[2510.00612] Empirical validation of the polarization transition in a double-random field model of elections

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arXiv:2510.00612 (physics)

[Submitted on 1 Oct 2025 (v1), last revised 10 Mar 2026 (this version, v4)]

Title:Empirical validation of the polarization transition in a double-random field model of elections

Authors:Jan Korbel, Remah Dahdoul, Stefan Thurner<br>View a PDF of the paper titled Empirical validation of the polarization transition in a double-random field model of elections, by Jan Korbel and Remah Dahdoul and Stefan Thurner

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Abstract:We model bipartisan elections where voters are exposed to two forces: local homophilic interactions and external influence from two political campaigns. The model is mathematically equivalent to the random field Ising model with a bimodal field. When both parties exceed a critical campaign spending, the system undergoes a phase transition to a highly polarized state where homophilic influence becomes negligible, and election outcomes mirror the proportion of voters aligned with each campaign, independent of total spending. The model predicts a hysteresis region, where the election results are not determined by campaign spending but by incumbency. Calibrating the model with historical data from US House elections between 1980 and 2020, we find the critical campaign spending to be $\sim 1.8$ million USD. Campaigns exceeding critical expenditures increased in 2018 and 2020, suggesting a boost in political polarization.

Comments:<br>accepted to Physical Review Letters

Subjects:

Physics and Society (physics.soc-ph)

Cite as:<br>arXiv:2510.00612 [physics.soc-ph]

(or<br>arXiv:2510.00612v4 [physics.soc-ph] for this version)

https://doi.org/10.48550/arXiv.2510.00612

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arXiv-issued DOI via DataCite

Journal reference:<br>Phys. Rev. Lett. 136 (2025) 127402

Related DOI:

https://doi.org/10.1103/9gjj-1df6

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DOI(s) linking to related resources

Submission history<br>From: Jan Korbel [view email]<br>[v1]<br>Wed, 1 Oct 2025 07:38:39 UTC (4,453 KB)

[v2]<br>Thu, 2 Oct 2025 07:59:18 UTC (4,453 KB)

[v3]<br>Thu, 27 Nov 2025 10:27:16 UTC (11,507 KB)

[v4]<br>Tue, 10 Mar 2026 08:02:36 UTC (7,680 KB)

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