Regensburg 2025 – scientific programme

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 4: Urban systems, Scaling, and Social Systems

SOE 4.6: Talk

Tuesday, March 18, 2025, 11:15–11:30, H45

The noisy voter model with complete and partial aging — •Raul Toral — Institute for Cross-Disciplinary Physics and Complex Systems IFISC (CSIC-UIB), Campus UIB, 07122 Palma de Mallorca, Spain

Many agent-based models of social interaction use the Markovian assumption, namely that the transition rates from one to another state depend only on the current state of the system and not on its previous history. This, being obviously wrong in many situations, it is widely used because of its mathematical simplicity. In this work, I will consider the effect that a particular non-Markovian effect, known in the literature as “aging” or “inertia” has on the paradigmatic noisy voter model. This is a widely used model in social and economics situations to describe transitions to consensus or synchronized behavior. While the standard version of the model displays a discontinuous change of behavior from unsynchronized to consensus as a function of a parameter which depends on the free-will, or tendency to act independently on the neighbors, this transition is size-dependent and disappears in the thermodynamic limit. I will show that a genuine -second order- phase transition can appear as a consequence of aging, modeled as a reluctance to change state as a function of the length of time that has been spent in the current state. We investigate the situation where aging acts on both socially influenced and random opinion changes (complete aging), and compare it with previous results where aging acts only on pairwise interactions (partial aging).

Keywords: Voter model; non-Markovian effects; Aging