Aperiodic dynamics in a deterministic model of attitude formation in social groups

TL;DR

This paper introduces a new deterministic model for attitude formation in social groups, revealing that homophily and social influence can lead to complex, aperiodic long-term behaviors like polarization and subgroup formation.

Contribution

It presents a novel mathematical framework combining homophily and social influence, demonstrating complex dynamics such as quasi-periodicity and polarization in social attitude evolution.

Findings

Long-term dynamics are quasi-periodic with sensitive dependence on initial conditions.

Homophily and social influence can prevent consensus, leading to polarization.

The model exhibits Turing instability affecting attitude dynamics.

Abstract

Homophily and social influence are the fundamental mechanisms that drive the evolution of attitudes, beliefs and behaviour within social groups. Homophily relates the similarity between pairs of individuals' attitudinal states to their frequency of interaction, and hence structural tie strength, while social influence causes the convergence of individuals' states during interaction. Building on these basic elements, we propose a new mathematical modelling framework to describe the evolution of attitudes within a group of interacting agents. Specifically, our model describes sub-conscious attitudes that have an activator-inhibitor relationship. We consider a homogeneous population using a deterministic, continuous-time dynamical system. Surprisingly, the combined effects of homophily and social influence do not necessarily lead to group consensus or global monoculture. We observe that sub-group formation and polarisation-like effects may be transient, the long-time dynamics being quasi-periodic with sensitive dependence to initial conditions. This is due to the interplay between the evolving interaction network and Turing instability associated with the attitudinal state dynamics.