Summary: 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.