{"id":"https://openalex.org/W2167710837","doi":"https://doi.org/10.1002/malq.200810027","title":"The Computational Complexity of Choice Sets","display_name":"The Computational Complexity of Choice Sets","publication_year":2009,"publication_date":"2009-07-17","ids":{"openalex":"https://openalex.org/W2167710837","doi":"https://doi.org/10.1002/malq.200810027","mag":"2167710837"},"language":"en","primary_location":{"id":"doi:10.1002/malq.200810027","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200810027","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001200543","display_name":"Felix Brandt","orcid":"https://orcid.org/0000-0002-4179-9897"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Felix Brandt","raw_affiliation_strings":["Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Oettingenstr. 67, 80538 M\u00fcnchen, Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen, Oettingenstr. 67, 80538 M\u00fcnchen, Germany#TAB#","institution_ids":["https://openalex.org/I8204097"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041652507","display_name":"Felix Fischer","orcid":"https://orcid.org/0000-0002-8403-9273"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Felix Fischer","raw_affiliation_strings":["Ludwig-Maximilians-Universita\u0308t Mu\u0308nchen, Oettingenstr. 67, 80538 Mu\u0308nchen, Germany"],"affiliations":[{"raw_affiliation_string":"Ludwig-Maximilians-Universita\u0308t Mu\u0308nchen, Oettingenstr. 67, 80538 Mu\u0308nchen, Germany","institution_ids":["https://openalex.org/I8204097"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017927930","display_name":"Paul Harrenstein","orcid":"https://orcid.org/0000-0001-9766-7618"},"institutions":[{"id":"https://openalex.org/I8204097","display_name":"Ludwig-Maximilians-Universit\u00e4t M\u00fcnchen","ror":"https://ror.org/05591te55","country_code":"DE","type":"education","lineage":["https://openalex.org/I8204097"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Paul Harrenstein","raw_affiliation_strings":["Ludwig-Maximilians-Universita\u0308t Mu\u0308nchen, Oettingenstr. 67, 80538 Mu\u0308nchen, Germany"],"affiliations":[{"raw_affiliation_string":"Ludwig-Maximilians-Universita\u0308t Mu\u0308nchen, Oettingenstr. 67, 80538 Mu\u0308nchen, Germany","institution_ids":["https://openalex.org/I8204097"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5001200543"],"corresponding_institution_ids":["https://openalex.org/I8204097"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":22.3286,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.99183148,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"55","issue":"4","first_page":"444","last_page":"459"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9993000030517578,"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":0.9993000030517578,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9624999761581421,"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"}},{"id":"https://openalex.org/T10050","display_name":"Multi-Criteria Decision Making","score":0.9128000140190125,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/social-choice-theory","display_name":"Social choice theory","score":0.8162868618965149},{"id":"https://openalex.org/keywords/condorcet-method","display_name":"Condorcet method","score":0.8141131401062012},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6431277394294739},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.6285568475723267},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.622633695602417},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.6144604086875916},{"id":"https://openalex.org/keywords/von-neumann-architecture","display_name":"Von Neumann architecture","score":0.5254147052764893},{"id":"https://openalex.org/keywords/preference-relation","display_name":"Preference relation","score":0.4973800480365753},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.415897935628891},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2401350438594818},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.23389428853988647},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17296218872070312},{"id":"https://openalex.org/keywords/voting","display_name":"Voting","score":0.1266167163848877},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07885634899139404},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07323464751243591}],"concepts":[{"id":"https://openalex.org/C189352744","wikidata":"https://www.wikidata.org/wiki/Q1971461","display_name":"Social choice theory","level":2,"score":0.8162868618965149},{"id":"https://openalex.org/C140940377","wikidata":"https://www.wikidata.org/wiki/Q868720","display_name":"Condorcet