On the Buyability of Voting Bodies

We study vote buying by competing interest groups in a variety of electoral and contractual settings. While increasing the size of a voting body reduces its buyability in the absence of competition, we show that larger voting bodies may be more buyable than smaller voting bodies when interest groups compete. In contrast, imposing the secret ballot---which we model as forcing interest groups to contract on outcomes rather than votes---is an effective way to fight vote buying in the presence of competition, but much less so in its absence. We also study more sophisticated vote buying contracts. We show that, regardless of competition, the option to contract on both votes and outcomes is worthless, as it does not affect buyability as compared to contracting only on votes. In contrast, when interest groups can contract on votes and vote shares, we show that voting bodies are uniquely at risk of being bought.