Geometry, Inference, Complexity, and Democracy

TL;DR

This paper surveys recent mathematical advances in understanding fair districting, highlighting how new tools influence political decisions and discussing remaining challenges in the intersection of geometry, inference, and democracy.

Contribution

It provides an overview of recent progress in mathematical approaches to fair districting and their impact on political decision-making.

Findings

Mathematical tools are increasingly used in districting decisions

Recent advances have influenced real political processes

Challenges remain in fully understanding fair districting

Abstract

Decisions about how the population of the United States should be divided into legislative districts have powerful and not fully understood effects on the outcomes of elections. The problem of understanding what we might mean by "fair districting" intertwines mathematical, political, and legal reasoning; but only in recent years has the academic mathematical community gotten directly involved in the process. I'll report on recent progress in this area, how newly developed mathematical tools have affected real political decisions, and what remains to be done. This survey represents the content of a lecture presented by the author in the Current Events Bulletin session of the Joint Mathematics Meetings in January 2020.