We consider a nonlinear kinetic equation of Boltzmann type, which takes into account the influence of conviction during the formation of opinion in a system of agents, which interact through the binary exchanges, introduced by Toscani [G. Toscani, Commun. Math. Sci. 4, 481 (2006)]. The original exchange mechanism, which is based on the human tendency to compromise and change of opinion through self-thinking, is here modified in the parameters of the compromise and diffusion terms, which now are assumed to depend on the personal degree of conviction. The numerical simulations show that the presence of conviction has the potential to break symmetry, and to produce clusters of opinions. The model is partially inspired by the recent work [L. Pareschi and G. Toscani, Phil. Trans. R. Soc. A 372, 20130396 (2014)], in which the role of knowledge in the formation of wealth distribution has been investigated.

• Received 1 April 2015

DOI:https://doi.org/10.1103/PhysRevE.92.052818