On the choice of a power index

Resumen

In this paper, we review and compare the main power indices to be found in the literature, that is to say, the Shapley-Shubik index, the Banzhaf index, the Johnston index, the Deegan-Packel index, and the Holler-Packel index. Three diferent approaches are used. First, the power indices are compared on the basis of a priori properties that they should satisfy. Second, a players power indices are compared on the basis of a priori properties that they shoud satisfy. Second, a players power is interpreted as the probability of her or his vote being necessary to pass a proposal. We present two models consistent with this approach: a model in which this probability arises from the assumptions made on the coalition formation and model, in which it arises from the assumptions made on the players voting behavior. Third, a players power is dened as her or his probability of playing a crucial role. Some power indices are derived from diferent assessments concerning the probability of playing such a role. Illustrations of the choice of an index are given for actual decision-making processes.