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Hyper-stable social welfare functions

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  • Jean Lainé

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  • Ali Ozkes
  • Remzi Sanver

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 Ozkes & Remzi Sanver, 2016. "Hyper-stable social welfare functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(1), pages 157-182, January.
  • Handle: RePEc:spr:sochwe:v:46:y:2016:i:1:p:157-182
    DOI: 10.1007/s00355-015-0908-1
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. Kikuchi, Kazuya, 2016. "Comparing preference orders: Asymptotic independence," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 1-5.
    4. 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.
    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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