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Maximum likelihood approach to vote aggregation with variable probabilities

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  • Mohamed Drissi-Bakhkhat

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  • Michel Truchon

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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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    References listed on IDEAS

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    1. Ladha, Krishna K., 1995. "Information pooling through majority-rule voting: Condorcet's jury theorem with correlated votes," Journal of Economic Behavior & Organization, Elsevier, vol. 26(3), pages 353-372, May.
    2. Berg, Sven, 1994. "Evaluation of some weighted majority decision rules under dependent voting," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 71-83, October.
    3. Truchon, M., 1998. "Figure Skating and the Theory of Social Choice," Papers 9814, Laval - Recherche en Politique Economique.
    4. Nitzan, Shmuel & Paroush, Jacob, 1982. "Optimal Decision Rules in Uncertain Dichotomous Choice Situations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 289-297, June.
    5. Truchon, Michel, 1998. "An Extension of the Concordet Criterion and Kemeny Orders," Cahiers de recherche 9813, Université Laval - Département d'économique.
    6. Donald G. Saari & Vincent R. Merlin, 2000. "A geometric examination of Kemeny's rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 403-438.
    7. Wit, Jorgen, 1998. "Rational Choice and the Condorcet Jury Theorem," Games and Economic Behavior, Elsevier, vol. 22(2), pages 364-376, February.
    8. Peyton Young, 1995. "Optimal Voting Rules," Journal of Economic Perspectives, American Economic Association, vol. 9(1), pages 51-64, Winter.
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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. Stephen Gordon & Michel Truchon, 2008. "Social choice, optimal inference and figure skating," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, pages 265-284.
    3. Conitzer, Vincent, 2012. "Should social network structure be taken into account in elections?," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 100-102.
    4. Marcus Hagedorn & Tzuo Hann Law & Iourii Manovskii, 2017. "Identifying Equilibrium Models of Labor Market Sorting," Econometrica, Econometric Society, vol. 85, pages 29-65, January.
    5. Truchon, Michel, 2008. "Borda and the maximum likelihood approach to vote aggregation," Mathematical Social Sciences, Elsevier, vol. 55(1), pages 96-102, January.
    6. Michel Truchon, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0414, CIRPEE.
    7. Jean-François Laslier, 2009. "In Silico Voting Experiments," Working Papers hal-00390376, HAL.
    8. Truchon, Michel & Gordon, Stephen, 2009. "Statistical comparison of aggregation rules for votes," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 199-212, March.
    9. 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.
    10. Michel Truchon, 2004. "Aggregation of Rankings in Figure Skating," Cahiers de recherche 0414, CIRPEE.

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