Lattice Studies of Gerrymandering Strategies

TL;DR

This paper introduces three new gerrymandering algorithms that incorporate spatial voter data, uses lattice models to compare strategies, and demonstrates the importance of compactness tests for legal districting.

Contribution

It presents novel algorithms for gerrymandering that ensure connected districts and employs lattice models to evaluate their effectiveness and the impact of spatial data.

Findings

Algorithms effectively pack opposition voters to gerrymander districts.

Spatial data inclusion leads to more connected districts.

Compactness tests are supported as effective measures for legal redistricting.

Abstract

We propose three novel gerrymandering algorithms which incorporate the spatial distribution of voters with the aim of constructing gerrymandered, equal-population, connected districts. Moreover, we develop lattice models of voter distributions, based on analogies to electrostatic potentials, in order to compare different gerrymandering strategies. Due to the probabilistic population fluctuations inherent to our voter models, Monte Carlo methods can be applied to the districts constructed via our gerrymandering algorithms. Through Monte Carlo studies we quantify the effectiveness of each of our gerrymandering algorithms and we also argue that gerrymandering strategies which do not include spatial data lead to (legally prohibited) highly disconnected districts. Of the three algorithms we propose, two are based on different strategies for packing opposition voters, and the third is a new approach to algorithmic gerrymandering based on genetic algorithms, which automatically guarantees that all districts are connected. Furthermore, we use our lattice voter model to examine the effectiveness of isoperimetric quotient tests and our results provide further quantitative support for implementing compactness tests in real-world political redistricting.