Despite the fact that in the 2012 presidential election, two-thirds of voters waited less than 10 min and a mere 3% waited longer than an hour to cast their ballots, media accounts of excruciating waits have left a misleading impression on the general public. At the root of the problem is the allocation of voting machines based on efficiency as measured by average waiting time. This method does not account for the damaging consequences of the rare events that cause extremely long waits. We propose an extreme-value robust optimization model that can explicitly consider nominal and worst-case waiting times beyond the single-point estimate commonly seen in the literature. We benchmark the robust model against the published deterministic model using a real case from the 2008 presidential election in Franklin County, Ohio. The results demonstrate that the proposed robust model is superior in accounting for uncertainties in voter turnout and machine availability, reducing the number of voters experiencing waits that exceed two hours by 61%.