When social networks polarize: On the number of clusters in the Hegselmann-Krause model

Wout De Vos (), Michel Grabisch () and Agnieszka Rusinowska ()
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Wout De Vos: CentER and Department of Econometrics and Operations Research, Tilburg University
Michel Grabisch: Centre d'Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, Paris School of Economics, https://centredeconomiesorbonne.cnrs.fr
Agnieszka Rusinowska: Centre d'Economie de la Sorbonne, CNRS, Université Paris 1 Panthéon-Sorbonne, Paris School of Economics, https://centredeconomiesorbonne.cnrs.fr

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

Abstract: In the present paper, we study opinion dynamics in a social network, where individuals only listen to those with opinion not farther away than a given threshold from their own opinion (known as bounded confidence models, proposed by Hegselmann and Krause). It is well known that in bounded confidence models consensus does not always exist, and that agents split in clusters (polarization), with convergence to consensus in each cluster. We are precisely interested in the effect of bounded confidence on polarization in the network. Our main focus concerns the formation of clusters and their number, as well as its non-monotonicity with respect to the value of the threshold. First, a framework with a finite number of agents is considered. We study analytically disintegration of various types of opinion chains (clusters), and investigate by simulation the likelihood of chains of a certain length and their disintegration. Next, we analyze in a formal way the formation of clusters in a model with a continuum of agents. Finally, we examine the (non-)monotonicity of the number of clusters with respect to the threshold for a given initial vector of opinions and in expectation

Keywords: opinion dynamics; polarization; clusters; bounded confidence; non-monotonicity; network formation; continuous opinion (search for similar items in EconPapers)
JEL-codes: D72 D85 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2025-07
New Economics Papers: this item is included in nep-net
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