Axelrod Model of Social Influence With Cultural Hybridization

Abstract

Since cultural interactions between a pair of social agents involve changes in both individuals, we present simulations of a new model based on Axelrod's homogenization mechanism that includes hybridization or mixture of the agents' features. In this new hybridization model, once a cultural feature of a pair of agents has been chosen for the interaction, the average of the values for this feature is reassigned as the new value for both agents after interaction. Moreover, a parameter representing social tolerance is implemented in order to quantify whether agents are similar enough to engage in interaction, as well as to determine whether they belong to the same cluster of similar agents after the system has reached the frozen state. The transitions from a homogeneous state to a fragmented one decrease in abruptness as tolerance is increased. Additionally, the entropy associated to the system presents a maximum within the transition, the width of which increases as tolerance does. Moreover, a plateau was found inside the transition for a low-tolerance system of agents with only two cultural features.

Another phase transition in the Axelrod model

“…In a monocultural (ordered) state, S max /L 2 ≈ 1, a single cultural region covers almost the entire lattice; in a multicultural (disordered) state, multiple cultural regions exist. Other order parameters that have been used include the number of cultural domains [1,24], mean density of cultural domains [67], entropy [68], overlap between neighboring sites [63], and activity (number of changes) per agent [69].…”

“…If the features are distributed uniformly from 1 to q, then ρ 0 = 1/q. It is sometimes assumed that the features have a Poisson distribution [5,36,44,67,68] with mean q, so then application of the Skellam distribution gives ρ 0 = e −2q I 0 (2q), where I 0 is a modified Bessel function of the first kind. For the single bond, the number of common features is a binomial random variable, so…”