Signs of universality in the structure of culture

Abstract

Abstract. Understanding the dynamics of opinions, preferences and of culture as whole requires more use of empirical data than has been done so far. It is clear that an important role in driving this dynamics is played by social influence, which is the essential ingredient of many quantitative models. Such models require that all traits are fixed when specifying the "initial cultural state". Typically, this initial state is randomly generated, from a uniform distribution over the set of possible combinations of traits. However, recent work has shown that the outcome of social influence dynamics strongly depends on the nature of the initial state. If the latter is sampled from empirical data instead of being generated in a uniformly random way, a higher level of cultural diversity is found after long-term dynamics, for the same level of propensity towards collective behavior in the short-term. Moreover, if the initial state is randomized by shuffling the empirical traits among people, the level of long-term cultural diversity is in-between those obtained for the empirical and uniformly random counterparts. The current study repeats the analysis for multiple empirical data sets, showing that the results are remarkably similar, although the matrix of correlations between cultural variables clearly differs across data sets. This points towards robust structural properties inherent in empirical cultural states, possibly due to universal laws governing the dynamics of culture in the real world. The results also suggest that this dynamics might be characterized by criticality and involve mechanisms beyond social influence.

Ultrametricity increases the predictability of cultural dynamics

“…If the distance d ij between their cultural vectors is smaller than ω and if these vectors are different with respect to at least one feature, then an interaction successfully occurs with probability 1−d ij : one of the agents switches its trait to match the trait of the other agent, with respect to one of the features that differentiates between them. This is exactly the model used in [15,17,18] and partly in [16]. As anticipated in sections 1 and 2, this model converges to a random final, absorbing state, one that consists of groups (cultural domains) of internally identical and externally non-interacting cultural vectors-distances within such groups are zero, while distances across are larger or equal to ω, as illustrated at the bottom of figure 1.…”

“…In practice, an ultrametric representation can be produced as the output of a hierarchical clustering algorithm applied to a matrix of pairwise distances between objects [19]. For the purpose of this work, these objects are the cultural vectors, whose pairwise cultural distances are computed in the same manner as in [15][16][17][18], based on a combination between the Hamming distance and the Manhattan distance, which are used in association with nominal and ordinal cultural featues, respectively-also see equation (A2) and the associated description for more details. The following explanations concerning ultrametricity are mostly restricted to cultural vectors, although many of the concepts have a wide range of applicability.…”

“…However, any ultrametric, shuffled or random state is generated in a stochastic way, conditionally on a given empirical state, so one could say that these three classes are composite, each one being a collection of statistical ensembles, one for each empirical state. Most of this study focuses on an empirical cultural state constructed from Eurobarometer 38.1 [25,26] data (collected via face-to-face interviews with people in the EU), formatted according to the procedure in [17], whose cultural features are associated to survey questions dealing with opinions on various topics concerning science, technology, the environment and the European community. The associated ultrametric cultural state is generated using the new procedure mentioned in section 2 and explained in detail in appendix A, which retains, in a certain sense, the empirical ultrametric structure.…”

“…On the other hand, recent studies have investigated the model starting from different classes of initial conditions, beyond the uniformly random one. In particular, emphasis has been put on using initial conditions constructed from empirical data [15][16][17] and their randomized, trait-shuffled counterparts-obtained by randomly shuffling, for each component of the cultural vectors, the empirical values (traits) of all individuals in the sample. These studies have emphasized a strong dependence of the final outcome on the initial conditions.…”

“…For instance, certain model outcomes that have an interesting interpretation in terms of enabling the coexistence of short-term social collective behavior and long-term cultural diversity [15] (more details are provided later in this paper) are found to vary significantly across the classes of empirical, trait-shuffled, and uniformly random initial conditions, while remaining largely stable when considering different instances belonging to the same class. This stability implies that empirical cultural data share certain remarkably universal properties, independent of the specific sample considered and at the same time significantly different from those exhibited by random and randomized data [17]. This has stimulated the introduction of stochastic, structural models aimed at capturing the essential properties of the empirical cultural data [16,18].…”