On partisan bias in redistricting: computational complexity meets the science of gerrymandering

Abstract

The main topic of this paper is "gerrymandering", namely the curse of deliberate creations of district maps with highly asymmetric electoral outcomes to disenfranchise voters, and it has a long legal history going back as early as 1812. Measuring and eliminating gerrymandering has enormous far-reaching implications to sustain the backbone of democratic principles of a country or society.Although there is no dearth of legal briefs filed in courts involving many aspects of gerrymandering over many years in the past, it is only more recently that mathematicians and applied computational researchers have started to investigate this topic. However, it has received relatively little attention so far from the computational complexity researchers (where by "computational complexity researchers" we mean researchers dealing with theoretical analysis of computational complexity issues of these problems, such as polynomial-time solvabilities, approximability issues, etc.). There could be several reasons for this, such as descriptions of these problem non-CS non-math (often legal or political) journals that are not very easy for theoretical CS (TCS) people to follow, or the lack of effective collaboration between TCS researchers and other (perhaps non-CS) researchers that work on these problems accentuated by the lack of coverage of these topics in TCS publication venues. One of our modest goals in writing this article is to improve upon this situation by stimulating further interactions between the science of gerrymandering and the TCS researchers. To this effect, our main contributions in this article are twofold:We provide formalization of several models, related concepts, and corresponding problem statements using TCS frameworks from the descriptions of these problems as available in existing non-CS-theory (perhaps legal) venues.We also provide computational complexity analysis of some versions of these problems, leaving other versions for future research.The goal of writing article is not to have the final word on gerrymandering, but to introduce a series of concepts, models and problems to the TCS community and to show that science of gerrymandering involves an intriguing set of partitioning problems involving geometric and combinatorial optimization.

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

“…Optimal political districting is well known to be an NP -hard computational problem [24,55,65]. 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.…”

Fairmandering: A column generation heuristic for fairness-optimized political districting

“…Exact optimization methods are intractable for all but the smallest problems because optimal political districting is N P -hard for any useful objective function [42,30,13]. Optimization approaches for fairness therefore either rely on local search techniques [47,29] or embed a heuristic in some stage of the optimization.…”