In the past few years, there has been an explosion of research by mathematicians and computer scientists developing formal methods to detect and combat gerrymandering. While interesting and powerful, the relationship that these methods bear to the democratic values they are intended to uphold is unclear, especially to policy-makers who are rarely equipped to understand them. Bridging the gap will be a major interdisciplinary undertaking. In this talk, I present a formal theoretical framework for understanding the problems of districting and the tools being developed to resolve them. I discuss how philosophical considerations of the role of districting in democracy can productively guide how these tools can be put to use, and indicate directions for the production of future tools that more faithfully reflect pro-democratic aims.