{"id":"https://openalex.org/W7134286960","doi":"https://doi.org/10.1287/deca.2025.0512","title":"Characterizing Fractional-Degree Stochastic Dominance by Invariance Laws","display_name":"Characterizing Fractional-Degree Stochastic Dominance by Invariance Laws","publication_year":2026,"publication_date":"2026-03-09","ids":{"openalex":"https://openalex.org/W7134286960","doi":"https://doi.org/10.1287/deca.2025.0512"},"language":"en","primary_location":{"id":"doi:10.1287/deca.2025.0512","is_oa":false,"landing_page_url":"https://doi.org/10.1287/deca.2025.0512","pdf_url":null,"source":{"id":"https://openalex.org/S33235364","display_name":"Decision Analysis","issn_l":"1545-8490","issn":["1545-8490","1545-8504"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Decision Analysis","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/A5128492061","display_name":"Tiantian Mao","orcid":null},"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":false,"raw_author_name":"Tiantian Mao","raw_affiliation_strings":["School of Management, University of Science and Technology of China, Hefei 230026, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Management, University of Science and Technology of China, Hefei 230026, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032727911","display_name":"Ruodu Wang","orcid":"https://orcid.org/0000-0003-3849-4555"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Ruodu Wang","raw_affiliation_strings":["Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":null,"display_name":"Lin Zhao","orcid":"https://orcid.org/0000-0003-3117-7610"},"institutions":[{"id":"https://openalex.org/I204831749","display_name":"Southwestern University of Finance and Economics","ror":"https://ror.org/04ewct822","country_code":"CN","type":"education","lineage":["https://openalex.org/I204831749"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin Zhao","raw_affiliation_strings":["School of Business Administration, Southwestern University of Finance and Economics, Chengdu 611130, China"],"raw_orcid":"https://orcid.org/0000-0003-3117-7610","affiliations":[{"raw_affiliation_string":"School of Business Administration, Southwestern University of Finance and Economics, Chengdu 611130, China","institution_ids":["https://openalex.org/I204831749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31302748,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"2","first_page":"149","last_page":"171"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.8323000073432922,"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":0.8323000073432922,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.051100000739097595,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10315","display_name":"Decision-Making and Behavioral Economics","score":0.019300000742077827,"subfield":{"id":"https://openalex.org/subfields/1800","display_name":"General Decision Sciences"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/stochastic-dominance","display_name":"Stochastic dominance","score":0.7937999963760376},{"id":"https://openalex.org/keywords/dominance","display_name":"Dominance (genetics)","score":0.621399998664856},{"id":"https://openalex.org/keywords/natural-science","display_name":"Natural science","score":0.5600000023841858},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.4860999882221222},{"id":"https://openalex.org/keywords/natural-law","display_name":"Natural law","score":0.42559999227523804},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.38339999318122864},{"id":"https://openalex.org/keywords/foundation","display_name":"Foundation (evidence)","score":0.36169999837875366},{"id":"https://openalex.org/keywords/expected-utility-hypothesis","display_name":"Expected utility hypothesis","score":0.34290000796318054}],"concepts":[{"id":"https://openalex.org/C33252445","wikidata":"https://www.wikidata.org/wiki/Q3713315","display_name":"Stochastic dominance","level":2,"score":0.7937999963760376},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.680899977684021},{"id":"https://openalex.org/C151913843","wikidata":"https://www.wikidata.org/wiki/Q3454555","display_name":"Dominance (genetics)","level":3,"score":0.621399998664856},{"id":"https://openalex.org/C193235544","wikidata":"https://www.wikidata.org/wiki/Q7991","display_name":"Natural science","level":2,"score":0.5600000023841858},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.4860999882221222},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45089998841285706},{"id":"https://openalex.org/C155785087","wikidata":"https://www.wikidata.org/wiki/Q29524","display_name":"Natural law","level":2,"score":0.42559999227523804},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.38339999318122864},{"id":"https://openalex.org/C2780966255","wikidata":"https://www.wikidata.org/wiki/Q5474306","display_name":"Foundation (evidence)","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36149999499320984},{"id":"https://openalex.org/C205706631","wikidata":"https://www.wikidata.org/wiki/Q2319304","display_name":"Expected