Gerrymandering and Convexity

Hodge, Jonathan; Marshall, Emily C.; Patterson, Geoff

doi:10.4169/074683410x510317

Cited by 16 publications

(15 citation statements)

References 7 publications

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“…Hodge et al use a “simpler” version of the measure of Chambers and Miller, which they call the convexity coefficient. The convexity coefficient χ (p) is simply the probability that two randomly selected points are visible from each other.…”

Section: The Measurementsmentioning

confidence: 99%

“…Here, the probability that a randomly selected point k in D will be visible from a point k 0 in p is given by A p (k 0 )/A p , where A p is the area of p and A p (k 0 ) is the area of the region visible from k o . However, as the authors indicate, “Calculating the exact value of the convexity coefficient of a region can be difficult, even for relatively simple shapes” (see the work of Hodge et al24(p315)). Therefore, this would be hard for the public, and legislators, to understand.…”

Section: The Measurementsmentioning

confidence: 99%

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Redistricting without gerrymandering, utilizing the convexity ratio, and other applications to business and industry

Bozeman

Davey

Hutchins

et al. 2018

Appl Stoch Models Bus & Ind

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We exhibit the convexity ratio of voting districts in many states of the USA, which have had their plans challenged. The convexity ratio confirms that these states have likely been gerrymandered. We then redistrict the largest of these states, Texas, avoiding gerrymandering by starting with counties and their populations and only adding or deleting municipalities as necessary. The voting districts themselves are made as nicely shaped as possible, using the convexity ratio as a guide. Those districts with immovable boundaries that cause a poorly shaped designation, a topic of much current research, are dealt with appropriately in the context of the convexity ratio. Algorithms for finding the convexity ratio and designing non-gerrymandered districts are shown. Other more probabilistic convexity measures are discussed. Finally, we comment on how the convexity ratio can be used in other countries, both politically and in other contexts, for example, in territory design for geomarketing and on the electrical or police districting problem.

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Section: The Measurementsmentioning

confidence: 99%

Section: The Measurementsmentioning

confidence: 99%

Redistricting without gerrymandering, utilizing the convexity ratio, and other applications to business and industry

Bozeman

Davey

Hutchins

et al. 2018

Appl Stoch Models Bus & Ind

View full text Add to dashboard Cite

show abstract

“…To the best of the authors' knowledge, the literature has a lack of models that tackle the problem of optimizing convex partitions, that is, partitioning a graph into convex subgraphs while optimizing an objective function or a set of criteria. In fact, optimization of convex partitions is a prerogative of the districting problem, a special case of the graph partitioning problem to which the MC-PDP belongs, and most of the research in the area focused on proposing metrics of convexity for districting problems (see, e.g., [28][29][30]). With respect to the Police Districting Problem, the only model that includes a measure of graph convexity in the optimization process, apart from the MC-PDP, is that proposed by D' Amico et al [18].…”

Section: Related Workmentioning

confidence: 99%

A Comparison of Local Search Methods for the Multicriteria Police Districting Problem on Graph

Liberatore

Camacho‐Collados

2016

Mathematical Problems in Engineering

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In the current economic climate, law enforcement agencies are facing resource shortages. The effective and efficient use of scarce resources is therefore of the utmost importance to provide a high standard public safety service. Optimization models specifically tailored to the necessity of police agencies can help to ameliorate their use. The Multicriteria Police Districting Problem (MC-PDP) on a graph concerns the definition of sound patrolling sectors in a police district. The objective of this problem is to partition a graph into convex and continuous subsets, while ensuring efficiency and workload balance among the subsets. The model was originally formulated in collaboration with the Spanish National Police Corps. We propose for its solution three local search algorithms: a Simple Hill Climbing, a Steepest Descent Hill Climbing, and a Tabu Search. To improve their diversification capabilities, all the algorithms implement a multistart procedure, initialized by randomized greedy solutions. The algorithms are empirically tested on a case study on the Central District of Madrid. Our experiments show that the solutions identified by the novel Tabu Search outperform the other algorithms. Finally, research guidelines for future developments on the MC-PDP are given.

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“…Hodge et al [6] devise a simpler version of the measure in [3] they call the convexity coefficient. Let P ⊂ R 2 be a polygon and A its area.…”

Section: Chapter 2 Review Of Gerrymandering Measuresmentioning

confidence: 99%

“…The goal is to engineer artificial landslides for the opposition in a few districts while winning smaller yet secure majorities for their own party in many districts [11]. forbids the dilution of minority districts, which can lead to the creation of oddly shaped districts such as Illinois' 4th Congressional District in Figure 3 [11,6]. This district provides a good example of packing because it was created to connect to geographically separated groups of voters.…”

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confidence: 99%

A Boundary-Based Measure for Gerrymandering

Sprock

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A BOUNDARY-BASED MEASURE FOR GERRYMANDERING by Carson Sprock This paper presents a new measure for quantifying legislative gerrymandering based intuitive observation that in a non-gerrymandered district a randomly placed observer should be able to walk in a straight line and only cross the boundary of the district once, when the district is exited. We make this notion precise in terms of the expected value of such crossings. The result is the Boundary Intersection Number, or BIN. Properties of the BIN score are proven and its computational properties discussed.

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Gerrymandering and Convexity

Cited by 16 publications

References 7 publications

Redistricting without gerrymandering, utilizing the convexity ratio, and other applications to business and industry

Redistricting without gerrymandering, utilizing the convexity ratio, and other applications to business and industry

A Comparison of Local Search Methods for the Multicriteria Police Districting Problem on Graph

A Boundary-Based Measure for Gerrymandering

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