Ultrametric distribution of culture vectors in an extended Axelrod model of cultural dissemination

Abstract

The Axelrod model of cultural diffusion is an apparently simple model that is capable of complex behaviour. A recent work used a real-world dataset of opinions as initial conditions, demonstrating the effects of the ultrametric distribution of empirical opinion vectors in promoting cultural diversity in the model. Here we quantify the degree of ultrametricity of the initial culture vectors and investigate the effect of varying degrees of ultrametricity on the absorbing state of both a simple and extended model. Unlike the simple model, ultrametricity alone is not sufficient to sustain long-term diversity in the extended Axelrod model; rather, the initial conditions must also have sufficiently large variance in intervector distances. Further, we find that a scheme for evolving synthetic opinion vectors from cultural " prototypes" shows the same behaviour as real opinion data in maintaining cultural diversity in the extended model; whereas neutral evolution of cultural vectors does not.