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Social Choice under Fuzziness: A Perspective

  • Chapter
Preferences and Decisions under Incomplete Knowledge

Part of the book series: Studies in Fuzziness and Soft Computing ((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.

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Author information

Authors and Affiliations

  1. Department of Political Science, University of Turku, FIN-20014, Turku, Finland

    Hannu Nurmi

  2. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

Authors
  1. Hannu Nurmi
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  2. Janusz Kacprzyk
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Editors and Affiliations

  1. Department of Biomathematics and Informatics, Faculty of Veterinary Science, Szent István University, István u. 2, 1078, Budapest, Hungary

    János Fodor

  2. Department of Applied Mathematics, Biometrics and Process Control, University of Gent, Coupure Links 653, 9000, Gent, Belgium

    Bernard De Baets

  3. Case 169, LIP 6 (Paris 6 University), 4 Place Jussieu, 75252, Paris Cedex 05, France

    Patrice Perny

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Nurmi, H., Kacprzyk, J. (2000). Social Choice under Fuzziness: A Perspective. In: Fodor, J., De Baets, B., Perny, P. (eds) Preferences and Decisions under Incomplete Knowledge. Studies in Fuzziness and Soft Computing, vol 51. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1848-2_7

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  • DOI: https://doi.org/10.1007/978-3-7908-1848-2_7

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2474-2

  • Online ISBN: 978-3-7908-1848-2

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