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Dummy Players and the Quota in Weighted Voting Games

Author

Listed:
  • Fabrice Barthelemy

    (Cemotev - Centre d'études sur la mondialisation, les conflits, les territoires et les vulnérabilités - UVSQ - Université de Versailles Saint-Quentin-en-Yvelines)

  • Dominique Lepelley

    (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion)

  • Mathieu Martin

    (THEMA - Théorie économique, modélisation et applications - CNRS - Centre National de la Recherche Scientifique - CY - CY Cergy Paris Université)

  • Hatem Smaoui

    (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion)

Abstract

In a weighted voting game, each voter has a weight and a proposal is accepted if the sum of the weights of the voters in favor of that proposal is at least as large as a certain quota. It is well-known that, in this kind of voting process, it can occur that the vote of a player has no efect on the outcome of the game; such a player is called a "dummy" player. This paper studies the role of the quota on the occurrence of dummy players in weighted voting games. Assuming that every admissible weighted voting game is equally likely to occur, we compute the probability of having a player without voting power as a function of the quota for three, four and fve players. It turns out that this probability is very sensitive to the choice of the quota and can be very high. The quota values that minimize (or maximize) the likelihood of dummy players are derived (Some technical details are voluntarily omitted in this version of our study. These details can be found in the online appendix associated with this paper at https://bit.ly/2MVVuBW).

Suggested Citation

  • Fabrice Barthelemy & Dominique Lepelley & Mathieu Martin & Hatem Smaoui, 2021. "Dummy Players and the Quota in Weighted Voting Games," Post-Print hal-03797495, HAL.
    • Handle: RePEc:hal:journl:hal-03797495
    DOI: 10.1007/s10726-020-09705-y
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Cooperative game theory; Weighted voting games; Dummy player; Probability of voting paradoxes;
    All these keywords.

    JEL classification:

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

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