By integrating multilateral social influence with Axelrod’s original postulation of homophily, Flache et al [ 21 ] proposed, to the best of our knowledge, the thus far most successful model, facilitating the emergence of cultural diversity and stabilizing Axelrod’s original model [ 5 ] against the two sources of noise. It will therefore serve, along with Axelrod's model, as a comparison point in our results.

Finally, Axelrod’s original idea of testing the model against random noise was implemented, in the form of "mutation rates" [ 20 , 23 ], and later, “selection error” [ 21 ]. Klemm et al [ 23 , 24 ] introduced various rates of noise into Axelrod's model and found that even at the smallest rate of perturbations, the model quickly destabilized and converged into a monoculture without any diversity, while at a larger rate of perturbation, it devolved into anomie, the complete cultural isolation of each individual from their neighbors [ 25 , 26 ]. The “selection error”, which is based on the assumption of an occasional perception error of a neighbour’s similarity (or dissimilarity), was added to cultural drift as another level of noise, and produced a similar instability [ 21 ].

In recent research, mass media has been shown to increase cultural diversity when the mass media messages are strong enough, whereas weaker messages were more likely to lead to global homogeneity [ 18 , 19 ]. A change in geography, such as modelling mountains that minimize contact between groups of agents, increased levels of diversity as well [ 20 ]. The types of interaction between agents have been also explored: while in Axelrod’s original model, interactions were of dyadic nature, i.e. individuals interacted with and influenced each other on one-on-one basis, Parisi et al [ 20 ] and Flache et al [ 21 ] implemented multilateral social influence models based on Richardson et al [ 22 ], in which agents consider opinions of multiple neighbors around them (instead of just one), before changing their traits.

He found that cultural diversity emerges and persists under homophily, because groups of agents with similar characteristics grow more similar inside each group, until the groups don't share any common characteristics. Once complete dissimilarity between two groups is reached, they no longer interact. Initial parameters, such as population size, neighbourhood interaction size, and number of cultural features and traits, impacted the emergence of cultural diversity, for example, a smaller population size was conducive to diversity, while an increase in neighbourhood size increased cultural homogeneity [ 5 , 17 ].

One example of a social process that has yielded valuable insights is homophily, the principle of "like attracts like": the higher the similarity between two individuals, the more likely they are to influence each other [ 13 , 14 ]. Schelling used this idea to show that a small "dislike" for a dissimilar neighbor could lead to complete segregation in an agent-based model [ 15 , 16 ]. Following this, Axelrod's seminal paper [ 5 ] introduced an agent-based model that integrated both, the proposed network structure of previous models [ 4 ] and homophily [ 13 ], but instead of looking at segregation by movement like Schelling [ 16 ], he studied segregation by attitude change, in particular the question: when individuals change their values and opinions based on similarities with each other, do cultures become more alike or more diverse?

Formal mathematical models of social influence illustrated that, when everyone in a network is connected, a global monoculture is inevitable—all cultures converge to a global consensus and become homogenous [ 4 , 10 , 11 ]. Cultural simulations, among them artificial societies [ 5 , 12 ], have since then been adopted to facilitate the study of patterns of cultural transmission. They have enhanced our understanding of how diversity and global consensus emerge in societies, and how societies can fluctuate between one and the other, exploring these dynamics by introducing various factors to social influence to find ways by which diversity can be preserved.

In light of inherent tensions in international integration [ 1 ] and a contemporary trend towards cultural policy [ 2 , 3 ], factors that impact cultural globalization and the preservation of diversity have been a recent focus in computational modeling. The question how diversity, i.e. the co-existence of many varied cultures, can be sustained in the face of a growing tendency towards globalization has been explored with various approaches [ 4 – 8 ]. Culture is here construed as the information which is transmitted between individuals in a social manner (such as music, customs, and language). The process of transmission is also known as social influence [ 9 ].

Models of institutions

Following cultural drift, limited communication, terrain effects, technology and broadcasting, with the present paper, we would like to introduce a novel question to extend Axelrod’s original model: what role do institutions play in the emergence and resilience of diversity?

First analyses of institutional influence supposed that a diminishing impact of social institutions on values and behavior would increase individualistic tendencies and could, in extreme cases, lead to anomie [26]. Since then, much research into social institutions has investigated their effects in terms of social networks [27,28] and theory of games approaches, such as prisoner’s dilemma and coordination games [29–31]. Very little research has looked at the impact of institutions on culture and its underlying processes of social influence. To our knowledge, only three major projects have used agent-based models in this context: (1) one study showcases how individuals hide their true beliefs in authoritarian regimes (institutions), and how the regimes are affected by this [32]; (2) one platform exists that allows an integration of information repositories, and lets researchers analyze patterns of cultural dynamics [33], and (3) a line of research exists that investigates mass media influence [18,19,34], which can be interpreted as institutional influence and shows several methodological similarities to ours.

