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Hyper-Stable Social Welfare Functions

Author

Listed:
  • Jean Lainé

    (Department of Economics, Bilgi University - Istanbul Bilgi University)

  • Ali Ihsan Ozkes

    (Department of Economics, Bilgi University - Istanbul Bilgi University, Department of Economics, Ecole Polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

  • Remzi Sanver

    (Department of Economics, Bilgi University - Istanbul Bilgi University)

Abstract

We introduce a new consistency condition for neutral social welfare functions, called hyperstability. A social welfare function a selects a complete weak order from a profile PN of linear orders over any finite set of alternatives, given N individuals. Each linear order P in PN generates a linear order over orders of alternatives,called hyper-preference, by means of a preference extension. Hence each profile PN generates a hyper-profile ˙PN. We assume that all preference extensions are separable: the hyper-preference of some order P ranks order Q above order Q0 if the set of alternative pairs P and Q agree on contains the one P and Q0 agree on. A special sub-class of separable extensions contains all Kemeny extensions, which build hyper-preferences by using the Kemeny distance criterion. A social welfare function a is hyper-stable (resp. Kemeny-stable) if at any profile PN, at least one linearization of a(PN) is ranked first by a( ˙PN), where ˙PN is any separable (resp. Kemeny) hyper-profile induced from PN. We show that no scoring rule is hyper-stable, and that no unanimous scoring rule is Kemeny-stable, while there exists a hyper-stable Condorcet social welfare function.

Suggested Citation

  • Jean Lainé & Ali Ihsan Ozkes & Remzi Sanver, 2014. "Hyper-Stable Social Welfare Functions," Working Papers hal-00871312, HAL.
  • Handle: RePEc:hal:wpaper:hal-00871312
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00871312v2
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    References listed on IDEAS

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    1. Binmore, K. G., 1975. "An example in group preference," Journal of Economic Theory, Elsevier, vol. 10(3), pages 377-385, June.
    2. Herrade Igersheim, 2007. "Du paradoxe libéral-parétien à un concept de métaclassement des préférences," Recherches économiques de Louvain, De Boeck Université, vol. 73(2), pages 173-192.
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    5. Semih Koray, 2000. "Self-Selective Social Choice Functions Verify Arrow and Gibbarad- Satterthwaite Theorems," Econometrica, Econometric Society, vol. 68(4), pages 981-996, July.
    6. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
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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. Kikuchi, Kazuya, 2016. "Comparing preference orders: Asymptotic independence," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 1-5.
    3. 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.

    More about this item

    Keywords

    Stability; Social Welfare Functions; Kemeny distance; Hyperpreferences;

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