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Strategic Social Choice

Stable Representations of Constitutions

  • Book
  • © 2010

Overview

Authors:
  1. Bezalel Peleg

    1. Center for the Study of Rationality, Interactive Decision Theory, Hebrew University of Jerusalem, Jerusalem, Israel

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    You can also search for this author in PubMed   Google Scholar

  2. Hans Peters

    1. Dept. Quantitative Economics, Maastricht University, Maastricht, Netherlands

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • This is the first monograph on the subject of constitutions modeled by effectivity functions
  • It reviews and extends the literature on this issue from the beginning, around 30 years ago
  • It is especially relevant for researchers, including PhD students, in the area of game theory and social choice theory

Part of the book series: Studies in Choice and Welfare (WELFARE)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Representations of constitutions

    1. Front Matter

      Pages 1-1
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    2. Introduction to Part I

      • Bezalel Peleg, Hans Peters
      Pages 3-6

    3. Constitutions, effectivity functions, and game forms

      • Bezalel Peleg, Hans Peters
      Pages 7-20

    4. Nash consistent representations

      • Bezalel Peleg, Hans Peters
      Pages 21-43

    5. Acceptable representations

      • Bezalel Peleg, Hans Peters
      Pages 45-57

    6. Strongly consistent representations

      • Bezalel Peleg, Hans Peters
      Pages 59-66

    7. Nash consistent representation through lottery models

      • Bezalel Peleg, Hans Peters
      Pages 67-79

    8. On the continuity of representations of constitutions

      • Bezalel Peleg, Hans Peters
      Pages 81-94

  3. Consistent voting

    1. Front Matter

      Pages 95-95
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    2. Introduction to Part II

      • Bezalel Peleg, Hans Peters
      Pages 97-103

    3. Feasible elimination procedures

      • Bezalel Peleg, Hans Peters
      Pages 105-112

    4. Exactly and strongly consistent representations of effectivity functions

      • Bezalel Peleg, Hans Peters
      Pages 113-121

    5. Consistent voting systems with a continuum of voters

      • Bezalel Peleg, Hans Peters
      Pages 123-145

  4. Back Matter

    Pages 147-154
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Keywords

About this book

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

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)

Authors and Affiliations

  • Center for the Study of Rationality, Interactive Decision Theory, Hebrew University of Jerusalem, Jerusalem, Israel

    Bezalel Peleg

  • Dept. Quantitative Economics, Maastricht University, Maastricht, Netherlands

    Hans Peters

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