A new power index based on minimal winning coalitions without any surplus

Abstract

In this paper we propose a new power index useful for the evaluation of each member in a committee, or democratic institution, and the degree of influence over the voting decision making system. The proposed solution is based on the observation that democratic organizations not only tend to form coalitions which can by themselves guarantee the control of the organization, but that they also do it in an extremely efficient way that avoids the inclusion of powerful members if they can be replaced by weaker ones. The mathematical foundation of the new measure is based on two different axiomatizations. A comparison with other well-known measures is also done.