POSTULATES AND PARADOXES OF RELATIVE VOTING POWER - A CRITICAL REAPPRAISAL

This paper re-evaluates the problem of measuring the a priori relative voting power of a voter in an assembly. We propose several new intuit ively compelling postulates that any reasonable index of voting power ought to satisfy. At the same time we argue that most of the paradoxes of voting power discussed in the literature are paradoxical only in a weak sense, if at all. This Leaves three crippling paradoxes - the we ll-known paradox of weighted voting, and two new ones presented here: the bloc and donation paradoxes. We evaluate the four main relative po wer indices discussed in the literature with respect to these three se vere paradoxes. The Shapley-Shubik index is seen to be immune to all t hree paradoxes, while the Deegan-Packel index is vulnerable to all thr ee. The Banzhaf and the Johnston indices are demonstrably immune to th e paradox of weighted voting. However, they are shown to suffer from b oth the bloc and the donation paradoxes. We argue that this seriously undermines these indices in a hitherto unsuspected way. Several other theoretical issues relating to voting power are discussed.