{"id":"https://openalex.org/W4415421005","doi":"https://doi.org/10.3390/e27111087","title":"Winning Opinion in the Voter Model: Following Your Friends\u2019 Advice or That of Their Friends?","display_name":"Winning Opinion in the Voter Model: Following Your Friends\u2019 Advice or That of Their Friends?","publication_year":2025,"publication_date":"2025-10-22","ids":{"openalex":"https://openalex.org/W4415421005","doi":"https://doi.org/10.3390/e27111087","pmid":"https://pubmed.ncbi.nlm.nih.gov/41294931"},"language":"en","primary_location":{"id":"doi:10.3390/e27111087","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27111087","pdf_url":"https://www.mdpi.com/1099-4300/27/11/1087/pdf?version=1761128043","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/11/1087/pdf?version=1761128043","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022501938","display_name":"Francisco J. Mu\u00f1oz","orcid":"https://orcid.org/0000-0002-0874-6275"},"institutions":[{"id":"https://openalex.org/I182083151","display_name":"Universidad Rey Juan Carlos","ror":"https://ror.org/01v5cv687","country_code":"ES","type":"education","lineage":["https://openalex.org/I182083151"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Francisco J. Mu\u00f1oz","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, Ciencia e Ingenier\u00eda de Materiales y Tecnolog\u00eda Electr\u00f3nica, Universidad Rey Juan Carlos, 28933 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0002-0874-6275","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Ciencia e Ingenier\u00eda de Materiales y Tecnolog\u00eda Electr\u00f3nica, Universidad Rey Juan Carlos, 28933 Madrid, Spain","institution_ids":["https://openalex.org/I182083151"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032215497","display_name":"Juan Carlos Nu\u00f1o","orcid":"https://orcid.org/0000-0003-4708-980X"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Juan Carlos Nu\u00f1o","raw_affiliation_strings":["Departamento de Matem\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0003-4708-980X","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica Aplicada, Universidad Polit\u00e9cnica de Madrid, 28040 Madrid, Spain","institution_ids":["https://openalex.org/I88060688"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022501938"],"corresponding_institution_ids":["https://openalex.org/I182083151"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2160534,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"11","first_page":"1087","last_page":"1087"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10557","display_name":"Social Media and Politics","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/3315","display_name":"Communication"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9873999953269958,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6851000189781189},{"id":"https://openalex.org/keywords/voter-model","display_name":"Voter model","score":0.5976999998092651},{"id":"https://openalex.org/keywords/asymmetry","display_name":"Asymmetry","score":0.5683000087738037},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.46779999136924744},{"id":"https://openalex.org/keywords/network-topology","display_name":"Network topology","score":0.45590001344680786},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4551999866962433},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.4544999897480011},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.35120001435279846},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.34299999475479126}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6851000189781189},{"id":"https://openalex.org/C2781396049","wikidata":"https://www.wikidata.org/wiki/Q7942158","display_name":"Voter model","level":2,"score":0.5976999998092651},{"id":"https://openalex.org/C38976095","wikidata":"https://www.wikidata.org/wiki/Q752641","display_name":"Asymmetry","level":2,"score":0.5683000087738037},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.46779999136924744},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45910000801086426},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.45590001344680786},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4551999866962433},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.4544999897480011},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3817000091075897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3799000084400177},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.35120001435279846},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3441999852657318},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34299999475479126},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C2779955035","wikidata":"https://www.wikidata.org/wiki/Q4686785","display_name":"Advice (programming)","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.2743000090122223},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2680000066757202},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2628999948501587},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.25769999623298645},{"id":"https://openalex.org/C2776292839","wikidata":"https://www.wikidata.org/wiki/Q5179217","display_name":"Coverage probability","level":3,"score":0.25189998745918274}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e27111087","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27111087","pdf_url":"https://www.mdpi.com/1099-4300/27/11/1087/pdf?version=1761128043","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:41294931","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/41294931","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:844a0857972246f1a89bb7c282fc3570","is_oa":true,"landing_page_url":"https://doaj.org/article/844a0857972246f1a89bb7c282fc3570","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 11, p 1087 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e27111087","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27111087","pdf_url":"https://www.mdpi.com/1099-4300/27/11/1087/pdf?version=1761128043","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415421005.pdf","grobid_xml":"https://content.openalex.org/works/W4415421005.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1965044289","https://openalex.org/W1969871566","https://openalex.org/W1971842701","https://openalex.org/W1984813754","https://openalex.org/W1998692453","https://openalex.org/W2008620264","https://openalex.org/W2037930661","https://openalex.org/W2051510192","https://openalex.org/W2058105398","https://openalex.org/W2062868500","https://openalex.org/W2108758170","https://openalex.org/W2112090702","https://openalex.org/W2761309159","https://openalex.org/W3037826211","https://openalex.org/W4243813765","https://openalex.org/W4251085314","https://openalex.org/W4411370469"],"related_works":[],"abstract_inverted_index":{"We":[0,200],"investigate":[1],"a":[2,28],"variation":[3],"of":[4,12,27,31,41,53,87,107,123,130,162,167,179,206],"the":[5,10,57,78,85,105,121,160,165,174,190,196,204],"classical":[6],"voter":[7],"model":[8],"where":[9],"set":[11],"influencing":[13],"agents":[14,181],"depends":[15,172],"on":[16,120,169,173],"an":[17,155],"individual's":[18],"current":[19],"opinion.":[20],"The":[21,61,177],"initial":[22],"population":[23],"is":[24,125],"made":[25],"up":[26],"random":[29],"sample":[30],"equally":[32],"sized":[33],"sub-populations":[34],"for":[35,209],"each":[36],"state,":[37,193],"and":[38,48,89,135,212],"two":[39],"types":[40],"interactions":[42,97],"are":[43],"considered:":[44],"(i)":[45],"direct":[46,54,58,95],"neighbors":[47,51,59],"(ii)":[49],"second":[50],"(friends":[52],"neighbors,":[55],"excluding":[56],"themselves).":[60],"neighborhood":[62],"size,":[63],"reflecting":[64,114],"regular":[65],"network":[66,131,175],"connectivity,":[67,94,151],"remains":[68],"constant":[69],"across":[70],"all":[71],"agents.":[72],"Our":[73],"findings":[74,208],"show":[75,154],"that":[76,83],"varying":[77],"interaction":[79],"range":[80],"introduces":[81],"asymmetries":[82],"affect":[84],"probability":[86,106,122,161],"consensus":[88,111,124],"convergence":[90,141,170],"time.":[91],"At":[92],"low":[93],"neighbor":[96],"dominate,":[98],"leading":[99],"to":[100,127,198],"consensus.":[101,199],"As":[102],"connectivity":[103],"increases,":[104],"either":[108],"state":[109],"reaching":[110,163],"becomes":[112],"equal,":[113],"symmetric":[115,144],"dynamics.":[116],"This":[117],"asymmetric":[118,152],"effect":[119],"shown":[126],"be":[128],"independent":[129],"topology":[132],"in":[133,215],"small-world":[134],"scale-free":[136],"networks.":[137],"Asymmetry":[138],"also":[139],"influences":[140],"time:":[142],"while":[143],"cases":[145,153],"display":[146],"decreasing":[147],"times":[148],"with":[149],"increased":[150],"almost":[156],"linear":[157],"increase.":[158],"Unlike":[159],"consensus,":[164],"impact":[166],"asymmetry":[168],"time":[171,197],"topology.":[176],"introduction":[178],"stubborn":[180],"further":[182],"magnifies":[183],"these":[184,207],"effects,":[185],"especially":[186],"when":[187],"they":[188],"favor":[189],"less":[191],"dominant":[192],"significantly":[194],"lengthening":[195],"conclude":[201],"by":[202],"discussing":[203],"implications":[205],"decision-making":[210],"processes":[211],"political":[213],"campaigns":[214],"human":[216],"populations.":[217]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-24T00:00:00"}
