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 that to achieve 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 for the probability of passing the issue at hand, is a good tool with which to acquire the answer. An axiomatic characterization of this index is given in this paper, and its relation to other classical power indices is shown.

Keywords:

• game theory
• potential decisiveness index
• a measure for bribes
• axiomatization
• standard power indices
• relationship among several measures

Notes

1 This game can also be represented by the weighted game with representation [3, 2, 1, 1, 1].