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Maximum likelihood approach to vote aggregation with variable probabilities

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  • Mohamed Drissi-Bakhkhat

    ()

  • Michel Truchon

    ()

Abstract

The Condorcet-Kemeny-Young statistical approach to vote aggregation is based on the assumption that voters have the same probability of comparing correctly two alternatives and that this probability is the same for any pair of alternatives. We relax the second part of this assumption by letting the probability of comparing correctly two alternatives be increasing with the distance between two alternatives in the allegedly true ranking. This leads to a rule in which the majority in favor of one alternative against another one is given a larger weight the larger the distance between the two alternatives in the true ranking, i.e., the larger the probability that the voters compare them correctly. This rule is not Condorcet consistent and does not satisfy local independence of irrelevant alternatives. Yet, it is anonymous, neutral, and paretian. It also appears that its performance in selecting the alternative most likely to be the best improves with the rate at which the probability increases. Copyright Springer-Verlag 2004

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File URL: http://hdl.handle.net/10.1007/s00355-003-0242-x
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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 23 (2004)
Issue (Month): 2 (October)
Pages: 161-185

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Handle: RePEc:spr:sochwe:v:23:y:2004:i:2:p:161-185

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Cited by:
  1. Marcus Hagedorn & Tzuo Hann Law & Iourii Manovskii, 2012. "Identifying Equilibrium Models of Labor Market Sorting," NBER Working Papers 18661, National Bureau of Economic Research, Inc.
  2. Michel Truchon & Stephen Gordon, 2006. "Statistical Comparison of Aggregation Rules for Votes," Cahiers de recherche 0625, CIRPEE.
  3. Truchon, Michel, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0402, Université Laval - Département d'économique.
  4. Truchon, Michel, 2008. "Borda and the maximum likelihood approach to vote aggregation," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 96-102, January.
  5. Conitzer, Vincent, 2012. "Should social network structure be taken into account in elections?," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 100-102.
  6. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer, vol. 40(2), pages 581-630, February.
  7. T. Tideman & Florenz Plassmann, 2014. "Which voting rule is most likely to choose the “best” candidate?," Public Choice, Springer, vol. 158(3), pages 331-357, March.
  8. Jean-François Laslier, 2009. "In Silico Voting Experiments," Working Papers hal-00390376, HAL.

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