Dummy Players and the Quota in Weighted Voting Games

Fabrice Barthélémy (), Dominique Lepelley, Mathieu Martin and Hatem Smaoui ()
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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

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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).

Keywords: Cooperative game theory; Weighted voting games; Dummy player; Probability of voting paradoxes (search for similar items in EconPapers)
Date: 2021-02
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Published in Group Decision and Negotiation, 2021, 30 (1), pp.43-61. ⟨10.1007/s10726-020-09705-y⟩

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Journal Article: Dummy Players and the Quota in Weighted Voting Games (2021)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03797495

DOI: 10.1007/s10726-020-09705-y

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