Opinion polarisation in social networks

TL;DR

This paper introduces a kinetic model for opinion formation on social networks that accounts for network connectivity, analyzing conditions for opinion polarization shifts and validating findings with simulations.

Contribution

It presents a novel Boltzmann-type kinetic framework for opinion dynamics on complex networks, incorporating connectivity distributions and analytical criteria for polarization switches.

Findings

Polarization switch depends on initial opinion and connectivity correlation.

Analytical conditions for opinion sign change are derived.

Monte Carlo simulations confirm theoretical predictions.

Abstract

In this paper, we propose a Boltzmann-type kinetic description of opinion formation on social networks, which takes into account a general connectivity distribution of the individuals. We consider opinion exchange processes inspired by the Sznajd model and related simplifications but we do not assume that individuals interact on a regular lattice. Instead, we describe the structure of the social network statistically, assuming that the number of contacts of a given individual determines the probability that their opinion reaches and influences the opinion of another individual. From the kinetic description of the system, we study the evolution of the mean opinion, whence we find precise analytical conditions under which a \textit{polarisation switch} of the opinions, i.e. a change of sign between the initial and the asymptotic mean opinions, occurs. In particular, we show that a non-zero correlation between the initial opinions and the connectivity of the individuals is necessary to observe polarisation switch. Finally, we validate our analytical results through Monte Carlo simulations of the stochastic opinion exchange processes on the social network.