{"id":"https://openalex.org/W4416982927","doi":"https://doi.org/10.1017/jpr.2025.10043","title":"Negative dependence in knockout tournaments","display_name":"Negative dependence in knockout tournaments","publication_year":2025,"publication_date":"2025-12-04","ids":{"openalex":"https://openalex.org/W4416982927","doi":"https://doi.org/10.1017/jpr.2025.10043"},"language":"en","primary_location":{"id":"doi:10.1017/jpr.2025.10043","is_oa":false,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10043","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005817228","display_name":"Yuting Su","orcid":"https://orcid.org/0000-0001-6629-939X"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuting Su","raw_affiliation_strings":["University of Science and Technology of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057822040","display_name":"Zhenfeng Zou","orcid":"https://orcid.org/0009-0007-5774-726X"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhenfeng Zou","raw_affiliation_strings":["University of Science and Technology of China"],"raw_orcid":"https://orcid.org/0009-0007-5774-726X","affiliations":[{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023576850","display_name":"Taizhong Hu","orcid":"https://orcid.org/0000-0002-9426-2348"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Taizhong Hu","raw_affiliation_strings":["University of Science and Technology of China"],"raw_orcid":"https://orcid.org/0000-0002-9426-2348","affiliations":[{"raw_affiliation_string":"University of Science and Technology of China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005817228","https://openalex.org/A5023576850","https://openalex.org/A5057822040"],"corresponding_institution_ids":["https://openalex.org/I126520041"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.43557913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"63","issue":"2","first_page":"536","last_page":"551"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.3221000134944916,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.3221000134944916,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11674","display_name":"Sports Analytics and Performance","score":0.1460999995470047,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10845","display_name":"Advanced Causal Inference Techniques","score":0.11159999668598175,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tournament","display_name":"Tournament","score":0.9753000140190125},{"id":"https://openalex.org/keywords/orthant","display_name":"Orthant","score":0.718500018119812},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5102999806404114},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5052000284194946},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.38690000772476196}],"concepts":[{"id":"https://openalex.org/C136975688","wikidata":"https://www.wikidata.org/wiki/Q1320634","display_name":"Tournament","level":2,"score":0.9753000140190125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7813000082969666},{"id":"https://openalex.org/C2780016784","wikidata":"https://www.wikidata.org/wiki/Q2714507","display_name":"Orthant","level":2,"score":0.718500018119812},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5102999806404114},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5052000284194946},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4307999908924103},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42879998683929443},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.38690000772476196},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C165661538","wikidata":"https://www.wikidata.org/wiki/Q7829327","display_name":"Tournament selection","level":3,"score":0.2547000050544739}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/jpr.2025.10043","is_oa":false,"landing_page_url":"https://doi.org/10.1017/jpr.2025.10043","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1966695467","https://openalex.org/W1972034621","https://openalex.org/W1981604690","https://openalex.org/W1984416451","https://openalex.org/W1990068454","https://openalex.org/W1997988698","https://openalex.org/W2043189488","https://openalex.org/W2083196069","https://openalex.org/W2091021910","https://openalex.org/W2101251294","https://openalex.org/W2329190018","https://openalex.org/W2584846892","https://openalex.org/W2950148913","https://openalex.org/W4206510499","https://openalex.org/W4213232880","https://openalex.org/W4233783080","https://openalex.org/W4245777296","https://openalex.org/W4319439643","https://openalex.org/W4378674802","https://openalex.org/W4393042404"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Negative":[1],"dependence":[2,16,116,120,125],"in":[3,8,51,199],"tournaments":[4,34,37],"has":[5],"received":[6],"attention":[7],"the":[9,52,111],"literature.":[10],"The":[11],"property":[12],"of":[13,113,139],"negative":[14,59,114,118,123],"orthant":[15],"(NOD)":[17],"was":[18],"proved":[19],"for":[20,28,127],"different":[21],"tournament":[22,65,130,145],"models":[23],"with":[24,38,66,131,136,146,151],"a":[25,56,63,67,128,132,143,147],"special":[26],"proof":[27,102],"each":[29],"model.":[30],"For":[31,62,142],"general":[32],"round-robin":[33],"and":[35,42,46,122,135,150,177],"knockout":[36,64,129,144],"random":[39,133],"draws,":[40],"Malinovsky":[41],"Rinott":[43],"(2023)":[44],"unified":[45],"simplified":[47],"many":[48],"existing":[49],"results":[50],"literature":[53],"by":[54],"proving":[55],"stronger":[57],"property,":[58],"association":[60],"(NA).":[61],"non-random":[68,148],"draw,":[69],"they":[70],"presented":[71],"an":[72],"example":[73],"to":[74],"illustrate":[75],"that":[76,156],"bold":[77,157,180],"italic":[78,158,181],"upper":[79,159,182],"S":[80,160,183],"<mml:math":[81,161,184],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"":[82,162,185],"xmlns:mnf=\"http://cambridge.org/core/manifest\"":[83,163,186],"xmlns:cup=\"http://contentservices.cambridge.org\"":[84,164,187],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[85,165,188],"xmlns:m=\"http://cambridge.org/core/metadata\"":[86,166,189],"xmlns:core=\"http://cambridge.org/core\"":[87,167,190],"xmlns:c=\"http://cambridge.org/core/content\">":[88,168,191],"<mml:mrow>":[89,169,192],"<mml:mi":[90,170,193],"mathvariant=\"bold-italic\">S</mml:mi>":[91,171,194],"</mml:mrow>":[92,172,195],"</mml:math>":[93,173,196],"${\\boldsymbol{S}}$":[94,174,197],"is":[95,103,175],"NOD":[96],"but":[97],"not":[98,104,201],"NA.":[99],"However,":[100],"their":[101],"correct.":[105],"In":[106],"this":[107],"paper,":[108],"we":[109,154],"establish":[110],"properties":[112],"regression":[115],"(NRD),":[117],"left-tail":[119],"(NLTD),":[121],"right-tail":[124],"(NRTD)":[126],"draw":[134,149],"players":[137],"being":[138],"equal":[140,152],"strength.":[141],"strength,":[153],"prove":[155],"NA":[176],"NRTD,":[178],"while":[179],"is,":[198],"general,":[200],"NRD":[202],"or":[203],"NLTD.":[204]},"counts_by_year":[],"updated_date":"2026-06-25T06:16:34.145877","created_date":"2025-12-04T00:00:00"}
