Kinetic models of opinion formation in the presence of personal conviction

TL;DR

This paper introduces a kinetic opinion formation model incorporating personal conviction, showing through simulations that conviction influences opinion clustering and symmetry breaking, extending previous models by linking conviction to opinion dynamics.

Contribution

The paper develops a modified kinetic model where conviction affects exchange parameters, revealing its role in opinion clustering and symmetry breaking, which was not addressed in prior models.

Findings

Conviction influences the formation of opinion clusters.

The model demonstrates symmetry breaking due to conviction.

Numerical simulations confirm the impact of conviction on opinion dynamics.

Abstract

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.