Modeling public opinion control by a charismatic leader

TL;DR

This paper models how a charismatic leader influences public opinion over time using a generalized Ising model, revealing temperature-dependent metastable states and opinion dynamics.

Contribution

It introduces a mean-field approach to analyze the impact of a persuadable leader on social opinion, considering both global and local interactions.

Findings

Opinion sign depends on initial conditions and temperature.

Metastable states influence long-term social mood.

Local interactions also exhibit the temperature-dependent effect.

Abstract

We study the average long-time behavior of the binary opinions of a social group with peer-to-peer interactions under the influence of an external bias and a persuadable leader, a strongly-biased agent with a dynamic opinion with the intention of spreading it across the system. We use a generalized, fully-connected Ising model, with each spin representing the binary opinion of an agent at a given time and a single, super spin representing the opinion of the leader. External fields and interaction constants model the opinion bias and peer-to-peer interactions, respectively, while the temperature $T$ models an idealized social climate, representing an authoritarian regime if $T$ is low or a liberal one if $T$ is high. We derive a mean-field solution for the average magnetization $m$, the "social mood", and investigate how $m$ and the super spin magnetization vary as a function of $T$. We find that, depending on the initial conditions, due to the presence of metastable states, the sign of the average magnetization depends on the temperature. Finally, we verify that this effect is also present even if we consider only nearest-neighbor interactions within the social group.