Diversity in Axelrod's social adaptation model

TL;DR

This paper analyzes Axelrod's social adaptation model, revealing that cultural diversity peaks at the phase transition point and that multiculturalism does not necessarily equate to high cultural diversity.

Contribution

It introduces the concept of Cultural Diversity $D$ and links it to phase transitions, providing new insights into the complexity of social dynamics in Axelrod's model.

Findings

Maximum cultural diversity occurs at the critical point.

Entropy peaks at the phase transition, indicating an order-order transition.

Multiculturalism is not equivalent to cultural diversity.

Abstract

In this paper, we study Axelrod's model of social dynamics, introducing the concept of Cultural Diversity ($D$), defined as the variety of sizes of clusters or cultural domains formed, which measures the complexity of the system. We find that the maximum of $D$ agrees with the critical point where the monocultural/multicultural phase transition occurs, tending to a minimum value when the system's degrees of freedom, cultural traits $q$, are far from the critical point $q_c$. We show that at $q_c$ the entropy also reaches its maximum value, that is, the phase transition for this model is of the order-order type. Thus, multiculturalism is not synonymous with cultural diversity, as is commonly assumed in the literature.