Measuring Power in Voting Bodies: Linear Constraints, Spatial Analysis, and a Computer Program

Abstract

The purpose of this contribution is to present some extensions of an established method for measuring the distribution of power among the various groups within any voting body. If there are no formal alignments of individual voters — like parliamentary groups or fractions — within such a unit, and if voting occurs on a purely individual basis according to a “one man one vote” rule, all members obviously possess the same voting power in that they are all equally decisive for voting outcomes. If, on the other hand, voting patterns are mediated, so to speak, by a division of the voting body into several voting blocs with a fairly high probability of joint voting, as is the case for parliamentary groups within legislatures, then the voting power of individual members can vary between blocs depending upon the number of individuals in each bloc and the decision rule. In highly simplified economic terms this means that if one wants to “buy” the one decisive vote for a particular motion, then in the former case each member would be worth the same amount of money whereas in the latter case this amount would have to be weighted by the odds that an individual member will belong to the decisive voting bloc. In other words, the “price” paid for each voting bloc should covary with its probability of turning the outcome which is a straightforward measure of its power.