Graphical Metrics for Analyzing District Maps

Abstract

For the past several decades, political scientists have sought to understand the impact of legislative redistricting and gerrymandering on a variety of outcomes. However, traditional metrics such as compactness scores and newer metrics such as aggregated simulations impose very strong assumptions that make their use difficult. In this study, we propose a new graphical framework for analyzing districts that relaxes current assumptions while allowing analysts to focus on the choices that redistricting parties may potentially make. We then leverage the newest advances in district simulation algorithms to extend this framework to propose four new metrics. These new metrics are Edge Cut Growth (ECG), Excess Edge (EE), and Edge per District Gain (EDG), and Internal Boundary Growth (IBG). These new metrics are then compared to several existing metrics, allowing us to test the attributes that our approach is similar to. In doing so, we demonstrate that the four new metrics are best seen as theoretical and technical advances on current metrics that focus on district geometry.