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On the stability of a triplet of scoring rules

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  • 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)

Abstract

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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Bibliographic Info

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

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Keywords: Self-selectivity ; Stability ; Instability ; Scoring rules ; Impartial Culture assumption;

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  1. Thierry Marchant, 2001. "The probability of ties with scoring methods: Some results," Social Choice and Welfare, Springer, Springer, vol. 18(4), pages 709-735.
  2. Barbera, Salvador & Bevia, Carmen, 2002. "Self-Selection Consistent Functions," Journal of Economic Theory, Elsevier, vol. 105(2), pages 263-277, August.
  3. Merlin, V. & Tataru, M. & Valognes, F., 2000. "On the Likelihood of Condorcet's Profiles," Papers, Notre-Dame de la Paix, Sciences Economiques et Sociales 223, Notre-Dame de la Paix, Sciences Economiques et Sociales.
  4. Fabrice Valognes & William V. Gehrlein, 2001. "Condorcet efficiency: A preference for indifference," Social Choice and Welfare, Springer, Springer, vol. 18(1), pages 193-205.
  5. Donald G. Saari & Maria M. Tataru, 1999. "The likelihood of dubious election outcomes," Economic Theory, Springer, Springer, vol. 13(2), pages 345-363.
  6. Tataru, Maria & Merlin, Vincent, 1997. "On the relationship of the Condorcet winner and positional voting rules," Mathematical Social Sciences, Elsevier, Elsevier, vol. 34(1), pages 81-90, August.
  7. Merlin, Vincent & Valognes, Fabrice, 2004. "The impact of indifferent voters on the likelihood of some voting paradoxes," Mathematical Social Sciences, Elsevier, Elsevier, vol. 48(3), pages 343-361, November.
  8. Semih Koray, 2000. "Self-Selective Social Choice Functions Verify Arrow and Gibbarad- Satterthwaite Theorems," Econometrica, Econometric Society, Econometric Society, vol. 68(4), pages 981-996, July.
  9. 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.
  10. Nicolas Houy, 2004. "A note on the impossibility of a set of constitutions stable at different levels," Cahiers de la Maison des Sciences Economiques, Université Panthéon-Sorbonne (Paris 1) v04039, Université Panthéon-Sorbonne (Paris 1).
  11. Semih Koray & Bulent Unel, 2003. "Characterization of self-selective social choice functions on the tops-only domain," Social Choice and Welfare, Springer, Springer, vol. 20(3), pages 495-507, 06.
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Cited by:
  1. Diss, Mostapha & Louichi, Ahmed & Merlin, Vincent & Smaoui, Hatem, 2012. "An example of probability computations under the IAC assumption: The stability of scoring rules," Mathematical Social Sciences, Elsevier, Elsevier, vol. 64(1), pages 57-66.
  2. Mostapha Diss, 2013. "Strategic manipulability of self-­selective social choice rules," Working Papers halshs-00785366, HAL.
  3. Mostapha Diss, 2013. "Strategic manipulability of self-selective social choice rules," Working Papers, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure 1302, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.

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