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In this paper we investigate the possibility of reducing the complexity of asystem composed of a large number of interacting agents, whose dynamics featurea symmetry breaking. We consider first order stochastic differential equationsdescribing the behavior of the system at the particle (i.e., Lagrangian) leveland we get its continuous (i.e., Eulerian) counterpart via a kineticdescription. However, the resulting continuous model alone fails to describeadequately the evolution of the system, due to the loss of granularity whichprevents it from reproducing the symmetry breaking of the particle system. Bysuitably coupling the two models we are able to reduce considerably thenecessary number of particles while still keeping the symmetry breaking andsome of its large-scale statistical properties. We describe such a multiscaletechnique in the context of opinion dynamics, where the symmetry breaking isinduced by the results of some opinion polls reported by the media.

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