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arXiv · 2607.21662

Reconstructing the Probability Measure of a Multi-group Curie-Weiss Model with Interacting Groups

Miguel Ballesteros·Gerardo Franco Cordova·Fedro Guillen·Gabor Toth
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Abstract

We study the problem of reconstructing the probability measure of a multi-group version of the Curie-Weiss or mean-field model of ferromagnetism from a sample of the voting behaviour the population. While originally used to study phase transitions in statistical mechanics, the Curie-Weiss or mean-field model has been applied to study phenomena where many agents interact with each other, in particular in case of a heterogeneous population with identifiable subpopulations. The degree of social cohesion within social groups manifests in the way the members of the group influence each others' decisions as well as how they behave under outside influence from voters belonging to another group. Contrary to single-group Curie-Weiss models, here we have a larger number of coupling parameters which have to be estimated. While the maximum likelihood estimator of the coupling parameters has desirable statistical properties in theory, computational challenges make applications to larger populations impractical. Therefore, we analyse an estimator based on asymptotic approximations to the behaviour of the Curie-Weiss model valid for large populations. Due to the wide applicability of models such as Curie-Weiss, the estimator is potentially useful in disciplines such as political science, sociology, automated voting, and preference aggregation.

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Miguel Ballesteros, Gerardo Franco Cordova, Fedro Guillen, Gabor Toth. 2026-07-23. Reconstructing the Probability Measure of a Multi-group Curie-Weiss Model with Interacting Groups. https://arxiv.org/abs/2607.21662

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