Unlocking Democratic Efficiency: How Coordinated Outcome-Contingent Promises Shape Decisions

We consider a committee voting on whether to adopt a reform under a quota rule, where members differ in how much they value the reform some supporting it, others opposing it. We examine how members can influence each other's votes through coordinated non-negative transfer promises, made prior to voting and contingent on the vote outcome. In equilibrium, these transfers are structured to prevent any coalition from profitably deviating in a coordinated way, while minimizing total transfers. We provide a complete characterization of these `strong' equilibria and show that they exist, are indeterminate, efficient, and involve transfers from high- to low-utility members. Such transfers prevent opponents from swaying less enthusiastic supporters and may be directed not only to opponents but also to lukewarm supporters.