Continuous model of opinion dynamics with convictions

Vinh Nguyen; Roman Shvydkoy

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arXiv · 2211.09199

Continuous model of opinion dynamics with convictions

Vinh Nguyen·Roman Shvydkoy

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Abstract

In this note we study a new kinetic model of opinion dynamics. The model incorporates two forces -- alignment of opinions under all-to-all communication driving the system to a consensus, and Rayleigh type friction force that drives each `player' to its fixed conviction value. The balance between these forces creates a non-trivial limiting outcome. We establish existence of a global mono-opinion state, whereby any initial distribution of opinions for each conviction value aggregates to the Dirac measure concentrated on a single opinion. We identify several cases where such a state is unique and depends continuously on the initial distribution of convictions. Several regularity properties of the limiting distribution of opinions are presented.

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Vinh Nguyen, Roman Shvydkoy. 2022-11-16. Continuous model of opinion dynamics with convictions. https://arxiv.org/abs/2211.09199

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