  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.
