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On the likelihood of dummy players in weighted majority games

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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Submitted on : Tuesday, December 15, 2015 - 7:37:26 AM
Last modification on : Tuesday, October 19, 2021 - 11:33:18 PM

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Fabrice Barthélémy, Dominique Lepelley, Mathieu Martin. On the likelihood of dummy players in weighted majority games. Social Choice and Welfare, Springer Verlag, 2012, 41 (2), pp.263--279. ⟨10.1007/s00355-012-0683-1⟩. ⟨hal-01243433⟩

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