THIS PAPER EXAMINES ANOTHER IMPLICATION OF THE PROBABILISTIC RELATIONSHIP BETWEEN THE POTENTIAL CHOICE OF THE INDIVIDUAL VOTER, AND THE ULTIMATE COLLECTIVE OUTCOME: THE MUTUALLY ADVANTAGEOUS OPPORTUNITIES FOR THE BUYING AND SELLING OF VOTES THAT MAY EMERGE AS THE PROBABILITIES OF INFLUENCE OVER COLLECTIVE OUTCOMES VARY. THE ANALYSIS IS INDIRECTLY RELATED TO THEORIES OF COALITION FORMATION.
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.
In a recent paper, Banks (2000), adopting the framework of our model (Groseclose & Snyder 1996), derives several new & 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. 3 References. Adapted from the source document.
THIS REPLY ANSWERS ABRAHAM'S COMMENT ON THE PAPER, BUCHANAN AND LEE (1986). IT ACKNOWLEDGES AND APPRECIATES THE ATTENTION CALLED TO AN OVERSIGHT THEN STATES THAT ABRAHAM OVERSTATES THE PROBLEMS CAUSED BY THE INFORMATION GENERATED BY THE STRUCTURE OF THE MODEL. THE MAIN POINT OF THE PAPER IS THAT THERE EXIST MUTUAL GAINS FROM VOTE TRADING THAT DO NOT DEPEND ON DIFFERENCES IN HOW PEOPLE ASSESS THE PROBABILITIES OF RANDOMLY CHOSEN INDIVIDUALS VOTING YES OR NO, OR DIFFERENCES IN HOW THEY VALUE BEING ON THE WINNING SIDE OF AN ELECTION. THERE IS NO DOUBT THAT THIS RESULT HOLDS UNDER OUR INITIAL ASSUMPTION THAT VOTE MARKETS ARE BLIND ON BOTH SIDES; I.E., NEITHER BUYER NOR SELLER KNOWS THE VOTING CHOICE OF THE OTHER.
Minimal winning coalitions have appeared as a key prediction or as an essential assumption of virtually all formal models of coalition formation, vote buying, and logrolling. Notwithstanding this research, we provide a model showing that supermajority coalitions may be cheaper than minimal winning coalitions. Specifically, if vote buyers move sequentially, and if the losing vote buyer is always granted a last chance to attack the winner's coalition, then minimal winning coalitions will generally not be cheapest, and equilibrium coalitions will generally not be minimal winning. We provide results relating equilibrium coalition size with preferences of the legislators and vote buyers, and we show that minimal winning coalitions should occur in only rare cases. We discuss these results in light of empirical work on coalition size and suggest other possible avenues for testing our model. (American Political Science Review / FUB)
