We discuss possible criteria that may qualify or disqualify power indices for applications. Instead of providing final answers we merely ask questions that are relevant from our point of view and summarize some material from the literature

This paper studies power indices based on average representations of a weighted game. If restricted to account for the lack of power of dummy voters, average representations become coherent measures of voting power, with power distributions being proportional to the distribution of weights in...

For the classical power indices there is a disproportion between power and relative weights, in general. We introduce two new indices, based on weighted representations, which are proportional to suitable relative weights and which also share several important properties of the classical power...