The Blocker Postulates for Measures of Voting Power

TL;DR

This paper evaluates various voting power measures against a set of postulates related to blockers, finding that the Recursive Measure uniquely satisfies all, thus supporting its plausibility as a voting power metric.

Contribution

It introduces five postulates for voting power measures concerning blockers and demonstrates that only the Recursive Measure satisfies all of them.

Findings

Recursive Measure satisfies all five postulates

Penrose-Banzhaf measure fails four postulates

Shapley-Shubik index fails two postulates

Abstract

A proposed measure of voting power should satisfy two conditions to be plausible: first, it must be conceptually justified, capturing the intuitive meaning of what voting power is; second, it must satisfy reasonable postulates. This paper studies a set of postulates, appropriate for a priori voting power, concerning blockers (or vetoers) in a binary voting game. We specify and motivate five such postulates, namely, two subadditivity blocker postulates, two minimum-power blocker postulates, each in weak and strong versions, and the added-blocker postulate. We then test whether three measures of voting power, namely the classic Penrose-Banzhaf measure, the classic Shapley-Shubik index, and the newly proposed Recursive Measure, satisfy these postulates. We find that the first measure fails four of the postulates, the second fails two, while the third alone satisfies all five postulates. This work consequently adds to the plausibility of the Recursive Measure as a reasonable measure of voting power.