# Reducing complexity of multiagent systems with symmetry breaking: an application to opinion dynamics with polls

## TL;DR

This paper presents a multiscale approach combining particle and continuous models to efficiently simulate large multiagent systems with symmetry breaking, demonstrated through opinion dynamics influenced by polls.

## Contribution

It introduces a coupled multiscale modeling technique that reduces particle number requirements while preserving symmetry breaking in opinion dynamics.

## Key findings

- Coupled models effectively reproduce symmetry breaking.
- Reduced particle count maintains large-scale statistical properties.
- Method applicable to opinion dynamics influenced by media polls.

## Abstract

In this paper we investigate the possibility of reducing the complexity of a system composed of a large number of interacting agents, whose dynamics feature a symmetry breaking. We consider first order stochastic differential equations describing the behavior of the system at the particle (i.e., Lagrangian) level and we get its continuous (i.e., Eulerian) counterpart via a kinetic description. However, the resulting continuous model alone fails to describe adequately the evolution of the system, due to the loss of granularity which prevents it from reproducing the symmetry breaking of the particle system. By suitably coupling the two models we are able to reduce considerably the necessary number of particles while still keeping the symmetry breaking and some of its large-scale statistical properties. We describe such a multiscale technique in the context of opinion dynamics, where the symmetry breaking is induced by the results of some opinion polls reported by the media.