Scaling limits for continuous opinion dynamics systems

TL;DR

This paper investigates the large-population behavior of stochastic continuous opinion dynamics models, demonstrating that empirical opinion distributions converge exponentially fast to a mean-field limit described by a probability-measure ODE, with analysis of bounded-confidence and heterogeneous influence scenarios.

Contribution

It provides a rigorous analysis of the scaling limits of gossip models, establishing exponential convergence to a mean-field description and exploring their long-term behavior under various influence conditions.

Findings

Empirical opinion densities concentrate exponentially fast around the mean-field solution.

The mean-field dynamics are characterized by a probability-measure-valued ODE.

Asymptotic analysis reveals behavior under bounded-confidence and heterogeneous influence environments.

Abstract

Scaling limits are analyzed for stochastic continuous opinion dynamics systems, also known as gossip models. In such models, agents update their vector-valued opinion to a convex combination (possibly agent- and opinion-dependent) of their current value and that of another observed agent. It is shown that, in the limit of large agent population size, the empirical opinion density concentrates, at an exponential probability rate, around the solution of a probability-measure-valued ordinary differential equation describing the system's mean-field dynamics. Properties of the associated initial value problem are studied. The asymptotic behavior of the solution is analyzed for bounded-confidence opinion dynamics, and in the presence of an heterogeneous influential environment.