The Deffuant model on Z with higher-dimensional opinion spaces

Research output: Contribution to journalArticlepeer-review

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. We consider this model on the line graph 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. As in the univariate case there turns out to exist a critical value θc for θ at which a phase transition in the long-term behavior takes place, but θc depends on the initial distribution in a more intricate way than in the univariate case.

Original languageEnglish
Pages (from-to)409-444
Number of pages36
JournalAlea
Volume11
Issue number1
Publication statusPublished - 2014
Externally publishedYes

Subject classification (UKÄ)

  • Probability Theory and Statistics

Free keywords

  • Consensus formation
  • Deffuant model
  • Vector-valued opinions

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