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Hyper-Stable Social Welfare Functions

  • 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 - Polytechnique - X - CNRS)

  • Remzi Sanver

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

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.

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Paper provided by HAL in its series Working Papers with number hal-00871312.

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Date of creation: 03 Mar 2014
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Handle: RePEc:hal:wpaper:hal-00871312
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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. Sen, Amartya, 1970. "The Impossibility of a Paretian Liberal," Journal of Political Economy, University of Chicago Press, vol. 78(1), pages 152-57, Jan.-Feb..
  3. Semih Koray, 2000. "Self-Selective Social Choice Functions Verify Arrow and Gibbarad- Satterthwaite Theorems," Econometrica, Econometric Society, vol. 68(4), pages 981-996, July.
  4. Bossert, Walter & Sprumont, Yves, 2014. "Strategy-proof preference aggregation: Possibilities and characterizations," Games and Economic Behavior, Elsevier, vol. 85(C), pages 109-126.
  5. Semih Koray & Bulent Unel, 2003. "Characterization of self-selective social choice functions on the tops-only domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 495-507, 06.
  6. Sen, Amartya Kumar, 1970. "The Impossibility of a Paretian Liberal," Scholarly Articles 3612779, Harvard University Department of Economics.
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