CULTURAL EVOLUTION IN A LATTICE: THE MAJORITY-VOTE MODEL AS A FREQUENCY-DEPENDENT BIAS MODEL OF CULTURAL TRANSMISSION

摘要

The pertinence of culture for understanding the hominid evolutionary process has been persuasively advocated by many authors using the biological concept of niche construction. Hence understanding how opinions and, more generally, cultural traits disseminate through a population is crucial to fully comprehend human evolution. Of particular interest here is the understanding of the mechanisms that lead to the appearance of stable domains characterized by distinct cultural traits, given that people's beliefs have a tendency to become more similar to each other's as people interact repeatedly. Here we study an extreme version of the frequency-dependent bias model in which an individual adopts the trait/opinion shared by the majority of its neighbors - the majority-vote rule model. We assume that the individuals are fixed in the sites of a square lattice of linear size L and that they can interact with their four nearest neighbors only. Within a mean-field framework, we derive the equations of motion for the density of individuals adopting a particular opinion in the single-site and pair approximations. Although the single-site approximation predicts a single cultural domain that takes over the entire lattice, the pair approximation yields a qualitatively correct picture with the coexistence of different opinions and a strong dependence on the initial conditions. In addition, extensive Monte Carlo simulations indicate the existence of a rich distribution of cultural domains or clusters, the number of which grows with L2 whereas the size of the largest cluster grows with In L. The analysis of the sizes of the cultural domains shows that they obey a power-law distribution for not too large sizes but they are exponentially distributed in the asymptotic limit.