The incremental voter model: mean-field analysis and convergence to equilibrium

Fuente: arXiv
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Main Authors: Cao, Fei, Gong, Xiaoqian
Format: Preprint
Published: 2026
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author Cao, Fei
Gong, Xiaoqian
author_facet Cao, Fei
Gong, Xiaoqian
contents We introduce the incremental voter model (IVM), a discrete-opinion multi-agent system where agents undergo step-wise transitions biased by the opinion of a randomly selected persuader. Our incremental voter model comprises a large population of interacting agents, each holding an opinion represented by an element of the discrete set $\{-k,\ldots,0,\ldots,k\}, k \in \mathbb{N}_{+}$. At each update step as time progresses, a pair of distinct agents are selected independently and uniformly at random from the population, and the first agent (viewed as the ``listener'') updates its opinion based on that of the second (viewed as the ``persuader''), adopting a new opinion that differs from its current one by at most one unit. By deriving the mean-field system of nonlinear ordinary differential equations (ODEs) that governs the large-population limit of the agent-based model, we develop a rigorous mathematical framework to study the asymptotic behavior of the opinion distribution in the mean-field limit. These results contribute to a deeper understanding of social influence processes in complex systems, particularly in modeling opinion polarization, and may guide the formulation of more advanced models in future research.
format Preprint
id arxiv_https___arxiv_org_abs_2605_28984
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The incremental voter model: mean-field analysis and convergence to equilibrium
Cao, Fei
Gong, Xiaoqian
Multiagent Systems
91D25, 91D30, 82C31, 82C22
We introduce the incremental voter model (IVM), a discrete-opinion multi-agent system where agents undergo step-wise transitions biased by the opinion of a randomly selected persuader. Our incremental voter model comprises a large population of interacting agents, each holding an opinion represented by an element of the discrete set $\{-k,\ldots,0,\ldots,k\}, k \in \mathbb{N}_{+}$. At each update step as time progresses, a pair of distinct agents are selected independently and uniformly at random from the population, and the first agent (viewed as the ``listener'') updates its opinion based on that of the second (viewed as the ``persuader''), adopting a new opinion that differs from its current one by at most one unit. By deriving the mean-field system of nonlinear ordinary differential equations (ODEs) that governs the large-population limit of the agent-based model, we develop a rigorous mathematical framework to study the asymptotic behavior of the opinion distribution in the mean-field limit. These results contribute to a deeper understanding of social influence processes in complex systems, particularly in modeling opinion polarization, and may guide the formulation of more advanced models in future research.
title The incremental voter model: mean-field analysis and convergence to equilibrium
topic Multiagent Systems
91D25, 91D30, 82C31, 82C22
url https://arxiv.org/abs/2605.28984