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

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... ing 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.