Discussion paper // Center for Mathematical Studies in Economics and Management Science 1386
We examine the consequences of vote buying, assuming this practice were allowed and free of stigma. Two parties competing in a binary election may purchase votes in a sequential bidding game via up-front binding payments and/or campaign promises (platforms) that are contingent upon the outcome of the election. We analyze the role of the parties' budget constraints and voter preferences. For instance, if only campaign promises are allowed, then the winning party depends not only on the relative size of the budgets, but also on the excess support of the party with the a priori majority, where the excess support is measured in terms of the (minimal) total utility of supporting voters who are in excess of the majority needed to win. If up front vote buying is permitted, and voters care directly about how they vote (as a legislator would), then the determination of the winning party depends on a weighted comparison of the two parties' budgets plus half of the total utility of their supporting voters. These results suggest that vote buying can lead to an inefficient party winning in equilibrium. We find that under some circumstances, if parties budgets are raised through donations, then vote buying can be efficient. Finally, we provide some results on vote buying in the face of uncertainty.