C. E. La Rocca, L. A. Braunstein, F. Vazquez, EPL 106, 40004 (2014)
We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number k that expresses its level of agreement on a given issue, from totally against k = −M to totally in favor k = M. Same-orientation agents persuade each other with probability p, becoming more extreme, while opposite-orientation agents become more moderate as they reach a compromise with probability q. The population initially evolves to (a) a polarized state for r = p/q > 1, where opinions’ distribution is peaked at the extreme values k = ±M, or (b) a centralized state for r < 1, with most opinions around k = ±1. When r >> 1, polarization lasts for a time that diverges as r M ln N, where N is the population’s size. Finally, an extremist consensus (k = M or −M) is reached in a time that scales as r -1 for r << 1.