Vote buying, supermajorities, and flooded coalitions

In a recent paper, Banks (2000), adopting the framework of our model (Groseclose and Snyder 1996), derives several new and noteworthy results. In addition, he provides a counterexample to our proposition 4. Here we explain the error in our proposition but note that we can correct it easily if we invoke and additional assumption. In equilibrium the winning vote buyer constructs a nonflooded coalition, that is, she does not bribe every member of her coalition. We conclude with a brief discussion of the substantive implications of Bank's proposition 1; we note that it provides additional support for our general claim that minimal winning coalitions should be rare in a vote-buying game.