The Deffuant model on Z with higher-dimensional opinion spaces
Hirscher, Timo LU
(2014)
In Alea
11(1).
p.409-444
- 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... (More)
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.
(Less)
- author
- Hirscher, Timo
LU
- publishing date
- 2014
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Consensus formation, Deffuant model, Vector-valued opinions
- in
- Alea
- volume
- 11
- issue
- 1
- pages
- 36 pages
- publisher
- Instituto Nacional de Matematica Pura e Aplicada
- external identifiers
-
- scopus:85010918288
- ISSN
- 1980-0436
- language
- English
- LU publication?
- no
- id
- 451845ba-2453-40d0-aeaf-c93de29d3e37
- alternative location
- https://alea.impa.br/articles/v11/11-18.pdf
- date added to LUP
- 2023-12-14 13:20:34
- date last changed
- 2025-10-14 09:03:10
@article{451845ba-2453-40d0-aeaf-c93de29d3e37,
abstract = {{<p>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 θ<sub>c</sub> for θ at which a phase transition in the long-term behavior takes place, but θ<sub>c</sub> depends on the initial distribution in a more intricate way than in the univariate case.</p>}},
author = {{Hirscher, Timo}},
issn = {{1980-0436}},
keywords = {{Consensus formation; Deffuant model; Vector-valued opinions}},
language = {{eng}},
number = {{1}},
pages = {{409--444}},
publisher = {{Instituto Nacional de Matematica Pura e Aplicada}},
series = {{Alea}},
title = {{The Deffuant model on Z with higher-dimensional opinion spaces}},
url = {{https://alea.impa.br/articles/v11/11-18.pdf}},
volume = {{11}},
year = {{2014}},
}