The incremental voter model: mean-field analysis and convergence to equilibrium
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| Format: | Preprint |
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2026
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| _version_ | 1866910267388985344 |
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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 |