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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

Suggested Citation

  • Mohamed Drissi-Bakhkhat & Michel Truchon, 2004. "Maximum likelihood approach to vote aggregation with variable probabilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(2), pages 161-185, October.
    • Handle: RePEc:spr:sochwe:v:23:y:2004:i:2:p:161-185
    DOI: 10.1007/s00355-003-0242-x
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    Cited by:

    1. Marcus Pivato, 2013. "Voting rules as statistical estimators," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 581-630, February.
    2. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
    3. Marcus Hagedorn & Tzuo Hann Law & Iourii Manovskii, 2017. "Identifying Equilibrium Models of Labor Market Sorting," Econometrica, Econometric Society, vol. 85, pages 29-65, January.
    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. Truchon, Michel, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0402, Université Laval - Département d'économique.
    6. Jean-François Laslier, 2010. "In Silico Voting Experiments," Studies in Choice and Welfare, in: Jean-François Laslier & M. Remzi Sanver (ed.), Handbook on Approval Voting, chapter 0, pages 311-335, Springer.
    7. Conitzer, Vincent, 2012. "Should social network structure be taken into account in elections?," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 100-102.
    8. 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.
    9. Yuta Nakamura, 2015. "Maximum Likelihood Social Choice Rule," The Japanese Economic Review, Japanese Economic Association, vol. 66(2), pages 271-284, June.

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