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On the Likelihood of Dummy players in Weighted Majority Games

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  • Fabrice Barthelemy
  • Dominique Lepelley
  • Mathieu Martin

    ()
    (THEMA, Universite de Cergy-Pontoise
    CEMOI,universite de la réunion
    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.

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Paper provided by THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise in its series THEMA Working Papers with number 2011-17.

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Date of creation: 2011
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Handle: RePEc:ema:worpap:2011-17

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

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  1. Dominique Lepelley & Ahmed Louichi & Hatem Smaoui, 2006. "On Ehrhart Polynomials and Probability Calculations in Voting Theory," Economics Working Paper Archive (University of Rennes 1 & University of Caen), Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS 200610, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
  2. Wilson, Mark C. & Pritchard, Geoffrey, 2007. "Probability calculations under the IAC hypothesis," Mathematical Social Sciences, Elsevier, Elsevier, vol. 54(3), pages 244-256, December.
  3. William V. Gehrlein, 2002. "Obtaining representations for probabilities of voting outcomes with effectively unlimited precision integer arithmetic," Social Choice and Welfare, Springer, Springer, vol. 19(3), pages 503-512.
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