problems, 117
119 Concave function, 366 Condorcet’s Jury Theorem. See Jury theorem Conjoint analysis, 65 Conjoint measurement, 65 Conjunctive strategy (CON), 116, 143 Constant-sum scale, 60 Consummation sensitivity, analysis of, 305
306 Consumption vector, 71
72 Contingency, 414
415 on description, 414 of human relations, 414 of internal states, 415 to other external environments, 414 of place, 414 Contingent decision-making, 413 Contingent focus model, 343, 349
351, 404
407, 493 expected utility theory, 391
394 counterexample to, 394
396 formulation, 351
354 framing effect as situation-dependent preference reversal, 344
347 inadequacy of utility theory, 347
348 nonadditive probability and nonlinear utility theory, 396
399 prospect theory, 348
349 representation theorem of, 354
357 situation dependence of decision-making and bad decisions, 343
344 Contingent judgment, 413
414 existing models, 416
417 problems, 417
418

511

and problems in modeling, 414
418 by utility theory, 415
416 Contingent weighting model, 353 Continuity axiom, 393 Continuous categorical evaluation, 417 Continuous function, 63 Conventional normative decision theory, 95
96 Convergence of probability, 325 Convergence theorem, 324 Convex function, 348
349, 367 Correlation analysis, 262
265, 281, 292
293, 304 Correlation coefficient between desirability of decision and process in meetings, 283 Correspondence, 56
57 bias, 70 Counterbalancing of questionnaire, 221 Covid-19, 9
11 global epidemic, 495 Crisis rate by strategy, 196
198 Cumulative prospect theory, 402 D Decision frame model, 416 Decision heuristics, 115 Decision strategy, 141, 180, 247 findings and problems of previous research on, 114
119 psychological functions of, 113
114 Decision task, 331
332 Decision time, 189
192, 195
196, 200
203 Decision weights, 403
404 Decision-making, 17, 449 conditions for guaranteeing preference relations of worst and best options, 24
26 experiment on situation dependence of, 330
339 framework to, 17
21 indicators, 143
144 model to explain nontransitivity, 87
88 necessary and sufficient conditions for existence of worst and best options, 26
28 pluralism in, 11
12 prescriptive approach of, 5
7

512

Decision-making (Continued) under risk, 467 strategy, 225 for individual decision-making and majority rule, 311
319 under uncertainty, 398 worst option, best option, and bad decision, 21
23 Degree of concentration, 449
450 Degree of focusing, 381 Deliberative democracy theory, 492
493 Democracy, 91 Description invariance, 344
345, 349 Descriptive contingency, 415 Descriptive theory, 400 Desirability, 304
305 Desirability of meeting decision, analysis of, 278
282, 293
294 Desirability of meeting process, analysis of, 280
282, 294
296, 305 DIF strategy (additive difference strategy), 143 Direct probability test, 335
336 Direct product, 18 Disjunctive decision strategy (DIS decision strategy), 116, 119, 143, 155, 171, 176, 311
312, 491 Dissonance. See Cognitive dissonance Distributed agenda form, 229 Dominance principle, 97 Dominance structure, 422
423 Double cancellation, 107 Double exponential distribution, 454 E Economic deprivation, 9
10 Economic man, 31
33 Editing phase, 401 Elementary information processes (EIP), 143 Elimination by aspects (EBA) strategy, 116, 143 Ellsberg’s paradox, 347
348 Emotion, 94
95 Emotional-rational acts, 32 Empirical relational system, 58 Empirical testing of acyclic preference relations, 84
88 decision-making model to explain nontransitivity, 87
88

