B. Gibilisco, M., M. Gowen, A., E. Albert, K., N. Mordeson, J., J. Wierman, M., D. Clark, T.
2014, XVIII, 185 p. 7 illus.
Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.
You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.
After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.
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
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.
Content Level »Research
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
Fuzzy Social Choice.- Classical Social Choice Theorems.- Rationality of Fuzzy Preferences.- Arrow and the Aggregation of Fuzzy Preferences.- Characteristics of Strategy-Proof Fuzzy Social Choice.- Fuzzy Black’s Median Voter Theorem.- Representing Thick Indifference in Spatial Models.- Conclusion.