utility hypothesis","level":2,"score":0.34290000796318054},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.32690000534057617},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.31380000710487366},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C191935318","wikidata":"https://www.wikidata.org/wiki/Q148","display_name":"China","level":2,"score":0.2937000095844269},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.2856000065803528},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C2781043087","wikidata":"https://www.wikidata.org/wiki/Q939761","display_name":"Preference theory","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C28901747","wikidata":"https://www.wikidata.org/wiki/Q177571","display_name":"Decision theory","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C84839998","wikidata":"https://www.wikidata.org/wiki/Q5249245","display_name":"Decision rule","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.26010000705718994},{"id":"https://openalex.org/C2778648169","wikidata":"https://www.wikidata.org/wiki/Q967768","display_name":"Compatibility (geochemistry)","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.2574000060558319},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2508000135421753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1287/deca.2025.0512","is_oa":false,"landing_page_url":"https://doi.org/10.1287/deca.2025.0512","pdf_url":null,"source":{"id":"https://openalex.org/S33235364","display_name":"Decision Analysis","issn_l":"1545-8490","issn":["1545-8490","1545-8504"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Decision Analysis","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":40,"referenced_works":["https://openalex.org/W1583280453","https://openalex.org/W1966823320","https://openalex.org/W1967658623","https://openalex.org/W1975687818","https://openalex.org/W1995118028","https://openalex.org/W1996926988","https://openalex.org/W2001842060","https://openalex.org/W2004226444","https://openalex.org/W2009749785","https://openalex.org/W2028465076","https://openalex.org/W2050905651","https://openalex.org/W2058860749","https://openalex.org/W2059597350","https://openalex.org/W2070539891","https://openalex.org/W2081081544","https://openalex.org/W2085274538","https://openalex.org/W2087460341","https://openalex.org/W2091803403","https://openalex.org/W2116558675","https://openalex.org/W2120166589","https://openalex.org/W2142504616","https://openalex.org/W2157699542","https://openalex.org/W2171543997","https://openalex.org/W2221453696","https://openalex.org/W2547703543","https://openalex.org/W2749733103","https://openalex.org/W2906913962","https://openalex.org/W2938317532","https://openalex.org/W2962769750","https://openalex.org/W3012080916","https://openalex.org/W3121406782","https://openalex.org/W3121428746","https://openalex.org/W3121958765","https://openalex.org/W3122010017","https://openalex.org/W3122754327","https://openalex.org/W3123005068","https://openalex.org/W4245777296","https://openalex.org/W4252707658","https://openalex.org/W4310251704","https://openalex.org/W4404713048"],"related_works":[],"abstract_inverted_index":{"Classic":[0],"notions":[1],"of":[2,21,84,98,107,122,140,156],"stochastic":[3,23,51],"dominance":[4,24,52],"have":[5,10],"integer":[6],"degrees.":[7],"Recent":[8],"studies":[9],"imposed":[11],"distinct":[12],"preference":[13,27],"conditions":[14,28],"for":[15,42],"refinement,":[16],"resulting":[17],"in":[18],"a":[19,39,60],"range":[20],"fractional-degree":[22,50],"rules.":[25,93],"However,":[26],"are":[29],"generally":[30],"not":[31],"mutually":[32],"exclusive,":[33],"making":[34],"it":[35],"challenging":[36],"to":[37,66,75,87,104],"establish":[38,49],"strict":[40],"criterion":[41],"rule":[43],"selection.":[44,110],"To":[45],"address":[46],"this,":[47],"we":[48],"rules":[53],"based":[54],"exclusively":[55],"on":[56,78],"invariance":[57,85],"laws":[58],"under":[59],"general":[61],"condition":[62],"that":[63],"is":[64,114,130,148],"applicable":[65],"all":[67],"intermediate":[68],"utility":[69],"sets.":[70],"This":[71],"approach":[72,100],"enables":[73],"practitioners":[74],"rely":[76],"solely":[77],"the":[79,91,96,105,117,133,151],"mutual":[80,108],"compatibility":[81],"and":[82,89,126,136,144,160],"exclusivity":[83],"properties":[86],"compare":[88],"select":[90],"appropriate":[92],"We":[94],"illustrate":[95],"usefulness":[97],"our":[99],"through":[101],"an":[102],"application":[103],"problem":[106],"fund":[109],"Funding:":[111],"T.":[112],"Mao":[113],"supported":[115,131,149],"by":[116,132,150],"National":[118,152],"Natural":[119,134,153],"Science":[120,154],"Foundation":[121,155],"China":[123,157],"[Grants":[124,142,158],"12371476":[125],"71921001].":[127],"R.":[128],"Wang":[129],"Sciences":[135],"Engineering":[137],"Research":[138],"Council":[139],"Canada":[141],"CRC-2022-00141":[143],"RGPIN-2024-03728].":[145],"L.":[146],"Zhao":[147],"72125003":[159],"72131003].":[161]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-10T00:00:00"}
