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Social Choice under Fuzziness: A Perspective

  • Hannu Nurmi
  • Janusz Kacprzyk
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 51)

Summary

The mainstream of social choice (group decision making) theory takes as its point of departure the assumption that each individual is endowed with a connected and transitive binary relation of weak preference over the set of decision alternatives (options, variants, ...). The theory focuses on social choice correspondences (functions) which map the individual preference relations to the set of social choices (alternatives). In social choice (group decision making) theory under fuzziness the starting point is the concept of an individual fuzzy preference relation. Moreover, a fuzzy majority may also be included. The aim is to find plausible aggregation methods using fuzzy preference relations, and possibly a fuzzy majority. First, we will show how the introduction of fuzzy preference relations may provide means for a way out of basic incompatibility results and paradoxes in social choice. Moreover, we will deal with ways of solving compound majority paradoxes using fuzzy preference relations. Then, taking into account the perspective adopted, we will sketch some known definitions of social choice solution concepts under fuzzy preference relations and fuzzy majority, and present three basic approaches: (1) one based on first aggregating the individual preference relations into collective preference relations and then defining various solutions, i.e. subsets of alternatives called social choices, (2) one based on defining solutions directly from individual fuzzy preference relations, and (3) one based on fuzzy tournaments.

Keywords

Social Choice Choice Probability Social Choice Function Condorcet Winner Preference Profile 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Hannu Nurmi
    • 1
  • Janusz Kacprzyk
    • 2
  1. 1.Department of Political ScienceUniversity of TurkuTurkuFinland
  2. 2.Systems Research InstitutePolish Academy of SciencesWarsawPoland

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