Phase Transition in Democratic Opinion Dynamics

Consider a community where initially, each individual is positive or negative regarding a reform proposal. In each round, individuals gather randomly in fixed rooms of different sizes, and all individuals in a room agree on the majority opinion in the room (with ties broken in favor of the negative opinion). The Galam model---introduced in statistical physics, specifically sociophysics---approximates this basic random process. We approach the model from a more mathematical perspective and study the threshold behavior and the consensus time of the model.