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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 an 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 Banks'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.