This paper develops a new axiomatic characterization of the Banzhaf index of power using four axioms from four different contributions to the area. A nice feature of the characterization is independence of the axioms showing importance of each of them in the exercise.

In this paper we establish equivalence between six collections of axioms that all characterize the Carreras-Coleman decisiveness index. Axioms in each of the different sets are shown to be independent.

Coleman [Coleman, J.S., 1971. Control of collectivities and the power of a collectivity to act. In: Leberman, B. (Ed.), Social Choice. Gordon and Breach, New York] proposed a measure of the power that a decision-making body has to pass any bill that comes before it. He termed it "the power of a...