Collective Decision Making : Views from Social Choice and Game Theory (Hardcover)--by Adrian Van Deemen [2010 Edition] ISBN: 9783642028649

This book discusses collective decision making from the perspective of social choice and game theory. The chapters are written by well-known scholars in the field. The topics range from Arrow’s Theorem to the Condorcet and Ostrogorski Paradoxes, from vote distributions in the European Council to influence processes and information sharing in collective decision making networks; from cardinal utility to restricted domains for social welfare functions; from rights and game forms to responsibility in committee decision making; and from dueling to bargaining. The book reflects the richness and diversity of the field of collective decision making and shows the usefulness and adequacy of social choice and game theory for the study of it. It starts with typical social choice themes like Arrow’s Theorem and ends with typical game theoretical topics, like bargaining and interval games. In between there is a mixture of views on collective decision making in which both social choice and game theoretic aspects are brought in. The book is dedicated to Harrie de Swart, who organized the well-known Social Choice Colloquia at the University of Tilburg in the Netherlands. Cover 1 THEORY AND DECISION LIBRARY SERIES C: GAME THEORY, MATHEMATICAL PROGRAMMING AND OPERATIONS RESEARCH 2 Collective Decision Making: Views from Social Choice and Game Theory 4 Copyright 5 3642028640 5 Preface and Introduction 6 Contents 12 Contributors 14 From Black's Advice and Arrow's Theoremto the Gibbard--Satterthewaite Result 16 Donald G. Saari 16 1 Black's Advice 17 2 New Interpretations of Arrow's Result 19 2.1 What Causes Arrow's Result 20 2.2 Positive Assertions 21 3 Strategic Voting 23 3.1 Can Strategic Voting Be Avoided? 24 3.2 Illustrating Examples 25 3.3 Lessons Learned 26 3.4 Minimizing Strategic Behavior 28 4 Concluding Comments 30 References 30 The Impact of Forcing Preference Rankings When Indifference Exists 32 William V. Gehrlein 32 1 Introduction 32 2 The Possible Existence of Voter Indifference 34 3 The Impact of Requiring Forced Rankings 38 4 Conclusion 43 References 44 Connections and Implications of the Ostrogorski Paradox for Spatial Voting Models 46 Hannu Nurmi and Donald G. Saari 46 1 Introduction 46 2 Ostrogorski's Paradox 47 3 The Anscombe and Exam Paradoxes 49 4 Core Conditions and Aggregation Paradoxes 50 5 Resolving Kelly's Conjecture 54 6 Differences Between Dichotomous and Spatial Models 56 7 Relating and Explaining the Paradoxes 57 8 Supermajority Voting 61 9 Simpson's Paradox: A Shadow Over the Sure-Thing Principle 65 10 Conclusion 68 References 69 Maximal Domains for Maskin Monotone Pareto Optimal and Anonymous Choice Rules 72 Olivier Bochet and Ton Storcken 72 1 Introduction 72 2 Maskin Monotonic Choice Rules 74 3 Three or More Agents 75 4 Two Agents and Maskin Monotonicity 78 5 Conclusion 81 References 82 Extremal Restriction, Condorcet Sets, and Majority Decision Making 84 Adrian Van Deemen and M. Elena Saiz 84 1 Introduction 84 2 Notation, Definitions, and the Sen-Pattanaik Theorem 86 3 Extremal Restriction: What It Excludes 88 4 Extremal Restriction: What It Includes 91 5 Zero Assignments and Counter-Examples for the Sen-Pattanaik Theorem 93 6 Condorcet Sets 94 7 Conclusion 96 References 97 Rights Revisited, and Limited 100 Maurice Salles and Feng Zhang 100 1 Introduction 100 2 Necessary Concepts 101 3 Sen's Theorem 102 4 Limited Rights 104 4.1 The Social Preference Framework 105 4.2 The Choice-Theoretic Framework 107 5 Discussion and Remarks 109 6 Conclusion 110 References 111 Some General Results on Responsibility for Outcomes 114 Martin van Hees 114 1 Introduction 114 2 The Formal Framework 116 3 Conditions for Responsibility 117 4 Responsibility Voids 120 5 Equivalence of Efficacy and Responsibility 121 6 Full Responsibility 122 7 Conclusion 123 References 124 Existence of a Dictatorial Subgroup in Social Choice with Independent Subgroup Utility Scales, an Alternative