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In many proportional parliamentary elections, electoral thresholds (typically 3-5%) are used to promote stability and governability by preventing the election of parties with very small representation. However, these thresholds often result…

Computer Science and Game Theory · Computer Science 2025-03-24 Théo Delemazure , Rupert Freeman , Jérôme Lang , Jean-François Laslier , Dominik Peters

We compare federal election results for each state versus the USA in every second year from 1992 to 2018, to model partisan lean of each state and its dependence on the nationwide popular vote. For each state, we model both its current…

Applications · Statistics 2019-10-09 Andrey Sarantsev

In an election in which each voter ranks all of the candidates, we consider the head-to-head results between each pair of candidates and form a labeled directed graph, called the margin graph, which contains the margin of victory of each…

Theoretical Economics · Economics 2020-09-08 Matthew Harrison-Trainor

In the computational study of political redistricting, feasibility necessitates the use of a discretization of regions such as states, counties, and towns. In nearly all cases, researchers use a dual graph, whose vertices represent small…

Discrete Mathematics · Computer Science 2026-04-08 Sara Anderson , Sarah Cannon , Brooke Feinberg , Anne Friedman

We propose a method for redistricting, decomposing a geographical area into subareas, called districts, so that the populations of the districts are as close as possible and the districts are compact and contiguous. Each district is the…

Data Structures and Algorithms · Computer Science 2018-01-09 Vincent Cohen-Addad , Philip N. Klein , Neal E. Young

In redistricting litigation, effective enforcement of the Voting Rights Act has often involved providing the court with districting plans that display a larger number of majority-minority districts than the current proposal (as was true,…

Data Structures and Algorithms · Computer Science 2025-09-08 Daniel Brous , David Shmoys

The related concepts of partisan belief systems, issue alignment, and partisan sorting are central to our understanding of politics. These phenomena have been studied using measures of alignment between pairs of topics, or how much…

Social and Information Networks · Computer Science 2025-01-14 Letizia Iannucci , Ali Faqeeh , Ali Salloum , Ted Hsuan Yun Chen , Mikko Kivelä

Granular geographic data present new opportunities to understand how neighborhoods are formed, and how they influence politics. At the same time, the inherent subjectivity of neighborhoods creates methodological challenges in measuring and…

Applications · Statistics 2024-11-20 Cory McCartan , Jacob R. Brown , Kosuke Imai

Representative democracy in the United States relies on election systems that transmit votes into representatives in three key bodies: the two chambers of the federal legislature (House of Representatives and Senate) and the Electoral…

Applications · Statistics 2025-09-25 Lee Kennedy-Shaffer

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 show how to use automated computation of election margins to assess the number of votes that would need to change in order to alter a parliamentary outcome for single-member preferential electorates. In the context of increasing…

Data Structures and Algorithms · Computer Science 2017-08-02 Michelle Blom , Peter J. Stuckey , Vanessa Teague

The outcome of the British General Election to be held in just over one week's time is widely regarded as the most difficult in living memory to predict. Current polls suggest that the two main parties are neck and neck but that there will…

Physics and Society · Physics 2015-05-04 Carlos Molinero , Elsa Arcaute , Duncan Smith , Michael Batty

This past decade has seen a noticeable uptick in asymmetric election results along with the inevitable claims of gerrymandering and litigation. Research, too, has followed, giving rise to intense scrutiny of elections, where the goal is to…

Physics and Society · Physics 2019-01-28 Ray J Wallin

The paper considers a general model of electoral systems combining district-based elections with a compensatory mechanism in order to create any outcome between strictly majoritarian and purely proportional seat allocation. It contains vote…

Computer Science and Game Theory · Computer Science 2017-10-27 László Csató

In this paper, we propose to use the concept of local fairness for auditing and ranking redistricting plans. Given a redistricting plan, a deviating group is a population-balanced contiguous region in which a majority of individuals are of…

Computer Science and Game Theory · Computer Science 2022-11-22 Shao-Heng Ko , Erin Taylor , Pankaj K. Agarwal , Kamesh Munagala

We describe an electoral system for distributing seats in a parliament. It gives proportionality for the political parties and close to proportionality for constituencies. The system suggested here is a version of the system used in Sweden…

Optimization and Control · Mathematics 2013-10-31 Svante Linusson , Gustav Ryd

Despite extensive theoretical research on proportionality in approval-based multiwinner voting, its impact on which committees and candidates can be selected in practice remains poorly understood. We address this gap by (i) analyzing the…

Computer Science and Game Theory · Computer Science 2025-11-13 Niclas Boehmer , Lara Glessen , Jannik Peters

Participatory budgeting is one of the exciting developments in deliberative grassroots democracy. We concentrate on approval elections and propose proportional representation axioms in participatory budgeting, by generalizing relevant…

Computer Science and Game Theory · Computer Science 2017-11-23 Haris Aziz , Barton Lee , Nimrod Talmon

We present an increasingly stringent set of replications of Ghitza & Gelman (2013), a multilevel regression and poststratification analysis of polls from the 2008 U.S. presidential election campaign, focusing on a set of plots showing the…

Applications · Statistics 2016-07-15 Rayleigh Lei , Andrew Gelman , Yair Ghitza

In the apportionment problem, a fixed number of seats must be distributed among parties in proportion to the number of voters supporting each party. We study a generalization of this setting, in which voters can support multiple parties by…

Computer Science and Game Theory · Computer Science 2022-03-31 Markus Brill , Paul Gölz , Dominik Peters , Ulrike Schmidt-Kraepelin , Kai Wilker