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On the likelihood of dummy players in weighted majority games

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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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Authors and Affiliations

  1. THEMA, Université de Cergy Pontoise, 33 boulevard du Port, 95011, Cergy-Pontoise Cedex, France

    Fabrice Barthélémy & Mathieu Martin

  2. CEMOI, Université de la Réunion, 97715, Saint Denis Cedex 9, France

    Dominique Lepelley

Authors
  1. Fabrice Barthélémy
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  2. Dominique Lepelley
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  3. Mathieu Martin
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Correspondence to Mathieu Martin.

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Barthélémy, F., Lepelley, D. & Martin, M. On the likelihood of dummy players in weighted majority games. Soc Choice Welf 41, 263–279 (2013). https://doi.org/10.1007/s00355-012-0683-1

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  • DOI: https://doi.org/10.1007/s00355-012-0683-1

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