{"id":"https://openalex.org/W4362608684","doi":"https://doi.org/10.1007/s00355-023-01453-7","title":"Proportional representation in matching markets: selecting multiple matchings under dichotomous preferences","display_name":"Proportional representation in matching markets: selecting multiple matchings under dichotomous preferences","publication_year":2023,"publication_date":"2023-04-05","ids":{"openalex":"https://openalex.org/W4362608684","doi":"https://doi.org/10.1007/s00355-023-01453-7"},"language":"en","primary_location":{"id":"doi:10.1007/s00355-023-01453-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00355-023-01453-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00355-023-01453-7.pdf","source":{"id":"https://openalex.org/S107325288","display_name":"Social Choice and Welfare","issn_l":"0176-1714","issn":["0176-1714","1432-217X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Social Choice and Welfare","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00355-023-01453-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052325149","display_name":"Niclas Boehmer","orcid":"https://orcid.org/0000-0001-5102-449X"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Niclas Boehmer","raw_affiliation_strings":["Algorithmics and Computational Complexity, Technische Universit\u00e4t Berlin, 10587, Berlin, Germany","Algorithmics and Computational Complexity, Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5102-449X","affiliations":[{"raw_affiliation_string":"Algorithmics and Computational Complexity, Technische Universit\u00e4t Berlin, 10587, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Algorithmics and Computational Complexity, Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031193164","display_name":"Markus Brill","orcid":"https://orcid.org/0000-0001-9509-7017"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Markus Brill","raw_affiliation_strings":["Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK","Efficient Algorithms, Technische Universit\u00e4t Berlin, 10587, Berlin, Germany","Department of Computer Science, University of Warwick, Coventry, UK","Efficient Algorithms, Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0001-9509-7017","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Warwick, Coventry, CV4 7AL, UK","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"Efficient Algorithms, Technische Universit\u00e4t Berlin, 10587, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Department of Computer Science, University of Warwick, Coventry, UK","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"Efficient Algorithms, Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027081283","display_name":"Ulrike Schmidt-Kraepelin","orcid":"https://orcid.org/0000-0002-9213-7746"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]},{"id":"https://openalex.org/I69737025","display_name":"University of Chile","ror":"https://ror.org/047gc3g35","country_code":"CL","type":"education","lineage":["https://openalex.org/I69737025"]}],"countries":["CL","DE"],"is_corresponding":true,"raw_author_name":"Ulrike Schmidt-Kraepelin","raw_affiliation_strings":["Centro de Modelamiento Matem\u00e1tico, Universidad de Chile, Santiago, Chile","Efficient Algorithms, Technische Universit\u00e4t Berlin, 10587, Berlin, Germany","Efficient Algorithms, Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9213-7746","affiliations":[{"raw_affiliation_string":"Centro de Modelamiento Matem\u00e1tico, Universidad de Chile, Santiago, Chile","institution_ids":["https://openalex.org/I69737025"]},{"raw_affiliation_string":"Efficient Algorithms, Technische Universit\u00e4t Berlin, 10587, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Efficient Algorithms, Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5027081283"],"corresponding_institution_ids":["https://openalex.org/I4577782","https://openalex.org/I69737025"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.1167,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.87305013,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"64","issue":"1-2","first_page":"179","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9998999834060669,"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":0.9998999834060669,"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/T11182","display_name":"Auction Theory and Applications","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/axiom","display_name":"Axiom","score":0.7326983213424683},{"id":"https://openalex.org/keywords/voting","display_name":"Voting","score":0.6575570702552795},{"id":"https://openalex.org/keywords/approval-voting","display_name":"Approval voting","score":0.6498953104019165},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.644037127494812},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5816658139228821},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5538392066955566},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5143950581550598},{"id":"https://openalex.org/keywords/proportional-representation","display_name":"Proportional representation","score":0.5103756785392761},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5030810236930847},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4493088722229004},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4305485486984253},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3856620490550995},{"id":"https://openalex.org/keywords/condorcet-method","display_name":"Condorcet method","score":0.3784927725791931},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3337171673774719},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08493447303771973},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.07999840378761292}],"concepts":[{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7326983213424683},{"id":"https://openalex.org/C520049643","wikidata":"https://www.wikidata.org/wiki/Q189760","display_name":"Voting","level":3,"score":0.6575570702552795},{"id":"https://openalex.org/C100479058","wikidata":"https://www.wikidata.org/wiki/Q526530","display_name":"Approval voting","level":5,"score":0.6498953104019165},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.644037127494812},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5816658139228821},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5538392066955566},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5143950581550598},{"id":"https://openalex.org/C119588120","wikidata":"https://www.wikidata.org/wiki/Q13365595","display_name":"Proportional representation","level":4,"score":0.5103756785392761},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5030810236930847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4493088722229004},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4305485486984253},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3856620490550995},{"id":"https://openalex.org/C140940377","wikidata":"https://www.wikidata.org/wiki/Q868720","display_name":"Condorcet