Subject Index

empirical investigation of acyclicity, 84
86 nontransitivity and thresholds, 86
87 End points, 420 Epistemic democracy, 330 Epistemology bad decision, 489
490 Equal weight strategy (EQW), 110 Equally-weighted additive type (EQW type), 115 Equivalence class, 51 relation, 51 Escape from freedom, 499
500 Essentiality, 109 Estimation method assuming utility with error term, 372
374 Evaluability hypothesis, 434 Evaluation function, 427
428, 439 Evaluation phase, 401 EVexpected value choice, 118 EVheuristic rule choice, 118 Exhaustiveness of categories, 59 Existence condition of best option, 25 of worst option, 24 Expected utility, 348 Expected utility theory, 6
7, 347
348, 391
394, 400 counterexample to, 394
396 Experimental design, 273 Experimental instructions, 260
262 Experimental operations, 449 Exploratory behavior, 449
450 Expressive measurement, 64 Extensional definition, 17
18 Extensive structure, 64
65 Eye gaze method, 182 Eye movement, 469
470 measurement results, 336
338 Eye-tracking, 207, 210f data, 217
218 decision-making issues, 209
211 experiment, 209
214, 219 experimental procedures, 212
213 experimental trial, 212
213 eye-tracker setup and calibration, 212 instruction, 212 practice trial, 212

Subject Index

experimental setup, 209 instructional content, 213
214 experimental trial, 214 introductory instruction, 213 practice trials, 214 setup, 214 results, 214
219 EyeLink CL Illuminator TT-890, 209, 334
335 F Fast and frugal heuristics, 8
9, 495 Fatal risk, 208 Favorableness evaluation, 451
452 Fechner’s law, 62
63 Finite additive probability measure, 392 First-stage strategy, 122, 192
193, 198
199 Focus of attention, 343
344 Focusing hypothesis. See Category focusing hypothesis Food choice problems, 222
223 task, 221 Food decision-making, 207 choice results and decision time in food decision-making task, 214
215 gazed behavior, 218
219 questionnaire food choice scores and eyetracking data, 217
218 Food safety, 208
209 evaluation of knowledge about, 221 Forced choice method, 19
21 Formal rationality, 31
32 Formalism scale, 220 Framing effect, 311, 330, 347
348, 368, 370, 399
400 and prospect theory, 400
404 as situation-dependent preference reversal, 344
347 Freedom, 92 Frequency principle, 477 Fundamental attribution error, 70 Fuzzy integrals, 397 Fuzzy measure, 396
397 G Gain, 401 Gamble, 363
364

513

Gaze Cascade Hypothesis, 450
451 Gaze time ratio, 469
470 Gazed behavior, 218
219 beef liver task, 218 lettuce task, 219 mushroom task, 218 rice task, 218 spinach task, 218 water task, 219 General possibility theorem, 100 Generalized expected utility theory, 396 Good decisions, 178 good decision making, 12
13 Graduation of mental ruler, 419
420 Great East Japan Earthquake, 11 Greatest element rationalizability, 31, 33
40. See also Maximal-element rationalizability and best option, 33 criteria of irrationality and weak order, 35
37 criteria of rationality and irrationality, 37
40 criteria of rationality and weak order, 33
35 Greedoid-Languages, 142 Group decision, 225
227, 247, 285 strategies, 490
493 Group decision-making, 247 cognitive processes and groupthink in, 247
249 implementation of experiment, 275
278 analysis, 278 instruction, 276
278 procedure, 276 irrationality and bad decision-making in, 269
271 method for group decision-making experiment, 273
278 method of experiment, 258
262 creation of experimental stimuli for experiment, 258 implementation, 259
262 pilot study, 249
258 preliminary survey, 271
273 implementation of preliminary survey, 272 purpose, 271 questionnaire, 271
272

514

Group decision-making (Continued) results, 272
273 psychological process, 247 results, 278
281 Group meeting experiment experimental procedures, 231
232 experimental stimuli distributed agenda forms, 229 procedures, 230
231 group decision, 225
227 groupthink, 225
227 instruction, 232
234 method of experiment, 227
234 participants in experiment, 228 procedures, 228
229 preliminary survey, 229 questionnaire, 231 results, 234
242 agreement rate, 235 analyzing experimental results, 234
235 bad option in majority-based choice, 237 logistic regression analysis on irrational decision-making, 237
242 tabulations of bad decisions, 235
237 Groupthink, 225
227, 269
270, 285
287, 328 in group decision-making, 247
249 in social psychology, 1 H Hazard, 207
208 Heuristics, 449 Homoeconomicas, 31 Human rationality, 32
33 Hypothetical tracking technique, 182 I Impossibility theorem, 489 of multiattribute decision-making, 98
101 Impulsivity, 3 Incommutability, 11
12 Independence, 106 within attributes, 106 axiom, 393 of irrelevant alternatives, 489 Indicators, 189, 190t of decision-making, 143
144

