The influence of persuasion in opinion formation and polarization - la Rocca, Cristian Ernesto (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 $r=p/q\gt 1$ , 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 $r \gg 1$ , 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 $r \ll 1$.