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 Neumann-Morgenstern utility functions. Our axioms admit meaningful interpretations in the setting proposed by Roth in terms of different attitudes toward risk involving roles in collective decision procedures under the veil of ignorance. In particular, an illuminating interpretation of `efficiency', up to now missing in this set up, as well as of the corresponding axiom for the Banzhaf index, is provided. November 7, 2002 RID="*" ID="*"  We want to thank M. Maschler, J. M. Zarzuelo and two referees for their comments. This research has been supported by the IVIE, and by the DGES of the Spanish Ministerio de Educación y Cultura, under project PB96-0247. The first author also acknowledges the financial support from the Ramón y Cajal Program initiated by the Spanish MCyT.