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On the stability of a triplet of scoring rules

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  • Mostapha Diss

    ()

  • Vincent Merlin

    ()

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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File URL: http://hdl.handle.net/10.1007/s11238-009-9187-6
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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 69 (2010)
Issue (Month): 2 (August)
Pages: 289-316

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Handle: RePEc:kap:theord:v:69:y:2010:i:2:p:289-316

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Web page: http://www.springerlink.com/link.asp?id=100341

Related research

Keywords: Self-selectivity; Stability; Instability; Scoring rules; Impartial Culture assumption; D72;

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References

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  1. Donald G. Saari & Maria M. Tataru, 1999. "The likelihood of dubious election outcomes," Economic Theory, Springer, vol. 13(2), pages 345-363.
  2. Salvador Barbera & Carmen Bevia, 2000. "Self-Selection Consistent Choices," Econometric Society World Congress 2000 Contributed Papers 1322, Econometric Society.
  3. 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.
  4. Barbera, Salvador & Bevia, Carmen, 2002. "Self-Selection Consistent Functions," Journal of Economic Theory, Elsevier, vol. 105(2), pages 263-277, August.
  5. Gehrlein, W. & Valognes, F., 2000. "Condorcet Efficiency: A Preference for Indifference," Papers 224, Notre-Dame de la Paix, Sciences Economiques et Sociales.
  6. 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.
  7. 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).
  8. 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.
  9. 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.
  10. 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.
  11. Thierry Marchant, 2001. "The probability of ties with scoring methods: Some results," Social Choice and Welfare, Springer, vol. 18(4), pages 709-735.
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Citations

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Cited by:
  1. Mostapha Diss, 2013. "Strategic manipulability of self-­selective social choice rules," Working Papers halshs-00785366, HAL.
  2. Mostapha Diss, 2013. "Strategic manipulability of self-selective social choice rules," Working Papers 1302, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  3. 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, vol. 64(1), pages 57-66.

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