Computational approaches to studying the broader social context can be found in work on the emergence and diffusion of communities in cultural system. Spicer makes an anthropological appeal for the study of such systems, arguing that cultural change can only be properly considered in relation to more stable elements of culture. These persistent cultural elements, he argues, can best be understood as ‘identity systems,’ in which individuals bestow meaning to symbols. Spicer notes that there are collective identity systems (i.e., culture) as well as individual systems, and chooses to focus his attention on the former. Spicer talks about these systems in implicitly network terms: identity systems capture “relationships between human beings and their cultural products” (Spicer, 1971). To the extent that individuals share the same relationships with the same cultural products, they are united under a common culture; they are, as Spicer says, “a people.”
Axelrod presents a more robust mathematical model for studying these cultural systems. Similar to Schelling’s dynamic models of segregation, Axelrod imagines individuals interacting through processes of social influence and social selection (Axelrod, 1997). Agents are described with n-length vectors, with each element initialized to a value between 0 and m. The elements of the vector represent cultural dimensions (features), and the value of each element represents an individual’s state along that dimension (traits). Two individuals with the exact same vector are said to share a culture, while, in general, agents are considered culturally similar to the extent to which they hold the same trait for the same feature. Agents on a grid are then allowed to interact: two neighboring agents are selected at random. With a probability equal to their cultural similarity, the agents interact. An interaction consists of selecting a random feature on which the agents differ (if there is one), and updating one agent’s trait on this feature to its neighbor’s trait on that feature. This simple model captures both the process of choice homophily, as agents are more likely to interact with similar agents, and the process of social influence, as interacting agents become more similar over time. Perhaps the most surprising finding of Axelrod’s approach is just how complex this cultural system turns out to be. Despite the model’s simple rules, he finds that it is difficult to predict the ultimate number of stable cultural regions based on the system’s n and m parameters.
This concept of modeling cultural convergence through simple social processes has maintained a foothold in the literature and has been slowly gaining more widespread attention. Bednar and Page take a game theoretic approach, imagining agents who must play multiple cognitively taxing games simultaneously. Their finding that in these scenarios “culturally distinct behavior is likely and in many cases unavoidable” (Bednar & Page, 2007) is notable because classic game-theoretic models fail to explain the emergence of culture at all: rather rational agents simply maximize their utility and move on. In their simultaneous game scenarios, however, cognitively limited agents adopt the strategies that can best be applied across the tasks they face. Cultures, then, emerge as “agents evolve behaviors in strategic environments.” This finding underscores Granovetter’s argument of embeddedness (M. Granovetter, 1985): distinctive cultures emerge because regional contexts influence adaptive choices, which in turn influence an agent’s environment.
Moving beyond Axelrod’s grid implementation, Flache and Macy (Flache & Macy, 2011) consider agent interaction on the small world network proposed by Watts and Strogatz (Watts & Strogatz, 1998). This model randomly rewires a grid with select long-distance ties. Following Granovetter’s strength of weak ties theory (M. S. Granovetter, 1973), the rewired edges in the Watts-Strogatz model should bridge clusters and promote cultural diffusion. Flache and Macy also introduce the notion of the valiance of interaction, considering social influence along dimensions of assimilation and differentiation, and taking social selection to consist of either attraction or xenophobia. In systems with only positively-valenced interaction (assimilation and attraction), they find that the ‘weak’ ties have the expected result: cultural signals diffuse and the system tends towards cultural integration. However, introduction of negatively valenced interactions (differentiation and xenophobia), leads to cultural polarization; resulting in deep disagreement between communities which themselves have high internal consensus.