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Jan Zápal, Ph.D.

CERGE-EI

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Authors: Ying Chen and Jan Zápal

Abstract: A leader wants to enact a general-interest policy but needs the support of q members of a committee who oppose the policy with heterogenous intensities. The leader sequentially approaches the committee members: in each period, she chooses which member to approach and what offer to make in exchange for his vote. We analyze two variants, depending on the nature of the offer. In the transfer-promise model, the leader pays the accepted offers only if she puts the policy to a vote; in the up-front-payment model, she pays the accepted offers immediately even if she does not put the policy to a vote eventually. In the transfer-promise model, the policy passes in equilibrium if and only if the leader's gain is higher than the sum of the losses of the q members who are least opposed; whenever the policy passes in equilibrium, the leader makes offers close to zero to the set of members who are least opposed to the policy, and the optimal sequence may require her to first approach the most-opposed member among the set. In the up-front-payment model, however, the leader does not necessarily buy the votes of the least-opposed members. The equilibrium now features two phases: in the first phase, each approached member is indispensable and thus compensated fully for his vote; in the second phase, each approached member is dispensable and thus offered a payment close to zero. Even though the leader may pay a significant amount for a vote, she is better off with the instrument of up-front payments because it is a commitment device that allows her to pass policy that she would not be able to with transfer promises. We also discuss extensions that allow simultaneous offers and bargaining with coalitions.
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Full Text: “Sequential Vote Buying”