In a seminal paper on electoral equilibrium under majority rule, Ledyard (1984) demonstrates that strategic participation by voters results in an electoral equilibrium at the proposal that maximizes the utility of a randomly selected voter. Palfrey and Rosenthal (1985) limit the usefulness of this result by showing that strategic participation rates are miniscule in large electorates, and that the incentive to participate vanishes completely as the electorate grows without bound. The most reasonable modification of Ledyard’s approach that circumvents these criticisms is to allow for a negative cost of voting. We show that when voters can have even an arbitrarily small negative cost of voting, there is an electorate sufficiently large so that any proposal is defeated or tied by the median proposal. This observation raises questions about the existence of electoral equilibrium under strategic participation, and is relevant to the efficiency of elections.