We analyze two-candidate elections in which some voters are uncertain about the realization of a state variable that affects the utility of all voters. We demonstrate the existence of a swing voter's curse: less informed indifferent voters strictly prefer to abstain rather than vote for either candidate even when voting is costless. The swing voter's curse leads to the equilibrium result that a substantial fraction of the electorate will abstain even though all abstainers strictly prefer voting for one candidate over voting for another.