Proof 126 Anna B. Khmelnitskaya 126 1 Introduction 126 2 The Framework 127 3 Existence of a Dictatorial Subgroup 131 References 138 Making (Non-standard) Choices 140 Wulf Gaertner 140 1 Introduction 140 2 Three Particular Choice Functions 142 2.1 Sequential Rationalizability 142 2.2 Picking the Second Largest 145 2.3 The Choice of the Median Element 147 3 Some Other Non-Standard Choice Functions 148 4 Concluding Remarks 149 References 151 Puzzles and Paradoxes Involving Averages: An Intuitive Approach 152 Scott L. Feld and Bernard Grofman 152 1 Three Insights into Aggregation 152 2 Parts and Wholes 154 2.1 Types of Households 155 2.2 Family and per Capita Income 156 2.3 Standardized Test Scores 157 2.4 Crowded Roads 158 2.5 Class Sizes 158 2.6 Bush v. Gore: The 2000 US Presidential Election 160 2.7 Friendship Networks 161 3 Different Types of Averages 161 3.1 Median 161 3.2 Geometric Mean 162 3.3 Harmonic Mean 163 4 Discussion 164 References 164 Voting Weights, Thresholds and Population Size: Member State Representation in the Council of the European Union 166 Madeleine O. Hosli 166 1 Introduction 166 2 Characteristics of Voting Rules 167 3 Former Vote Allocations in the Council 169 4 Government Preferences for the Council Decision Threshold 174 5 Recent Adaptations: Nice and Lisbon Treaty Provisions 175 6 Conclusions 181 References 182 Stabilizing Power Sharing 184 Steven J. Brams and D. Marc Kilgour 184 1 Introduction 184 2 Notation and Assumptions 186 3 Sequential Interaction 187 4 Simultaneous Interaction 190 5 How Should Power Be Shared to Induce Stability? 192 5.1 Sequential Interaction 192 5.2 Simultaneous Interaction 195 6 Conclusions 197 References 199 Different Approaches to Influence Based on Social Networksand Simple Games 200 Michel Grabisch and Agnieszka Rusinowska 200 1 Introduction 200 1.1 Aim of the Paper 200 1.2 Overview of Research on Influence 201 1.3 Structure of the Paper 203 2 The Model of Influence in a Social Network 203 2.1 Description of the Model and Weighted Influence Indices 203 2.2 Follower Functions and Influence Functions 205 2.3 Example 208 3 The Command Games 209 3.1 Command Games and Command Functions 209 3.2 Command Games and Influence Functions 211 3.3 Example Continued 212 3.4 Power and Influence Indices 212 4 Enlarging the Set of Possible Yes/No Actions 214 4.1 The Influence Model with an Ordered Set of Possible Actions 214 4.2 Example Continued 217 4.3 The Influence Model with a Continuum of Actions 219 5 Levels of Knowledge and the Identification Problem 220 6 Future Research on Influence 222 References 223 Networks, Information and Choice 226 René Janssen and Herman Monsuur 226 1 Introduction 226 2 Network Value of Nodes 228 3 Situational Awareness in Networks 232 3.1 Deterministic Behaviour of Nodes 233 3.2 Stochastic Behaviour of Nodes 236 4 Network Dynamics 239 5 A Choice Mechanism for Network Evolution 241 5.1 The Uncovered Set 242 5.2 Forming or Severing Links 242 6 Conclusions 244 References 244 Characterizations of Bargaining Solutions by Properties of Their Status Quo Sets 246 Hans Peters 246 1 Introduction 246 2 Bargaining and Status Quo 246 3 Basic Definitions and Properties 248 4 The Nash Solution 251 5 The Kalai--Rosenthal Solution 253 6 The Kalai--Smorodinsky Solution 254 7 The Egalitarian Solution 255 8 The Continuous Raiffa Solution 256 9 Overview, Comparison and Independence of the Properties 259 10 Overview of Related Literature 261 References 262 Monotonicity Properties of Interval Solutions and the Dutta--Ray Solution for Convex Interval Games 264 Elena Yanovskaya, Rodica Branzei, and Stef Tijs 264 1 Introduction 264 2 Definitions and Notation 266 3 Monotonicity Properties of TU Game Valuesand of the Corresponding Generated Interval Values 268 3.1 Existence of Interval Values Generated by TU Game Values 268 3.2 Inheritance of Monotonicity Properties by Interval Values 270 4 The Interval Dutta--Ray Solution on the Class of Convex Interval Games 271 4.1 Properties of the Interval Dutta--Ray Solution 271 5 Consistency of the Dutta--Ray Solution