Polling locations are often unequally distributed and public policies have the potential to exasperate the disparity even if the intent is to improve access. We develop a facility location integer program to decide where to open precincts with the objective of minimizing the Kolm-Pollak Equally Distributed Equivalent (EDE) – an inequality aversion metric that captures the benefits of a statistical mean and standard deviation in a single statistic. Limitations in optimization solver technology make it impossible to optimize over the nonlinear EDE directly on city-size model instances which require millions of binary variables.  We develop a linear objective function as a proxy for the EDE that allows us to optimize the EDE exactly with the same computational burden as minimizing the population-weighted average distance.  Like the EDE, this objective function allows the user to specify a desired level of inequality aversion. We employ the EDE in two ways: to compare precinct accessibility before and after the Shelby v. Holder decision, a Supreme Court ruling that struck down a key section of the Voting Rights Act of 1965, and to optimize precinct locations in a variety of scenarios. We examine a pseudo-city to demonstrate the optimization effects on a smaller scale and then expand to U.S. cities. Computational experiments demonstrate that optimizing over the EDE results in a much more equitable distribution while maintaining a nearly-optimal population-weighted average distance. Public officials should consider placing precincts or voter drop boxes in the locations that correspond to producing the lowest Kolm-Pollak EDE for their jurisdiction.