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Behavioral social choice: probabilistic models, statistical inference and applications

Author: Regenwetter, Michel ; Grofman, Bernard ; Tsetlin, IliaINSEAD Area: Decision SciencesPublisher: Cambridge University Press (CUP) 2006.Language: EnglishDescription: 240 p. ; 24 cm.ISBN: 0521536669Type of document: INSEAD BookBibliography/Index: Includes bibliographical references and indexAbstract: This book develops a mathematical modeling and statistical inference framework that allows us to construct descriptive (as opposed to normative) theories of social choice behavior and to test these theories against empirical data. The authors believe that this work provides a first systematic attempt toward a formal behavioral theory of social choice behavior, in the spirit of behavioral economics and of behavioral decision theory (à la Kahneman and Tversky). Their empirical work on majority rule decision making demonstrates that some influential strands of theoretical research (the impartial culture assumption, and domain restriction conditions, such as Sen's value restriction and Black's single peakedness) are descriptively invalid. They also show that their behaviorally plausible conditions, which they validate on empirical data, predict that majority rule decision making is extremely unlikely to generate cycles (among sincere preferences) for realistic distributions in mass electorates. A major implication is that majority rule provides a 'solution' (in practice) to Arrow's impossibility theorem. The authors also discuss how statistical considerations of social choice processes can dramatically redefine important research questions (e.g., finding the correct winner may be a bigger concern than avoiding cycles) and reverse policy implications (e.g., high turnout, not low turnout, as often argued, is desirable when using majority rule). In follow-up work, the authors show how Condorcet's majority rule and Borda's scoring rule are in almost perfect agreement with each other in some major empirical data sets. These findings suggest that behavioral approaches to social choice processes can dramatically alter their focus: rather than emphasize impossibilities of universally feasible solutions and pessimistic predictions about what might go wrong in a social choice process in the worst case scenario, they may investigate redundancies among social choice procedures in actual elections and how to choose social choice procedures that are easy for the voter to use. As indicated above, the authors must also turn their attention to problems that have been widely ignored in the theoretical, social choice literature, such as the susceptibility of social choice procedures to erroneous election outcomes 1) when voters experience preference uncertainty, 2) when ballots are complex to fill out or 3) when tally procedures contain probabilistic components. They illustrate their theoretical and empirical arguments using attitudinal survey data, single transferable vote ballot and approval voting ballot data from real elections.
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Includes bibliographical references and index

This book develops a mathematical modeling and statistical inference framework that allows us to construct descriptive (as opposed to normative) theories of social choice behavior and to test these theories against empirical data. The authors believe that this work provides a first systematic attempt toward a formal behavioral theory of social choice behavior, in the spirit of behavioral economics and of behavioral decision theory (à la Kahneman and Tversky).
Their empirical work on majority rule decision making demonstrates that some influential strands of theoretical research (the impartial culture assumption, and domain restriction conditions, such as Sen's value restriction and Black's single peakedness) are descriptively invalid. They also show that their behaviorally plausible conditions, which they validate on empirical data, predict that majority rule decision making is extremely unlikely to generate cycles (among sincere preferences) for realistic distributions in mass electorates. A major implication is that majority rule provides a 'solution' (in practice) to Arrow's impossibility theorem.
The authors also discuss how statistical considerations of social choice processes can dramatically redefine important research questions (e.g., finding the correct winner may be a bigger concern than avoiding cycles) and reverse policy implications (e.g., high turnout, not low turnout, as often argued, is desirable when using majority rule).
In follow-up work, the authors show how Condorcet's majority rule and Borda's scoring rule are in almost perfect agreement with each other in some major empirical data sets. These findings suggest that behavioral approaches to social choice processes can dramatically alter their focus: rather than emphasize impossibilities of universally feasible solutions and pessimistic predictions about what might go wrong in a social choice process in the worst case scenario, they may investigate redundancies among social choice procedures in actual elections and how to choose social choice procedures that are easy for the voter to use.
As indicated above, the authors must also turn their attention to problems that have been widely ignored in the theoretical, social choice literature, such as the susceptibility of social choice procedures to erroneous election outcomes 1) when voters experience preference uncertainty, 2) when ballots are complex to fill out or 3) when tally procedures contain probabilistic components.
They illustrate their theoretical and empirical arguments using attitudinal survey data, single transferable vote ballot and approval voting ballot data from real elections.

