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An Extension of the Concordet Criterion and Kemeny Orders

Listed author(s):
  • 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.

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Paper provided by Université Laval - Département d'économique in its series Cahiers de recherche with number 9813.

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Date of creation: 1998
Handle: RePEc:lvl:laeccr:9813
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  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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