Pair approximation for the noisy threshold $q$-voter model

Abstract

In the standard $q$-voter model, a given agent can change its opinion only if there is a full consensus of the opposite opinion within a group of influence of size $q$. A more realistic extension is the threshold $q$-voter, where a minimal agreement (at least $0<q_0\le q$ opposite opinions) is sufficient to flip the central agent's opinion, including also the possibility of independent (non conformist) choices. Variants of this model including non-conformist behavior have been previously studied in fully connected networks (mean-field limit). Here we investigate its dynamics in random networks. Particularly, while in the mean-field case it is irrelevant whether repetitions in the influence group are allowed, we show that this is not the case in networks, and we study the impact of both cases, with or without repetition. Furthermore, the results of computer simulations are compared with the predictions of the pair approximation derived for uncorrelated networks of arbitrary degree distributions.

arXiv comment13 pages, 12 figures

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• Spontaneous symmetry breaking of active phase in coevolving nonlinear voter model
• Species exclusion and coexistence in a noisy voter model with a competition-colonization tradeoff
• Ferromagnetic and spin-glass like transition in the $q$-neighbor Ising model on random graphs
• The threshold model with anticonformity under random sequential updating
• Nonlinear $q$-voter model involving nonconformity on networks
• $Q$-voter model with independence on signed random graphs: homogeneous approximations
• The $q$-neighbor Ising model on multiplex networks with partial overlap of nodes
• Large population limits of Markov processes on random networks
• Shannon information criterion for low-high diversity transition in Moran and Voter models
• When heterogeneity drives hysteresis: Anticonformity in the multistate $q$-voter model on networks
• Complete aging in the noisy voter model enhances consensus formation
• Competition between private and expressed opinions in binary choice: the $\alpha$-EPO $q$-voter model
• When Does Population Diversity Matter? A Unified Framework for Binary-Choice Dynamics