Legislative Bargaining under Weighted Voting1

Voting institutions commonly assign di®erent weights across voters. Most analyses of such systems assume that the relative in°uence of each player is non-linear in her voting weight. We reassess this assumption with a distributive bargaining game that closely resembles the closed-rule, in ̄nite-horizon Baron-Ferejohn (1989) model. In equilibrium, voters with lower weights are typically perfect substitutes for voters with higher weights. Hence, each voter's power is exactly proportional to her voting weight. An exception occurs when su±cient numbers of high-weight voters exist. In this case, low-weight voters are relatively more powerful than high-weight voters because their probabilities of being recognized to make a proposal are equal to those of high-weight voters. These results call into question the applicability of power indices such as the Banzhaf index and Shapley-Shubik value, which are often convex in voting weights.