Mathematical Analysis of Redistricting in Utah

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.

Keywords

• Ensemble methods
• Gerrymander
• Markov chain Monte Carlo
• Partisan symmetry
• Redistricting
• Utah