Peer influence breaks ergodicity in an opinion dynamics model with external information

TL;DR

This paper introduces a stochastic opinion model showing how social influence and external information cause a phase transition between adaptable and persistent consensus states, with memory effects lowering the threshold for ergodicity breaking.

Contribution

The study presents a novel opinion dynamics model incorporating memory and external signals, revealing a critical social sensitivity threshold for ergodicity breaking and demonstrating robustness across network structures.

Findings

Memory in decision-making smooths the phase transition.

A critical social sensitivity threshold determines ergodic vs. non-ergodic phases.

Model robustness confirmed across various network topologies.

Abstract

We present a stochastic imitation-based model of opinion dynamics in which agents balance social conformity with responsiveness to an external signal. The model captures how populations evolve between two binary opinion states, driven by peer influence and noisy external information. Through both memory-less and memory-based implementations, we identify a critical threshold of social sensitivity that separates an ergodic phase--where agents collectively track the external signal--from a non-ergodic phase characterized by persistent consensus and reduced adaptability to external changes. Analytical results and simulations reveal that memory in decision-making smooths the transition and lowers the critical threshold for ergodicity breaking. Extending the model to various network structures confirms the robustness of the observed phase transition. We further discuss empirical methodologies for estimating the critical threshold and show how the model may be applied to real-world domains. Our findings contribute to understanding how social conformity, memory effects and randomness jointly shape collective behaviour, with implications for predicting social tipping points and influencing large-scale social dynamics.