An axiomatic characterization of the potential decisiveness index

Abstract

Let us consider that somebody is extremely interested in increasing the probability of a proposal to be approved by a certain committee and let us assume that for achieving this goal he/she is prepared to pay off one member of the committee. In a situation like this one, and assuming that vote-buying is allowed and free of stigma, which voter should be offered a bribe? The potential decisiveness index for simple games, which measures the effect that ensuring one positive vote produces in the probability to pass the issue at hand, is a good tool to get the answer. An axiomatic characterization of this index is given in this paper, and its relation to other classical power indices is showed.

A note on multinomial probabilistic values

“…can be viewed as the increment on the probability of acceptance of the proposal when only player i changes his probability of voting yes from p i to 1 and becomes therefore a magnetic player for the new multinomial value arising after the change of tendency of this player. This proves the close relationship between the multinomial values on simple games and the potential decisiveness index Ω p introduced by Freixas and Pons [13] and defined, for each i ∈ N , by…”