Fei Cao: The fractal geometry of opinion formation 

Speaker Website:

https://feicao1995.github.io/

Institution: 

Amherst College

Title:

The fractal geometry of opinion formation 

Abstract: 

In this manuscript, we introduce and study a variant of the agent-based opinion dynamics proposed in a recent work [8], within the framework of an interacting multi-agent system, where agents are assumed to interact with each other and update their opinions after each pairwise encounter. Specifically, our opinion model involves a large crowd of N indistinguishable agents, each characterized by an opinion value ranging within the interval [-1,1]. At each update time, two agents are picked uniformly at random and the opinion of one agent will either shift by a proportion μ_+ ∈ (0,1] towards +1, or by a proportion μ_{-} ∈ (0,1] towards -1, with probabilities depending on the other agent's opinion. We rigorously derive the mean-field limit PDE that governs the large-population limit of the agent-based model and present several quantitative results demonstrating convergence to the unique equilibrium distribution. Remarkably, for a suitable choice of model parameters, the long-term equilibrium opinion profile displays a striking self-similar structure that generalizes the celebrated Bernoulli convolution, a topic extensively studied in the context of fractal geometry [23,44]. These findings also enhance our understanding of the opinion fragmentation phenomenon and may provide valuable insights for the development of more sophisticated models in future research.