Do Stubborn Users Always Cause More Polarization and Disagreement? A Mathematical Study

TL;DR

This paper investigates how user stubbornness affects opinion polarization in social networks, revealing that increasing stubbornness generally raises polarization but can reduce it when involving neutral users, supported by theoretical proofs and real-world data.

Contribution

It provides a mathematical analysis of stubbornness effects on opinion dynamics, showing that increasing stubbornness can both increase and decrease polarization depending on user roles.

Findings

Higher stubbornness increases polarization in homogeneous networks.

In inhomogeneous networks, stubbornness of neutral users can reduce polarization.

Experimental results support theoretical predictions.

Abstract

We study how the stubbornness of social network users influences opinion polarization and disagreement. Our work is in the context of the popular Friedkin-Johnson opinion formation model, where users update their opinion as a function of the opinion of their connections and their own innate opinion. Stubbornness then is formulated in terms of the stress a user puts on its innate opinion. We examine two scenarios: one where all nodes have uniform stubbornness levels (homogeneous) and another where stubbornness varies among nodes (inhomogeneous). In the homogeneous scenario, we prove that as the network's stubbornness factor increases, the polarization and disagreement index grows. In the more general inhomogeneous scenario, our findings surprisingly demonstrate that increasing the stubbornness of some users (particularly, neutral/unbiased users) can reduce the polarization and disagreement. We characterize specific conditions under which this phenomenon occurs. Finally, we conduct an extensive set of experiments on real-world network data to corroborate and complement our theoretical findings.