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May 2020 Strictly weak consensus in the uniform compass model on $\mathbb{Z}$
Nina Gantert, Markus Heydenreich, Timo Hirscher
Bernoulli 26(2): 1269-1293 (May 2020). DOI: 10.3150/19-BEJ1155

Abstract

We investigate a model for opinion dynamics, where individuals (modeled by vertices of a graph) hold certain abstract opinions. As time progresses, neighboring individuals interact with each other, and this interaction results in a realignment of opinions closer towards each other. This mechanism triggers formation of consensus among the individuals. Our main focus is on strong consensus (i.e., global agreement of all individuals) versus weak consensus (i.e., local agreement among neighbors). By extending a known model to a more general opinion space, which lacks a “central” opinion acting as a contraction point, we provide an example of an opinion formation process on the one-dimensional lattice $\mathbb{Z}$ with weak consensus but no strong consensus.

Citation

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Nina Gantert. Markus Heydenreich. Timo Hirscher. "Strictly weak consensus in the uniform compass model on $\mathbb{Z}$." Bernoulli 26 (2) 1269 - 1293, May 2020. https://doi.org/10.3150/19-BEJ1155

Information

Received: 1 April 2019; Revised: 1 August 2019; Published: May 2020
First available in Project Euclid: 31 January 2020

zbMATH: 07166563
MathSciNet: MR4058367
Digital Object Identifier: 10.3150/19-BEJ1155

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

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Vol.26 • No. 2 • May 2020
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