Buying Supermajorities

Abstract

M inimal 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.

Legislative Bargaining and Coalition Formation

“…See for example Riker [14], Shepsle [16], or, more recently, Baron and Ferejohn [2,3]. For an interesting strategic model where winning majorities are oversized, see Groseclose and Snyder [8].…”

Foreign aid and voting in international organizations: Evidence from the IWC

“…For tractability, I make two simplifying assumptions: First, Pro begins, Anti moves second, and then countries make their attendance and voting decisions. This sequential structure is common in the theoretical vote-buying literature (Groseclose and Snyder [1996], Dekel et al [2008]). I secondly assume that only Pro can pay positive bribes, while Anti is politically constrained to only punish.…”

“…There is a participation cost c p , so that equilibrium-abstainers do not attend. 26 Following the setup in Groseclose and Snyder [1996] and Dekel et al [2008], members get direct utility from voting but do not care about the outcome. This is a reasonable assumption if members are legislators, who care primarily how their actions appear in the eyes of their constituencies.…”

“…Abstention, non-attendance and non-membership are therefore synonymous in the model (as well as in the data). 27 In Groseclose and Snyder [1996] and Dekel et al [2008] the second lobby can counter-bribe before members vote. However, non-attendance is not an option in those papers.…”

Corruption and bicameral reforms

“…In particular, similarly to Diermeier and Myerson (1999) and Groseclose and Snyder (1996), we assume that a lobbyist can buy the legislators' vote to obtain the implementation of a given policy, and we study how constitutional rules, affecting the bargaining process, have an impact on the cost of buying legislators (external hurdle factor ).…”