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On the likelihood of dummy players in weighted majority games

Author

Listed:
  • Fabrice Barthélémy

    ()

  • Dominique Lepelley

    ()

  • Mathieu Martin

    ()

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. Copyright Springer-Verlag 2013

Suggested Citation

  • Fabrice Barthélémy & Dominique Lepelley & Mathieu Martin, 2013. "On the likelihood of dummy players in weighted majority games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 263-279, July.
  • Handle: RePEc:spr:sochwe:v:41:y:2013:i:2:p:263-279
    DOI: 10.1007/s00355-012-0683-1
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    File URL: http://hdl.handle.net/10.1007/s00355-012-0683-1
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    References listed on IDEAS

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    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

    JEL classification:

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

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