An axiomated family of power indices for simple n-person games

In this probabilistic generalization of the Deegan-Packel power index, a new family of power indices based on the notions of minimal winning coalitions and equal division of pay offs is developed. The family of indices is parameterized by allowing minimal winning coalitions to form in accordance with varying probability functions. These indices are axiomatically characterized and compared to other similarly characterized indices. Additionally, a dual family of minimal blocking coalition indices and their characterization axioms is presented.