{"id":"https://openalex.org/W7204459296","doi":"https://doi.org/10.3390/axioms15090639","title":"Constrained Bayesian Reconstruction of Latent Public Preferences Under Dynamic Elimination Rules: An Uncertainty-Aware Expert\u2013Public Fusion Framework","display_name":"Constrained Bayesian Reconstruction of Latent Public Preferences Under Dynamic Elimination Rules: An Uncertainty-Aware Expert\u2013Public Fusion Framework","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204459296","doi":"https://doi.org/10.3390/axioms15090639"},"language":"en","primary_location":{"id":"doi:10.3390/axioms15090639","doi":"https://doi.org/10.3390/axioms15090639","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15090639","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"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":"Axioms","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms15090639","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025213616","display_name":"Fang Liang","orcid":"https://orcid.org/0000-0002-0372-8027","observed_orcids":["https://orcid.org/0000-0002-0372-8027"]},"institutions":[{"id":"https://openalex.org/I31683504","display_name":"Beijing Forestry University","ror":"https://ror.org/04xv2pc41","country_code":"CN","type":"education","lineage":["https://openalex.org/I1327237609","https://openalex.org/I31683504","https://openalex.org/I4210127390"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang Fang","raw_affiliation_strings":["School of Economics and Management, Beijing Forestry University, Beijing 100083, China"],"raw_orcid":"https://orcid.org/0000-0002-0372-8027","affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing Forestry University, Beijing 100083, China","institution_ids":["https://openalex.org/I31683504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147679841","display_name":"Xiaoyu Wang","orcid":"https://orcid.org/0009-0000-6193-9896","observed_orcids":["https://orcid.org/0009-0000-6193-9896"]},"institutions":[{"id":"https://openalex.org/I31683504","display_name":"Beijing Forestry University","ror":"https://ror.org/04xv2pc41","country_code":"CN","type":"education","lineage":["https://openalex.org/I1327237609","https://openalex.org/I31683504","https://openalex.org/I4210127390"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoyu Wang","raw_affiliation_strings":["School of Economics and Management, Beijing Forestry University, Beijing 100083, China"],"raw_orcid":"https://orcid.org/0009-0000-6193-9896","affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing Forestry University, Beijing 100083, China","institution_ids":["https://openalex.org/I31683504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147669418","display_name":"Jiashuo Fan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I31683504","display_name":"Beijing Forestry University","ror":"https://ror.org/04xv2pc41","country_code":"CN","type":"education","lineage":["https://openalex.org/I1327237609","https://openalex.org/I31683504","https://openalex.org/I4210127390"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiashuo Fan","raw_affiliation_strings":["School of Technology, Beijing Forestry University, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Technology, Beijing Forestry University, Beijing 100083, China","institution_ids":["https://openalex.org/I31683504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147670001","display_name":"Shengyu He","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I31683504","display_name":"Beijing Forestry University","ror":"https://ror.org/04xv2pc41","country_code":"CN","type":"education","lineage":["https://openalex.org/I1327237609","https://openalex.org/I31683504","https://openalex.org/I4210127390"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shengyu He","raw_affiliation_strings":["School of Landscape Architecture, Beijing Forestry University, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Landscape Architecture, Beijing Forestry University, Beijing 100083, China","institution_ids":["https://openalex.org/I31683504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5148435405","display_name":"Wenhui Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I31683504","display_name":"Beijing Forestry University","ror":"https://ror.org/04xv2pc41","country_code":"CN","type":"education","lineage":["https://openalex.org/I1327237609","https://openalex.org/I31683504","https://openalex.org/I4210127390"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenhui Chen","raw_affiliation_strings":["School of Economics and Management, Beijing Forestry University, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economics and Management, Beijing Forestry University, Beijing 