A Computational Approach to Measuring Vote Elasticity and Competitiveness

Abstract

The recent wave of attention to partisan gerrymandering has come with a push to refine or replace the laws that govern political redistricting around the country. A common element in several states' reform efforts has been the inclusion of competitiveness metrics, or scores that evaluate a districting plan based on the extent to which district-level outcomes are in play or are likely to be closely contested. In this article, we examine several classes of competitiveness metrics motivated by recent reform proposals and then evaluate their potential outcomes across large ensembles of districting plans at the Congressional and state Senate levels. This is part of a growing literature using MCMC techniques from applied statistics to situate plans and criteria in the context of valid redistricting alternatives. Our empirical analysis focuses on five states-Utah, Georgia, Wisconsin, Virginia, and Massachusetts-chosen to represent a range of partisan attributes. We highlight situation-specific difficulties in creating good competitiveness metrics and show that optimizing competitiveness can produce unintended consequences on other partisan metrics. These results demonstrate the importance of (1) avoiding writing detailed metric constraints into long-lasting constitutional reform and (2) carrying out careful mathematical modeling on real geo-electoral data in each redistricting cycle.

Implementing Partisan Symmetry: Problems and Paradoxes

“…Compactness, at levels comparable to those observed in humanmade plans, is an automatic consequence of the spanning-tree-based recombination step. For more information about the Markov chain used here, see (DeFord, Duchin, and Solomon 2019).…”

Combatting Gerrymandering with Social Choice: the Design of Multi-member Districts

“…Therefore, to study redistricting, researchers have developed ensemble methods [10,25,33,48,57] that generate huge quantities of legal district plans to explore the exponentially large space of feasible maps. Such techniques are commonly used to detect gerrymandering [27,37,39,50] or to study the impact of different redistricting rules on the distribution of outcomes [32,34]. However, even under neutral ensembles, the natural geographic segregation among partisan voters can create skewed political outcomes [18,25].…”

“…There are many proposed definitions of (un)fairness metrics in redistricting such as the efficiency gap [71], the mean-median gap [79], partisan-symmetry [80], competitiveness [34], and most simply, proportionality. Such metrics can be used as the objective function of an optimization algorithm to generate district maps with (un)fair outcomes [48,53,73].…”

Geometry, Inference, Complexity, and Democracy

“…There are districts like that in real life, but it turns out requiring districts to be roughly round 8 is also not sufficient to prevent strong partisan gerrymandering. Ensemble methods have also shown that rules which are facially neutral to party, like maximization of the number of competitive districts, can introduce partisan bias [8]. What's more, the ensemble method speaks to much more than the number of seats each party winsthat's just one statistic attached to the maps in the ensemble.…”