Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise

TL;DR

This paper presents an agent-based model where opinions and social positions co-evolve under multiplicative noise, revealing how feedback loops influence group formation and consensus, supported by simulations and PDE analysis.

Contribution

It introduces a novel co-evolving opinion and social dynamics model with multiplicative noise, including a PDE approximation validated by numerical simulations.

Findings

Emergence of group formation and opinion consensus

PDE model accurately approximates the agent-based model

Feedback loops significantly influence social and opinion dynamics

Abstract

We introduce an agent-based model for co-evolving opinion and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents' movements are governed by positions and opinions of other agents and similarly, the opinion dynamics is influenced by agents' spatial proximity and their opinion similarity. Using numerical simulations and formal analysis, we study this feedback loop between opinion dynamics and mobility of agents in a social space. We investigate the behavior of this ABM in different regimes and explore the influence of various factors on appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution and in the limit of infinite number of agents we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples we show that a resulting PDE model is a good approximation of the original ABM.