Contrarian Majority Rule Model with External Oscillating Propaganda and Individual Inertias

Abstract

We study the Galam majority rule dynamics with contrarian behavior and an oscillating external propaganda in a population of agents that can adopt one of two possible opinions. In an iteration step, a random agent interacts with three other random agents and takes the majority opinion among the agents with probability p(t) (majority behavior) or the opposite opinion with probability 1−p(t) (contrarian behavior). The probability of following the majority rule p(t) varies with the temperature T and is coupled to a time-dependent oscillating field that mimics a mass media propaganda, in a way that agents are more likely to adopt the majority opinion when it is aligned with the sign of the field. We investigate the dynamics of this model on a complete graph and find various regimes as T is varied. A transition temperature Tc separates a bimodal oscillatory regime for T<Tc, where the population’s mean opinion m oscillates around a positive or a negative value from a unimodal oscillatory regime for T>Tc in which m oscillates around zero. These regimes are characterized by the distribution of residence times that exhibit a unique peak for a resonance temperature T*, where the response of the system is maximum. An insight into these results is given by a mean-field approach, which also shows that T* and Tc are closely related.

Aging in Some Opinion Formation Models: A Comparative Study

“…Similar ideas appear in other areas. In the context of opinion formation, for example, one expects, on the one hand, that social influences reduce differences between individuals via social contagion, but, on the other, interactions can also produce differentiation via repulsive forces, associated with anticonformist "contrarian" agents that tend to deviate from the behavior adopted by the neighbors in the network of connections [6,7]. Another example is Galam's model for minority opinion spread [8,9] that, although based on local majority rule, can lead to the hostile minority views having an advantage.…”