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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 14: Social Systems, Opinion and Group Formation
SOE 14.1: Vortrag
Donnerstag, 19. März 2020, 11:30–11:45, GÖR 226
Consensus and diversity in multi-state noisy voter models — •Tobias Galla1,2 and Francisco Herrerías-Azcué2 — 1Instituto de Fisica Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), 07122 Palma de Mallorca, Spain — 2Theoretical Physics, Department of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK
We study a variant of the voter model with multiple opinions; individuals can imitate each other and also change their opinion randomly in mutation events. We focus on the case of a population with all-to-all interaction. A noise-driven transition between regimes with multi-modal and unimodal stationary distributions is observed. In the former, the population is mostly in consensus states; in the latter opinions are mixed. We derive an effective death-birth process, describing the dynamics from the perspective of one of the opinions, and use it to analytically compute marginals of the stationary distribution. These calculations are exact for models with homogeneous imitation and mutation rates, and an approximation if rates are heterogeneous. Our approach can be used to characterize the noise-driven transition and to obtain mean switching times between consensus states. We also discuss the influence of zealots on the transition between unimodal and multi-modal stationary distributions.
Reference: Francisco Herrerías-Azcué, Tobias Galla, Phys. Rev. E 100, 022304 (2019)