Approval quorums dominate participation quorums

We study direct democracy with population uncertainty. Voters' participation is often among the desiderata by the election designer. We show that with a participation quorum, i.e. a threshold on the fraction of participating voters below which the status quo is kept, the status quo may be kept in situations where the planner would prefer the reform, or the reform is passed when the planner prefers the status quo. On the other hand, using an approval quorum, i.e. a threshold on the number of voters expressing a ballot in favor of the reform below which the status quo is kept, we show that those drawbacks of participation quorums are avoided. Moreover, an electoral system with approval quorum performs better than one with participation quorum even when the planner wishes to implement the corresponding participation quorum social choice function.