Social power evolution in influence networks with stubborn individuals

TL;DR

This paper introduces models for the evolution of social power in influence networks that incorporate stubborn individuals, analyzing their equilibrium states and convergence properties, and demonstrating that stubbornness prevents autocratic dominance.

Contribution

It is the first to analyze social power evolution with stubborn individuals using the reflected appraisal mechanism, extending the DeGroot-Friedkin model.

Findings

More stubborn individuals have higher equilibrium social power.

Models with stubbornness prevent autocracy, enabling democracy under any network topology.

Equilibria depend only on influence and stubbornness levels.

Abstract

This paper studies the evolution of social power in influence networks with stubborn individuals. Based on the Friedkin-Johnsen opinion dynamics and the reflected appraisal mechanism, two models are proposed over issue sequences and over a single issue, respectively. These models generalize the original DeGroot-Friedkin (DF) model by including stubbornness. To the best of our knowledge, this paper is the first attempt to investigate the social power evolution of stubborn individuals basing on the reflected appraisal mechanism. Properties of equilibria and convergence are provided. We show that the models have same equilibrium social power and convergence property, where the equilibrium social power depends only upon interpersonal influence and individuals' stubbornness. Roughly speaking, more stubborn individual has more equilibrium social power. Moreover, unlike the DF model without stubbornness, we prove that for the models with stubbornness, autocracy can never be achieved, while democracy can be achieved under any network topology.