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A survey on the complexity of tournament solutions

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  • Hudry, Olivier
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    Abstract

    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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    Bibliographic Info

    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

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    Web page: http://www.elsevier.com/locate/inca/505565

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    Keywords: Voting theory Tournament solutions Majority tournament Complexity;

    References

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    1. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    2. Brandt, Felix & Fischer, Felix, 2008. "Computing the minimal covering set," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 254-268, September.
    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. 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.
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    Cited by:
    1. Vincent Anesi, 2010. "A New Old Solution for Weak Tournaments," Discussion Papers 2010-04, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    2. Rudolf Berghammer & Agnieszka Rusinowska & Harrie De Swart, 2013. "Computing tournament solutions using relation algebra and RelView," PSE - Labex "OSE-Ouvrir la Science Economique" hal-00756696, HAL.
    3. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
    4. repec:hal:cesptp:hal-00756696 is not listed on IDEAS
    5. Marc Pauly, 2014. "Can strategizing in round-robin subtournaments be avoided?," Social Choice and Welfare, Springer, vol. 43(1), pages 29-46, June.
    6. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2013. "Computing tournament solutions using relation algebra and RelView," European Journal of Operational Research, Elsevier, vol. 226(3), pages 636-645.
    7. repec:hal:wpaper:hal-00756696 is not listed on IDEAS
    8. Hudry, Olivier, 2012. "On the computation of median linear orders, of median complete preorders and of median weak orders," Mathematical Social Sciences, Elsevier, vol. 64(1), pages 2-10.

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