{"id":"https://openalex.org/W4288037860","doi":"https://doi.org/10.1007/s10107-022-01852-1","title":"Approval-based apportionment","display_name":"Approval-based apportionment","publication_year":2022,"publication_date":"2022-07-26","ids":{"openalex":"https://openalex.org/W4288037860","doi":"https://doi.org/10.1007/s10107-022-01852-1"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-022-01852-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-022-01852-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01852-1.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","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/s10107-022-01852-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031193164","display_name":"Markus Brill","orcid":"https://orcid.org/0000-0001-9509-7017"},"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":true,"raw_author_name":"Markus Brill","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Research Group Efficient Algorithms, Berlin, Germany","TU - Technical University of Berlin / Technische Universit\u00e4t Berlin (Stra\u00dfe des 17. Juni 135 10623 Berlin - Allemagne)"],"raw_orcid":"https://orcid.org/0000-0001-9509-7017","affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Research Group Efficient Algorithms, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"TU - Technical University of Berlin / Technische Universit\u00e4t Berlin (Stra\u00dfe des 17. Juni 135 10623 Berlin - Allemagne)","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044570084","display_name":"Paul G\u00f6lz","orcid":"https://orcid.org/0000-0002-8101-6818"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul G\u00f6lz","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, PA, USA","CMU - Carnegie Mellon University [Pittsburgh] (5000 Forbes Ave,  Pittsburgh, PA 15213 - \u00c9tats-Unis)"],"raw_orcid":"https://orcid.org/0000-0002-8101-6818","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"CMU - Carnegie Mellon University [Pittsburgh] (5000 Forbes Ave,  Pittsburgh, PA 15213 - \u00c9tats-Unis)","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015162351","display_name":"Dominik Peters","orcid":"https://orcid.org/0000-0001-9418-7571"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210137929","display_name":"Lamsade","ror":"https://ror.org/03pnp1a74","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2746051580","https://openalex.org/I4210137929","https://openalex.org/I4210159245","https://openalex.org/I56435720"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dominik Peters","raw_affiliation_strings":["CNRS, LAMSADE, Universit\u00e9 Paris Dauphine\u2013PSL, Paris, France","LAMSADE - Laboratoire d'analyse et mod\u00e9lisation de syst\u00e8mes pour l'aide \u00e0 la d\u00e9cision (Place de Lattre de Tassigny 75775 PARIS CEDEX 16 - France)"],"raw_orcid":"https://orcid.org/0000-0001-9418-7571","affiliations":[{"raw_affiliation_string":"CNRS, LAMSADE, Universit\u00e9 Paris Dauphine\u2013PSL, Paris, France","institution_ids":["https://openalex.org/I56435720","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LAMSADE - Laboratoire d'analyse et mod\u00e9lisation de syst\u00e8mes pour l'aide \u00e0 la d\u00e9cision (Place de Lattre de Tassigny 75775 PARIS CEDEX 16 - France)","institution_ids":["https://openalex.org/I4210137929"]}]},{"author_position":"middle","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"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ulrike Schmidt-Kraepelin","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Research Group Efficient Algorithms, Berlin, Germany","TU - Technical University of Berlin / Technische Universit\u00e4t Berlin (Stra\u00dfe des 17. Juni 135 10623 Berlin - Allemagne)"],"raw_orcid":"https://orcid.org/0000-0002-9213-7746","affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Research Group Efficient Algorithms, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"TU - Technical University of Berlin / Technische Universit\u00e4t Berlin (Stra\u00dfe des 17. Juni 135 10623 Berlin - Allemagne)","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086429338","display_name":"Kai Wilker","orcid":null},"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":"Kai Wilker","raw_affiliation_strings":["Technische Universit\u00e4t Berlin, Research Group Efficient Algorithms, Berlin, Germany","TU - Technical University of Berlin / Technische Universit\u00e4t Berlin (Stra\u00dfe des 17. Juni 135 10623 Berlin - Allemagne)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Berlin, Research Group Efficient Algorithms, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"TU - Technical University of Berlin / Technische Universit\u00e4t Berlin (Stra\u00dfe des 17. Juni 135 10623 Berlin - Allemagne)","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5031193164"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":3.565,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.93638193,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"203","issue":"1-2","first_page":"77","last_page":"105"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9872999787330627,"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/T10108","display_name":"Electoral Systems and Political Participation","score":0.9779000282287598,"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/apportionment","display_name":"Apportionment","score":0.9955115914344788},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.6954337954521179},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6796408891677856},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.6415769457817078},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5893754959106445},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5296753644943237},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5061947703361511},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5059682726860046},{"id":"https://openalex.org/keywords/operations-research","display_name":"Operations