Authors:
- 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
Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 315)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
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.
Authors and Affiliations
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Rochester, USA
Michael B. Gibilisco
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Papillion, USA
Annie M. Gowen
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Lincoln, USA
Karen E. Albert
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Department of Mathematics, Creighton University, Omaha, USA
John N. Mordeson
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Department of Computer Science, Creighton University, Omaha, USA
Mark J. Wierman
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Department of Political Science, Creighton University, Omaha, USA
Terry D. Clark
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
DOI: https://doi.org/10.1007/978-3-319-05176-5
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-05175-8Published: 07 March 2014
Softcover ISBN: 978-3-319-35671-6Published: 03 September 2016
eBook ISBN: 978-3-319-05176-5Published: 24 February 2014
Series ISSN: 1434-9922
Series E-ISSN: 1860-0808
Edition Number: 1
Number of Pages: XVIII, 185
Number of Illustrations: 7 b/w illustrations
Topics: Computational Intelligence, Political Theory, Mathematics in the Humanities and Social Sciences