Persistent individual bias in a voter model with quenched disorder

TL;DR

This paper investigates how individual biases can persist over time in a voter model with fixed heterogeneity and antagonistic relationships, revealing that sparse and heterogeneous interactions can sustain long-term opinion biases at the individual level.

Contribution

It introduces a modified voter model incorporating quenched disorder and antagonistic links, showing how these factors enable persistent individual biases.

Findings

Long-lived individual biases arise from network sparsity and heterogeneity.

Eigenvalue spectrum analysis explains the conditions for sustained biases.

Population-averaged bias may not reflect individual-level dynamics.

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.