Persistent individual bias in a voter model with quenched disorder

Abstract

Many theoretical studies of the voter model (or variations thereupon) involve order parameters that are population-averaged. While enlightening, such quantities may obscure important statistical features that are only apparent on the level of the individual. In this work, we ask which factors contribute to a single voter maintaining a long-term statistical bias for one opinion over the other in the face of social influence. To this end, a modified version of the network voter model is proposed, which also incorporates quenched disorder in the interaction strengths between individuals and the possibility of antagonistic relationships. We find that a sparse interaction network and heterogeneity in interaction strengths give rise to the possibility of arbitrarily long-lived individual biases, even when there is no population-averaged bias for one opinion over the other. This is demonstrated by calculating the eigenvalue spectrum of the weighted network Laplacian using the theory of sparse random matrices.

arXiv comment15 pages, 7 figures

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• Eigenvalue spectra and stability of directed complex networks
• Consensus, polarisation and coexistence in a continuous opinion dynamics model with quenched disorder
• Pair approximation for the q-voter models with quenched disorder on networks
• $Q$-voter model with independence on signed random graphs: homogeneous approximations
• When heterogeneity drives hysteresis: Anticonformity in the multistate $q$-voter model on networks
• A path integral approach to sparse non-Hermitian random matrices