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arXiv · 1505.07433

Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation

Bertram Düring·Marie-Therese Wolfram
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Abstract

We propose and investigate different kinetic models for opinion formation, when the opinion formation process depends on an additional independent variable, e.g. a leadership or a spatial variable. More specifically, we consider:(i) opinion dynamics under the effect of opinion leadership, where each individual is characterised not only by its opinion, but also by another independent variable which quantifies leadership qualities; (ii) opinion dynamics modelling political segregation in the `The Big Sort', a phenomenon that US citizens increasingly prefer to live in neighbourhoods with politically like-minded individuals. Based on microscopic opinion consensus dynamics such models lead to inhomogeneous Boltzmann-type equations for the opinion distribution. We derive macroscopic Fokker-Planck-type equations in a quasi-invariant opinion limit and present results of numerical experiments.

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Bertram Düring, Marie-Therese Wolfram. 2015-05-27. Opinion dynamics: inhomogeneous Boltzmann-type equations modelling opinion leadership and political segregation. https://doi.org/10.1098/rspa.2015.0345

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