Regensburg 2022 – scientific programme

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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 5: Social Systems, Opinion and Group Dynamics

SOE 5.4: Talk

Monday, September 5, 2022, 13:15–13:30, H11

Ordering dynamics and path to consensus in multi-state voter models — Lucía Ramirez, Maxi San Miguel, and •Tobias Galla — Instituto de Física Interdisciplinary Sistemas Complejos, IFISC (CSIC-UIB), Campus Universitat Illes Balears, E-07122 Palma de Mallorca, Spain

We investigate the time evolution of the density of active interfaces and of the entropy of the distribution of agents among opinions in multi-state voter models. Individual realisations undergo a sequence of extinctions until consensus is reached. After each elimination the population remains in a meta-stable state. The density of active interfaces and the entropy in these states varies from realisation to realisation. Making some simple assumptions we are able to analytically calculate the average density of active interfaces and the average entropy in each of these states. We also show that, averaged over realisations, the density of active interfaces decays exponentially, with a time scale set by the size and geometry of the interaction graph, but independent of the initial number of opinion states. The decay of the average entropy is exponential only at long times when there are at most two opinions left in the network. Finally, we show how meta-stable states comprised of only a subset of opinions can be engineered as genuinely stationary states by introducing precisely one zealot in each of the prevailing opinions.