Regensburg 2025 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 4: Urban systems, Scaling, and Social Systems
SOE 4.5: Talk
Tuesday, March 18, 2025, 11:00–11:15, H45
Statistical mechanics of a voter model with an evolving number of opinion states — Jeehye Choi1, Byungjoon Min1,2, and •Tobias Galla3 — 1Department of Physics, Chungbuk National University, Cheongju, Chungbuk, Korea — 2Department of Medicine, University of Florida, Gainesville FL, USA — 3Institute for Cross-Disciplinary Physics and Complex Systems IFISC, Palma de Mallorca, Spain
The voter model (VM) describes population of interacting individuals. At each step a randomly chosen individual copies the state ("the opinion") of a neighbour.
Here, we introduce and study a VM in which new opinion states can be introduced spontaneously. Opinions can also go extinct via the voter dynamics. This leads to stationary states with a variable number of opinions in the population or network.
We use statistical physics methods to characterise these stationary states, drawing parallels to the evolution of "mating types" in biological populations. Mating types are forms of the sperm-egg system. Unlike for true sexes, there can be more than two mating types (some fungi have thousands). We transfer methods from number theory, previously used to characterise the evolution of mating types [1], to compute how many opinions will ultimately be present in a VM with a dynamic number of states.
[1] E. Berríos-Caro, T. Galla, G. W.A. Constable, Switching environments, synchronous sex, and the evolution of mating types, Theor. Pop. Biol. 138, 28 (2021)
Keywords: voter model; statistical physics; stochastic processes; biological evolution of mating types