Diversity in Axelrod's social adaptation model

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.