Semisimple games,enactment power and generalized power indices

By allowing for individual abstention, the classC of simplen-person games is extended to the class ofsemisimple gamesS. Using this extension, any given index of individual power onC gives rise to a measure of individual power onS in the form of a vector function with 2 ⁿ ?1 components. After developing an axiomatic characterization of Coleman's notion of collective power, thisenactment power is combined with any index of individual power to provide a general nonnormalized meausre of individual power. Using these results, enactment and individual power in different games can be meaningfully compared. In the presence of abstention, various “paradoxes” associated with power indices lose some of the impact.