{"id":"https://openalex.org/W7206157992","doi":"https://doi.org/10.48550/arxiv.2609.01580","title":"Weighted Fair Division of Indivisible Mixed Manna","display_name":"Weighted Fair Division of Indivisible Mixed Manna","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7206157992","doi":"https://doi.org/10.48550/arxiv.2609.01580"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01580","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01580","pdf_url":"https://arxiv.org/pdf/2609.01580","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.01580","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037242857","display_name":"Nicholas Teh","orcid":"https://orcid.org/0000-0002-9698-466X","observed_orcids":["https://orcid.org/0000-0002-9698-466X"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Teh, Nicholas","raw_affiliation_strings":["University of Oxford , UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Oxford , UK","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037242857"],"corresponding_institution_ids":["https://openalex.org/I40120149"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9994999766349792,"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":0.9994999766349792,"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/T12288","display_name":"Optimization and Search Problems","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/indivisible-goods","display_name":"indivisible goods","score":0.8180000185966492},{"id":"https://openalex.org/keywords/additive-valuations","display_name":"additive valuations","score":0.7429999709129333},{"id":"https://openalex.org/keywords/entitlement","display_name":"entitlement","score":0.6019999980926514},{"id":"https://openalex.org/keywords/price-of-fairness","display_name":"price of fairness","score":0.7820000052452087},{"id":"https://openalex.org/keywords/polynomial-time-algorithms","display_name":"polynomial-time algorithms","score":0.6610000133514404},{"id":"https://openalex.org/keywords/flow-algorithms","display_name":"flow algorithms","score":0.5590000152587891},{"id":"https://openalex.org/keywords/chores","display_name":"chores","score":0.48100000619888306},{"id":"https://openalex.org/keywords/welfare-guarantees","display_name":"welfare guarantees","score":0.39800000190734863}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7404000163078308},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.6075999736785889},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5975000262260437},{"id":"https://openalex.org/C184659173","wikidata":"https://www.wikidata.org/wiki/Q1511081","display_name":"Fair division","level":2,"score":0.5960000157356262},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5720000267028809},{"id":"https://openalex.org/C94982200","wikidata":"https://www.wikidata.org/wiki/Q5380545","display_name":"Entitlement (fair division)","level":2,"score":0.5049999952316284},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.49619999527931213},{"id":"https://openalex.org/C186027771","wikidata":"https://www.wikidata.org/wiki/Q4008379","display_name":"Valuation (finance)","level":2,"score":0.43560001254081726},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.34700000286102295},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34470000863075256},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3147999942302704},{"id":"https://openalex.org/C58468513","wikidata":"https://www.wikidata.org/wiki/Q1201165","display_name":"Determinacy","level":2,"score":0.2824999988079071},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2750000059604645},{"id":"https://openalex.org/C2780339515","wikidata":"https://www.wikidata.org/wiki/Q3074698","display_name":"Arrow","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01580","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01580","pdf_url":"https://arxiv.org/pdf/2609.01580","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.01580","doi":"https://doi.org/10.48550/arxiv.2609.01580","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01580","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.01580","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01580","pdf_url":"https://arxiv.org/pdf/2609.01580","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7206157992.pdf","grobid_xml":"https://content.openalex.org/works/W7206157992.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7207798055","https://openalex.org/W4403578839","https://openalex.org/W4415345314","https://openalex.org/W4416017127","https://openalex.org/W2989970888","https://openalex.org/W4378501534","https://openalex.org/W3183710841","https://openalex.org/W2973654306","https://openalex.org/W7124247511","https://openalex.org/W4387107393"],"abstract_inverted_index":{"We":[0,46],"study":[1],"weighted":[2,21,121],"fair":[3],"division":[4],"of":[5,61],"indivisible":[6],"mixed":[7],"manna":[8],"under":[9,188],"additive":[10,165],"valuations.":[11],"First,":[12],"we":[13],"resolve":[14],"the":[15,58,89,172,177],"general":[16],"existence":[17,50],"open":[18],"question":[19],"for":[20,66,108,117,145,220],"envy-freeness":[22],"up":[23],"to":[24,137,150,176],"one":[25],"item":[26,74,110],"(WEF1),":[27],"and":[28,76,133],"show":[29,48],"that":[30,49,105],"every":[31,158,191],"instance":[32],"with":[33,70,218],"arbitrary":[34,118],"positive":[35,200],"entitlements":[36],"admits":[37],"a":[38,80,84,101,120,151,162,198],"complete":[39],"WEF1":[40,62,86,159,192,219],"allocation":[41,87,125,160,193],"computable":[42,129],"in":[43,79,88,130],"polynomial":[44,131],"time.":[45],"then":[47],"does":[51],"not":[52],"imply":[53],"any":[54,109,212],"welfare":[55],"guarantee,":[56],"i.e.,":[57],"utilitarian":[59],"price":[60],"is":[63,91,111,128,194],"infinite,":[64],"even":[65],"two":[67],"unweighted":[68],"agents":[69,183],"normalized":[71],"valuations,":[72],"common":[73],"signs,":[75],"singleton":[77],"values":[78],"fixed":[81,213],"four-value":[82],"set;":[83],"welfare-maximizing":[85],"construction":[90],"fractionally":[92,139],"Pareto":[93,140],"optimal.":[94,141],"Second,":[95],"suppose":[96],"each":[97,146],"agent":[98],"$i$":[99],"has":[100],"number":[102],"$a_i>0$":[103],"such":[104],"their":[106],"valuation":[107],"$-a_i$,":[112],"$0$,":[113],"or":[114],"$a_i$.":[115],"Then,":[116],"entitlements,":[119,190],"maximin":[122],"share":[123],"(WMMS)":[124],"always":[126],"exists,":[127],"time,":[132],"can":[134,202],"be":[135,138],"chosen":[136],"An":[142],"exact":[143,185,204],"formula":[144],"WMMS":[147,166,186,215],"value":[148],"leads":[149],"polynomial-time":[152],"flow":[153],"algorithm.":[154],"In":[155],"this":[156],"class,":[157],"satisfies":[161],"best":[163],"possible":[164],"guarantee":[167,216],"whose":[168],"loss":[169],"depends":[170],"on":[171],"agent's":[173],"entitlement":[174,182,208],"relative":[175],"largest":[178],"entitlement.":[179],"Thus":[180],"maximum":[181],"receive":[184],"and,":[187],"equal":[189],"also":[195],"MMS-fair.":[196],"Allowing":[197],"second":[199],"magnitude":[201],"violate":[203],"WMMS,":[205],"while":[206],"unrestricted":[207],"ratios":[209],"rule":[210],"out":[211],"multiplicative":[214],"compatible":[217],"chores.":[221]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-03T00:00:00"}