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The process of legislative redistricting in New Hampshire, along with many other states across the country, was particularly contentious during the 2020 census cycle. In this paper we present an ensemble analysis of the enacted districts to…

Social and Information Networks · Computer Science 2025-09-12 Atticus McWhorter , Daryl DeFord

We develop a theory of distributive competition under redistricting that explains both electoral outcomes and the equilibrium allocation of policy benefits by endogenizing voter pivotality. In a multi-district model with primaries, general…

General Economics · Economics 2026-04-03 Thomas Groll , Sharyn O'Halloran

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

Recently, scholars from law and political science have introduced metrics which use only election outcomes (and not district geometry) to assess the presence of partisan gerrymandering. The most high-profile example of such a tool is the…

Physics and Society · Physics 2018-03-15 Ellen Veomett

Recently, a proposal has been advanced to detect unconstitutional partisan gerrymandering with a simple formula called the efficiency gap. The efficiency gap is now working its way towards a possible landmark case in the Supreme Court. This…

Physics and Society · Physics 2017-06-01 Mira Bernstein , Moon Duchin

Decisions about how the population of the United States should be divided into legislative districts have powerful and not fully understood effects on the outcomes of elections. The problem of understanding what we might mean by "fair…

Physics and Society · Physics 2020-06-22 Jordan S. Ellenberg

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

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 introduce a non-partisan probability distribution on congressional redistricting of North Carolina which emphasizes the equal partition of the population and the compactness of districts. When random districts are drawn and the results…

Physics and Society · Physics 2014-11-03 Jonathan C. Mattingly , Christy Vaughn

Redistricting is the process by which electoral district boundaries are drawn, and a common normative assumption in this process is that districts should be drawn so as to capture coherent communities of interest (COIs). While states rely…

Social and Information Networks · Computer Science 2023-09-26 Jacob Kruse , Song Gao , Yuhan Ji , Daniel P. Szabo , Kenneth Mayer

Ensemble analysis has become central to redistricting litigation, but parameter effects remain understudied. We analyze 315 ReCom ensembles across the three legislative chambers in 7 states, systematically varying the population tolerance,…

Physics and Society · Physics 2025-05-28 Kristopher Tapp , Todd Proebsting , Alec Ramsay

We explore the Declination, a new metric intended to detect partisan gerrymandering. We consider instances in which each district has equal turnout, the maximum turnout to minimum turnout is bounded, and turnout is unrestricted. For each of…

Physics and Society · Physics 2018-12-17 Marion Campisi , Andrea Padilla , Thomas C. Ratliff , Ellen Veomett

We use voting precinct and election data to analyze the political geography of New Hampshire and Maine. We find that the location of dividing line between Congressional districts in both states are significantly different than what we would…

This preprint is an exploration in how a single mathematical idea - entropy - can be applied to redistricting in a number of ways. It's meant to be read not so much as a call to action for entropy, but as a case study illustrating one of…

Information Theory · Computer Science 2020-11-05 Larry Guth , Ari Nieh , Thomas Weighill

Suppose a researcher observes individuals within a county within a state. Given concerns about correlation across individuals, it is common to group observations into clusters and conduct inference treating observations across clusters as…

Econometrics · Economics 2022-01-24 Yong Cai

The space of connected graph partitions underlies statistical models used as evidence in court cases and reform efforts that analyze political districting plans. In response to the demands of redistricting applications, researchers have…

Physics and Society · Physics 2022-02-09 Elle Najt , Daryl DeFord , Justin Solomon

While manipulative attacks on elections have been well-studied, only recently has attention turned to attacks that account for geographic information, which are extremely common in the real world. The most well known in the media is…

Computer Science and Game Theory · Computer Science 2020-03-17 Zack Fitzsimmons , Omer Lev

This article introduces the 50stateSimulations, a collection of simulated congressional districting plans and underlying code developed by the Algorithm-Assisted Redistricting Methodology (ALARM) Project. The 50stateSimulations allow for…

Gerrymandering is the practice of drawing biased electoral maps that manipulate the voter population to gain an advantage. The most recent time gerrymandering became an issue was 2019 when the U.S. Federal Supreme Court decided that the…

Computers and Society · Computer Science 2023-12-08 Noah Lee , Hyunwoo Park , Sangho Shim

Ensembles of random legislative districts are a valuable tool for assessing whether a proposed district plan is an outlier or gerrymander. Expert witnesses have presented these in litigation using various methods, and unsurprisingly, they…

Computers and Society · Computer Science 2022-08-29 P. Dingus , C. Zhu , C. Gonatas