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Overly determined agents prevent consensus in a generalized Deffuant model on ℤ with dispersed opinions

Part of: Time-dependent statistical mechanics (dynamic and nonequilibrium) Special processes Stochastic processes

Published online by Cambridge University Press:  08 September 2017

Timo Hirscher
Timo Hirscher*
Affiliation:
Goethe-Universität Frankfurt am Main
*
* Postal address: Institute of Mathematics, Goethe-Universität, 60054 Frankfurt am Main, Germany. Email address: hirscher@math.uni-frankfurt.de
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Abstract

During the last decades, quite a number of interacting particle systems have been introduced and studied in the crossover area of mathematics and statistical physics. Some of these can be seen as simplistic models for opinion formation processes in groups of interacting people. In the model introduced by Deffuant et al. (2000), agents that are neighbors on a given network graph, randomly meet in pairs and approach a compromise if their current opinions do not differ by more than a given threshold value θ. We consider the two-sided infinite path ℤ as the underlying graph and extend existing models to a setting in which opinions are given by probability distributions. Similar to what has been shown for finite-dimensional opinions, we observe a dichotomy in the long-term behavior of the model, but only if the initial narrow mindedness of the agents is restricted.

Keywords

Deffuant modelopinion dynamicsrandom measuretotal variation distance

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60G57: Random measures 82C22: Interacting particle systems
Type
Research Article
Information
Advances in Applied Probability , Volume 49 , Issue 3 , September 2017 , pp. 722 - 744
Copyright
Copyright © Applied Probability Trust 2017 

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