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.

In this project, we develop a Q-learning algorithm for a simple non-deterministic environment. In particular, our algorithm teaches an agent to navigate to a defined location while avoiding non-stationary obstacles. Deep reinforcement learning is typically used for complex non-deterministic tasks like autonomous driving, but can require significant computing requirements and time to train. Q-learning is a relatively simple algorithm that requires less computational investment and has been proven to work efficiently in deterministic environments. To our knowledge, Q-learning has not been widely tested for non-deterministic environments for path planning and maneuvering. Our Q-learning algorithm taught the agent to reach its target approximately 77% of the time, which is insufficient for autonomous control. However, as an additional metric for military platforms, a modified Q-learning algorithm could provide recommendations to crew members aboard ships or troops on land. An algorithm of this type could be developed to make recommendations based on data from many sources and sensors, which may be difficult to track manually.