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A survey on the complexity of tournament solutions

  • Hudry, Olivier
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    In voting theory, the result of a paired comparison method such as the one suggested by Condorcet can be represented by a tournament, i.e.,a complete asymmetric directed graph. When there is no Condorcet winner, i.e.,a candidate preferred to any other candidate by a majority of voters, it is not always easy to decide who is the winner of the election. Different methods, called tournament solutions, have been proposed for defining the winners. They differ in their properties and usually lead to different winners. Among these properties, we consider in this survey the algorithmic complexity of the most usual tournament solutions: some are polynomial, some are NP-hard, while the complexity status of others remains unknown.

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    File URL: http://www.sciencedirect.com/science/article/B6V88-4V59TW4-1/2/d10513dc742953eb40f8da4dbbb82b4e
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    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 57 (2009)
    Issue (Month): 3 (May)
    Pages: 292-303

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    Handle: RePEc:eee:matsoc:v:57:y:2009:i:3:p:292-303
    Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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    1. Pierre Barthelemy, Jean & Monjardet, Bernard, 1981. "The median procedure in cluster analysis and social choice theory," Mathematical Social Sciences, Elsevier, vol. 1(3), pages 235-267, May.
    2. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    3. Gerhard J. Woeginger, 2003. "Banks winners in tournaments are difficult to recognize," Social Choice and Welfare, Springer, vol. 20(3), pages 523-528, 06.
    4. Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
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