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

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posted on 2023-06-08, 22:41 authored by Bertram Duering, Marie-Therese Wolfram
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.

Funding

Novel discretisations for higher-order nonlinear PDE; Leverhulme Trust; RPG-2015-069

History

Publication status

  • Published

File Version

  • Submitted version

Journal

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science

ISSN

1364-5021

Publisher

The Royal Society

Issue

2182

Volume

471

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2015-10-05

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