Some chance for consensus: voting methods for which consensus is an equilibrium

We introduce the following basic voting method: Voters submit both a “consensus” and a “fall-back” ballot. If all “consensus” ballots name the same option, it wins; otherwise a randomly drawn “fall-back” ballot decides. If there is one potential consensus option that everyone prefers to the benchmark lottery which picks the favourite of a randomly drawn voter, then naming that option on all “consensus” ballots builds a very strong form of correlated equilibrium. Unlike common consensus procedures, ours is not biased towards the status quo and removes incentives to block consensus. Variants of the method allow for large groups, partial consensus, and choosing from several potential consensus options.