Scaling limits for continuous opinion dynamics systems
(2009) 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 In 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009 p.1562-1566- Abstract
A class of large-scale stochastic discrete-time continuous-opinion dynamical systems is analyzed. Agents have pairwise random interactions in which their vector-valued opinions are updated to a weighted average of their current values. The intensity of the interactions is allowed to depend on the agents' opinions themselves through an interaction kernel. This class of models includes as a special case the bounded-confidence opinion dynamics models recently introduced by Deffuant et al., in which agents interact only when their opinions differ by less than a given threshold, as well as more general interaction kernels. It is shown that, in the limit as the population size increases, upon a proper rescaling of the time index, the... (More)
A class of large-scale stochastic discrete-time continuous-opinion dynamical systems is analyzed. Agents have pairwise random interactions in which their vector-valued opinions are updated to a weighted average of their current values. The intensity of the interactions is allowed to depend on the agents' opinions themselves through an interaction kernel. This class of models includes as a special case the bounded-confidence opinion dynamics models recently introduced by Deffuant et al., in which agents interact only when their opinions differ by less than a given threshold, as well as more general interaction kernels. It is shown that, in the limit as the population size increases, upon a proper rescaling of the time index, the trajectories of such stochastic processes concentrate, at an exponential rate, around the solution of a measure-valued differential equation. The asymptotic properties of the solution of such a differential equation are then studied, and convergence is proven to a convex combination of delta measures whose number depends on the interaction kernel.
(Less)
- author
- Como, Giacomo LU and Fagnani, Fabio
- publishing date
- 2009
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
- series title
- 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
- article number
- 5394488
- pages
- 5 pages
- conference name
- 2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009
- conference location
- Monticello, IL, United States
- conference dates
- 2009-09-30 - 2009-10-02
- external identifiers
-
- scopus:77949597588
- ISBN
- 9781424458714
- DOI
- 10.1109/ALLERTON.2009.5394488
- language
- English
- LU publication?
- no
- id
- ec915c43-4fc9-4e27-9dbb-18cc20576b34
- date added to LUP
- 2022-03-22 13:16:08
- date last changed
- 2022-06-07 23:55:18
@inproceedings{ec915c43-4fc9-4e27-9dbb-18cc20576b34,
abstract = {{<p>A class of large-scale stochastic discrete-time continuous-opinion dynamical systems is analyzed. Agents have pairwise random interactions in which their vector-valued opinions are updated to a weighted average of their current values. The intensity of the interactions is allowed to depend on the agents' opinions themselves through an interaction kernel. This class of models includes as a special case the bounded-confidence opinion dynamics models recently introduced by Deffuant et al., in which agents interact only when their opinions differ by less than a given threshold, as well as more general interaction kernels. It is shown that, in the limit as the population size increases, upon a proper rescaling of the time index, the trajectories of such stochastic processes concentrate, at an exponential rate, around the solution of a measure-valued differential equation. The asymptotic properties of the solution of such a differential equation are then studied, and convergence is proven to a convex combination of delta measures whose number depends on the interaction kernel.</p>}},
author = {{Como, Giacomo and Fagnani, Fabio}},
booktitle = {{2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009}},
isbn = {{9781424458714}},
language = {{eng}},
pages = {{1562--1566}},
series = {{2009 47th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2009}},
title = {{Scaling limits for continuous opinion dynamics systems}},
url = {{http://dx.doi.org/10.1109/ALLERTON.2009.5394488}},
doi = {{10.1109/ALLERTON.2009.5394488}},
year = {{2009}},
}