method","level":4,"score":0.3784927725791931},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3337171673774719},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08493447303771973},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.07999840378761292},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C555826173","wikidata":"https://www.wikidata.org/wiki/Q7174","display_name":"Democracy","level":3,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00355-023-01453-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00355-023-01453-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00355-023-01453-7.pdf","source":{"id":"https://openalex.org/S107325288","display_name":"Social Choice and Welfare","issn_l":"0176-1714","issn":["0176-1714","1432-217X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Social Choice and Welfare","raw_type":"journal-article"},{"id":"pmh:oai:econstor.eu:10419/309812","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/309812","pdf_url":"https://www.econstor.eu/bitstream/10419/309812/1/s00355-023-01453-7.pdf","source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:econstor.eu:10419/318562","is_oa":true,"landing_page_url":"https://hdl.handle.net/10419/318562","pdf_url":"https://www.econstor.eu/bitstream/10419/318562/1/00355_2023_Article_1453.pdf","source":{"id":"https://openalex.org/S4306401696","display_name":"Econstor (Econstor)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"doc-type:article"},{"id":"pmh:oai:RePEc:spr:sochwe:v:64:y:2025:i:1:d:10.1007_s00355-023-01453-7","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00355-023-01453-7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:3e9a97ed-75e2-48cf-9801-1567f5f02afe","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"OpenAlex","raw_type":"http://purl.org/coar/resource_type/c_dcae04bc"}],"best_oa_location":{"id":"doi:10.1007/s00355-023-01453-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00355-023-01453-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00355-023-01453-7.pdf","source":{"id":"https://openalex.org/S107325288","display_name":"Social Choice and Welfare","issn_l":"0176-1714","issn":["0176-1714","1432-217X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Social Choice and Welfare","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.5199999809265137,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1814917559","display_name":null,"funder_award_id":"NI 369/22","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5947282477","display_name":null,"funder_award_id":"BR 4744/2-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8056830759","display_name":null,"funder_award_id":"NI 369/19","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4362608684.pdf"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1666585835","https://openalex.org/W2006912660","https://openalex.org/W2011039300","https://openalex.org/W2033301836","https://openalex.org/W2047846903","https://openalex.org/W2048285065","https://openalex.org/W2063292248","https://openalex.org/W2063341202","https://openalex.org/W2068115726","https://openalex.org/W2096797149","https://openalex.org/W2102669784","https://openalex.org/W2107944092","https://openalex.org/W2134660637","https://openalex.org/W2168987865","https://openalex.org/W2241862190","https://openalex.org/W2322270235","https://openalex.org/W2346933546","https://openalex.org/W2490950911","https://openalex.org/W2558040216","https://openalex.org/W2559235980","https://openalex.org/W2788250535","https://openalex.org/W2944024625","https://openalex.org/W2952554568","https://openalex.org/W2997616944","https://openalex.org/W3004995474","https://openalex.org/W3034326317","https://openalex.org/W3035692363","https://openalex.org/W3040736983","https://openalex.org/W3176515086","https://openalex.org/W4213094076","https://openalex.org/W4233756358","https://openalex.org/W4288037860","https://openalex.org/W4292027170","https://openalex.org/W4309635574","https://openalex.org/W4362608684"],"related_works":["https://openalex.org/W3122597229","https://openalex.org/W3121552910","https://openalex.org/W2091916991","https://openalex.org/W2159183006","https://openalex.org/W1968242356","https://openalex.org/W2812810142","https://openalex.org/W2095742142","https://openalex.org/W2741845716","https://openalex.org/W3142750683","https://openalex.org/W2980481925"],"abstract_inverted_index":{"Abstract":[0],"Given":[1],"a":[2,48,153,178],"set":[3,53],"of":[4,16,31,54,57,59,79,108,118,188,196],"agents":[5],"with":[6,200],"approval":[7,120],"preferences":[8,64,71],"over":[9,65,72],"each":[10,66],"other,":[11],"we":[12,27,43,123,146],"study":[13],"the":[14,29,45,52,60,76,105,116,119,136],"task":[15],"finding":[17],"k":[18],"matchings":[19,58],"fairly":[20],"representing":[21],"everyone\u2019s":[22],"preferences.":[23,121],"To":[24,40],"formalize":[25],"fairness,":[26],"apply":[28],"concept":[30],"proportional":[32],"representation":[33],"as":[34,47,92,183],"studied":[35],"in":[36,81,135,175],"approval-based":[37,138],"multiwinner":[38,49,139],"elections.":[39],"this":[41],"end,":[42],"model":[44],"problem":[46],"election":[50],"where":[51],"candidates":[55,80],"consists":[56],"agents,":[61],"and":[62,97,127,163],"agents\u2019":[63],"other":[67,194],"are":[68,99,144],"lifted":[69],"to":[70,75,193],"matchings.":[73],"Due":[74],"exponential":[77,202],"number":[78],"such":[82],"elections,":[83],"standard":[84],"algorithms":[85],"for":[86],"classical":[87,137],"sequential":[88,166],"voting":[89,158],"rules":[90,110],"(such":[91],"those":[93,133],"proposed":[94],"by":[95,114],"Thiele":[96],"Phragm\u00e9n)":[98],"rendered":[100],"inefficient.":[101],"We":[102],"show":[103,147],"that":[104,130,142,148,164],"computational":[106],"tractability":[107],"these":[109],"can":[111],"be":[112],"regained":[113],"exploiting":[115],"structure":[117],"Moreover,":[122],"establish":[124],"algorithmic":[125,190],"results":[126,191],"axiomatic":[128],"guarantees":[129,174],"go":[131],"beyond":[132],"obtainable":[134],"setting:":[140],"Assuming":[141],"approvals":[143],"symmetric,":[145],"Proportional":[149],"Approval":[150],"Voting":[151],"(PAV),":[152],"well-established":[154],"but":[155],"computationally":[156],"intractable":[157],"rule,":[159],"becomes":[160],"polynomial-time":[161],"computable,":[162],"its":[165],"variant,":[167],"which":[168],"does":[169],"not":[170],"provide":[171],"any":[172],"proportionality":[173],"general,":[176],"fulfills":[177],"rather":[179],"strong":[180],"guarantee":[181],"known":[182],"extended":[184],"justified":[185],"representation.":[186],"Some":[187],"our":[189],"extend":[192],"types":[195],"compactly":[197],"representable":[198],"elections":[199],"an":[201],"candidate":[203],"space.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}