Phase Transition and Pattern Formation in a Model of Collective Choice Dynamics

We present a model for the emergence of collective decision in a system composed of interacting agents, each of whom is free to choose one of two possible alternatives at every time instant. The choice of each agent is influenced by those of its neighbors, as well as by its personal preference. The agent's preference, in turn, is not fixed, but adjusts to changing circumstances, based on the choices it has made previously (adaptation), as well as whether such choices accorded with those of the majority (learning). We observe a phase transition in the distribution of the collective decision in the presence of learning dynamics. The system gets polarized although individuals may continue to alternate among the choices. This indicates the existence of long-range correlations among the behavior of agents, and is observed in two-dimensional lattices as spatial patterns in the shape of vortices or spirals. Results of our model corroborate with empirical data on movie popularity, financial markets and voting behavior.