Voting rules and efficiency in one-dimensional bargaining games with endogenous protocol

We analyze a rent-seeking contest that determines the bargaining protocol in a one-dimensional bargaining game, where agents preferences over social outcomes are single-peaked. We relate the incentives of agents to make unproductive and costly efforts/investments to the quota rules that are required to implement agreements. When the contest assigns persistent recognition probabilities, we find that simple majority minimizes the total investments and, hence, inefficiency. In case that the contest recurs each period, multiple equilibria exist with the particularity that in each equilibrium only one agent controls the agenda of the bargaining process.