Arrow and the Aggregation of Fuzzy Preferences

  • Michael B. Gibilisco
  • Annie M. Gowen
  • Karen E. Albert
  • John N. Mordeson
  • Mark J. Wierman
  • Terry D. Clark
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 315)

Abstract

This chapter builds off of chapter 3 by examining the aggregation of fuzzy weak preference relations in order to determine how a social preference relation emerges. Specifically, this chapter focuses on Arrow’s theorem which employs a deductive analysis of aggregation rules and establishes five necessary conditions for an ideal aggregation rule.When Arrow’s theorem is applied with fuzzy preferences, not only do serious complications arise when conceiving the fuzzy definitions of an ideal aggregation rule, but there exist specific combinations of conditions that allow for a fuzzy aggregation rule to satisfy all of the fuzzy counterparts of Arrow’s conditions. Moreover, this chapter shows that a fuzzy aggregation rule exists which satisfies all five Arrowian conditions including non-dictatorship.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Michael B. Gibilisco
    • 1
  • Annie M. Gowen
    • 2
  • Karen E. Albert
    • 3
  • John N. Mordeson
    • 4
  • Mark J. Wierman
    • 5
  • Terry D. Clark
    • 6
  1. 1.New YorkUSA
  2. 2.PapillionUSA
  3. 3.LincolnUSA
  4. 4.Department of Mathematics Creighton UniversityOmahaUSA
  5. 5.Department of Computer Science Creighton UniversityOmahaUSA
  6. 6.Department of Political Science Creighton UniversityOmahaUSA

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