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 in [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, 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.Comment: arXiv admin note: text overlap with arXiv:1401.455
