Measuring Congressional District Meandering

TL;DR

This paper introduces a novel geometric method to quantify the irregularity of Congressional districts by measuring their meandering through medial axis analysis, providing a new metric for district shape complexity.

Contribution

It proposes the medial-hull ratio as a new, dimensionless measure of district irregularity, and applies it to analyze numerous Congressional districts.

Findings

Medial-hull ratio effectively quantifies district irregularity.

Many districts exhibit high meandering, indicating complex shapes.

The method offers a new tool for evaluating district drawing practices.

Abstract

In recent decades, state legislatures have often drawn U.S. Congressional voting districts that look---to the human eye---to be rather twisted. In this paper, we propose a method to measure how much districts "meander" via a computation of the medial axis of the region. We then compare this to the medial axis of the convex hull of the district to obtain the {\em medial-hull ratio}: a dimensionless quantity that captures the district's irregularity. We compute this quantity for many example Congressional districts.