Subject Index

Indifference, 71
72 Indifference curves, 71
76, 354 groups of neutral goods, 75
76 for noneconomic goods, 75 Individual behavior, 225 Individual decision strategies, 490
493 Information cascade, 328 Information monitoring acquisition method, 182, 381
384 Information overload, 179 Information search, 92
93 Interlocking condition, 356 Internal consistency of preference, 31
32 Interpretation of evaluation experiment on value of saved lives, 434
435 of experimental results, 431
434 of perceptual judgment experiment, 435
436 of price judgment experiment, 436
438 of probability weighting function, 439
444 Interval scale, 59
60 Intransitivity of preference, 94 Involvement, 283 Irrational choice, 36
37, 49, 489 and revealed preference, 82 Irrational decision, 31
32 Irrational decision-making, 1, 49 Irrational meetings, 247
248 Irrational preference, 49 Irrationality, 2, 31 criteria of, 35
37 in group decision-making, 269
271 weak order, 35
37 J Judgments, 49
51, 413 Jury theorem, 320
328 K Kamikaze Special Attack Team, 4 Kamikaze Suicide Attack. See Kamikaze Special Attack Team Knowledge confidence survey items, 221 L Least squares method, 66 Lebesgue integral for stochastic measures, 397

Subject Index

Lettuce task, 219 Lexicographic decision strategy (LEX decision strategy), 116, 118
119, 143, 225, 227, 490
491 in multiattribute decision-making, 141
143 screening, 207 Lexicographic semiorder decision strategy (LEX-SEMI), 116, 120
121, 143 Limited attention, 82
83 Linear function, 367 Linear order preference relation, 21 Linear regression analysis, 458
459 Linear utility model, 393 Linguistic communication, 329 Logarithm of odds ratio of choice probability, 373 Logistic regression analysis on irrational decision-making, 237
242, 373 analysis of difference between options, 239
240 analysis of ease of choosing bad option, 237
239 multiple regression analysis of discussion evaluation, 240
242 Loss, 348
349 Lottery, 441 M Macroeconomics, 491 Majority of confirming dimensions (MCD) strategy, 116
117, 143 Majority rule, 320
321, 330 Marginal rate of substitution, 74 Marginal utility for good, 74 Mathematical model of attention rate to social events, 453
454 Maximal option, 41, 43 Maximal-element irrational choice theorem, 43
44 Maximal-element rationalizability, 31, 40
45. See also Greatest element rationalizability and bad decision, 42
44 maximal option and quasiorder, 41 maximal-element rational choice, 40
42 and not inferior option, 40
41 and not superior option, 42 and rationality, 44
45 theorem, 42

515

Measurement, 56
57 experiment of contingent focus model and, 368
374 scale level, 58
61 Meeting video, 257 Meetings, 269 Mental accounting, 471 Mental box model, 449, 471 category-focusing hypothesis and, 472
477 empirical study, 477
483 prospect theory, 471 Mental ruler, 96 basic function, 419
421 basic hypothesis of model and property of, 418
419 composition, 476
477 contingent judgment, 413
414 experimental findings, 431
444 explanation using set theory and mathematical description, 422
431 situation, 422 subjective situation, 422
423 model, 413, 421, 443
444, 493
494 model of category focusing and construction of, 471
483 category-focusing hypothesis and mental box model, 472
477 prospect theory and mental box model, 471 people construct, 419
420 qualitative description, 418
422 restructure of subjective situation and, 427
428 as set function, 429
431 structure, 423
424 subadditivity of mental ruler and mathematical description, 424
426 threshold as graduation of mental ruler, 426
427 Metacognition, 495
496 Metacognitive model of decision-making process, 496
499 Ministry of Health, Labor and Welfare (MHLW), 209
211 Monitoring information acquisition method, 94, 182 Monotone analysis of variance (MONANOVA), 66

