Structural Properties of Realistic Cultural Space Distributions

An interesting sociophysical research problem consists of the compatibility between collective social behavior in the short term and cultural diversity in the long term. Recently, it has been shown that, when studying a model of short term collective behavior in parallel with one of long term cultural diversity, one is lead to the puzzling conclusion that the 2 aspects are mutually exclusive. However, the compatibility is restored when switching from the randomly generated cultural space distribution to an empirical one for specifying the initial conditions in those models. This calls for understanding the extent to which such a compatibility restoration is independent of the empirical data set, as well as the relevant structural properties of such data. Firstly, this work shows that the restoration patterns are largely robust across data sets. Secondly, it provides a possible mechanism explaining the restoration, for the special case when the cultural space is formulated only in terms of nominal variables. The proposed model assumes that a realistic distribution in cultural space is governed by the existence of several "cultural prototype", a hypothesis already used in previous work, provided that every individual's sequence of cultural traits is a combination of the sequences associated to the prototypes. This can be considered indirect empirical evidence in favor of social science theories having inspired the model.