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

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Multicriteria and Multiagent Decision Making with Applications to Economics and Social Sciences

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

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Author information

Authors and Affiliations

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

    Janusz Kacprzyk & Sławomir Zadrożny

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

    Hannu Nurmi

  3. Dipartimento di Informatica e Studi Aziendali, Universitá degli Studi di Trento via Inama 5, I-38100, Trento, Italy

    Mario Fedrizzi

Authors
  1. Janusz Kacprzyk
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  2. Sławomir Zadrożny
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  3. Hannu Nurmi
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  4. Mario Fedrizzi
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Corresponding author

Correspondence to Janusz Kacprzyk .

Editor information

Editors and Affiliations

  1. , Department of Architecture, Second University of Napoli, Via San Lorenzo s/n, Aversa, 81031, Italy

    Aldo G. S. Ventre

  2. “G. d’Annunzio", Department of Letters, Arts and, University of Chieti-Pescara, Via dei Vestini 31, Chieti, 66100, Italy

    Antonio Maturo

  3. Faculty of Military Technology, Department of Mathematics and Physics, University of Defence, Kounicova 65, Brno, 66210, Czech Republic

    Šárka Hošková-Mayerová

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

    Janusz Kacprzyk

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Kacprzyk, J., Zadrożny, S., Nurmi, H., Fedrizzi, M. (2013). On Some Voting Paradoxes: A Fuzzy Preference and a Fuzzy Majority Perspective. In: Ventre, A., Maturo, A., Hošková-Mayerová, Š., Kacprzyk, J. (eds) Multicriteria and Multiagent Decision Making with Applications to Economics and Social Sciences. Studies in Fuzziness and Soft Computing, vol 305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35635-3_17

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  • DOI: https://doi.org/10.1007/978-3-642-35635-3_17

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  • Print ISBN: 978-3-642-35634-6

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