Approval vs. participation quorums

Using a pivotal costly voting model, we analyze how participation and approval quorum requirements, applied separately or jointly, affect turnout, election outcomes, and welfare. To characterize an optimal quorum rule, we first show that equally strict participation and approval quorums often yield similar outcomes, unless the two settings result in equilibria that differ in terms of whether voters can coordinate on participation. Second, any combination of quorum types can be replaced by either an approval or participation quorum alone, with negligible or no impact on equilibrium. Using these results, we suggest that to maximize turnout, no quorum is optimal unless low status quo support is expected, in which case a strict approval quorum is preferred. To increase the status quo’s chances of winning, a strict approval quorum or no quorum works best. From a voter welfare perspective, an approval quorum near half the electorate or no quorum at all are reasonable choices. These results hold whether we use Bayesian Nash equilibrium or quantal response equilibrium as the solution concept.