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Resolute refinements of social choice correspondences

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  • Bubboloni, Daniela
  • Gori, Michele

Abstract

Many classical social choice correspondences are resolute only in the case of two alternatives and an odd number of individuals. Thus, in most cases, they admit several resolute refinements, each of them naturally interpreted as a tie-breaking rule, satisfying different properties. In this paper we look for classes of social choice correspondences which admit resolute refinements fulfilling suitable versions of anonymity and neutrality. In particular, supposing that individuals and alternatives have been exogenously partitioned into subcommittees and subclasses, we find out arithmetical conditions on the sizes of subcommittees and subclasses that are necessary and sufficient for making any social choice correspondence which is efficient, anonymous with respect to subcommittees, neutral with respect to subclasses and possibly immune to the reversal bias admit a resolute refinement sharing the same properties.

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  • Bubboloni, Daniela & Gori, Michele, 2016. "Resolute refinements of social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 37-49.
    • Handle: RePEc:eee:matsoc:v:84:y:2016:i:c:p:37-49
    DOI: 10.1016/j.mathsocsci.2016.08.007
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    1. Michele Gori, 2014. "Selecting anonymous, neutral and reversal symmetric minimal majority rules," Working Papers - Mathematical Economics 2014-04, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    2. 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.
    3. Campbell, Donald E. & Kelly, Jerry S., 2015. "The finer structure of resolute, neutral, and anonymous social choice correspondences," Economics Letters, Elsevier, vol. 132(C), pages 109-111.
    4. Bubboloni, Daniela & Gori, Michele, 2016. "On the reversal bias of the Minimax social choice correspondence," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 53-61.
    5. Bubboloni, Daniela & Gori, Michele, 2015. "Symmetric majority rules," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 73-86.
    6. Campbell, Donald E. & Kelly, Jerry S., 2013. "Anonymity, monotonicity, and limited neutrality: Selecting a single alternative from a binary agenda," Economics Letters, Elsevier, vol. 118(1), pages 10-12.
    7. Campbell, Donald E. & Kelly, Jerry S., 2011. "Majority selection of one alternative from a binary agenda," Economics Letters, Elsevier, vol. 110(3), pages 272-273, March.
    8. Onur Doğan & Ayça Ebru Giritligil, 2015. "Anonymous and Neutral Social Choice:Existence Results on Resoluteness," Working Papers 201501, Murat Sertel Center for Advanced Economic Studies, Istanbul Bilgi University.
    9. Moulin, Herve, 1988. "Condorcet's principle implies the no show paradox," Journal of Economic Theory, Elsevier, vol. 45(1), pages 53-64, June.
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    1. Bubboloni, Daniela & Gori, Michele, 2016. "On the reversal bias of the Minimax social choice correspondence," Mathematical Social Sciences, Elsevier, vol. 81(C), pages 53-61.
    2. Onur Doğan & Ayça Ebru Giritligil, 2022. "Anonymous and neutral social choice: a unified framework for existence results, maximal domains and tie-breaking," Review of Economic Design, Springer;Society for Economic Design, vol. 26(3), pages 469-489, September.
    3. Lirong Xia, 2022. "Most Equitable Voting Rules," Papers 2205.14838, arXiv.org, revised Jul 2023.
    4. Daniela Bubboloni & Michele Gori, 2018. "The flow network method," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 621-656, December.
    5. 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.
    6. McMorris, F.R. & Mulder, Henry Martyn & Novick, Beth & Powers, Robert C., 2021. "Majority rule for profiles of arbitrary length, with an emphasis on the consistency axiom," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 164-174.
    7. Ali I. Ozkes & M. Remzi Sanver, 2021. "Anonymous, neutral, and resolute social choice revisited," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 97-113, July.

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