# Gerrymandering and Compactness: Implementation Flexibility and Abuse

## TL;DR

This paper examines how implementation choices affect compactness measures in districting, revealing their susceptibility to manipulation and noise, and introduces reliable software tools for their calculation.

## Contribution

It demonstrates the instability of common compactness measures due to implementation and adversarial manipulation, and provides open-source packages for accurate computation.

## Key findings

- Compactness measures are affected by irrelevant implementation factors.
- Adversaries can manipulate compactness scores to influence assessments.
- The paper releases software packages for reproducible compactness calculations.

## Abstract

Political districts may be drawn to favor one group or political party over another, or gerrymandered. A number of measurements have been suggested as ways to detect and prevent such behavior. These measures give concrete axes along which districts and districting plans can be compared. However, measurement values are affected by both noise and the compounding effects of seemingly innocuous implementation decisions. Such issues will arise for any measure. As a case study demonstrating the effect, we show that commonly-used measures of geometric compactness for district boundaries are affected by several factors irrelevant to fairness or compliance with civil rights law. We further show that an adversary could manipulate measurements to affect the assessment of a given plan. This instability complicates using these measurements as legislative or judicial standards to counteract unfair redistricting practices. This paper accompanies the release of packages in C++, Python, and R that correctly, efficiently, and reproducibly calculate a variety of compactness scores.