Power indices when players can commit to reject coalitions

Power indices have been used to evaluate the allocation of power in a wide range of voting situations. While they use the language of game theory known measures of a priori voting power are hardly more than statistical expectations assuming the random behaviour of the players. We introduce a model where players can reject certain partnerships in cooperation. For normalised indices strategic rejection may increase power. Our notion of a strategic power index is well dened if power is measured by an index that takes only minimal winning coalitions into account. Keywords and phrases: quarrelling, rejected coalitions, a priori voting power, power indices, minimal winning coalitions, rational players.