An axiomatic characterization of the potential decisiveness index

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.