Digitized

Behavioral Social Choice Probabilistic Models, Statistical Inferences, and Applications Contents List of Figures and Tables Acknowledgments Introduction and Summary Introduction Summary I PROBABILISTIC MODELS OF SOCIAL CHOICE BEHAVIOR 1 The Lack of Theoretical and Practical Support for Majority Cycles 1.1 The impartial culture and majority cycles 1.1.1 Background 1.1.2 For three candidates the impartial culture generates the most cycles 1.1.3 Does the impartial culture generate the most cycles regardless of the number of candidates? 1.2 Net value restriction and net preference majority 1.2.1 Majority rule and probabilistic preferences 1.2.2 Probabilistic reformulation and generalizations of Sen's value restriction 1.3 Empirical illustrations 1.4 Discussion 2 A General Concept of Majority Rule 2.1 A general definition of majority rule 2.1.1 Majority rule based on deterministic or probabilistic preference relations page ix xi 1 1 10 23 26 29 32 35 37 37 41 44 49 52 53 56 v vi Contents 2.1.2 Majority rule based on utility functions or random utility representations 2.2 Generalizations of the impartial culture 2.3 General concepts of value restriction and preference majority 2.3.1 A generalization of Theorem 1.2.15 beyond linear orders 2.3.2 Generalizations of net value restriction and net preference majority 2.3.3 Visualizations using the partial order graph on three alternatives 2.4 Empirical illustrations 2.5 Discussion II APPLICATIONS OF PROBABILISTIC MODELS TO EMPIRICAL DATA 3 On the Model Dependence versus Robustness of Social Choice Results 3.1 Model dependence versus robustness 3.2 Empirical illustrations 3.3 Near net value restriction 3.4 Discussion 4 Constructing Majority Preferences from Subset Choice Data 4.1 Majority rule preferences constructed via two probabilistic models of subset choice data 4.1.1 Evaluating net value restriction and net preference majority from subset choices via the size-independent model 4.1.2 Majority preferences constructed from the topset voting model 4.2 Model dependendence of majority preference constructed from subset choice data 4.3 Empirical illustrations 4.3.1 Analyses using the size-independent model 4.3.2 Analyses using the topset voting model 4.3.3 Model dependence of majority outcomes, net value restriction, and net majority 4.4 Discussion III A GENERAL STATISTICAL SAMPLING AND BAYESIAN INFERENCE FRAMEWORK 5 Majority Rule in a Statistical Sampling and Bayesian Inference Framework 63 73 75 77 80 85 95 103 109 111 113 117 120 124 127 130 132 133 135 137 147 148 149 155 Contents 5.1 Majority rule in a general sampling framework 5.1.1 Pairwise majority in a sample of binary relations 5.1.2 Upper and lower bounds on the probabilities of majority preference relations 5.2 The Condorcet efficiency of majority rule 5.3 Majority rule in a Bayesian inference framework 5.4 Empirical illustrations 5.4.1 Majority misestimation 5.4.2 Majority outcomes in random samples from the 1996 ANES 5.4.3 Majority outcomes in random samples from the 1969 GNES 5.4.4 Majority outcomes in random samples from the 1988 FNES for Communist Party identifiers 5.4.5 Summary of results for samples from ANES, GNES, and FNES surveys 5.4.6 Bayesian inference about majority outcomes for the full 1988 FNES 5.5 Discussion 6 Conclusions and Directions for Future Behavioral Social Choice Research 6.1 Conclusions 6.2 Directions for future behavioral social choice research A Definitions of Cultures of Preference Distributions B Definitions and Notation for Binary Relations C Proofs of Theorems and Observations Bibliography Author Index Subject Index vii 157 160 163 168 170 174 174 177 181 181 183 186 187 191 191 194 199 202 204 217 233 236

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