🤖 AI Summary
This paper investigates the dynamics of individual opinion evolution in social networks, focusing on the impact of the weighted median update rule on stationary opinion distributions. Unlike conventional mean-based models, it introduces the weighted median—novel in network opinion dynamics—to more realistically capture consensus formation and echo chamber emergence. Employing the configuration model, the authors develop an infinite-size mean-field asymptotic theory, complemented by numerical simulations and probabilistic distributional dynamics modeling. Their analysis reveals that network structure fundamentally determines the stationary distribution: it can drive either global consensus or multimodal fragmentation. The resulting asymptotic evolution equation is analytically tractable, providing a new theoretical framework and quantitative tools for understanding opinion polarization and social consensus formation.
📝 Abstract
Social interactions influence people's opinions. In some situations, these interactions result in a consensus opinion; in others, they result in opinion fragmentation and the formation of different opinion groups in the form of"echo chambers". Consider a social network of individuals, who hold continuous-valued scalar opinions and change their opinions when they interact with each other. In such an opinion model, it is common for an opinion-update rule to depend on the mean opinion of interacting individuals. However, we consider an alternative update rule - which may be more realistic in some situations - that instead depends on a weighted median opinion of interacting individuals. Through numerical simulations of our opinion model, we investigate how the limit opinion distribution depends on network structure. For configuration-model networks, we also derive a mean-field approximation for the asymptotic dynamics of the opinion distribution when there are infinitely many individuals in a network.