Overview
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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Full Product Details
Author: Bezalel Peleg ,
Hans Peters
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition: 2010 ed.
Dimensions:
Width: 15.50cm
, Height: 0.90cm
, Length: 23.50cm
Weight: 0.454kg
ISBN: 9783642265051
ISBN 10: 3642265057
Pages: 154
Publication Date: 05 November 2012
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
From the reviews: The book studies stable representations of constitutions. ... the book is very well written and perfectly organized ... . I can highly recommend the book by Bezalel Peleg and Hans Peters: a real pleasure for scholars working on effectivity functions and social choice functions, and a great learning opportunity for those who are not that familiar with the topics in question. It is an excellent contribution, bringing together a lot of material in a single manuscript in a coherent way. (Agnieszka Rusinowska, Social Choice and Welfare, Vol. 40, 2013) The book presents in terms of effectivity functions (i.e. coalitional game forms) a very deep, clear and consistent exposition of the most important social choice problem--coalitional decision making. ... Written by two authors who have made outstanding contributions to the developed theory, the book will be very useful for game and social choice experts, lecturers, and master's and Ph.D. students in these fields. (Fouad T. Aleskerov, Mathematical Reviews, Issue 2012 b)
From the reviews: The book presents in terms of effectivity functions (i.e. coalitional game forms) a very deep, clear and consistent exposition of the most important social choice problem--coalitional decision making. ... Written by two authors who have made outstanding contributions to the developed theory, the book will be very useful for game and social choice experts, lecturers, and master's and Ph.D. students in these fields. (Fouad T. Aleskerov, Mathematical Reviews, Issue 2012 b)
From the reviews: The book presents in terms of effectivity functions (i.e. coalitional game forms) a very deep, clear and consistent exposition of the most important social choice problem -coalitional decision making. ... Written by two authors who have made outstanding contributions to the developed theory, the book will be very useful for game and social choice experts, lecturers, and master's and Ph.D. students in these fields. (Fouad T. Aleskerov, Mathematical Reviews, Issue 2012 b)
"From the reviews: ""The book presents in terms of effectivity functions (i.e. coalitional game forms) a very deep, clear and consistent exposition of the most important social choice problem -coalitional decision making. ... Written by two authors who have made outstanding contributions to the developed theory, the book will be very useful for game and social choice experts, lecturers, and master's and Ph.D. students in these fields."" (Fouad T. Aleskerov, Mathematical Reviews, Issue 2012 b)"