516

Monotonicity, 75, 101 Multiattribute decision-making, 3, 9, 91, 113, 181 additive and lexicographic strategy in, 141
143 and additive conjoint structure, 105
106 best decision, and worst decision, 93
94 computer simulation studies of multiattribute decision-making process and problems, 117
119 difficulties, 92
96 and psychological cause, 94
96 and information search, 92
93 and intransitivity of preference, 94 multioptimization, 101
104 plurality of values and, 92 theoretical examination, 96
101 Multiattribute utility theory, 95
96 Multiattribute value function, 99 Multiobjective analysis, 102 Multiobjective optimization, 101
104 Multiobjective optimization problem (MOP), 102 Multioptimization, 101
102 Multiple objective functions, 102 Multiple regression analysis of discussion evaluation, 240
242 Multistage decision-making, 117 Mushroom task, 218 Mutual exclusiveness, 59 N Neutral goods, indifference curve group of, 75
76 Nominal scale, 59 Nonadditive probability, 396
399 Noncompensatory decision strategies, 117, 207 Noncompensatory decision-making, 207 Noneconomic goods, indifference curve groups for, 75 Nonlinear expected utility theory, 404
407 Nonlinear utility theory, 396
399 framing effect, 399
400 Nontransitivity, 86
87 decision-making model to explain nontransitivity, 87
88 Normative decision theory, 95
96

Subject Index

Nudges, 8, 495
496 Nudging, 7
9 O One-dimensional ruler, 419, 421 standards, 96 Optimization problem, 102 Order, 50
51 Ordering decisions aspects of, 50
56 equivalence relation, 51 properties of preference relations, 50
51 relationship system, 51
52 total order and representation theorem, 52
54 weak order and representation theorem, 54
56 preference relationships through, 49
50 Ordering judgment, 19 Ordering relation, 51 Ordinal scale, 59
60 Ordinal utility, 54
55 theory, 49 Organizational structural deficiencies, 248 P Paired-comparison scale, 59
60 Paradox. See Allais paradox; Ellsberg paradox Parameter estimation, 363 Pareto optimal solution, 102 Pareto solution, 103 Partial utility function, 66 Paternalistic or nudge approach, 9 Path dependency, 343
344 Perceptual judgment. See also Contingent judgment interpretation of perceptual judgment experiment, 435
436 task, 451
452 Perfect completeness good, 74 Perfect substitute goods, 72
74 Pilot study, 179
181, 249
258 making videos of meeting scene, 249
250 method, 180, 250, 253
254

Subject Index

overview of experiment, 249, 253 previous research on choice accuracy and problem, 179 purpose, 180, 249, 252 results, 180
181, 251
252, 254
255 Pluralism in decision-making, 11
12 Plurality of values, 92 Point-of-purchase (POP), 415 Preference based on dominance principle, 97 Preference based on principle of maximum number of dominant attributes, 97
98 Preference ordering and measurement aspects of ordering decisions, 50
56 measurement of preference relations, 56
61 preference relationships through ordering decisions and behavioral observations, 49
50 quantitative representation of psychophysical laws and preference relations in terms of scale levels, 62
66 Preference relation, 49 conditions for guaranteeing preference relations of worst and best options, 24
26 on measurement and representation of, 57
58 measurement of, 56
61 correspondence and measurement, 56
57 uniqueness and measurement scale, 58
61 properties of, 50
51 and set theory, 18
19 Preference relations through ordering decisions and behavioral observations, 49
50 Preference reversal, 311 Preliminary study, 333
334 method, 333 results, 334 Prescriptive approach of decision-making, 5
7 Prescriptive decision-making, 1 Prescriptive pluralistic decision-making, 12
13

