Simple ¬Smarket Value� Bargaining Model for Weighted Voting Games: Characterization and Limit Theorems

Abstract

Feld, Grofman and Ray (2003) offer a bargaining model for weighted voting games that is a close relative of the nucleolus and the kernel. They look for a set of weights that preserves winning coalitions that has the property of minimizing the difference between the weight of the smallest and the weight of the largest Minimum Winning Coalition. They claim that such a set of weights provides an a priori measure of a weighted voterâ¬"s bribeworthiness or marketvalue. Here, after reviewing the basic elements of their model, we provide acharacterization result for this model and show its links to other bargaining modelapproaches in the literature. Then we offer some limit results showing that, with certain reasonable conditions on the distributions of weights, as the size of the voting body increases, the values of bribeworthiness we calculate will approach both the weights themselves and the Banzhaf scores for the weighted voting game. We also show that, even for relatively small groups using weighted voting, such as the membership of the European Council of Ministers (and itsprecedessors) 1958-2003, similarities among the usual a priori power scores,bribeworthiness/market value, and the weights themselves, will be quite strong.