on the Class of Convex Interval Games and Its Axiomatic Characterization 274 6 Concluding Remarks and Perspectives 280 References 281 9783642028649 Springer Harrie de Swart is a Dutch logician and mathematician with a great and open int- est in applications of logic. After being confronted with Arrow's Theorem, Harrie became very interested in social choice theory. In 1986 he took the initiative to start up a group of Dutch scientists for the study of social choice theory. This initiative grew out to a research group and a series of colloquia, which were held approximately every month at the University of Tilburg in The Netherlands. The organization of the colloquia was in the hands of Harrie and under his guidance they became more and more internationally known. Many international scholars liked visiting the social choice colloquia in Tilburg and enjoyed giving one or more presentations about their work. They liked Harrie's kindness and hospitality, and the openness of the group for anything and everything in the eld of social choice. The Social Choice Theory Group started up by Harrie consisted, and still c- sists, of scholars from several disciplines; mostly economics, mathematics, and (mathematical) psychology. It was set up for the study of and discussion about anything that had to do with social choice theory including, and not in the least, the supervision of PhD students in the theory. Members of the group were, among o- ers, Thom Bezembinder (psychologist), Hans Peters (mathematician), Pieter Ruys (economist), Stef Tijs (mathematician and game theorist) and, of course, Harrie de Swart (logician and mathematician). Front Matter....Pages i-xiv From Black’s Advice and Arrow’s Theorem to the Gibbard–Satterthewaite Result....Pages 1-16 The Impact of Forcing Preference Rankings When Indifference Exists....Pages 17-29 Connections and Implications of the Ostrogorski Paradox for Spatial Voting Models....Pages 31-56 Maximal Domains for Maskin Monotone Pareto Optimal and Anonymous Choice Rules....Pages 57-68 Extremal Restriction, Condorcet Sets, and Majority Decision Making....Pages 69-83 Rights Revisited, and Limited....Pages 85-97 Some General Results on Responsibility for Outcomes....Pages 99-109 Existence of a Dictatorial Subgroup in Social Choice with Independent Subgroup Utility Scales, an Alternative Proof....Pages 111-123 Making (Non-standard) Choices....Pages 125-136 Puzzles and Paradoxes Involving Averages: An Intuitive Approach....Pages 137-150 Voting Weights, Thresholds and Population Size: Member State Representation in the Council of the European Union....Pages 151-167 Stabilizing Power Sharing....Pages 169-184 Different Approaches to Influence Based on Social Networks and Simple Games....Pages 185-209 Networks, Information and Choice....Pages 211-230 Characterizations of Bargaining Solutions by Properties of Their Status Quo Sets....Pages 231-247 Monotonicity Properties of Interval Solutions and the Dutta–Ray Solution for Convex Interval Games....Pages 249-266 The rich and diverse array of articles presented in this book result from workshops and seminars held by the Dutch Interuniversity Group at the Tilburg University. The articles represent a state-of-the-art overview from the field's most important researchers. This book brings together interesting contributions in Social Choice Theory of important researchers in the field. To mention: Steven Brams, William Gehrlein, Wulf Gaertner, Michel Grabisch, Bernie Grofman, Herman Monsuur, Hannu Nurmi, Hans Peters, Ton Storcken, Martin Van Hees, Donald Saari and Maurice Salles. The contributions show actual research topics in social choice and bring the reader to the state of the art in the theory. The book's richness and diversity is a reflection of the seminars and workshops held by the Dutch Interuniversity Group at the Tilburg University in The Netherlands. Because of its richness and state-of-the-art overview, it can be used for teaching in, e.g., micro-economics, public choice, political theory, and public finance at the Master and Ph.D level.