Barthélémy F. (CEMOTEV), Lepelley D., Martin M. & Smaoui H., "Dummy players and the quota in weighted voting games", Working Paper CEMOTEV n°03-2019, December 2019

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 eect 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 ve 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.

JEL classication: C7, D7

Keywords: Cooperative game theory, weighted voting games, dummy player, probability of voting paradoxes

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