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On the Likelihood of Dummy players in Weighted Majority Games

Author

Listed:
  • Fabrice Barthelemy

    () (THEMA, Universite de Cergy-Pontoise)

  • Dominique Lepelley

    () (CEMOI,universite de la réunion)

  • Mathieu Martin

    () (THEMA, Universite de Cergy-Pontoise)

Abstract

When the number of players is small in a weighted majority voting game, it can occur that one of the players has no influence on the result of the vote, in spite of a strictly positive weight. Such a player is called a “dummy” player in game theory. The purpose of this paper is to investigate the conditions that give rise to such a phenomenon and to compute its likelihood. It is shown that the probability of having a dummy player is surprisingly high and some paradoxical results are observed.

Suggested Citation

  • Fabrice Barthelemy & Dominique Lepelley & Mathieu Martin, 2011. "On the Likelihood of Dummy players in Weighted Majority Games," THEMA Working Papers 2011-17, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  • Handle: RePEc:ema:worpap:2011-17
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    File URL: http://thema.u-cergy.fr/IMG/documents/2011-17.pdf
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    References listed on IDEAS

    as
    1. William V. Gehrlein, 2002. "Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(3), pages 503-512.
    2. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2008. "On Ehrhart polynomials and probability calculations in voting theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(3), pages 363-383, April.
    3. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, vol. 54(3), pages 244-256, December.
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    Cited by:

    1. Dominique Lepelley & Vincent R Merlin & Jean-louis Rouet & Laurent Vidu, 2014. "Referendum paradox in a federal union with unequal populations: the three state case," Economics Bulletin, AccessEcon, vol. 34(4), pages 2201-2207.

    More about this item

    Keywords

    Cooperative game theory; weighted voting games; dummy player; likelihood of voting paradoxes.;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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