Proportionality and the power of unequal parties

In this paper we introduce the concept of an overall power function that is meant to combine two sources of a party’s power in a parliament. The first source is based on the possibilities for the party to be part of a majority coalition and it is typically modeled using a cooperative simple game. The second source takes into account parties’ asymmetries outside the cooperative game and it is displayed by a vector of exogenously given weights. We adopt a normative point of view and provide an axiomatic characterization of a specific overall power function, in which the weights enter in a proportional fashion.