The addition of institutions to an agent-based model of cultural patterns, as we propose, can add insight into processes of cultural diversity emergence and resilience by for example analyzing the impact of varying levels of institutional influence and institutional loyalty on culture. Furthermore, we can analyze the way in which individuals and institutions interact with each other inside different political systems, for example through means of democratic processes (like referenda), or organized dissemination of information (like propaganda), and then explore how this impacts the system’s composition.

In agent based models, the idea of "central authorities" has been mostly excluded from the methodology so far. This might be due to the assumption that they can only play the part of central coordinating agents [5,12]. To the contrary, we would like to establish that central authorities and institutions do not denote the same concept. At the center of institutional research lies the exchange between human autonomy (i.e. the agency in human behavior), and social structure (i.e. influences derived by institutions in society) [35]. Axelrod [5] explicitly excludes powerful authorities from his model because of their absolute coordinating impact on culture (where an authority influences individuals’ beliefs and values, but is not in turn influenced in any way). An example of a previous implementation of central authority is the inclusion of geography, such as a mountain range [20]. It impacts agents’ behaviour (by preventing interaction between neighbourhoods of agents), but cannot be impacted by agents itself.

However, authorities are not necessarily absolute. With our present work, we aim at a use of institutions which exert influence on individuals and govern people's behavior and are in turn influenced by individuals, especially in their creation [36]. We speak of institutions in terms of information centers, i.e. mechanisms of political, economic or social interactions [37]. They can be more formal, such as governments, marriage, organized religion, or informal agreements, such as vegetarianism or spiritual beliefs.

In general, space in which shared information is stored does not need to be tangible, but in artificial representations, there is a need to conceptualize a second level of information that lies beyond first level individual interaction patterns. This idea has been previously applied in cultural algorithms (a branch of evolutionary algorithms) in the way of “belief spaces” [38]. Belief spaces inherit cultural knowledge; they are the storage of agents’ shared beliefs, and are updated as those beliefs change. At the same time, belief spaces have an impact on how the agents evolve alongside each other; they impact who interacts with who and who is influenced in what way. In agent-based models, this particular kind of belief space has been termed a "cultural repository" [33].

In order to illustrate the relationship of these two levels of information storage, let us assume, for example, that Romeo interacts with Juliet, discussing the value of certain types of music. In Axelrod’s model [5], there is only one level: through homophily and social influence, Romeo can be convinced by Juliet that salsa music is better than hard rock, and Romeo and Juliet would then share a common "trait". In our model, both Romeo and Juliet still interact on an individual level, but they also have a belief space that represents the two different institutions that they belong to, for example their respective familial units, House Montague and House Capulet (Fig 1). When Romeo interacts with Juliet, he is not only aware of their interpersonal similarity and their own traits, he is also pressured by how representative his institution (i.e. his family) is of him, and how much influence this has on him. The level of institutional influence that Romeo perceives can prevent him from liking salsa music. He needs to check whether his family approves of salsa music, and if it doesn’t, whether his homophily with Juliet is strong enough to ignore his family.

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larger image TIFF original image Download: Fig 1. Model of institutions, Romeo and Juliet example. "R" represents agent Romeo, "J" represents agent Juliet, "M" and "C" their respective houses, Montague and Capulet. Agents from one cultural region (e.g. yellow, blue) are connected to the institution that they belong to (also colored yellow and blue). https://doi.org/10.1371/journal.pone.0153334.g001

If Romeo does change his trait, because he likes Juliet better than his family, he can then also choose to change his institution, i.e. see if becoming a Capulet will suit him better than being a Montague, as Juliet’s family, the Capulets, might be more representative of who he is than his own family. This choice will depend on Romeo's loyalty towards his family, i.e. how willing he is to give up his family name and connections.

The different levels of institutional influence and agent loyalty can be exemplified by different types of institutions. For example there are institutions that promote strong identification and exert a lot of influence, such as families or nationalities, or those that do less so, such the school one went to, or the TV channels one watches. Individuals can feel varying levels of loyalty to their institutions as well, for example when someone is part of a political party because it has always been this way in their family (conservatism), or when social punishment is normative (e.g. some familial structures or religious organizations).

With all these considerations in mind, we would like to propose our initial research questions: How is the diversity of a system impacted by varying amounts of influence that institutions exert on individuals? How is the system impacted by varying amounts of loyalty that institutions demand from their followers? And how does the inclusion of institutional influence and agent loyalty to an agent-based cultural dissemination model compare with results obtained by Axelrod [5] and Flache et al [21]?