🤖 AI Summary
This study addresses the challenge of modeling social influence and opinion polarization dynamics in discrete-opinion systems by proposing the Incremental Voter Model (IVM), wherein agents update their discrete opinions in unit steps (±1) under the influence of randomly selected persuaders. For the first time, a bounded-step updating mechanism is introduced into discrete-opinion interaction models, accompanied by a rigorous mean-field theoretical framework. Through multi-agent simulations and limiting analysis of stochastic processes, the authors derive a system of mean-field ordinary differential equations governing the evolution of opinion distributions in large populations, and rigorously establish its convergence and equilibrium properties. This work significantly advances the theoretical understanding of the mechanisms underlying opinion polarization.
📝 Abstract
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.