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We analyse two-tier voting systems with voters described by a multi-group mean-field model that allows for correlated voters both within groups as well as across group boundaries. In this model voters are influenced by voters within their…

Probability · Mathematics 2025-09-16 Werner Kirsch , Gabor Toth

We model voting behaviour in the multi-group setting of a two-tier voting system using sequences of de Finetti measures. Our model is defined by using the de Finetti representation of a probability measure (i.e. as a mixture of…

Probability · Mathematics 2026-01-14 Gabor Toth

A new game-theoretic approach for combining multiple classifiers is proposed. A short introduction in Game Theory and coalitions illustrate the way any collective decision scheme can be viewed as a competitive game of coalitions that are…

Computer Science and Game Theory · Computer Science 2015-02-10 Harris V. Georgiou

Collective decision-making is a process by which a group of individuals determines a shared outcome that shapes societal dynamics; from innovation diffusion to organizational choices. A common approach to model these processes is using…

Physics and Society · Physics 2025-04-03 Maciej Doniec , Pratik Mullick , Parongama Sen , Katarzyna Sznajd-Weron

We consider two-tier voting system and try to determine optimal weights for a fair representation in such systems. A prominent example of such a voting system is the Council of Ministers of the European Union. Under the assumption of…

Probability · Mathematics 2012-10-18 Werner Kirsch , Jessica Langner

We investigate a dynamical model of opinion formation in which an individual's opinion is influenced by interactions with a group of other agents. We introduce a bias towards one of the opinions in a manner not considered earlier to the…

Physics and Society · Physics 2024-09-17 Pratik Mullick , Parongama Sen

We study a model of a population making a binary decision based on information spreading within the population, which is fully connected or covering a square grid. We assume that a fraction of the population wants to make the choice of the…

Physics and Society · Physics 2016-05-24 Petter Holme , Hang-Hyun Jo

In this paper, we reconsider the spin model suggested recently to understand some features of collective decision making among higher organisms [A.T. Hartnett et al., Phys. Rev. Lett. 116 (2016) 038701]. Within the model, the state of an…

Statistical Mechanics · Physics 2023-06-28 Petro Sarkanych , Mariana Krasnytska , Luis Gómez-Nava , Pawel Romanczuk , Yurij Holovatch

Strongly opinionated minorities can have a dramatic impact on the opinion dynamics of a large population. Two factions of inflexible minorities, polarised into two competing opinions, could lead the entire population to persistent…

Biological Physics · Physics 2023-07-26 Andreagiovanni Reina , Raina Zakir , Giulia De Masi , Eliseo Ferrante

Background: It has repeatedly been reported that when making decisions under uncertainty, groups outperform individuals. In a lab setting, real groups are often replaced by simulated groups: Instead of performing an actual group discussion,…

Applications · Statistics 2021-06-08 Sascha Meyen , Dorothee M. B. Sigg , Ulrike von Luxburg , Volker H. Franz

A key question concerning collective decisions is whether a social system can settle on the best available option when some members learn from others instead of evaluating the options on their own. This question is challenging to study, and…

Physics and Society · Physics 2021-08-24 Vicky Chuqiao Yang , Mirta Galesic , Harvey McGuinness , Ani Harutyunyan

Two of the main factors shaping an individual's opinion are social coordination and personal preferences, or personal biases. To understand the role of those and that of the topology of the network of interactions, we study an extension of…

Physics and Society · Physics 2023-06-07 Filippo Zimmaro , Pierluigi Contucci , János Kertész

A recently proposed graph-theoretic metric, the influence gap, has shown to be a reliable predictor of the effect of social influence in two-party elections, albeit only tested on regular and scale-free graphs. Here, we investigate whether…

Social and Information Networks · Computer Science 2022-02-09 Jacques Bara , Omer Lev , Paolo Turrini

We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…

Computer Science and Game Theory · Computer Science 2025-09-24 Tomáš Masařík , Grzegorz Pierczyński , Piotr Skowron

Direct democracy is a special case of an ensemble of classifiers, where every person (classifier) votes on every issue. This fails when the average voter competence (classifier accuracy) falls below 50%, which can happen in noisy settings…

Computer Science and Game Theory · Computer Science 2018-07-23 Malik Magdon-Ismail , Lirong Xia

Voters from m disjoint constituencies (regions, federal states, etc.) are represented in an assembly which contains one delegate from each constituency and applies a weighted voting rule. All agents are assumed to have single-peaked…

Computer Science and Game Theory · Computer Science 2012-11-28 Sascha Kurz , Nicola Maaser , Stefan Napel

Decades of research suggest that information exchange in groups and organizations can reliably improve judgment accuracy in tasks such as financial forecasting, market research, and medical decision-making. However, we show that improving…

General Economics · Economics 2021-04-26 Joshua Becker , Douglas Guilbeault , Ned Smith

Many important decisions in societies such as school admissions, hiring, or elections are based on the selection of top-ranking individuals from a larger pool of candidates. This process is often subject to biases, which typically manifest…

Computers and Society · Computer Science 2024-07-02 Ivan Smirnov , Florian Lemmerich , Markus Strohmaier

A social system is susceptible to perturbation when its collective properties depend sensitively on a few pivotal components. Using the information geometry of minimal models from statistical physics, we develop an approach to identify…

Physics and Society · Physics 2020-07-06 Edward D. Lee , Daniel M. Katz , Michael J. Bommarito , Paul Ginsparg

A voting rule decides on a probability distribution over a set of m alternatives, based on rankings of those alternatives provided by agents. We assume that agents have cardinal utility functions over the alternatives, but voting rules have…

Computer Science and Game Theory · Computer Science 2024-01-23 Soroush Ebadian , Anson Kahng , Dominik Peters , Nisarg Shah
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