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© 2014

Fuzzy Social Choice Theory

  • Presents a comprehensive analysis of fuzzy set theoretic models of social choice

  • Paves the way for the development of a fuzzy social choice theory

  • Includes applications of the described theory and encourage future empirical research in the field

Book

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 315)

Table of contents

  1. Front Matter
    Pages 1-13
  2. Michael B. Gibilisco, Annie M. Gowen, Karen E. Albert, John N. Mordeson, Mark J. Wierman, Terry D. Clark
    Pages 1-9
  3. Michael B. Gibilisco, Annie M. Gowen, Karen E. Albert, John N. Mordeson, Mark J. Wierman, Terry D. Clark
    Pages 11-20
  4. Michael B. Gibilisco, Annie M. Gowen, Karen E. Albert, John N. Mordeson, Mark J. Wierman, Terry D. Clark
    Pages 21-52
  5. Michael B. Gibilisco, Annie M. Gowen, Karen E. Albert, John N. Mordeson, Mark J. Wierman, Terry D. Clark
    Pages 53-87
  6. Michael B. Gibilisco, Annie M. Gowen, Karen E. Albert, John N. Mordeson, Mark J. Wierman, Terry D. Clark
    Pages 89-116
  7. Michael B. Gibilisco, Annie M. Gowen, Karen E. Albert, John N. Mordeson, Mark J. Wierman, Terry D. Clark
    Pages 117-148
  8. Michael B. Gibilisco, Annie M. Gowen, Karen E. Albert, John N. Mordeson, Mark J. Wierman, Terry D. Clark
    Pages 149-172
  9. Michael B. Gibilisco, Annie M. Gowen, Karen E. Albert, John N. Mordeson, Mark J. Wierman, Terry D. Clark
    Pages 173-181
  10. Back Matter
    Pages 183-185

About this book

Introduction

This book offers a comprehensive analysis of the social choice literature and shows, by applying fuzzy sets, how the use of fuzzy preferences, rather than that of strict ones, may affect the social choice theorems. To do this, the book explores the presupposition of rationality within the fuzzy framework and shows that the two conditions for rationality, completeness and transitivity, do exist with fuzzy preferences. Specifically, this book examines: the conditions under which a maximal set exists; the Arrow’s theorem;  the Gibbard-Satterthwaite theorem; and the median voter theorem.  After showing that a non-empty maximal set does exists for fuzzy preference relations, this book goes on to demonstrating the existence of a fuzzy aggregation rule satisfying all five Arrowian conditions, including non-dictatorship. While the Gibbard-Satterthwaite theorem only considers individual fuzzy preferences, this work shows that both individuals and groups can choose alternatives to various degrees, resulting in a social choice that can be both strategy-proof and non-dictatorial. Moreover, the median voter theorem is shown to hold under strict fuzzy preferences,  but not under weak fuzzy preferences. By providing a standard model of fuzzy social choice and by drawing the necessary connections between the major theorems,  this book fills an important gap in the current literature and encourages future empirical research in the field.

Keywords

Fuzzy maximal set Fuzzy spatial model Fuzzy weak preference Group decision making Individual preference Social choice theorem Social preference relation Strategy-proof choice function

Authors and affiliations

  1. 1.RochesterUSA
  2. 2.PapillionUSA
  3. 3.LincolnUSA
  4. 4.Department of MathematicsCreighton UniversityOmahaUSA
  5. 5.Department of Computer ScienceCreighton UniversityOmahaUSA
  6. 6.Department of Political ScienceCreighton UniversityOmahaUSA

Bibliographic information

  • Book Title Fuzzy Social Choice Theory
  • Authors Michael B. Gibilisco
    Annie M. Gowen
    Karen E. Albert
    John N. Mordeson
    Mark J. Wierman
    Terry D. Clark
  • Series Title Studies in Fuzziness and Soft Computing
  • Series Abbreviated Title Studies in Fuzziness
  • DOI https://doi.org/10.1007/978-3-319-05176-5
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-319-05175-8
  • Softcover ISBN 978-3-319-35671-6
  • eBook ISBN 978-3-319-05176-5
  • Series ISSN 1434-9922
  • Series E-ISSN 1860-0808
  • Edition Number 1
  • Number of Pages XVIII, 185
  • Number of Illustrations 7 b/w illustrations, 0 illustrations in colour
  • Topics Computational Intelligence
    Political Theory
    Mathematics in the Humanities and Social Sciences
  • Buy this book on publisher's site
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