Approval vs. Participation Quorums

Using a pivotal costly voting model of elections between a status quo and a challenger alternative, we compare participation and approval quorum requirements in terms of how they shape voter incentives to cast votes, and how they ultimately impact voter turnout, election outcomes, and welfare. We first show that approval and participation quorum restrictions of equal strictness result in at most two types of stable non-trivial equilibria: “abstention,” in which status quo supporters strategically abstain from voting, and “coordination,” in which they vote with positive probability. While abstention equilibria are always identical in the two quorum settings, coordination equilibria may differ, but only when the cost of voting is sufficiently low and status quo support among voters is neither extremely high or low, nor is it close to the degree of support for the challenger. We show that, in those cases, the difference in the outcomes of interest between approval and participation quorum settings is quantitatively small. The main difference between the two settings therefore arises from the fact that, under an approval quorum, coordination equilibrium exists for a narrower range of status quo support levels than under a participation quorum. We discuss the implications of these findings for designing optimal quorum restrictions, suggesting that choosing an approval quorum over a participation quorum and setting its strictness close to half of the number of voters, or setting no quorum restrictions at all, are often welfare maximizing choices.