Opinion formation models on a gradient

TL;DR

This paper investigates opinion formation models influenced by spatial cultural gradients, revealing that opinion clusters often follow standard percolation universality, but some models exhibit different transition scaling and cluster behaviors.

Contribution

It demonstrates how a spatial gradient affects opinion cluster formation and clarifies the universality class of these clusters, resolving recent debates.

Findings

Opinion clusters are typically in the standard percolation universality class.

The transition width scales as g^{-1/4} in some models.

Cluster size distribution can be consistent with first-order percolation.

Abstract

Statistical physicists have become interested in models of collective social behavior such as opinion formation, where individuals change their inherently preferred opinion if their friends disagree. Real preferences often depend on regional cultural differences, which we model here as a spatial gradient $g$ in the initial opinion. The gradient does not only add reality to the model. It can also reveal that opinion clusters in two dimensions are typically in the standard (i.e.\ independent) percolation universality class, thus settling a recent controversy about a non-consensus model. However, using analytical and numerical tools, we also present a model where the width of the transition between opinions scales $\propto g^{-1/4}$, not $\propto g^{-4/7}$ as in independent percolation, and the cluster size distribution is consistent with first-order percolation.