Freezeout, compensation rules, and voting equilibria

A single proposer has the opportunity to generate a surplus by buying out the assets of a group of individuals. These individuals vote to accept or reject the monetary offer made to them by the proposer, who needs the agreement of a qualified majority. The voters rejecting the offer while the qualified majority is met are frozen out but they can claim compensation in exchange for their asset. This article analyses how compensation rules influence both the votes and the offer made by the proposer. The existence of a symmetric subgame perfect Nash equilibrium is ensured, and multiple equilibrium outcomes with the same offer can arise when compensation depends on the probability of acceptance by the voters. We show that increasing the offer does not always increase the probability of acceptance, in sharp contrast to many similar models. We identify the equilibrium offer when compensation does not depend on the proposal. Increasing compensation always reduces the expected social surplus and the proposer's expected profit, but does not always benefit the voters. Reinforcing the qualified majority always increases the proposer's expected profit, and can lower both the expected social surplus and the voters' expected utility.