Strategic Social Choice: Stable Representations of Constitutions

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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...