English

The Deffuant model on $\mathbb{Z}$ with higher-dimensional opinion spaces

Probability 2014-08-21 v2

Abstract

When it comes to the mathematical modelling of social interaction patterns, a number of different models have emerged and been studied over the last decade, in which individuals randomly interact on the basis of an underlying graph structure and share their opinions. A prominent example of the so-called bounded confidence models is the one introduced by Deffuant et al.: Two neighboring individuals will only interact if their opinions do not differ by more than a given threshold θ\theta. We consider this model on the line graph Z\mathbb{Z} and extend the results that have been achieved for the model with real-valued opinions by considering vector-valued opinions and general metrics measuring the distance between two opinion values. Just as in the univariate case, there exists a critical value for θ\theta at which a phase transition in the long-term behavior takes place.

Keywords

Cite

@article{arxiv.1402.1416,
  title  = {The Deffuant model on $\mathbb{Z}$ with higher-dimensional opinion spaces},
  author = {Timo Hirscher},
  journal= {arXiv preprint arXiv:1402.1416},
  year   = {2014}
}
R2 v1 2026-06-22T03:02:56.338Z