Further results on consensus formation in the Deffuant model

Olle Häggström (Chalmers University of Technology)
Timo Hirscher (Chalmers University of Technology)


The so-called Deffuant model describes a pattern for social interaction, in which two neighboring individuals randomly meet and share their opinions on a certain topic, if their discrepancy is not beyond a given threshold $\theta$. The major focus of the analyses, both theoretical and based on simulations, lies on whether these single interactions lead to a global consensus in the long run or not. First, we generalize a result of Lanchier for the Deffuant model on $\mathbb{Z}$, determining the critical value for $\theta$ at which a phase transition of the long term behavior takes place, to other distributions of the initial opinions than i.i.d. uniform on $[0,1]$. Then we shed light on the situations where the underlying line graph $\mathbb{Z}$ is replaced by higher-dimensional lattices $\mathbb{Z}^d,\ d\geq2$, or the infinite cluster of supercritical i.i.d. bond percolation on these lattices.

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Pages: 1-26

Publication Date: February 4, 2014

DOI: 10.1214/EJP.v19-3116


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