517

Price judgment experiment, interpretation of, 436
438 Price marketing policies, 436
437 Priority heuristics, 176
177 Probability, 392 measure, 392 Probability weighting function, 442 characteristics, 443 interpretation of, 439
444 Procedural invariance, 414 Procedural justice, 414 Process tracing, 179 effect of second stage decision-making strategy, 181
188 experiment, 182
184 issues, 181 method of monitoring information acquisition, 182 methods of experiment, 184
188 Prominence, 467 Prospect theory, 348
349, 369, 400
407, 471, 493 Pseudo-certainty effect, 437
438 Psychological experiment, 363, 425
426 control of attention by, 464
471 experiments on stimulus variability and attention, 467
471 speed and acceleration of change of target, 464
467 Psychological functions of decision strategies, 113
114 Psychological model of attention, 452
453 Psychological purse model, 416
418 Psychological scale, 54
55 structure of preference, 64 Psychometric measurement, 64 Psychometric model application for attention rate to covid-19 problem, 456
464 analysis and results, 457
459 purpose, 456
457 Psychometric research approaches, 101 Psychophysical laws, 62
64 Psychophysical quantity, 453
454 Psychophysics, 483 Psyschometric analysis of contingent focus model experiment of contingent focus model and measurement, 368
385

518

Q Quantitative analysis, 96, 379
381 Quantitative representation of psychophysical laws and preference relations, 62
66 Quasi best decision, 104
110 Quasiorder, 41, 43, 50
51 preference relation, 21 Quasitransitivity, 101 Question items, 222
223 Questionnaire, 195
196, 200
203, 231, 274
275 experiment, 219 food choice scores, 217
218 methodology, 220
221 evaluation of knowledge about food safety, 221 information sources, 221 knowledge confidence survey items, 221 randomization and counterbalancing of questionnaire, 221 scales for social behavior, 220 tasks for selecting foods, 220 results, 221
223 survey, 219
223 survey participants, 220 R Random utility model, 372 Randomization of questionnaire, 221 Range
frequency theory, 417, 472 Rank-dependent utility theory, 397 Ratio scale, 369
371 Rational choice, 31, 34
35, 49 function, 82 Rational decision-making, 31
33, 49, 91 Rational homo economics, 31 Rational preference, 69 Rationality, 31
32, 80
82 criteria, 33
35, 37
40 and revealed preference, 69
70 weak order, 33
35 Rationalizability, 33 Real-valued function, 392 Reference points, 401
402, 420 Reflection effect, 374
377 problem, 384 Reflectivity, 20, 24

Subject Index

Regression analysis, 124 Regret and maximization scale, 220 Relation of worst and best options, 25
26 Relational system, 51
52 Relative accuracy (RA), 118, 143 and cognitive effort, 122
125 difference from minimum value, 155
159 divided by cognitive effort, 160
171 first-stage strategies and, 122 relationship between number of attributes and cognitive effort and, 129
132 relationship between number of options, cognitive effort, and, 125
129 Representation theorem of additive conjoint structure, 109 of contingent focus model, 354
357 total order and, 52
54 weak order and, 54
56 Representational measurement, 64
66 theory, 64 Restricted solvability, 108 Revealed attention, 82
84 Revealed preference, 31
32, 69
71, 77
82 irrational choice and, 82 principle of, 77
78 rationality and, 80
82 rationality criteria and, 69
70 strong axiom of revealed preference, 79
80 WARP, 78
79 Rice task, 218 Richter’s rationalizability theorem, 81 Ridiculous meetings, 247
248 Risk, 207 attitudes, 363
368 properties, 366
367 aversion, 366 communication, 207
208 neutrality, 367 risk-seeking, 367 Riskless gamble, 363
364 Riskless lottery, 441 Risky lottery, 441 Rule compliance, 279, 281, 295
296 Rule noncompliance, 295 S S-shaped function, 425 Safety, 208

