Legislative bargaining with private information: A comparison of majority and unanimity rule

We investigate the effects of alternative voting rules in a three-person, two-period bargaining game with private information. A single proposer is seeking to secure agreement to a proposal under either majority or unanimity rule. Two responders have privately known disagreement payoffs. We characterize Bayesian equilibria in stagewise undominated strategies. Our central result is that responders are ‘more expensive’ under unanimity rule because they like to be perceived as high types. Inefficient delay and disagreement are more likely under unanimity rule, except under very restrictive parameter conditions. Our analysis provides a theoretical foundation for intuitions that have been stated informally before. In addition, it yields deeper insights into the underlying incentives and what they imply for optimal behavior in bargaining with private information.