Multistate voter model with imperfect copying

Autores
Vazquez, Federico; Loscar, Ernesto Selim; Baglietto, Gabriel
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter ψ in [0,1], depend on the amplitude η of the copying error or noise and the population size N . In the case of perfect copying η = 0 , the system reaches an absorbing configuration with complete order ( ψ = 1 ) for all values of N . However, for any degree of imperfection η > 0 , we show that the average value of ψ at the stationary state decreases with N as ⟨ ψ ⟩ ≃ 6 / ( π 2 η 2 N ) for η ≪ 1 and η 2 N ≳ 1 , and thus the system becomes totally disordered in the thermodynamic limit N → ∞ . We also show that ⟨ ψ ⟩ ≃ 1 − π 2 6 η 2 N in the vanishing small error limit η → 0 , which implies that complete order is never achieved for η > 0 . These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.
Fil: Vazquez, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Loscar, Ernesto Selim. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina
Fil: Baglietto, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina
Materia
Complex Systems
Nonequilibrium statistical Mechanics
Active Matter
Social Systems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/143150

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network_name_str CONICET Digital (CONICET)
spelling Multistate voter model with imperfect copyingVazquez, FedericoLoscar, Ernesto SelimBaglietto, GabrielComplex SystemsNonequilibrium statistical MechanicsActive MatterSocial Systemshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter ψ in [0,1], depend on the amplitude η of the copying error or noise and the population size N . In the case of perfect copying η = 0 , the system reaches an absorbing configuration with complete order ( ψ = 1 ) for all values of N . However, for any degree of imperfection η > 0 , we show that the average value of ψ at the stationary state decreases with N as ⟨ ψ ⟩ ≃ 6 / ( π 2 η 2 N ) for η ≪ 1 and η 2 N ≳ 1 , and thus the system becomes totally disordered in the thermodynamic limit N → ∞ . We also show that ⟨ ψ ⟩ ≃ 1 − π 2 6 η 2 N in the vanishing small error limit η → 0 , which implies that complete order is never achieved for η > 0 . These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.Fil: Vazquez, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaFil: Loscar, Ernesto Selim. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaFil: Baglietto, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; ArgentinaAmerican Physical Society2019-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/143150Vazquez, Federico; Loscar, Ernesto Selim; Baglietto, Gabriel; Multistate voter model with imperfect copying; American Physical Society; Physical Review E; 100; 4; 10-2019; 1-462470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.042301info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.100.042301info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.07253v2info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:12:40Zoai:ri.conicet.gov.ar:11336/143150instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:12:41.152CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Multistate voter model with imperfect copying
title Multistate voter model with imperfect copying
spellingShingle Multistate voter model with imperfect copying
Vazquez, Federico
Complex Systems
Nonequilibrium statistical Mechanics
Active Matter
Social Systems
title_short Multistate voter model with imperfect copying
title_full Multistate voter model with imperfect copying
title_fullStr Multistate voter model with imperfect copying
title_full_unstemmed Multistate voter model with imperfect copying
title_sort Multistate voter model with imperfect copying
dc.creator.none.fl_str_mv Vazquez, Federico
Loscar, Ernesto Selim
Baglietto, Gabriel
author Vazquez, Federico
author_facet Vazquez, Federico
Loscar, Ernesto Selim
Baglietto, Gabriel
author_role author
author2 Loscar, Ernesto Selim
Baglietto, Gabriel
author2_role author
author
dc.subject.none.fl_str_mv Complex Systems
Nonequilibrium statistical Mechanics
Active Matter
Social Systems
topic Complex Systems
Nonequilibrium statistical Mechanics
Active Matter
Social Systems
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter ψ in [0,1], depend on the amplitude η of the copying error or noise and the population size N . In the case of perfect copying η = 0 , the system reaches an absorbing configuration with complete order ( ψ = 1 ) for all values of N . However, for any degree of imperfection η > 0 , we show that the average value of ψ at the stationary state decreases with N as ⟨ ψ ⟩ ≃ 6 / ( π 2 η 2 N ) for η ≪ 1 and η 2 N ≳ 1 , and thus the system becomes totally disordered in the thermodynamic limit N → ∞ . We also show that ⟨ ψ ⟩ ≃ 1 − π 2 6 η 2 N in the vanishing small error limit η → 0 , which implies that complete order is never achieved for η > 0 . These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.
Fil: Vazquez, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina
Fil: Loscar, Ernesto Selim. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina
Fil: Baglietto, Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentina
description The voter model with multiple states has found applications in areas as diverse as population genetics, opinion formation, species competition, and language dynamics, among others. In a single step of the dynamics, an individual chosen at random copies the state of a random neighbor in the population. In this basic formulation, it is assumed that the copying is perfect, and thus an exact copy of an individual is generated at each time step. Here, we introduce and study a variant of the multistate voter model in mean field that incorporates a degree of imperfection or error in the copying process, which leaves the states of the two interacting individuals similar but not exactly equal. This dynamics can also be interpreted as a perfect copying with the addition of noise: a minimalistic model for flocking. We found that the ordering properties of this multistate noisy voter model, measured by a parameter ψ in [0,1], depend on the amplitude η of the copying error or noise and the population size N . In the case of perfect copying η = 0 , the system reaches an absorbing configuration with complete order ( ψ = 1 ) for all values of N . However, for any degree of imperfection η > 0 , we show that the average value of ψ at the stationary state decreases with N as ⟨ ψ ⟩ ≃ 6 / ( π 2 η 2 N ) for η ≪ 1 and η 2 N ≳ 1 , and thus the system becomes totally disordered in the thermodynamic limit N → ∞ . We also show that ⟨ ψ ⟩ ≃ 1 − π 2 6 η 2 N in the vanishing small error limit η → 0 , which implies that complete order is never achieved for η > 0 . These results are supported by Monte Carlo simulations of the model, which allow to study other scenarios as well.
publishDate 2019
dc.date.none.fl_str_mv 2019-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
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://hdl.handle.net/11336/143150
Vazquez, Federico; Loscar, Ernesto Selim; Baglietto, Gabriel; Multistate voter model with imperfect copying; American Physical Society; Physical Review E; 100; 4; 10-2019; 1-46
2470-0053
CONICET Digital
CONICET
url http://hdl.handle.net/11336/143150
identifier_str_mv Vazquez, Federico; Loscar, Ernesto Selim; Baglietto, Gabriel; Multistate voter model with imperfect copying; American Physical Society; Physical Review E; 100; 4; 10-2019; 1-46
2470-0053
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.042301
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.100.042301
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.07253v2
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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