Topological bifurcations in a model society of reasonable contrarians

TL;DR

This paper models a society of reasonable contrarians using a cellular automaton with social norms, revealing complex bifurcation behaviors and the influence of network topology on collective opinion dynamics.

Contribution

It introduces a novel Ising-type cellular automaton model incorporating social norms and analyzes bifurcations and chaos in opinion dynamics across different network structures.

Findings

Mean field approximation shows bifurcations and chaos.

Small-world networks recover mean field behavior.

Bifurcation diagrams are similar across network types.

Abstract

People are often divided into conformists and contrarians, the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority. In practice, however, the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion, which denotes a social norm. Such reasonable contrarian behavior is often considered a mark of independent thought, and can be a useful strategy in financial markets. We present the opinion dynamics of a society of reasonable contrarian agents. The model is a cellular automaton of Ising type, with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms. We introduce the entropy of the collective variable as a way of comparing deterministic (mean-field) and probabilistic (simulations) bifurcation diagrams. In the mean field approximation the model exhibits bifurcations and a chaotic phase, interpreted as coherent oscillations of the whole society. However, in a one-dimensional spatial arrangement one observes incoherent oscillations and a constant average. In simulations on Watts-Strogatz networks with a small-world effect the mean field behavior is recovered, with a bifurcation diagram that resembles the mean-field one, but using the rewiring probability as the control parameter. Similar bifurcation diagrams are found for scale free networks, and we are able to compute an effective connectivity for such networks.