Fitness voter model: damped oscillations and anomalous consensus

Autores
Woolcock, A.; Connaughton, C.; Merali, Y.; Vazquez, Federico
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter k≥0, in addition to its + or - opinion state. The evolution of the distribution of k-values and the opinion dynamics are coupled together, so as to allow the system to dynamically develop heterogeneity and memory in a simple way. When two agents with different opinions interact, their k-values are compared, and with probability p the agent with the lower value adopts the opinion of the one with the higher value, while with probability 1-p the opposite happens. The agent that keeps its opinion (winning agent) increments its k-value by one. We study the dynamics of the system in the entire 0≤p≤1 range and compare with the case p=1/2, in which opinions are decoupled from the k-values and the dynamics is equivalent to that of the standard voter model. When 0≤p<1/2, agents with higher k-values are less persuasive, and the system approaches exponentially fast to the consensus state of the initial majority opinion. The mean consensus time τ appears to grow logarithmically with the number of agents N, and it is greatly decreased relative to the linear behavior τ∼N found in the standard voter model. When 1/2Instituto de Física de Líquidos y Sistemas Biológicos
Materia
Matemática
Ciencias Exactas
Damped oscillations
Consensus time
Linear behavior
Opinion dynamics
Opinion formation
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/87729
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/87729
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling Fitness voter model: damped oscillations and anomalous consensusWoolcock, A.Connaughton, C.Merali, Y.Vazquez, FedericoMatemáticaCiencias ExactasDamped oscillationsConsensus timeLinear behaviorOpinion dynamicsOpinion formationWe study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter k≥0, in addition to its + or - opinion state. The evolution of the distribution of k-values and the opinion dynamics are coupled together, so as to allow the system to dynamically develop heterogeneity and memory in a simple way. When two agents with different opinions interact, their k-values are compared, and with probability p the agent with the lower value adopts the opinion of the one with the higher value, while with probability 1-p the opposite happens. The agent that keeps its opinion (winning agent) increments its k-value by one. We study the dynamics of the system in the entire 0≤p≤1 range and compare with the case p=1/2, in which opinions are decoupled from the k-values and the dynamics is equivalent to that of the standard voter model. When 0≤p<1/2, agents with higher k-values are less persuasive, and the system approaches exponentially fast to the consensus state of the initial majority opinion. The mean consensus time τ appears to grow logarithmically with the number of agents N, and it is greatly decreased relative to the linear behavior τ∼N found in the standard voter model. When 1/2<p≤1, agents with higher k-values are more persuasive, and the system initially relaxes to a state with an even coexistence of opinions, but eventually reaches consensus by finite-size fluctuations. The approach to the coexistence state is monotonic for 1/2<p<po≃0.8, while for po≤p≤1 there are damped oscillations around the coexistence value. The final approach to coexistence is approximately a power law t-b(p) in both regimes, where the exponent b increases with p. Also, τ increases respect to the standard voter model, although it still scales linearly with N. The p=1 case is special, with a relaxation to coexistence that scales as t-2.73 and a consensus time that scales as τ∼Nβ, with β≃1.45.Instituto de Física de Líquidos y Sistemas Biológicos2017-09-25info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/87729enginfo:eu-repo/semantics/altIdentifier/issn/2470-0045info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.96.032313info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-15T11:09:06Zoai:sedici.unlp.edu.ar:10915/87729Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:09:07.067SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Fitness voter model: damped oscillations and anomalous consensus
title Fitness voter model: damped oscillations and anomalous consensus
spellingShingle Fitness voter model: damped oscillations and anomalous consensus
Woolcock, A.
Matemática
Ciencias Exactas
Damped oscillations
Consensus time
Linear behavior
Opinion dynamics
Opinion formation
title_short Fitness voter model: damped oscillations and anomalous consensus
title_full Fitness voter model: damped oscillations and anomalous consensus
title_fullStr Fitness voter model: damped oscillations and anomalous consensus
title_full_unstemmed Fitness voter model: damped oscillations and anomalous consensus
title_sort Fitness voter model: damped oscillations and anomalous consensus
dc.creator.none.fl_str_mv Woolcock, A.
