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Alternative Axioms in Group Identification Problems

Author

Listed:
  • Federico Fioravanti

    (Universidad Nacional del Sur, CONICET)

  • Fernando Tohmé

    (Universidad Nacional del Sur, CONICET)

Abstract

Group identification problems are introduced as the issue of classifying the members of a group in terms of the opinions of their potential members. This involves a finite set of agents N = {1, 2, … , n}, each one having an opinion about which agents should be classified as belonging to a specific subgroup J. A Collective Identity Function (CIF) aggregates those opinions yielding the class of members deemed J. A social planner postulate axioms, intended to ensure fair and socially desirable outcomes, characterizing different CIFs. We postulate axioms (classical and different to the ones found in the literature) constraining the spheres of influence of the agents. We show that some of them lead to different characterizations of the CIFs while in another instance we find an impossibility result.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jclass:v:38:y:2021:i:2:d:10.1007_s00357-020-09378-x
    DOI: 10.1007/s00357-020-09378-x
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    References listed on IDEAS

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    1. Cho, Wonki Jo & Ju, Biung-Ghi, 2017. "Multinary group identification," Theoretical Economics, Econometric Society, vol. 12(2), May.
    2. Dimitrov, D.A. & Sung, S.C., 2003. "On the Axiomatic Characterization of "Who is a J?"," Discussion Paper 2003-89, Tilburg University, Center for Economic Research.
    3. Samet, Dov & Schmeidler, David, 2003. "Between liberalism and democracy," Journal of Economic Theory, Elsevier, vol. 110(2), pages 213-233, June.
    4. Wonki Jo Cho & Alejandro Saporiti, 2015. "Incentives, Fairness, and Efficiency in Group Identification," Economics Discussion Paper Series 1501, Economics, The University of Manchester.
    5. Rubinstein, Ariel & Fishburn, Peter C., 1986. "Algebraic aggregation theory," Journal of Economic Theory, Elsevier, vol. 38(1), pages 63-77, February.
    6. Nicolas, Houy, 2007. ""I want to be a J!": Liberalism in group identification problems," Mathematical Social Sciences, Elsevier, vol. 54(1), pages 59-70, July.
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    Cited by:

    1. Federico Fioravanti, 2024. "Fuzzy Classification Aggregation," Working Papers 312, Red Nacional de Investigadores en Economía (RedNIE).
    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.
    3. Federico Fioravanti, 2024. "Expert Classification Aggregation," Papers 2409.11033, arXiv.org.
    4. Federico Fioravanti, 2024. "Fuzzy Classification Aggregation," Papers 2402.17620, arXiv.org, revised Aug 2024.

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