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An Extension of the Concordet Criterion and Kemeny Orders


  • Truchon, Michel



The usual Condorcet Criterion says that if an alternative is ranked ahead of all other alternatives by an absolute majority of voters, it should be declared the winner. The following partial extension of this criterion to other ranks is proposed: If an alternative is consistently ranked ahead of another alternative by an absolute majority of voters, it should be ahead in the final ranking. The term "consistently" refers to the absence of cycles in the majority relation involving these two alternatives. If there are cycles, this criterion gives partial orders that can be completed with the Kemeny rule. An algorithm to construct Kemeny orders is presented. It is based on a result saying that a complete Kemeny order over all alternatives can be obtained by splicing together Kemeny orders on the subsets of an admissible partition of the alternatives underlying the Extended Condorcet Criterion. Le critère usuel de Condorcet exige que, si une alternative est classée avant toutes les autres par une majorité de votants, elle devrait être déclarée vainqueur. Une extension partielle de ce critère aux autres rangs est proposée: Si une alternative est classée avant une autre de manière cohérente par une majorité de votants, elle devrait l'être dans le classement final. La cohérence réfère à l'absence de cycle dans la relation majoritaire impliquant ces deux alternatives. En cas de cycles, ce critère donne des ordres partiels, qui peuvent être complétés avec la règle de Kemeny. Un algorithme pour la construction des ordres de Kemeny est présenté. Il s'appuie sur un résultat affirmant qu'un ordre de Kemeny peut être obtenu en juxtaposant des ordres de Kemeny sur les sous-ensembles d'une partition des alternatives sous-jacente au critère de Condorcet généralisé.

Suggested Citation

  • Truchon, Michel, 1998. "An Extension of the Concordet Criterion and Kemeny Orders," Cahiers de recherche 9813, Université Laval - Département d'économique.
  • Handle: RePEc:lvl:laeccr:9813

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    References listed on IDEAS

    1. Barthelemy, J. P. & Guenoche, A. & Hudry, O., 1989. "Median linear orders: Heuristics and a branch and bound algorithm," European Journal of Operational Research, Elsevier, vol. 42(3), pages 313-325, October.
    2. I. Good, 1971. "A note on condorcet sets," Public Choice, Springer, vol. 10(1), pages 97-101, March.
    3. Truchon, M., 1998. "Figure Skating and the Theory of Social Choice," Papers 9814, Laval - Recherche en Politique Economique.
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    Cited by:

    1. Michel Truchon, 2002. "Choix social et comités de sélection : le cas du patinage artistique," CIRANO Burgundy Reports 2002rb-02, CIRANO.
    2. Truchon, Michel, 1999. "La démocratie : oui, mais laquelle?," L'Actualité Economique, Société Canadienne de Science Economique, vol. 75(1), pages 189-214, mars-juin.
    3. repec:wsi:ijitdm:v:03:y:2004:i:04:n:s0219622004001288 is not listed on IDEAS
    4. Truchon, Michel, 1998. "Figure Skating and the Theory of Social Choice," Cahiers de recherche 9814, Université Laval - Département d'économique.
    5. Gamboa, Gonzalo & Munda, Giuseppe, 2007. "The problem of windfarm location: A social multi-criteria evaluation framework," Energy Policy, Elsevier, vol. 35(3), pages 1564-1583, March.
    6. Giuseppe Munda, 2012. "Choosing Aggregation Rules for Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 109(3), pages 337-354, December.
    7. 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.
    8. Giuseppe Munda & Michela Nardo, 2009. "Noncompensatory/nonlinear composite indicators for ranking countries: a defensible setting," Applied Economics, Taylor & Francis Journals, vol. 41(12), pages 1513-1523.

    More about this item


    aggregation; Condorcet Criterion; Kemeny orders; algorithm;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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