Using a pivotal costly voting model of elections, we study how participation quorum require-
ments 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.