Freezeout, Compensation Rules and Voting Equilibria

A single proposer has the opportunity to generate a surplus by taking the assets of a group of individuals. These individuals are called upon to vote for accepting or rejecting the monetary offer made to them by the proposer, who needs the agreement of a qualified majority. The voters who rejected the offer while the qualified majority is met are frozen out but they can claim a compensation in exchange for their asset. This article analyses how compensation rules influence both the votes and the offer made by the proposer. We find that unanimity rule or compensation equals to the proposal or voters' initial wealth maximize the expected social surplus that entirely accrues to the proposer. We show that increasing the offer does not always increase the probability of acceptance, in sharp contrast to many close models. We identify the optimal offer when the compensation does not depend on the proposal. Increasing the compensation always reduces the expected social surplus and the expected profit of the proposer, but does not always benefit to the voters. Reinforcing the qualified majority always increases the expected profit of the proposer, and can decrease both the expected social surplus and the expected utility of the voters. When the compensation is based on the proposal we find that the success or the failure of the proposition depends crucially of the compensation's shape.