Don't Trust A Single Gerrymandering Metric

TL;DR

This paper demonstrates that common gerrymandering metrics can be manipulated to produce extreme partisan maps, questioning their reliability as standalone measures for fairness in districting.

Contribution

It shows that widely used gerrymandering metrics are gameable and unreliable when used in isolation, highlighting the need for more robust assessment methods.

Findings

Metrics can be manipulated to produce extreme partisan maps.

Extreme metric values do not necessarily indicate extreme partisan outcomes.

Metrics perform no better than simply counting districts won by a party.

Abstract

In recent years, in an effort to promote fairness in the election process, a wide variety of techniques and metrics have been proposed to determine whether a map is a partisan gerrymander. The most accessible measures, requiring easily obtained data, are metrics such as the Mean-Median Difference, Efficiency Gap, Declination, and GEO metric. But for most of these metrics, researchers have struggled to describe, given no additional information, how a value of that metric on a single map indicates the presence or absence of gerrymandering. Our main result is that each of these metrics is gameable when used as a single, isolated quantity to detect gerrymandering (or the lack thereof). That is, for each of the four metrics, we can find district plans for a given state with an extremely large number of Democratic-won (or Republican-won) districts while the metric value of that plan falls within a reasonable, predetermined bound. We do this by using a hill-climbing method to generate district plans that are constrained by the bounds on the metric but also maximize or nearly maximize the number of districts won by a party. In addition, extreme values of the Mean-Median Difference do not necessarily correspond to maps with an extreme number of districts won. Thus, the Mean- Median Difference metric is particularly misleading, as it cannot distinguish more extreme maps from less extreme maps. The other metrics are more nuanced, but when assessed on an ensemble, none perform substantially differently from simply measuring number of districts won by a fixed party. One clear consequence of these results is that they demonstrate the folly of specifying a priori bounds on a metric that a redistricting commission must meet in order to avoid gerrymandering.