Connaughton, C.
Merali, Y.
Vazquez, Federico
author Woolcock, A.
author_facet Woolcock, A.
Connaughton, C.
Merali, Y.
Vazquez, Federico
author_role author
author2 Connaughton, C.
Merali, Y.
Vazquez, Federico
author2_role author
author
author
dc.subject.none.fl_str_mv Matemática
Ciencias Exactas
Damped oscillations
Consensus time
Linear behavior
Opinion dynamics
Opinion formation
topic Matemática
Ciencias Exactas
Damped oscillations
Consensus time
Linear behavior
Opinion dynamics
Opinion formation
dc.description.none.fl_txt_mv We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter k≥0, in addition to its + or - opinion state. The evolution of the distribution of k-values and the opinion dynamics are coupled together, so as to allow the system to dynamically develop heterogeneity and memory in a simple way. When two agents with different opinions interact, their k-values are compared, and with probability p the agent with the lower value adopts the opinion of the one with the higher value, while with probability 1-p the opposite happens. The agent that keeps its opinion (winning agent) increments its k-value by one. We study the dynamics of the system in the entire 0≤p≤1 range and compare with the case p=1/2, in which opinions are decoupled from the k-values and the dynamics is equivalent to that of the standard voter model. When 0≤p<1/2, agents with higher k-values are less persuasive, and the system approaches exponentially fast to the consensus state of the initial majority opinion. The mean consensus time τ appears to grow logarithmically with the number of agents N, and it is greatly decreased relative to the linear behavior τ∼N found in the standard voter model. When 1/2<p≤1, agents with higher k-values are more persuasive, and the system initially relaxes to a state with an even coexistence of opinions, but eventually reaches consensus by finite-size fluctuations. The approach to the coexistence state is monotonic for 1/2<p<po≃0.8, while for po≤p≤1 there are damped oscillations around the coexistence value. The final approach to coexistence is approximately a power law t-b(p) in both regimes, where the exponent b increases with p. Also, τ increases respect to the standard voter model, although it still scales linearly with N. The p=1 case is special, with a relaxation to coexistence that scales as t-2.73 and a consensus time that scales as τ∼Nβ, with β≃1.45.
Instituto de Física de Líquidos y Sistemas Biológicos
description We study the dynamics of opinion formation in a heterogeneous voter model on a complete graph, in which each agent is endowed with an integer fitness parameter k≥0, in addition to its + or - opinion state. The evolution of the distribution of k-values and the opinion dynamics are coupled together, so as to allow the system to dynamically develop heterogeneity and memory in a simple way. When two agents with different opinions interact, their k-values are compared, and with probability p the agent with the lower value adopts the opinion of the one with the higher value, while with probability 1-p the opposite happens. The agent that keeps its opinion (winning agent) increments its k-value by one. We study the dynamics of the system in the entire 0≤p≤1 range and compare with the case p=1/2, in which opinions are decoupled from the k-values and the dynamics is equivalent to that of the standard voter model. When 0≤p<1/2, agents with higher k-values are less persuasive, and the system approaches exponentially fast to the consensus state of the initial majority opinion. The mean consensus time τ appears to grow logarithmically with the number of agents N, and it is greatly decreased relative to the linear behavior τ∼N found in the standard voter model. When 1/2<p≤1, agents with higher k-values are more persuasive, and the system initially relaxes to a state with an even coexistence of opinions, but eventually reaches consensus by finite-size fluctuations. The approach to the coexistence state is monotonic for 1/2<p<po≃0.8, while for po≤p≤1 there are damped oscillations around the coexistence value. The final approach to coexistence is approximately a power law t-b(p) in both regimes, where the exponent b increases with p. Also, τ increases respect to the standard voter model, although it still scales linearly with N. The p=1 case is special, with a relaxation to coexistence that scales as t-2.73 and a consensus time that scales as τ∼Nβ, with β≃1.45.
publishDate 2017
dc.date.none.fl_str_mv 2017-09-25
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/87729
url http://sedici.unlp.edu.ar/handle/10915/87729
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/2470-0045
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.96.032313
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
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