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On the stability of a triplet of scoring rules

  • Mostapha Diss

    ()

    (CREM - Centre de Recherche en Economie et Management - CNRS : UMR6211 - Université de Rennes I - Université de Caen)

  • Vincent Merlin

    ()

    (CREM - Centre de Recherche en Economie et Management - CNRS : UMR6211 - Université de Rennes I - Université de Caen)

When choosing a voting rule to make subsequent decisions, the members of a committee may wish this rule to be self-selected when it is the object of a choice among a menu of different possible voting rules. Such concepts have recently been explored in Social Choice theory, and a menu of voting rule is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this article the menu constituted by the three well-known scoring rules {Borda, Plurality, and Antiplurality}. Under the Impartial Culture assumption, which proposes an a priori model to estimate the likelihood of the profiles, we will derive a probability for the stability of this triplet of voting rules.

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Paper provided by HAL in its series Post-Print with number halshs-00443854.

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Date of creation: 2010
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Publication status: Published, Theory and Decision, 2010, 69, 289-316
Handle: RePEc:hal:journl:halshs-00443854
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00443854/en/
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  1. Carmen Bevi? & Salvador Barber?, . "Self-Selection Consistent Functions," UFAE and IAE Working Papers 468.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Nicolas Houy, 2004. "A note on the impossibility of a set of constitutions stable at different levels," Cahiers de la Maison des Sciences Economiques v04039, Université Panthéon-Sorbonne (Paris 1).
  3. Tataru, Maria & Merlin, Vincent, 1997. "On the relationship of the Condorcet winner and positional voting rules," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 81-90, August.
  4. Merlin, V. & Tataru, M. & Valognes, F., 2000. "On the probability that all decision rules select the same winner," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 183-207, March.
  5. Thierry Marchant, 2001. "The probability of ties with scoring methods: Some results," Social Choice and Welfare, Springer, vol. 18(4), pages 709-735.
  6. Merlin, Vincent & Valognes, Fabrice, 2004. "The impact of indifferent voters on the likelihood of some voting paradoxes," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 343-361, November.
  7. Fabrice Valognes & William V. Gehrlein, 2001. "Condorcet efficiency: A preference for indifference," Social Choice and Welfare, Springer, vol. 18(1), pages 193-205.
  8. Fabrice Valognes & Vincent Merlin & Monica Tataru, 2002. "On the likelihood of Condorcet's profiles," Social Choice and Welfare, Springer, vol. 19(1), pages 193-206.
  9. Semih Koray, 2000. "Self-Selective Social Choice Functions Verify Arrow and Gibbarad- Satterthwaite Theorems," Econometrica, Econometric Society, vol. 68(4), pages 981-996, July.
  10. Semih Koray & Bulent Unel, 2003. "Characterization of self-selective social choice functions on the tops-only domain," Social Choice and Welfare, Springer, vol. 20(3), pages 495-507, 06.
  11. Donald G. Saari & Maria M. Tataru, 1999. "The likelihood of dubious election outcomes," Economic Theory, Springer, vol. 13(2), pages 345-363.
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