Mathematical Analysis of Redistricting in Utah

TL;DR

This paper introduces the LRVS metric for evaluating partisan gerrymandering in Utah, demonstrating its effectiveness over traditional measures by analyzing 2011 district plans with Markov chain Monte Carlo simulations.

Contribution

It proposes the LRVS as a new indicator for gerrymandering in Utah and applies it using ensemble analysis to assess the 2011 redistricting plan.

Findings

LRVS effectively measures partisan advantage in Utah.

Traditional metrics often fail in Utah's context.

2011 Utah districts show evidence of gerrymandering.

Abstract

We discuss difficulties of evaluating partisan gerrymandering in the congressional districts in Utah and the failure of many common metrics in Utah. We explain why the Republican vote share in the least-Republican district (LRVS) is a good indicator of the advantage or disadvantage each party has in the Utah congressional districts. Although the LRVS only makes sense in settings with at most one competitive district, in that setting it directly captures the extent to which a given redistricting plan gives advantage or disadvantage to the Republican and Democratic parties. We use the LRVS to evaluate the most common measures of partisan gerrymandering in the context of Utah's 2011 congressional districts. We do this by generating large ensembles of alternative redistricting plans using Markov chain Monte Carlo methods. We also discuss the implications of this new metric and our results on the question of whether the 2011 Utah congressional plan was gerrymandered.