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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
