Interplay between media and social influence in the collective behavior of opinion dynamics

Messages conveyed by media act as a major drive in shaping attitudes and inducing opinion shift. On the other hand, individuals are strongly affected by peer pressure while forming their own judgment. We solve a general model of opinion dynamics where individuals either hold one of two alternative opinions or are undecided and interact pairwise while exposed to an external influence. As media pressure increases, the system moves from pluralism to global consensus; four distinct classes of collective behavior emerge, crucially depending on the outcome of direct interactions among individuals holding opposite opinions. Observed nontrivial behaviors include hysteretic phenomena and resilience of minority opinions. Notably, consensus could be unachievable even when media and microscopic interactions are biased in favor of the same opinion: The unfavored opinion might even gain the support of the majority.