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Conclusion

  • 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 concluding chapter provides a summary of the findings from this book. After showing that a fuzzy maximal set exists, a fuzzy aggregation rule was shown to exist which satisfies all five Arrowian conditions including nondictatorship. Although the Gibbard-Satterthwaite Theorem has considered individual fuzzy preferences, this book shows that both individuals and groups can choose alternatives to varying degrees resulting in a social choice that can be both strategy proof and non-dictatorial.Under strict fuzzy preferences, the Median Voter Theorem is shown to hold; however, this is not found under weak fuzzy preferences.

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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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