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In parliamentary elections, parties compete for a limited, typically fixed number of seats. Most parliaments are assembled using apportionment methods that distribute the seats based on the parties' vote counts. Common apportionment methods…

In recent years, opinion dynamics has received an increasing attention, and various models have been introduced and evaluated mainly by simulation. In this study, we introduce and study a dynamical model inspired by the so-called `bounded…

Dynamical Systems · Mathematics 2018-11-07 Sergei Yu. Pilyugin , M. C. Campi

For a binary choice problem, the spatial coordination of decisions in an agent community is investigated both analytically and by means of stochastic computer simulations. The individual decisions are based on different local information…

Statistical Mechanics · Physics 2009-11-07 Frank Schweitzer , Joerg Zimmermann , Heinz Muehlenbein

Forecasting elections -- a challenging, high-stakes problem -- is the subject of much uncertainty, subjectivity, and media scrutiny. To shed light on this process, we develop a method for forecasting elections from the perspective of…

Physics and Society · Physics 2020-09-21 Alexandria Volkening , Daniel F. Linder , Mason A. Porter , Grzegorz A. Rempala

In this paper we extend some recent results on an operatorial approach to the description of alliances between political parties interacting among themselves and with a basin of electors. In particular, we propose and compare three…

Physics and Society · Physics 2017-05-24 F. Bagarello , F. Gargano

In elections, the vote shares or turnout rates show a strong spatial correlation. The logarithmic decay with distance suggests that a 2D noisy diffusive equation describes the system. Based on the study of U.S. presidential elections data,…

Physics and Society · Physics 2019-05-29 Shintaro Mori , Masato Hisakado , Kazuaki Nakayama

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

Political polarization can be beneficial to competing political parties. I study how electoral competition itself generates incentives to polarize voters, even when parties are ex ante identical and motivated purely by political power,…

General Economics · Economics 2026-02-02 Giampaolo Bonomi

Elections for public offices in democratic nations are large-scale examples of collective decision-making. As a complex system with a multitude of interactions among agents, we can anticipate that universal macroscopic patterns could emerge…

Physics and Society · Physics 2025-01-14 Ritam Pal , Aanjaneya Kumar , M. S. Santhanam

We model an electorate voting on the funding of a public good in a two-party system in an evolutionary game theory framework. Voters adopt one of four strategies: Consensus-makers, Gridlockers, Party 1 Zealots, and Party 2 Zealots, which…

Physics and Society · Physics 2026-03-27 Jonathan Engle , Bryce Morsky

We use causal inference to study how designing ballots with and without party designations impacts electoral outcomes when partisan voters rely on party-order cues to infer candidate affiliation in races without designations. If the party…

Applications · Statistics 2025-07-23 Alessandro Arlotto , Alexandre Belloni , Fei Fang , Saša Pekeč

Election data represent a precious source of information to study human behavior at a large scale. In proportional elections with open lists, the number of votes received by a candidate, rescaled by the average performance of all…

Physics and Society · Physics 2013-01-25 Arnab Chatterjee , Marija Mitrović , Santo Fortunato

Today, our more-than-ever digital lives leave significant footprints in cyberspace. Large scale collections of these socially generated footprints, often known as big data, could help us to re-investigate different aspects of our social…

Physics and Society · Physics 2023-01-05 Taha Yasseri , Jonathan Bright

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 explain the anomaly of election results between large cities and rural areas in terms of urban scaling in the 1948-2016 US elections and in the 2016 EU referendum of the UK. The scaling curves are all universal and depend on a single…

Physics and Society · Physics 2018-07-04 Eszter Bokányi , Zoltán Szállási , Gábor Vattay

We propose a computational framework for modeling opinion dynamics in electoral competitions that combines two realistic features: voter memory and exogenous shocks. The population is represented by a fully-connected network of agents, each…

Physics and Society · Physics 2026-02-05 Jaime L. C. da C. Filho , Nuno Crokidakis

Consider an undirected graph G, representing a social network, where each node is blue or red, corresponding to positive or negative opinion on a topic. In the voter model, in discrete time rounds, each node picks a neighbour uniformly at…

Social and Information Networks · Computer Science 2025-06-03 Abhiram Manohara , Ahad N. Zehmakan

The election control problem through social influence asks to find a set of nodes in a social network of voters to be the starters of a political campaign aiming at supporting a given target candidate. Voters reached by the campaign change…

Social and Information Networks · Computer Science 2020-07-14 Mohammad Abouei Mehrizi , Federico Corò , Emilio Cruciani , Gianlorenzo D'Angelo

Affective polarization and increasing social divisions affect social mixing and the spread of information across online and physical spaces, reinforcing social and electoral cleavages and influencing political outcomes. Here, using…

Social and Information Networks · Computer Science 2025-10-06 Marco Tonin , Bruno Lepri , Michele Tizzoni

We study a model of electoral accountability and selection whereby heterogeneous voters aggregate incumbent politician's performance data into personalized signals through paying limited attention. Extreme voters' signals exhibit an…

Theoretical Economics · Economics 2023-04-05 Anqi Li , Lin Hu