Commitment timing in coalitional bargaining

Most multilateral bargaining models predict bargaining power to emanate from pivotality—a party’s ability to form different majority coalitions. However, this prediction contrasts with the empirical observation that negotiations in parliamentary democracies typically result in payoffs proportional to parties’ vote shares. Proportionate profits suggest equality rather than pivotality drives results. We design an experiment to study when bargaining outcomes reflect pivotality versus proportionality. We find that commitment timing is a crucial institutional factor moderating bargaining power. Payoffs are close to proportional if bargainers can commit to majority coalitions before committing to how to share the pie, but pivotality dictates outcomes otherwise. Our results help explain Gamson’s Law, a long-standing puzzle in the legislative bargaining literature.