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Hyper-stable social welfare functions

Author

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  • Jean Lainé

    () (LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM], Murat Sertel Center for Advanced Economic Studies - Istanbul Bilgi University)

  • Ali Ihsan Ozkes

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique, Murat Sertel Center for Advanced Economic Studies - Istanbul Bilgi University)

  • Remzi Sanver

    (Murat Sertel Center for Advanced Economic Studies - Istanbul Bilgi University)

Abstract

We define a new consistency condition for neutral social welfare functions, called hyper-stability. A social welfare function (SWF) selects a weak order from a profile of linear orders over any finite set of alternatives. Each profile induces a profile of hyper-preferences, defined as linear orders over linear orders, in accordance with the betweenness criterion: the hyper-preference of some order P ranks order Q above order Q' if the set of alternative pairs P and Q agree on contains the one P and Q' agree on. A special sub-class of hyper-preferences satisfying betweenness is defined by using the Kemeny distance criterion. A neutral SWF is hyper-stable (resp. Kemeny-stable) if given any profile leading to the weak order R, at least one linear extension of R is ranked first when the SWF is applied to any hyper-preference profile induced by means of the betweenness (resp. Kemeny) criterion. We show that no scoring rule is hyper-stable, unless we restrict attention to the case of three alternatives. Moreover, no unanimous scoring rule is Kemeny-stable, while the transitive closure of the majority relation is hyper-stable. Copyright Springer-Verlag Berlin Heidelberg 2016

Suggested Citation

  • Jean Lainé & Ali Ihsan Ozkes & Remzi Sanver, 2016. "Hyper-stable social welfare functions," Post-Print hal-01505809, HAL.
  • Handle: RePEc:hal:journl:hal-01505809
    DOI: 10.1007/s00355-015-0908-1
    Note: View the original document on HAL open archive server: https://hal-amu.archives-ouvertes.fr/hal-01505809
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    References listed on IDEAS

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    Cited by:

    1. Stergios, Athanasoglou, 2017. "An investigation of weak-veto rules in preference aggregation," Working Papers 363, University of Milano-Bicocca, Department of Economics, revised 18 Feb 2017.
    2. Mihir Bhattacharya, 2019. "Constitutionally consistent voting rules over single-peaked domains," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 225-246, February.
    3. Gilbert Laffond & Jean Lainé & M. Remzi Sanver, 2020. "Metrizable preferences over preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 177-191, June.
    4. Kikuchi, Kazuya, 2016. "Comparing preference orders: Asymptotic independence," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 1-5.
    5. Katherine Baldiga Coffman, 2016. "Representative democracy and the implementation of majority-preferred alternatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 477-494, March.

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    Keywords

    Economie quantitative;

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