Competing Effects of Social Balance and Influence

TL;DR

This paper models social dynamics with three states, analyzing how external deradicalizing influence affects the stability and convergence of social opinions, revealing a critical threshold for consensus formation.

Contribution

It introduces a coupled three-state model combining social balance and external influence, identifying a critical external field strength that determines system behavior.

Findings

Existence of a critical external field $p_c$ separating different dynamical regimes.

Metastable states and saddle points occur when $p < p_c$.

Convergence time to consensus matches quasi-stationary distribution predictions.

Abstract

We study a three-state (leftist, rightist, centrist) model that couples the dynamics of social balance with an external deradicalizing field. The mean-field analysis shows that there exists a critical value of the external field $p_c$ such that for a weak external field ($p$$<$$p_c$), the system exhibits a metastable fixed point and a saddle point in addition to a stable fixed point. However, if the strength of the external field is sufficiently large ($p$$>$$p_c$), there is only one (stable) fixed point which corresponds to an all-centrist consensus state (absorbing state). In the weak-field regime, the convergence time to the absorbing state is evaluated using the quasi-stationary distribution and is found to be in agreement with the results obtained by numerical simulations.