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