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Fuzzy Classification Aggregation

Author

Listed:
  • Federico Fioravanti

    (University of Amsterdam/UNS-CONICET)

Abstract

We consider the problem where a set of individuals has to classify m objects into p categories and does so by aggregating the individual classifications. We show that if m = 3, m = p = 2, and classificationsare fuzzy, that is, objects belong to a category to a certain degree, then an independent aggregator rule that satisfies a weak unanimity condition belongs to the family of Weighted Arithmetic Means. Wealso obtain characterization results for m = p = 2.

Suggested Citation

  • Federico Fioravanti, 2024. "Fuzzy Classification Aggregation," Working Papers 312, Red Nacional de Investigadores en Economía (RedNIE).
    • Handle: RePEc:aoz:wpaper:312
    as

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    File URL: https://rednie.eco.unc.edu.ar/files/DT/312.pdf
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    References listed on IDEAS

    as
    1. Federico Fioravanti & Fernando Tohmé, 2021. "Alternative Axioms in Group Identification Problems," Journal of Classification, Springer;The Classification Society, vol. 38(2), pages 353-362, July.
    2. Cailloux, Olivier & Hervouin, Matthieu & Ozkes, Ali I. & Sanver, M. Remzi, 2024. "Classification aggregation without unanimity," Mathematical Social Sciences, Elsevier, vol. 128(C), pages 6-9.
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    4. Dutta, Bhaskan, 1987. "Fuzzy preferences and social choice," Mathematical Social Sciences, Elsevier, vol. 13(3), pages 215-229, June.
    5. Conal Duddy & Ashley Piggins, 2018. "On some oligarchy results when social preference is fuzzy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 717-735, December.
    6. Samet, Dov & Schmeidler, David, 2003. "Between liberalism and democracy," Journal of Economic Theory, Elsevier, vol. 110(2), pages 213-233, June.
    7. Dietrich, Franz & List, Christian, 2014. "Probabilistic Opinion Pooling," MPRA Paper 54806, University Library of Munich, Germany.
    8. Miguel A. Ballester & José Luis García-Lapresta, 2008. "A Model of Elitist Qualification," Group Decision and Negotiation, Springer, vol. 17(6), pages 497-513, November.
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    10. Maniquet, François & Mongin, Philippe, 2016. "A theorem on aggregating classifications," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 6-10.
    11. Cho, Wonki Jo & Park, Chang Woo, 2018. "Fractional group identification," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 66-75.
    12. Mishra, Debasis & Sen, Arunava, 2012. "Robertsʼ Theorem with neutrality: A social welfare ordering approach," Games and Economic Behavior, Elsevier, vol. 75(1), pages 283-298.
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    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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