A critical reappraisal of some voting power paradoxes

Abstract

Power indices are meant to assess the power that a voting rule confers a priori to each of the decision makers who use it. In order to test and compare them, some authors have proposed "natural" postulates that a measure of a priori voting power "should" satisfy, the violations of which are called "voting power paradoxes". In this paper two general measures of factual success and decisiveness based on the voting rule and the voters' behavior, and some of these postulates/paradoxes test each other. As a result serious doubts on the discriminating power of most voting power postulates are cast.