100083, China","institution_ids":["https://openalex.org/I31683504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I31683504"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2896},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2896},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.71039925,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"9","first_page":"639","last_page":"639"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.43849998712539673,"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"}},"topics":[{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.43849998712539673,"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"}},{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.11580000072717667,"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"}},{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.09939999878406525,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/public-preferences","display_name":"public preferences","score":0.42899999022483826},{"id":"https://openalex.org/keywords/identified-set","display_name":"identified set","score":0.5320000052452087},{"id":"https://openalex.org/keywords/metropolis-hastings-sampling","display_name":"Metropolis-Hastings sampling","score":0.7310000061988831},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.6700000166893005},{"id":"https://openalex.org/keywords/dancing-with-the-stars","display_name":"Dancing with the Stars","score":0.8119999766349792},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"uncertainty quantification","score":0.45100000500679016}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6834999918937683},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5365999937057495},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.46140000224113464},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.44290000200271606},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4228000044822693},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.37610000371932983},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.37070000171661377},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3675999939441681},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.36000001430511475},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.34200000762939453},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.33309999108314514},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3230000138282776},{"id":"https://openalex.org/C159744936","wikidata":"https://www.wikidata.org/wiki/Q1126730","display_name":"Spearman's rank correlation coefficient","level":2,"score":0.3127000033855438},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.3091000020503998},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.30660000443458557},{"id":"https://openalex.org/C2781280628","wikidata":"https://www.wikidata.org/wiki/Q5280766","display_name":"Dirichlet process","level":3,"score":0.299699991941452},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.29739999771118164},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2922999858856201},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.28700000047683716},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.2556000053882599},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms15090639","doi":"https://doi.org/10.3390/axioms15090639","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15090639","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3e54b677828d4e8394ecf44de62d22bd","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/3e54b677828d4e8394ecf44de62d22bd","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,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 15, Iss 9, p 639 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms15090639","doi":"https://doi.org/10.3390/axioms15090639","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15090639","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.47620001435279846}],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320335869","display_name":"National Social Science Fund