Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation

TL;DR

This paper develops kinetic models for opinion formation incorporating additional variables like leadership and spatial factors, leading to inhomogeneous Boltzmann equations and their macroscopic limits, with numerical validation.

Contribution

It introduces novel kinetic models for opinion dynamics that include leadership and spatial segregation, deriving new macroscopic equations and providing numerical analysis.

Findings

Models capture opinion leadership effects

Models explain political segregation phenomena

Numerical experiments validate theoretical results

Abstract

We propose and investigate different kinetic models for opinion formation, when the opinion formation process depends on an additional independent variable, e.g. a leadership or a spatial variable. More specifically, we consider:(i) opinion dynamics under the effect of opinion leadership, where each individual is characterised not only by its opinion, but also by another independent variable which quantifies leadership qualities; (ii) opinion dynamics modelling political segregation in the `The Big Sort', a phenomenon that US citizens increasingly prefer to live in neighbourhoods with politically like-minded individuals. Based on microscopic opinion consensus dynamics such models lead to inhomogeneous Boltzmann-type equations for the opinion distribution. We derive macroscopic Fokker-Planck-type equations in a quasi-invariant opinion limit and present results of numerical experiments.