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Symmetry groups for social preference functions

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  • Bubboloni, Daniela
  • Nardi, Francesco

Abstract

We introduce the anonymity group, the neutrality group and the symmetry group of a social preference function. Inspired by an unsolved problem posed by Kelly in 1991, we investigate the problem of recognizing which permutation groups may arise as anonymity, neutrality and symmetry groups of a social preference function. A complete description is provided for neutrality groups. In the case of anonymity groups, we derive a sufficient condition, which largely captures the desired class of objects. Our approach also is of relevance for the notion of representability by Boolean functions and, therefore, the results of this paper also shed some light on this field of study.

Suggested Citation

  • Bubboloni, Daniela & Nardi, Francesco, 2024. "Symmetry groups for social preference functions," Mathematical Social Sciences, Elsevier, vol. 132(C), pages 1-14.
    • Handle: RePEc:eee:matsoc:v:132:y:2024:i:c:p:1-14
    DOI: 10.1016/j.mathsocsci.2024.07.004
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    References listed on IDEAS

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    1. Daniela Bubboloni & Michele Gori, 2014. "Anonymous and neutral majority rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 377-401, August.
    2. Daniela Bubboloni & Michele Gori, 2021. "Breaking ties in collective decision-making," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 411-457, June.
    3. Kelly, Jerry S., 1992. "Abelian symmetry groups in social choice," Mathematical Social Sciences, Elsevier, vol. 25(1), pages 15-25, December.
    4. Bubboloni, Daniela & Gori, Michele, 2016. "Resolute refinements of social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 37-49.
    5. Bubboloni, Daniela & Gori, Michele, 2015. "Symmetric majority rules," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 73-86.
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