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

We present 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 "breakdown values" which determine their payoff in case of "breakdown". Breakdown occurs with some probability if the first proposal fails and with certainty if the second proposal fails. We characterize Bayesian Equilibria in Sequentially Weakly Undominated Strategies. Our central result is that responders have a signaling incentive to vote "no" on the first proposal under unanimity rule, whereas no such incentive exists under majority rule. The reason is that being perceived as a "high breakdown value type" is advantageous under unanimity rule, but disadvantageous under majority rule. As a consequence, responders are "more expensive" under unanimity rule and disagreement is more likely. These results confirm intuitions that have been stated informally before and in addition yield deeper insights into the underlying incentives and what they imply for optimal behavior in bargaining with private information.