Opinion Dynamics with Slowly Evolving Zealot Populations

Abstract

. We introduce and analyze a model for opinion dynamics comprised of nonlinear ODEs. The variables are the proportion of moderates in the population who hold opinion A, the proportion of zealots who hold opinion A, and the proportion of zealots who hold opinion B (not A). The zealots are willing to change their opinion at a much slower rate than the moderates. Our model takes into account such things as the inherent attractiveness of one opinion over the other, the indoctrination of moderates by the zealots, and deradicalization of the zealots by the moderates. A combination of theoretical and numerical analysis shows there are many different types of asymptotic configurations of the population. Many of these correspond to critical points of the system. The most intriguing finding is that if both A and B are roughly equally attractive, and the rate of indoctrination is roughly equal to the rate of deradicalization, then there will be a stable periodic orbit. The dynamics of this orbit show that a precursor to an opinion being dominant is that the proportion of zealots for the opinion must first grow to some critical value. Moreover, when the periodic orbit exists, there are no other solutions which allow for coexistence between the two opinions.