Giuseppe Toscani, Andrea Tosin, Mattia Zanella
Physical Review E, to appear. Preprint arXiv, 2018.
We introduce and discuss kinetic models of opinion formation on social networks in which the distribution function depends on both the opinion and the connectivity of the agents. The opinion formation model is subsequently coupled with a kinetic model describing the spreading of popularity of a product on the web through a social network. Numerical experiments on the underlying kinetic models show a good qualitative agreement with some measured trends of hashtags on social media websites and illustrate how companies can take advantage of the network structure to obtain at best the advertisement of their products.
Related popularization article for the Italian blog Madd:Math!: La popolarità delle opinioni
Lorenzo Pareschi, Pierluigi Vellucci, Mattia Zanella
Physica A: Statistical Mechanics and its Applications, 10(1):1-32, 2017. Preprint arXiv.
We introduce and discuss kinetic models describing the influence of the competence in the evolution of decisions in a multi-agent system. The original exchange mechanism, which is based on the human tendency to compromise and change opinion through self-thinking, is here modified to include the role of the agents’ competence. In particular, we take into account the agents’ tendency to behave in the same way as if they were as good, or as bad, as their partner: the so-called equality bias. This occurred in a situation where a wide gap separated the competence of group members. We discuss the main properties of the kinetic models and numerically investigate some examples of collective decision under the influence of the equality bias. The results confirm that the equality bias leads the group to suboptimal decisions.