{"id":"https://openalex.org/W4416552022","doi":"https://doi.org/10.48550/arxiv.2508.00811","title":"Justified Representation: From Hare to Droop","display_name":"Justified Representation: From Hare to Droop","publication_year":2025,"publication_date":"2025-08-01","ids":{"openalex":"https://openalex.org/W4416552022","doi":"https://doi.org/10.48550/arxiv.2508.00811"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2508.00811","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2508.00811","pdf_url":"https://arxiv.org/pdf/2508.00811","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2508.00811","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120467649","display_name":"Matthew M. Casey","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Casey, Matthew M.","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5050150656","display_name":"Edith Elkind","orcid":"https://orcid.org/0000-0001-6718-3436"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Elkind, Edith","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5120467649"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9922999739646912,"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":0.9922999739646912,"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/T11598","display_name":"Internet Traffic Analysis and Secure E-voting","score":0.001500000013038516,"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"}},{"id":"https://openalex.org/T10108","display_name":"Electoral Systems and Political Participation","score":0.0013000000035390258,"subfield":{"id":"https://openalex.org/subfields/3320","display_name":"Political Science and International Relations"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/proportionality","display_name":"Proportionality (law)","score":0.8586000204086304},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7501999735832214},{"id":"https://openalex.org/keywords/voting","display_name":"Voting","score":0.6401000022888184},{"id":"https://openalex.org/keywords/voltage-droop","display_name":"Voltage droop","score":0.5752000212669373},{"id":"https://openalex.org/keywords/social-choice-theory","display_name":"Social choice theory","score":0.5252000093460083},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.3928999900817871},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.329800009727478}],"concepts":[{"id":"https://openalex.org/C183763965","wikidata":"https://www.wikidata.org/wiki/Q603959","display_name":"Proportionality (law)","level":2,"score":0.8586000204086304},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7501999735832214},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.6733999848365784},{"id":"https://openalex.org/C520049643","wikidata":"https://www.wikidata.org/wiki/Q189760","display_name":"Voting","level":3,"score":0.6401000022888184},{"id":"https://openalex.org/C40760162","wikidata":"https://www.wikidata.org/wiki/Q10920295","display_name":"Voltage droop","level":4,"score":0.5752000212669373},{"id":"https://openalex.org/C189352744","wikidata":"https://www.wikidata.org/wiki/Q1971461","display_name":"Social choice theory","level":2,"score":0.5252000093460083},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4341999888420105},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.3928999900817871},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3312999904155731},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.329800009727478},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3118000030517578},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3068999946117401},{"id":"https://openalex.org/C100479058","wikidata":"https://www.wikidata.org/wiki/Q526530","display_name":"Approval voting","level":5,"score":0.29670000076293945},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2935999929904938},{"id":"https://openalex.org/C156160270","wikidata":"https://www.wikidata.org/wiki/Q1078003","display_name":"Ranked voting system","level":4,"score":0.2639999985694885},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C140940377","wikidata":"https://www.wikidata.org/wiki/Q868720","display_name":"Condorcet method","level":4,"score":0.2565999925136566},{"id":"https://openalex.org/C132778050","wikidata":"https://www.wikidata.org/wiki/Q2065430","display_name":"Weighted voting","level":4,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2508.00811","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2508.00811","pdf_url":"https://arxiv.org/pdf/2508.00811","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2508.00811","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2508.00811","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2508.00811","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2508.00811","pdf_url":"https://arxiv.org/pdf/2508.00811","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,57,133],"study":[1,141],"of":[2,23,33,44,52,77,122,135,142,157,163,187,240,259],"proportionality":[3,18,106,242],"in":[4,14,66,91,97,105,119,208],"multiwinner":[5,92],"voting":[6,93,146,180],"with":[7,94,249],"approval":[8,123],"ballots":[9],"has":[10],"received":[11],"much":[12],"attention":[13],"recent":[15],"years.":[16],"Typically,":[17],"is":[19,40,48,60,79,88,129,138,212,223],"captured":[20],"by":[21],"variants":[22],"the":[24,41,49,63,67,80,120,126,153,158,164,184,200,216,231,238],"Justified":[25],"Representation":[26],"axiom,":[27],"which":[28],"say":[29],"that":[30,148,182,254],"cohesive":[31],"groups":[32],"at":[34],"least":[35],"$\\ell\\cdot\\frac{n}{k}$":[36],"voters":[37,45],"(where":[38],"$n$":[39],"total":[42],"number":[43,51],"and":[46,104,175,207],"$k$":[47],"desired":[50],"winners)":[53],"deserve":[54],"$\\ell$":[55],"representatives.":[56],"quantity":[58],"$\\frac{n}{k}$":[59],"known":[61,197],"as":[62,84,100,109],"Hare":[64,159,202],"quota":[65,78,87,155],"social":[68],"choice":[69,76],"literature.":[70],"Another":[71],"--":[72,75],"more":[73,224,266],"demanding":[74,267],"Droop":[81,154,185,232,262],"quota,":[82,233],"defined":[83,151,229],"$\\lfloor\\frac{n}{k+1}\\rfloor+1$.":[85],"This":[86],"often":[89],"used":[90],"ranked":[95],"ballots:":[96],"algorithms":[98],"such":[99,108],"Single":[101],"Transferable":[102],"Voting,":[103],"axioms,":[107],"Droop's":[110],"Proportionality":[111],"Criterion.":[112],"A":[113],"few":[114],"authors":[115],"have":[116],"considered":[117],"it":[118,193,211],"context":[121],"ballots,":[124],"but":[125],"existing":[127],"analysis":[128],"far":[130],"from":[131,218],"comprehensive.":[132],"contribution":[134],"our":[136,235,246],"work":[137],"a":[139,179],"systematic":[140],"JR-style":[143],"axioms":[144,167],"(and":[145],"rules":[147,198,217],"satisfy":[149,227],"them)":[150],"using":[152,230],"instead":[156],"quota.":[160],"For":[161],"each":[162],"standard":[165,269],"JR":[166],"(namely,":[168],"JR,":[169],"PJR,":[170],"EJR,":[171],"FPJR,":[172],"FJR,":[173],"PJR+":[174],"EJR+),":[176],"we":[177],"identify":[178],"rule":[181],"satisfies":[183],"version":[186],"this":[188],"axiom.":[189],"In":[190],"some":[191],"cases,":[192],"suffices":[194],"to":[195,214,226],"consider":[196],"(modifying":[199],"corresponding":[201],"proof,":[203],"sometimes":[204],"quite":[205],"substantially),":[206],"other":[209],"cases":[210],"necessary":[213],"modify":[215],"prior":[219],"work.":[220],"Each":[221],"axiom":[222],"difficult":[225],"when":[228],"so":[234],"results":[236,248],"expand":[237],"frontier":[239],"satisfiable":[241],"axioms.":[243],"We":[244],"complement":[245],"theoretical":[247],"an":[250],"experimental":[251],"study,":[252],"showing":[253],"for":[255],"many":[256],"probabilistic":[257],"models":[258],"voter":[260],"approvals,":[261],"JR/EJR+":[263],"are":[264],"considerably":[265],"than":[268],"(Hare)":[270],"JR/EJR+.":[271]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}