Assessing success and decisiveness in voting situations

In this paper we propose a simple model for measuring success or decisiveness in voting situations. For an assessment of these features two inputs are claimed to be necessary: the voting rule and the voters behavior. The voting rule specifies when a proposal is to be accepted or rejected depending on the resulting vote configuration. Voting behavior is summarized by a distribution of probability over the vote configurations. This basic model provides a clear common conceptual basis for reinterpreting different power indices and some related game theoretic notions coherently from a unified point of view.The authors would like to thank to M. Braham, M. Machover, N. Megiddo and F. Steffen, for their comments, and to J. F. Mertens for pointing out a misstatement, in all cases referring to previous versions of this paper. This research has been supported by the DGES of the Spanish Ministerio de Educación y Cultura under project PB96-0247, by the Spanish Ministerio de Ciencia y Tecnología under project BEC2000-0875, and by the Universidad del País Vasco under project UPV/EHU00031.321-HA-7918/2000. The first author also acknowledges the financial support from a postdoctoral grant from the Basque Government (2000–2001) and the Spanish Ministerio de Ciencia y Tecnología under the Ramón y Cajal Program.