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We apply persistent homology, the dominant tool from the field of topological data analysis, to study electoral redistricting. Our method combines the geographic information from a political districting plan with election data to produce a…

Algebraic Topology · Mathematics 2020-07-07 Moon Duchin , Tom Needham , Thomas Weighill

Using an ensemble of redistricting plans, we evaluate whether a given political districting faithfully represents the geo-political landscape. Redistricting plans are sampled by a Monte Carlo algorithm from a probability distribution that…

We develop methods to evaluate whether a political districting accurately represents the will of the people. To explore and showcase our ideas, we concentrate on the congressional districts for the U.S. House of representatives and use the…

As a case study into an algorithmic approach to congressional districting, North Carolina provides a lot to explore. Statistical modeling has called into question whether recent North Carolina district plans are unbiased. In particular, the…

Optimization and Control · Mathematics 2023-11-21 Jimmy Risk , Jennifer Switkes , Ann Zhang

We apply persistent homology, the main method in topological data analysis, to the study of demographic data. Persistence diagrams efficiently summarize information about clusters or peaks in a region's demographic data. To illustrate how…

Algebraic Topology · Mathematics 2023-10-13 Jakini A. Kauba , Thomas Weighill

It is important to choose the geographical distributions of public resources in a fair and equitable manner. However, it is complicated to quantify the equity of such a distribution; important factors include distances to resource sites,…

Computational Geometry · Computer Science 2023-08-14 Abigail Hickok , Benjamin Jarman , Michael Johnson , Jiajie Luo , Mason A. Porter

Gerrymandering is a practice of manipulating district boundaries and locations in order to achieve a political advantage for a particular party. Lewenberg, Lev, and Rosenschein [AAMAS 2017] initiated the algorithmic study of a…

Data Structures and Algorithms · Computer Science 2020-02-19 Eduard Eiben , Fedor V. Fomin , Fahad Panolan , Kirill Simonov

Gerrymandering, the deliberate manipulation of electoral district boundaries for political advantage, is a persistent issue in U.S. redistricting cycles. This paper introduces and analyzes a new phenomenon, 'votemandering'- a strategic…

Computer Science and Game Theory · Computer Science 2023-08-17 Sanyukta Deshpande , Ian G Ludden , Sheldon H Jacobson

This paper is to obtain a simple dividing-diagram of the congressional districts, where the only limit is that each district should contain the same population if possibly. In order to solve this problem, we introduce three different…

Computers and Society · Computer Science 2007-08-17 Pan Kai , Tan Yue , Jiang Sheng

Partitioning a region into districts to favor a particular candidate or a party is commonly known as gerrymandering. In this paper, we investigate the gerrymandering problem in graph theoretic setting as proposed by Cohen-Zemach et al.…

Data Structures and Algorithms · Computer Science 2021-05-26 Sushmita Gupta , Pallavi Jain , Fahad Panolan , Sanjukta Roy , Saket Saurabh

In recent years, in an effort to promote fairness in the election process, a wide variety of techniques and metrics have been proposed to determine whether a map is a partisan gerrymander. The most accessible measures, requiring easily…

Physics and Society · Physics 2025-08-11 Thomas Ratliff , Stephanie Somersille , Ellen Veomett

We investigate the distribution of partisanship in a cross-section of ten diverse States to elucidate how votes translate into seats won and other metrics. Markov chain simulations taking into account partisanship distribution agree…

Physics and Society · Physics 2021-03-03 Constantine , Gonatas

Partisan gerrymandering, i.e., manipulation of electoral district boundaries for political advantage, is one of the major challenges to election integrity in modern day democracies. Yet most of the existing methods for detecting partisan…

Applications · Statistics 2023-06-06 Wojciech Słomczyński , Dariusz Stolicki , Stanisław Szufa

Racial segregation is a widespread social and physical phenomenon present in every city across the United States. Although prevalent nationwide, each city has a unique history of racial segregation, resulting in distinct "shapes" of…

Social and Information Networks · Computer Science 2024-10-16 Ori Friesen , Lori Ziegelmeier

Every representative democracy must specify a mechanism under which voters choose their representatives. The most common mechanism in the United States -- Winner takes all single-member districts -- both enables substantial partisan…

Computer Science and Game Theory · Computer Science 2026-02-23 Nikhil Garg , Wes Gurnee , David Rothschild , David Shmoys

Gerrymandering is a pervasive problem within the US political system. In the past decade, methods based on Markov Chain Monte Carlo (MCMC) sampling and statistical outlier tests have been proposed to quantify gerrymandering and were used as…

Computers and Society · Computer Science 2025-01-13 Ranthony A. Clark , Susan Glenn , Harlin Lee , Soledad Villar

Algorithmic and statistical approaches to congressional redistricting are becoming increasingly valuable tools in courts and redistricting commissions for quantifying gerrymandering in the United States. While there is existing literature…

Computers and Society · Computer Science 2021-11-18 Gilvir Gill

The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that they unfairly favor a particular political party, often…

Data Structures and Algorithms · Computer Science 2024-02-22 Jin-Yi Cai , Jacob Kruse , Kenneth Mayer , Daniel P. Szabo

Roughly speaking, gerrymandering is the systematic manipulation of the boundaries of electoral districts to make a specific (political) party win as many districts as possible. While typically studied from a geographical point of view,…

Data Structures and Algorithms · Computer Science 2021-02-18 Matthias Bentert , Tomohiro Koana , Rolf Niedermeier

Deciding whether a political districting plan was distorted by a hidden agenda, or whether it dilutes the voting power of some group, requires a neutral baseline for comparison. Remarkably, all nine U.S. Supreme Court justices have now…

Physics and Society · Physics 2025-11-18 Sarah Cannon , Moon Duchin , Dana Randall , Parker Rule
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