research","score":0.37893617153167725},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3642074167728424},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.26205506920814514},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.18321409821510315},{"id":"https://openalex.org/keywords/politics","display_name":"Politics","score":0.08804318308830261}],"concepts":[{"id":"https://openalex.org/C2778337684","wikidata":"https://www.wikidata.org/wiki/Q3173700","display_name":"Apportionment","level":2,"score":0.9955115914344788},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.6954337954521179},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6796408891677856},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.6415769457817078},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5893754959106445},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5296753644943237},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5061947703361511},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5059682726860046},{"id":"https://openalex.org/C42475967","wikidata":"https://www.wikidata.org/wiki/Q194292","display_name":"Operations research","level":1,"score":0.37893617153167725},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3642074167728424},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.26205506920814514},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.18321409821510315},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.08804318308830261},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"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/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10107-022-01852-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-022-01852-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01852-1.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:170677","is_oa":true,"landing_page_url":null,"pdf_url":"https://wrap.warwick.ac.uk/170677/1/s10107-022-01852-1.pdf","source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:HAL:hal-03816043v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03816043","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Programming, 2022, 203, pp.77--105. &#x27E8;10.1007/s10107-022-01852-1&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1007/s10107-022-01852-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-022-01852-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01852-1.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7799999713897705,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"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"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4288037860.pdf","grobid_xml":"https://content.openalex.org/works/W4288037860.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W587373156","https://openalex.org/W1666585835","https://openalex.org/W1993527581","https://openalex.org/W2017492304","https://openalex.org/W2017990047","https://openalex.org/W2050020465","https://openalex.org/W2060147086","https://openalex.org/W2093606268","https://openalex.org/W2094174358","https://openalex.org/W2127882486","https://openalex.org/W2132421331","https://openalex.org/W2153583058","https://openalex.org/W2330451690","https://openalex.org/W2521628013","https://openalex.org/W2531519033","https://openalex.org/W2558040216","https://openalex.org/W2559235980","https://openalex.org/W2597810180","https://openalex.org/W2604312315","https://openalex.org/W2788250535","https://openalex.org/W2796162322","https://openalex.org/W2889720540","https://openalex.org/W2904176157","https://openalex.org/W2944024625","https://openalex.org/W2962758382","https://openalex.org/W2963025088","https://openalex.org/W2963293785","https://openalex.org/W2991301029","https://openalex.org/W2998041510","https://openalex.org/W3010909211","https://openalex.org/W3022864194","https://openalex.org/W3034326317","https://openalex.org/W3037117897","https://openalex.org/W3040736983","https://openalex.org/W3137712949","https://openalex.org/W3185021214","https://openalex.org/W3189099075","https://openalex.org/W3192205305","https://openalex.org/W4253419473","https://openalex.org/W4293179730","https://openalex.org/W4293385687"],"related_works":["https://openalex.org/W2035775247","https://openalex.org/W3198848671","https://openalex.org/W2135080344","https://openalex.org/W4302333893","https://openalex.org/W4250564678","https://openalex.org/W2017109433","https://openalex.org/W1550552339","https://openalex.org/W1987932026","https://openalex.org/W1988972657","https://openalex.org/W3124869498"],"abstract_inverted_index":{"Abstract":[0],"In":[1,102],"the":[2,18,82,99,104,118],"apportionment":[3,45,49,73,84,100],"problem,":[4],"a":[5,27,52],"fixed":[6],"number":[7,19],"of":[8,20,29,55,67,94,115,121],"seats":[9],"must":[10],"be":[11,136],"distributed":[12],"among":[13],"parties":[14,38],"in":[15,32,98,117,138],"proportion":[16],"to":[17,132],"voters":[21,34],"supporting":[22],"each":[23],"party.":[24],"We":[25],"study":[26],"generalization":[28],"this":[30],"setting,":[31],"which":[33,91],"can":[35,135],"support":[36],"multiple":[37],"by":[39],"casting":[40],"approval":[41,60],"ballots.":[42],"This":[43],"approval-based":[44,56],"setting":[46,120],"generalizes":[47],"traditional":[48],"and":[50,74,86,134],"is":[51,148],"natural":[53],"restriction":[54],"multiwinner":[57,75,122],"elections,":[58,76],"where":[59],"ballots":[61],"range":[62],"over":[63],"individual":[64],"candidates":[65],"instead":[66],"parties.":[68],"Using":[69],"techniques":[70],"from":[71],"both":[72],"we":[77,106,125,142],"identify":[78],"rules":[79,105],"that":[80,87,111,127,144],"generalize":[81],"D\u2019Hondt":[83],"method":[85],"satisfy":[88],"strong":[89],"axioms":[90],"are":[92,112,130],"generalizations":[93],"properties":[95],"commonly":[96],"studied":[97],"literature.":[101],"fact,":[103],"discuss":[107],"provide":[108],"representation":[109,147],"guarantees":[110],"currently":[113],"out":[114],"reach":[116],"general":[119],"elections:":[123],"First,":[124],"show":[126],"core-stable":[128],"committees":[129],"guaranteed":[131],"exist":[133],"found":[137],"polynomial":[139],"time.":[140],"Second,":[141],"demonstrate":[143],"extended":[145],"justified":[146],"compatible":[149],"with":[150],"committee":[151],"monotonicity":[152],"(also":[153],"known":[154],"as":[155],"house":[156],"monotonicity).":[157]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
