Strategic Social Choice (eBook)

Stable Representations of Constitutions

Bezalel Peleg, Hans Peters (Autoren)

eBook Download: PDF

2010 | 2010
XVIII, 154 Seiten
Springer Berlin (Verlag)
978-3-642-13875-1 (ISBN)

Infos

This book was written mainly during the Spring periods of 2008 and 2009, when the ?rst author was visiting Maastricht University. Financial s- port both from the Dutch Science Foundation NWO (grants 040. 11. 013 and 0. 40. 11. 082) and from the research institute METEOR (Maastricht Univ- sity) is gratefully acknowledged. Jerusalem Bezalel Peleg Maastricht Hans Peters April 2010 v Contents Preview to this book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi Part I Representations of constitutions 1 Introduction to Part I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 2 Arrow's constitution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 3 Arrow's Impossibility Theorem and its implications. . . . . . . . . 4 1. 4 Ga ¨rdenfors's model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 5 Notes and comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Constitutions, e?ectivity functions, and game forms . . . . . . 7 2. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2. 2 Constitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2. 3 Constitutions and e?ectivity functions . . . . . . . . . . . . . . . . . . . . 12 2. 4 Game forms and a representation theorem. . . . . . . . . . . . . . . . . 16 2. 5 Representation and simultaneous exercising of rights. . . . . . . . 19 2. 6 Notes and comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3 Nash consistent representations. . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3. 2 Existence of Nash consistent representations: a general result 22 3. 3 The case of ?nitely many alternatives. . . . . . . . . . . . . . . . . . . . . 24 3. 4 Nash consistent representations of topological e?ectivity functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. 5 Veto functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3. 5. 1 Finitely many alternatives. . . . . . . . . . . . . . . . . . . . . . . . . 34 3. 5. 2 Topological veto functions. . . . . . . . . . . . . . . . . . . . . . . . . 36 3. 6 Liberalism and Pareto optimality of Nash equilibria. . . . . . . . . 40 3. 7 Notes and comments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 vii viii Contents 4 Acceptable representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4. 1 Motivation and summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Inhalt

Strategic Social Choice 3
Preface 5
Contents 7
Preview to this book 11
Part I Representations of constitutions 18
Chapter 1 Introduction to Part I 19
1.1 Motivation and summary 19
1.2 Arrow's constitution 19
1.3 Arrow's Impossibility Theorem and its implications 20
1.4 Gärdenfors's model 21
1.5 Notes and comments 22
Chapter 2 Constitutions, effectivity functions, and game forms 23
2.1 Motivation and summary 23
2.2 Constitutions 24
2.3 Constitutions and effectivity functions 28
2.4 Game forms and a representation theorem 32
2.5 Representation and simultaneous exercising of rights 35
2.6 Notes and comments 35
Chapter 3 Nash consistent representations 37
3.1 Motivation and summary 37
3.2 Existence of Nash consistent representations: a general result 38
3.3 The case of finitely many alternatives 40
3.4 Nash consistent representations of topological effectivity functions 45
3.5 Veto functions 50
3.5.1 Finitely many alternatives 50
3.5.2 Topological veto functions 52
3.6 Liberalism and Pareto optimality of Nash equilibria 56
3.7 Notes and comments 58
Chapter 4 Acceptable representations 60
4.1 Motivation and summary 60
4.2 Acceptable representations and minimal liberalism 61
4.3 Existence of acceptable representations 66
4.4 A game form with all Nash equilibrium outcomes Pareto optimal 67
4.5 Proof of Theorem 4.3.1 69
4.6 Notes and comments 72
Chapter 5 Strongly consistent representations 73
5.1 Motivation and summary 73
5.2 Necessary conditions for strongly consistent representations 74
5.3 Existence of strongly consistent representations 76
5.4 Strongly consistent representations of topological effectivity functions 78
5.5 Notes and comments 80
Chapter 6 Nash consistent representation through lottery models 81
6.1 Motivation and summary 81
6.2 Nash consistent representation: an extension 83
6.3 Lottery models 84
6.4 Neutral effectivity functions 88
6.5 Notes and comments 92
Chapter 7 On the continuity of representations of constitutions 94
7.1 Motivation and summary 94
7.2 Continuous representations may not exist 95
7.3 Finitely generated effectivity functions and 
97 
7.4 The reduction theorem 99
7.5 Semicontinuous representations on R 101
7.6 Representations of effectivity functions and modified Baire functions 105
7.7 Notes and comments 107
Part II Consistent voting 108
Chapter 8 Introduction to Part II 109
8.1 Motivation and summary 109
8.2 The Gibbard-Satterthwaite Theorem and its implications 110
8.3 Exactly and strongly consistent social choice functions 111
8.4 Strategyproofness and restricted preferences 112
8.5 Equilibrium with threats 113
8.6 Notes and comments 115
Chapter 9 Feasible elimination procedures 116
9.1 Motivation and summary 116
9.2 Feasible elimination procedures 117
9.3 Maximal alternatives and effectivity functions 119
9.4 A proof of Theorem 9.3.6 122
9.5 Notes and comments 123
Chapter 10 Exactly and strongly consistent representations of effectivity functions 124
10.1 Motivation and summary 124
10.2 Feasible elimination procedures revisited 125
10.3 Sufficient conditions for elimination stability 127
10.4 Necessary conditions for the existence of ESC representations 128
10.5 Necessity of elimination stability for the existence of ESC representations 130
10.6 Notes and comments 132
Chapter 11 Consistent voting systems with a continuum of voters 133
11.1 Motivation and summary 133
11.2 The basic model 134
11.3 The Gibbard-Satterthwaite Theorem 135
11.4 Exactly and strongly consistent social choice functions 139
11.4.1 Effectivity functions of ESC social choice functions 140
11.5 Blocking coefficients of anonymous ESC SCFs 141
11.6 Feasible elimination procedures 144
11.7 Core and feasible elimination procedures 148
11.8 Positive blocking coefficients 152
11.9 Notes and comments 155
References 156
Author Index 159
Subject Index 161

Produkt-Details

• Erscheint lt. Verlag: 25.8.2010
• Reihe/Serie: Studies in Choice and Welfare
• Reihe/Serie: Studies in Choice and Welfare
• Zusatzinfo: XVIII, 154 p. 2 illus.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Sozialwissenschaften ► Politik / Verwaltung
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Volkswirtschaftslehre
• Schlagworte: Constitutions • Effectivity functions • Game forms • Modeling • Nash and strong Nash equilibrium • Strategic stability
• ISBN-10: 3-642-13875-6 / 3642138756
• ISBN-13: 978-3-642-13875-1 / 9783642138751