Conclave

•In conclaves voting is repeated until sufficient supermajority is reached.•The greater supermajority is required, the more extreme the pivotal voters are.•Normative exercise is to maximize correlation between equilibrium and welfare.•Simple majority is inferior to some intermediate supermajority.

A committee is choosing between two alternatives. If the required supermajority is not reached, voting is repeated indefinitely, although there is a cost to delay. Under suitable assumptions the equilibrium analysis provides a sharp prediction. The result can be interpreted as a generalization of the seminal median voter theorem known from the simple majority case. If a supermajority is required instead, the power to select the outcome moves from the median voter to the more extreme voters. Normative analysis indicates that, in the utilitarian sense, simple majority is strictly inferior to some supermajorities. Even if unanimity is a bad voting rule, voting rules close to unanimity may be efficient. The more likely it is to have very many almost indifferent voters and some very opinionated ones, the more stringent a supermajority is required for efficiency.