Vote buying, supermajorities, and flooded coalitions

In a recent paper, Banks (2000), adopting the framework of our model (Grose close and Snyder 1996), derives several new and noteworthy results. In addi tion, he provides a counterexample to our proposition 4. Here we explain th e error in our proposition but note that we can correct it easily if we inv oke and additional assumption. In equilibrium the winning vote buyer constr ucts a nonflooded coalition, that is, she does not bribe every member of he r coalition. We conclude with a brief discussion of the substantive implica tions 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 v ote-buying game.