Power indices and the veil of ignorance

We provide an axiomatic foundation of the expected utility preferences over lotteries on roles in simple superadditive games represented by the two main power indices, the Shapley-Shubik index and the Banzhaf index, when they are interpreted as von NeumannMorgenstern utility functions. Our axioms admit meaningful interpretations in the setting proposed by Roth in terms of di®erent attitudes toward risk involving roles in collective decision procedures under the veil of ignorance. In particular, an illuminating interpretation of "e±ciency", up to now missing in this set up, as well as of the corresponding axiom for the Banzhaf index, is provided.