The exact lower bound for the Coleman index of the power of a collectivity for a special class of simple majority games

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 collectivity to act". In this paper we provide some numerical bounds on the values that this measure can take when the collectivity takes decisions under simple majority voting rule.