Mobilia, M orcid.org/0000-0002-1424-567X (2011) Fixation and polarization in a three-species opinion dynamics model. EPL, 95 (5). 50002. ISSN 0295-5075
Abstract
Motivated by the dynamics of cultural change and diversity, we generalize the three-species constrained voter model on a complete graph introduced in J. Phys. A, 37 (2004) 8479. In this opinion dynamics model, a population of size N is composed of "leftists" and "rightists" that interact with "centrists": a leftist and centrist can both become leftists with rate (1+q)/2 or centrists with rate (1−q)/2 (and similarly for rightists and centrists), where q denotes the bias towards extremism (q > 0) or centrism (q < 0). This system admits three absorbing fixed points and a "polarization" line along which a frozen mixture of leftists and rightists coexist. In the realm of Fokker-Planck equation, and using a mapping onto a population genetics model, we compute the fixation probability of ending in every absorbing state and the mean times for these events. We therefore show, especially in the limit of weak bias and large population size when |q| ~ N−1 and NGt1, how fluctuations alter the mean-field predictions: polarization is likely when q > 0, but there is always a finite probability to reach a consensus; the opposite happens when q < 0. Our findings are corroborated by stochastic simulations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Copyright (c) EPLA, 2011. This is an author produced version of a paper published in EPL. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Statistical Physics; Evolutionary Games; Voters; Complex Systems; Evolutionary dynamics; Mathematical and computational modelling; Dynamics of cultural change modelling |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Mar 2019 16:00 |
Last Modified: | 07 Mar 2019 16:00 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1209/0295-5075/95/50002 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:87674 |