of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W100464641","https://openalex.org/W1512208174","https://openalex.org/W1648907168","https://openalex.org/W1993865115","https://openalex.org/W1995875735","https://openalex.org/W2007423920","https://openalex.org/W2032916024","https://openalex.org/W2055325763","https://openalex.org/W2063248556","https://openalex.org/W2067392831","https://openalex.org/W2114990184","https://openalex.org/W2119515738","https://openalex.org/W2138309709","https://openalex.org/W2147453867","https://openalex.org/W2149498546","https://openalex.org/W2151729750","https://openalex.org/W2152828142","https://openalex.org/W2158392329","https://openalex.org/W2159026487","https://openalex.org/W2580299352","https://openalex.org/W2775363893","https://openalex.org/W2795604964","https://openalex.org/W2920804790","https://openalex.org/W3021341554","https://openalex.org/W3125298827","https://openalex.org/W4205465679","https://openalex.org/W4236474156"],"related_works":[],"abstract_inverted_index":{"Expert\u2013public":[0],"selection":[1],"systems":[2],"often":[3],"reveal":[4],"expert":[5],"scores,":[6],"institutional":[7,151],"rules,":[8,152],"and":[9,39,42,70,96,104,149,164,198,214,233,268,297],"discrete":[10],"elimination":[11,187],"outcomes":[12],"while":[13],"concealing":[14],"public-vote":[15],"information.":[16],"This":[17],"paper":[18],"develops":[19],"a":[20,63,113,165,302,309],"constrained":[21],"Bayesian":[22],"inverse-inference":[23],"framework":[24,293],"for":[25,91,159,304],"inferring":[26],"rule-compatible":[27,56],"latent":[28,37],"public-preference":[29],"distributions.":[30],"Public":[31],"preferences":[32],"are":[33,46,74,85,110],"represented":[34],"as":[35],"simplex-valued":[36],"variables,":[38],"rank-based,":[40],"percentage-based,":[41],"judges\u2019":[43,71,105],"save":[44,72,106],"mechanisms":[45],"encoded":[47],"through":[48],"rule-induced":[49],"likelihood":[50],"constraints.":[51],"We":[52],"formally":[53],"characterize":[54],"the":[55,59,68,121,124,136,160,185,189,200,247,278],"identified-set":[57],"geometry:":[58],"percentage-rule":[60,94],"set":[61],"is":[62,294],"compact":[64],"convex":[65],"polytope,":[66],"whereas":[67,266],"rank-based":[69],"sets":[73],"finite":[75],"unions":[76],"of":[77,244,255,289],"polyhedral":[78],"rank":[79,103],"cells.":[80],"Prior-free":[81],"sharp":[82],"coordinate":[83],"bounds":[84],"obtained":[86],"by":[87,97],"exact":[88,98,305],"linear":[89],"programming":[90],"all":[92],"170":[93],"weeks":[95],"weak-order":[99],"enumeration":[100],"in":[101,212,287],"representative":[102],"cases.":[107],"Posterior":[108],"distributions":[109],"approximated":[111],"using":[112],"mixed":[114,234],"Metropolis\u2013Hastings":[115,235],"sampler":[116],"whose":[117],"transition":[118],"kernel":[119],"preserves":[120],"target":[122],"posterior;":[123],"positive-probability":[125],"global":[126],"Dirichlet":[127],"component":[128],"provides":[129],"irreducibility":[130],"across":[131],"separated":[132],"positive-posterior-mass":[133],"regions.":[134],"In":[135,237],"primary":[137],"1800-case":[138],"factorial":[139],"synthetic":[140],"study":[141],"spanning":[142],"two":[143],"truth-generating":[144],"mechanisms,":[145],"three":[146,150],"contestant-set":[147],"sizes,":[148],"marginal":[153],"95%":[154],"credible-interval":[155],"coverage":[156,174],"was":[157],"similar":[158],"rule-constrained":[161,276],"posterior":[162,257],"(0.9400\u20130.9625)":[163],"newly":[166],"added":[167],"prior-only":[168],"benchmark":[169],"(0.9475\u20130.9617),":[170],"indicating":[171],"that":[172],"near-nominal":[173],"primarily":[175],"reflects":[176],"interval":[177],"calibration":[178],"rather":[179,300],"than":[180,301],"recovery":[181,307],"accuracy.":[182],"Conditioning":[183],"on":[184],"observed":[186],"reduced":[188],"overall":[190],"mean":[191,201,258],"total-variation":[192],"distance":[193],"from":[194,204],"0.4613":[195],"to":[196,208,241],"0.4353":[197],"increased":[199],"Spearman":[202],"correlation":[203],"approximately":[205],"zero":[206],"(\u22120.0206)":[207],"0.2147,":[209],"although":[210],"gains":[211],"Top-1":[213],"Top-3":[215],"identification":[216],"were":[217,260,271],"not":[218],"uniform":[219],"under":[220,262],"logistic-normal":[221],"misspecification.":[222],"A":[223],"54-case":[224],"validation":[225],"showed":[226],"close":[227],"agreement":[228],"between":[229],"vectorized":[230],"rejection":[231],"sampling":[232],"sampling.":[236],"an":[238],"empirical":[239],"application":[240],"34":[242],"seasons":[243],"Dancing":[245],"with":[246,284],"Stars,":[248],"multi-chain":[249],"diagnostics":[250],"provided":[251],"no":[252],"material":[253],"evidence":[254],"non-convergence;":[256],"shares":[259],"stable":[261],"moderate":[263],"specification":[264],"changes,":[265],"rankings":[267],"uncertainty":[269],"widths":[270],"more":[272],"sensitive.":[273],"Across":[274],"224":[275],"weeks,":[277],"Logistic":[279],"Dynamic":[280],"Weighting":[281],"System":[282],"agreed":[283],"percentage-based":[285],"decisions":[286],"86.66%":[288],"same-draw":[290],"comparisons.":[291],"The":[292],"therefore":[295],"uncertainty-aware":[296],"institutionally":[298],"transparent,":[299],"method":[303],"vote":[306],"or":[308],"universally":[310],"superior":[311],"aggregation":[312],"rule.":[313]},"counts_by_year":[],"updated_date":"2026-10-08T09:06:37.294493","created_date":"2026-08-28T00:00:00"}