Subject Index

Scalarization function, 91, 102
103 Scale construction, 58
59 Scales for social behavior, 220 Second-order desires, 3
5 Second-stage decision strategy, 179 results, 189
203 using process tracing on bad decisions, 181
188 experiment, 182
184 issues, 181 method of monitoring information acquisition as process tracing technique, 182 methods of experiment, 184
188 Second-stage strategy, 193, 199
200 Selective attention, 449
450 Self-control, 3 Sensitivity of consumption deadline, analysis of, 296
298 Set theory, 18
19 Simple parameter estimation method for contingent focus model, 368
369 Situation dependence of decision-making and bad decisions, 330
339, 343
344 of individual decision-making and psychological laws, 493
495 judgment phenomena, 474
476 Social action, 32 Social choice theory, 99 Social judgment, 475
476 Social psychological studies, 248 Social psychology, 1 Social welfare, 221 Space, 449 Speed and acceleration of change of target, 464
467 Spinach task, 218 Standard deviation (SD), 209, 333, 464 Stevens’ law, 63 Stimulus creation, 273
274 Stimulus variability, 467
471 Strength of preferences, 371
372 Strict partial order, 21 Strict partial order preference relation, 21 Strict quasiorder, 50
51 Strong axiom of revealed preference, 79
80 Subadditivity of mental ruler and mathematical description, 424
426

519

Subjective expected utility theory, 347
348, 400 Subjective situation, 422
423 restructure of, 427
428 Substantive rationality, 32 Supermarkets, 436
437 Symmetry, 20 T Tabulations of bad decisions, 235
237 Target decision strategy, 143 Tasks for selecting foods, 220 Thomsen condition, 107 Thresholds, 86
87 as graduation of mental ruler, 426
427 Time, 449 contingency, 414
415 discounting, 3 Total order, 50
51 and representation theorem, 52
54 Traditional economics, 31 Transitivity, 20, 54, 85 of social preferences, 100
101 Two-factor log-linear analysis, 376 Two-stage decision strategy, 141, 143 Two-stage decision-making process, 13 strategies, 113, 311
312 U Underwater suicide attacks, 4 Uniqueness, 58
61 Unrestricted solvability, 108 Upper contour set, 72 Utility, 49, 369
371, 399 curve, 72
74 functions, 71
76, 347 theory, 413 inadequacy of, 347
348 V Value function, 348
349, 367
368, 401 Value pluralism, 11 Value-rational acts, 32 Vector inequality, 103 Velocity, 449 Verbal protocol method, 182 Videos of meeting scene, 249
250

520

Voting analysis, 298
299, 306 detection of bad group decision-making, 285
287 groupthink, 285
287 method of experiment, 287
292, 299
303 experimental design, 288, 299
300 experimental stimuli, 288
289, 300 implementation, 290, 300
301 instruction, 290
292, 302
303 outline of experiment, 287 overview of experiment, 299 questionnaire, 289, 300 results, 292
299, 304
306 W Water suicide attacks, 4 Water task, 219 Weak axiom of revealed preference (WARP), 78
79, 83 necessary and sufficient condition theorem for WARP(LA), 84 Weak order, 33
37, 50
51 axiom, 393 preference relation, 21 and representation theorem, 54
56

Subject Index

Weak Pareto solution, 103 Weber’s law, 62 Weber’s theory, 32 Weighted-additive decision strategy (WAD strategy), 110, 115, 118
119, 180, 490
491 Weights, 403 Willingness to pay (WTP), 438 Worst choice, 31, 247, 318 adoption rate, 189
192, 195
196 rate, 192
195 first stage strategy, 192
193 second stage strategy, 193 Worst decisions, 6, 18, 93
94 idea of, 9
11 Worst options, 21
23, 238
239 conditions for guaranteeing preference relations, 24
26 existence condition of, 24 necessary and sufficient conditions for existence, 26
27 relation, 25
26 Wrist cutting, 3
4 Z Zero risk, 208 effect, 437
438