Effects of Stubbornness on Opinion Dynamics

TL;DR

This paper investigates how heterogeneous stubbornness influences opinion dynamics, showing it affects convergence, opinions, and polarization, and introduces efficient algorithms for quantifying social concepts in large networks.

Contribution

It provides a theoretical analysis of stubbornness effects, introduces new quantitative indicators, and develops scalable algorithms with guarantees for large networks.

Findings

Heterogeneous stubbornness significantly impacts convergence time and opinion formation.

Proposed algorithms efficiently approximate social conflict, disagreement, and polarization.

Experiments on large real networks demonstrate scalability and effectiveness.

Abstract

As an important factor governing opinion dynamics, stubbornness strongly affects various aspects of opinion formation. However, a systematically theoretical study about the influences of heterogeneous stubbornness on opinion dynamics is still lacking. In this paper, we study a popular opinion model in the presence of inhomogeneous stubbornness. We show analytically that heterogeneous stubbornness has a great impact on convergence time, expressed opinion of every node, and the overall expressed opinion. We provide an explanation of the expressed opinion in terms of stubbornness-dependent spanning diverging forests. We propose quantitative indicators to quantify some social concepts, including conflict, disagreement, and polarization by incorporating heterogeneous stubbornness, and develop a nearly linear time algorithm to approximate these quantities, which has a proved theoretical guarantee for the error of each quantity. To demonstrate the performance of our algorithm, we perform extensive experiments on a large set of real networks, which indicate that our algorithm is both efficient and effective, scalable to large networks with millions of nodes.