Participation quorum when voting is costly

Using a pivotal costly voting model of elections, we study how participation quorum requirements affect voters’ decisions to cast votes, and how they ultimately impact voter and candidate welfare. We solve the model analytically for the case of three voters and then provide numerical solutions for larger numbers of voters, and obtain several consistent results. First, we find that the effect of quorum requirements on voter turnout is non-monotonic and depends on ex-ante support for the candidates. When support for the status-quo is low, a stricter quorum requirement results in higher turnout, while when it is high, the relationship is reversed. Second, we show that a stricter quorum requirement does not necessarily benefit a status quo candidate and can sometimes decrease her chances of winning an election. Third, we characterize optimal quorum requirements from the perspective of voter welfare, and find that, while optimal requirements vary with support for the candidates, too strict and too lenient requirements can be very harmful to voter welfare. Therefore, setting moderate quorum requirements close to half of the number of voters or setting no quorum requirement at all may be reasonable choices.