Irrelevance of information outflow in opinion dynamics models

TL;DR

This paper demonstrates that the Sznajd opinion dynamics model's unique outflow feature is not fundamentally different from other models by introducing a generalized dynamics that produces similar results, and derives exact probabilities in one dimension.

Contribution

It introduces a generalized Glauber-type dynamics showing the irrelevance of outflow in opinion models and derives exact exit probabilities for the one-dimensional case.

Findings

Generalized dynamics match Sznajd model results

Exact exit probability derived in 1D

Questions raised about analytical approximation methods

Abstract

The Sznajd model for opinion dynamics has attracted a large interest as a simple realization of the psychological principle of social validation. As its most salient feature, it has been claimed that the Sznajd model is qualitatively different from other ordering processes, because it is the only one featuring outflow of information as opposed to inflow. We show that this claim is unfounded by presenting a generalized zero-temperature Glauber-type of dynamics which yields results indistinguishable from those of the Sznajd model. In one-dimension we also derive an exact expression for the exit probability of the Sznajd model, that turns out to coincide with the result of an analytical approach based on the Kirkwood approximation. This observation raises interesting questions about the applicability and limitations of this approach.