Sequential vote buying

To enact a policy, a leader needs votes from q committee members with heterogeneous opposition intensities. She sequentially offers transfers in exchange for votes. The transfers are either promises paid only if the policy passes or paid up front. With transfer promises, the policy passes in equilibrium when the leader's gain from the policy is larger than the sum of the losses of the q members least opposed to the policy. Under non-unanimity rule, if the members are patient enough, the payments are close to zero when the policy passes. Whenever the policy passes in equilibrium with transfer promises, it also passes with up-front payments, at a cost close to zero. Moreover, there are scenarios when the policy passes with up-front payments, but not with transfer promises. Hence the leader is better off and the members are worse off with up-front payments than with transfer promises. The leader does not necessarily buy the votes of those least opposed. The opposition structure most challenging to the leader involves homogeneous committees. Our results provide an explanation for several empirical regularities.