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 language | English |
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Pages (from-to) | 409-444 |
Number of pages | 36 |
Journal | Alea |
Volume | 11 |
Issue number | 1 |
Publication status | Published - 2014 |
Externally published | Yes |
Subject classification (UKÄ)
- Probability Theory and Statistics
Free keywords
- Consensus formation
- Deffuant model
- Vector-valued opinions