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On Some Voting Paradoxes: A Fuzzy Preference and a Fuzzy Majority Perspective

  • Janusz Kacprzyk
  • Sławomir Zadrożny
  • Hannu Nurmi
  • Mario Fedrizzi
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 305)

Abstract

Group decision making, as meant in this paper, is the following choice problem which proceeds in a multiperson setting. There is a group of individuals (decision makers, experts, …) who provide their testimonies concerning an issue in question as individual preference relations over some set of option (alternatives, variants, …). The problem is to find a solution, i.e., an alternative or a set of alternatives which best reflects the preferences of the group of individuals as a whole. First, we survey main developments in group decision making under fuzziness and outline some basic inconsistencies and negative results in group decision making and social choice, and show how they can be alleviated by some plausible modifications of underlying assumptions, mainly by introducing fuzzy preference relations and a fuzzy majority. We concentrate on how to derive solutions under individual fuzzy preference relations, and a fuzzy majority equated with a fuzzy linguistic quantifier (e.g., most, almost all, …), and discuss a related issue of how to define a “soft” degree of consensus in the group. Finally, we show how fuzzy preferences can help alleviate some known voting paradoxes.

Keywords

fuzzy logic linguistic quantifier fuzzy preference relation fuzzy majority group decision making social choice consensus 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Janusz Kacprzyk
    • 1
  • Sławomir Zadrożny
    • 1
  • Hannu Nurmi
    • 2
  • Mario Fedrizzi
    • 3
  1. 1.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  2. 2.Department of Political ScienceUniversity of TurkuTurkuFinland
  3. 3.Dipartimento di Informatica e Studi AziendaliUniversitá degli Studi di Trento via Inama 5TrentoItaly

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