Opinion inertia and coarsening in the persistent voter model.

Abstract

We consider the persistent voter model (PVM), a variant of the voter model (VM) that includes transient, dynamically induced zealots. Due to peer reinforcement, the internal confidence η_{i} of a normal voter increases in steps of size Δη. Once it surpasses a given threshold, it becomes a zealot. Its opinion remains frozen until enough interactions with the opposing opinion occur, resetting its confidence. No longer a zealot, the regular voter may change opinion once again. This mechanism of opinion inertia, though simplified, is responsible for an effective surface tension, and the PVM exhibits a crossover from a fluctuation-driven dynamics, as in the VM, to a curvature-driven one, akin to the Ising model at low temperature. The average time τ to attain consensus is nonmonotonic with respect to Δη and reaches a minimum at Δη_{min}. In this paper we elucidate the mechanisms that accelerate the system towards consensus close to Δη_{min}. Near the crossover at Δη_{min}, the intermediate region around the domains where the regular voters accumulate (the active region, AR) is large. The surface tension, albeit small, is sufficient to maintain the shape and reduce the domain fragmentation. The large size of the AR in the region of Δη_{min} has two important effects that accelerate the dynamics. First, it dislodges the zealots within the bulk of the domains. Secondly, it maximally suppresses the formation of slowly evolving stripes typical in Ising-like models. This suggests the importance of understanding the role of the AR, where opinion changes are facilitated, and the interplay between regular voters and zealots in disrupting polarized states.