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

Abstract

Every representative democracy must specify a mechanism under which voters choose their representatives. The most common mechanism in the United States -winner-take-all singlemember districts -both enables substantial partisan gerrymandering and constrains 'fair' redistricting, preventing proportional representation in legislatures. We study the design of multi-member districts (MMDs), in which each district elects multiple representatives, potentially through a non-winner-takes-all voting rule. We carry out large-scale analyses for the U.S. House of Representatives under MMDs with different social choice functions, under algorithmically generated maps optimized for either partisan benefit or proportionality. Doing so requires efficiently incorporating predicted partisan outcomes -under various multi-winner social choice functions -into an algorithm that optimizes over an ensemble of maps. We find that with threemember districts using Single Transferable Vote, fairness-minded independent commissions would be able to achieve proportional outcomes in every state up to rounding, and advantage-seeking partisans would have their power to gerrymander significantly curtailed. Simultaneously, such districts would preserve geographic cohesion, an arguably important aspect of representative democracies. In the process, we open up a rich research agenda at the intersection of social choice and computational redistricting.

Auditing for Gerrymandering by Identifying Disenfranchised Individuals

“…Gurnee and Shmoys [13] create a two-part linear programming algorithm that allows users to pick and choose a fairness metric to optimize. Garg et al [11] uses Gurnee and Shmoys' algorithm to create maps that optimize for either partisan benefit or proportionality in the case of multi-member districts (MMD). They find that MMDs using singletransferable vote can curtail legislators' ability to perform partisan gerrymandering and can allow for redistricting commissions to potentially create consistently proportionally representative maps.…”

“…It has the potential to cause social harm in the form of disenfranchisement to political and demographic groups [30]. Many studies in the quantitative sciences have attempted to characterize gerrymandering in terms of optimization criteria such as geographic compactness and proportional representation with respect to political parties [3,10,29,31], and many algorithms have been proposed to generate districts that optimize one or more of these criteria [4,5,11,13].…”