. so c - ph ] 2 8 Ju l 2 00 5 Binary and Multivariate Stochastic Models of Consensus Formation

Introduction A current paradigm in computer simulation studies of social sciences problems by physicists is the emergence of consensus [1, 2, 3, 4, 5, 6]. 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. The latter is called a polarized state. An important issue is to identify mechanisms producing a polarized state in spite of general convergent dynamics. When the agents are spatially distributed this problem shares many characteristics with the problem of domain growth in the kinetics of phase transitions [7]: Consensus emerges when a single spatial domain grows occupying the whole system, while polarization corresponds to a situation in which the system does not order and different spatial domains compete. We consider here stochastic dynamic models naturally studied by computer simulations. We will first review some basic results for the voter model [8]. This is a binary option stochastic model, and probably the simplest model of collective behavior. We focus on the dynamical effect of who interacts with whom, that is on the consequences of different networks of interaction. The fact whether consensus is reached or not depends on characteristics of the network such as dimensionality. Next we consider a model proposed by Axelrod [9] for the dissemination of culture. This model can be considered as a multivariable elaboration of the voter model dynamics. Time scales of evolution scale with system size in this model in the same way as for the voter model. We also discuss for this model the role of different networks of interaction. Finally we consider the effect of exogenous stochastic perturbations that account for cultural drift.