Imposing Contiguity Constraints in Political Districting Models

Validi, Hamidreza; Buchanan, Austin; Lykhovyd, Eugene

doi:10.1287/opre.2021.2141

Cited by 43 publications

(15 citation statements)

References 60 publications

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“…While it prevents the formation of noncompact districts, it also discounts many districts that would pass an eyeball test and generally reduces the space of feasible solutions. One item of future work is to profile different methods of enforcing contiguity [53].…”

Section: Stochastic Hierarchical Partitioning (Shp)mentioning

confidence: 99%

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

Gurnee¹,

Shmoys²

2021

Preprint

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The American winner-take-all congressional district system empowers politicians to engineer electoral outcomes by manipulating district boundaries. Existing computational solutions mostly focus on drawing unbiased maps by ignoring political and demographic input, and instead simply optimize for compactness. We claim that this is a flawed approach because compactness and fairness are orthogonal qualities, and introduce a scalable two-stage method to explicitly optimize for arbitrary piecewise-linear definitions of fairness. The first stage is a randomized divide-and-conquer column generation heuristic which produces an exponential number of distinct district plans by exploiting the compositional structure of graph partitioning problems. This district ensemble forms the input to a master selection problem to choose the districts to include in the final plan. Our decoupled design allows for unprecedented flexibility in defining fairness-aligned objective functions. The pipeline is arbitrarily parallelizable, is flexible to support additional redistricting constraints, and can be applied to a wide array of other regionalization problems. In the largest ever ensemble study of congressional districts, we use our method to understand the range of possible expected outcomes and the implications of this range on potential definitions of fairness.

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Section: Stochastic Hierarchical Partitioning (Shp)mentioning

confidence: 99%

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

Gurnee¹,

Shmoys²

2021

Preprint

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“…, V k is one of the oldest and fundamental problems in operations research and statistics, with the first work dating back to the seminal work of Weaver and Hess, to the best of our knowledge [51]. The solutions to this problem have created a huge impact in various applications ranging from drawing voting districts [47] and school districts [8] to police zones [24], clustering [39], and even divisions of large network problems for parallel computing [25].…”

Section: Introductionmentioning

confidence: 99%

“…Many different formulations for partitioning problems exist, dependent on the modeling choice for each of these objectives. Most of the existing literature, however, focuses on ensuring compactness and balance [7,47], but neglects contiguity of parts. Guaranteeing contiguity while ensuring tractability of districting over grids is the key contribution of our work.…”

Section: Introductionmentioning

confidence: 99%

Balanced Districting on Grid Graphs with Provable Compactness and Contiguity

Hettle,

Zhu,

Gupta

et al. 2021

Preprint

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Given a graph G = (V, E) with vertex weights w(v) and a desired number of parts k, the goal in graph partitioning problems is to partition the vertex set V into parts V 1 , . . . , V k . Metrics for compactness, contiguity, and balance of the parts V i are frequent objectives, with much existing literature focusing on compactness and balance. Revisiting an old method known as striping, we give the first polynomial-time algorithms with guaranteed contiguity and provable bicriteria approximations for compactness and balance for planar grid graphs. We consider several types of graph partitioning, including when vertex weights vary smoothly or are stochastic, reflecting concerns in various real-world instances. We show significant improvements in experiments for balancing workloads for the fire department and reducing over-policing using 911 call data from South Fulton, GA.

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“…Similarly, branch-and-bound algorithms might drop the integer constraint, resulting in a much easier (and typically convex) problem to solve algorithmically as well as a bound on the best possible objective value; then, various variables are pinned to nearby integers until the solution satisfies all the constraints[VBL19,MJN98].Integer programming algorithms and local search metaheuristics are similar in the sense that both navigate the space of feasible solutions while looking to improve an objective function. The main difference is that integer programming algorithms typically (but not always) aim to extract a global optimum via carefully-designed bounding and search strategies.…”

mentioning

confidence: 99%

Redistricting Algorithms

Becker¹,

Solomon²

2020

Preprint

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Why not have a computer just draw a map? This is something you hear a lot when people talk about gerrymandering, and it's easy to think at first that this could solve redistricting altogether. But there are more than a couple problems with this idea. In this chapter, two computer scientists survey what's been done in algorithmic redistricting, discuss what doesn't work and highlight approaches that show promise. This preprint was prepared as a chapter in the forthcoming edited volume Political Geometry, an interdisciplinary collection of essays on redistricting. (mggg.org/gerrybook)

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Imposing Contiguity Constraints in Political Districting Models

Cited by 43 publications

References 60 publications

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

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

Balanced Districting on Grid Graphs with Provable Compactness and Contiguity

Redistricting Algorithms

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