Social consensus through the influence of committed minorities

TL;DR

This paper demonstrates that a small, committed minority can rapidly reverse the majority opinion in a population, with the speed of change depending on the fraction of committed agents and the network structure.

Contribution

It introduces a model showing how a committed minority of about 10% can swiftly change societal opinions across different network types.

Findings

Critical minority fraction p_c is approximately 10%.

Time to consensus decreases dramatically when p > p_c.

Results are consistent across complete, Erdős-Rényi, and scale-free networks.

Abstract

We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value p_c \approx 10%, there is a dramatic decrease in the time, T_c, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < p_c, T_c \sim \exp(\alpha(p)N), while for p > p_c, T_c \sim \ln N. We conclude with simulation results for Erd\H{o}s-R\'enyi random graphs and scale-free networks which show qualitatively similar behavior.