On power distribution in weighted voting

We study here the strategic possibilities in a voting system where, in weight terms, there is a single main agent and the others are equivalent. As an alternative to the coalition formation, we suggest for the minor agents a more discreet, anonymous and solidary behavior based on commitments referred to the size of the coalitions that they would agree to form. In order to analyze, in a coherent way, the effects of such commitments on the a priori power distribution, we use as measures of power the Shapley value and a certain class of semivalues closely related to it.Research partially supported by Grant BFM 2003–01314 of the Science and Technology Spanish Ministry. The authors wish to thank Professor Maurice Salles and two anonymous referees for their stimulating comments.