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Timo Vilkas
Senior lecturer
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The Deffuant model on Z with higher-dimensional opinion spaces
Author
Summary, in English
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.
Publishing year
2014
Language
English
Pages
409-444
Publication/Series
Alea
Volume
11
Issue
1
Document type
Journal article
Publisher
Instituto Nacional de Matematica Pura e Aplicada (I M P A)
Topic
- Probability Theory and Statistics
Keywords
- Consensus formation
- Deffuant model
- Vector-valued opinions
Status
Published
ISBN/ISSN/Other
- ISSN: 1980-0436