Binary and Multivariate Stochastic Models of Consensus Formation

A current paradigm in computer simulation studies of social sciences problems by physicists is the emergence of consensus. The question is to establish when the dynamics of a set of interacting agents that can choose among several options (political vote, opinion, cultural features, etc.) leads to a consensus in one of these options, or when a state with several coexisting social options prevail. We consider here stochastic dynamic models naturally studied by computer simulations. We will first review some basic results for the voter model. This is a binary option stochastic model, and probably the simplest model of collective behavior. Next we consider a model proposed by Axelrod for the dissemination of culture. This model can be considered as a multivariable elaboration of the voter model dynamics.