Phase change in an opinion-dynamics model with separation of time scales

TL;DR

This paper introduces a 1D opinion dynamics model with agents whose opinions evolve through local interactions and occasional position exchanges, revealing a phase transition in undecided individuals driven by the frequency of these exchanges.

Contribution

It presents a novel opinion formation model with separated time scales for opinion updates and agent relocations, uncovering a phase change in opinion consensus.

Findings

Discovered a phase transition in the number of undecided agents.

Frequent agent exchanges lead to frustration in opinion formation.

Mean field analysis supports the phase transition phenomenon.

Abstract

We define an opinion formation model of agents in a 1d ring, where the opinion of an agent evolves due to its interactions with close neighbors and due to its either positive or negative attitude toward the overall mood of all the other agents. While the dynamics of the agent's opinion is described with an appropriate differential equation, from time to time pairs of agents are allowed to change their locations to improve the homogeneity of opinion (or comfort feeling) with respect to their short range environment. In this way the time scale of transaction dynamics and that of environment update are well separated and controlled by a single parameter. By varying this parameter we discovered a phase change in the number of undecided individuals. This phenomenon arises from the fact that too frequent location exchanges among agents result in frustration in their opinion formation. Our mean field analysis supports this picture.