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.