# Quantifying gerrymandering using the vote distribution

## TL;DR

This paper introduces a new, simple measure of partisan asymmetry for detecting gerrymandering that overcomes limitations of the efficiency gap and is applicable to various district plans.

## Contribution

The authors propose a novel measure of partisan asymmetry that is easy to compute, related to packing and cracking, and avoids proportional representation issues.

## Key findings

- The new measure effectively identifies gerrymandered districts.
- Application to US plans reveals potential gerrymandering cases.
- The generalized efficiency gap offers an alternative assessment method.

## Abstract

To assess the presence of gerrymandering, one can consider the shapes of districts or the distribution of votes. The "efficiency gap," which does the latter, plays a central role in a 2016 federal court case on the constitutionality of Wisconsin's state legislative district plan. Unfortunately, however, the efficiency gap reduces to proportional representation, an expectation that is not a constitutional right. We present a new measure of partisan asymmetry that does not rely on the shapes of districts, is simple to compute, is provably related to the "packing and cracking" integral to gerrymandering, and that avoids the constitutionality issue presented by the efficiency gap. In addition, we introduce a generalization of the efficiency gap that also avoids the equivalency to proportional representation. We apply the first function to US congressional and state legislative plans from recent decades to identify candidate gerrymanders.