Reducing Complexity of Multiagent Systems with Symmetry Breaking: An Application to Opinion Dynamics with 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.2010 Mathematics Subject Classification. 35Q20, 35Q84, 35Q91.

Hydrodynamic Models of Preference Formation in Multi-agent Societies

“…In conclusion, with the non-symmetric function P given by (18) we fully characterise the asymptotic distribution function as:…”

“…The preference, which is driven by, but need not coincide with, the opinion, is here understood as representative of the choice that an agent makes among some possible options, such as e.g. some candidates in an election or yes/no in a referendum [18]. As such, and unlike the opinion, the preference evolves towards necessarily polarised states, which reflect the available options.…”

Opinion modeling on social media and marketing aspects

“…Unlike classical modeling of opinion formation in a multi-agent society [5,10,12,13,16,36], where agents are considered indistinguishable, here we will take into account a further parameter, the network range, or connectivity, of the agents, which can be reasonably measured in terms of followers. Highly connected agents are identified as influencers, because, thanks to their large number of followers, their opinions can reach and influence many other users of the social media [20].…”

An interface-free multi-scale multi-order model for traffic flow

“…In this case, at the macroscopic level the flow is given by the classical LWR flux function f , while at the microscopic level the mass instantaneously (dis)appears at the passage of vehicles through the boundaries. The parameter θ is intended for tuning the contribution of the micro-and macro-scale, in the same spirit of [10,11,12,13,15]. Here we expect that large values of θ reduce the oscillations due to abrupt passage of microscopic vehicles across boundaries, while small values of θ increase the effectiveness of second-order dynamics.…”

“…In the framework of conservation laws and traffic flow models the conservation of the total mass is a crucial property which must be preserved at the discrete level. The multi-scale scheme (15) can be easily written in conservative form [38], therefore it preserves the mass.…”