A critical reappraisal of some voting power paradoxes

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 success and decisiveness based on the voting rule and voters' behavior and some of these postulates/paradoxes test each other. As a result serious doubts are cast on the discriminating power of most voting power postulates.