method","level":4,"score":0.8141131401062012},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6431277394294739},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6285568475723267},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.622633695602417},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.6144604086875916},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.5254147052764893},{"id":"https://openalex.org/C2777062324","wikidata":"https://www.wikidata.org/wiki/Q25036211","display_name":"Preference relation","level":3,"score":0.4973800480365753},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.415897935628891},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2401350438594818},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.23389428853988647},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17296218872070312},{"id":"https://openalex.org/C520049643","wikidata":"https://www.wikidata.org/wiki/Q189760","display_name":"Voting","level":3,"score":0.1266167163848877},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07885634899139404},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07323464751243591},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.200810027","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.200810027","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.7400000095367432,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G5192569469","display_name":null,"funder_award_id":"BR 2312/3-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5699381622","display_name":null,"funder_award_id":"BR 2312/3-2","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W70412040","https://openalex.org/W116064160","https://openalex.org/W583379360","https://openalex.org/W1484675474","https://openalex.org/W1506378440","https://openalex.org/W1533391239","https://openalex.org/W1586124026","https://openalex.org/W1592580500","https://openalex.org/W1644945789","https://openalex.org/W1968498770","https://openalex.org/W1975833254","https://openalex.org/W1978865199","https://openalex.org/W1982894918","https://openalex.org/W1983254396","https://openalex.org/W1986804393","https://openalex.org/W2013372570","https://openalex.org/W2019030315","https://openalex.org/W2019472348","https://openalex.org/W2021965161","https://openalex.org/W2024938564","https://openalex.org/W2027501230","https://openalex.org/W2037100948","https://openalex.org/W2047294939","https://openalex.org/W2049270305","https://openalex.org/W2054974335","https://openalex.org/W2057573268","https://openalex.org/W2070033045","https://openalex.org/W2070875744","https://openalex.org/W2074016826","https://openalex.org/W2081414680","https://openalex.org/W2081828561","https://openalex.org/W2085850898","https://openalex.org/W2091544162","https://openalex.org/W2098386424","https://openalex.org/W2144846366","https://openalex.org/W2166576712","https://openalex.org/W2263771924","https://openalex.org/W2313512971","https://openalex.org/W2326964644","https://openalex.org/W2327081444","https://openalex.org/W2328184904","https://openalex.org/W2913028927","https://openalex.org/W3121581278","https://openalex.org/W3124380835","https://openalex.org/W3145128584"],"related_works":["https://openalex.org/W2082491017","https://openalex.org/W2043607118","https://openalex.org/W4235406019","https://openalex.org/W4241879219","https://openalex.org/W2256553487","https://openalex.org/W4321602595","https://openalex.org/W2136888943","https://openalex.org/W1988244191","https://openalex.org/W4205262062","https://openalex.org/W1989284391"],"abstract_inverted_index":{"Abstract":[0],"Social":[1],"choice":[2,55,74,139],"rules":[3,140],"are":[4],"often":[5],"evaluated":[6],"and":[7,109,121],"compared":[8],"by":[9],"inquiring":[10],"whether":[11],"they":[12],"satisfy":[13],"certain":[14],"desirable":[15],"criteria":[16,48],"such":[17],"as":[18],"the":[19,37,64,67,81,88,92,96,105,110,116],"Condorcet":[20],"criterion":[21],",":[22,91,95,99,104,108],"which":[23,127],"states":[24],"that":[25,57],"an":[26],"alternative":[27],"should":[28],"always":[29],"be":[30,50],"chosen":[31],"when":[32],"more":[33],"than":[34],"half":[35],"of":[36,46,54,66,137],"voters":[38],"prefer":[39],"it":[40],"over":[41],"any":[42],"other":[43],"alternative.":[44],"Many":[45],"these":[47,119],"can":[49],"formulated":[51],"in":[52],"terms":[53],"sets":[56,75,86,103,120],"single":[58],"out":[59],"reasonable":[60],"alternatives":[61],"based":[62],"on":[63,80],"preferences":[65],"voters.":[68],"In":[69],"this":[70],"paper,":[71],"we":[72],"consider":[73],"whose":[76],"definition":[77],"merely":[78],"relies":[79],"pairwise":[82],"majority":[83],"relation.":[84],"These":[85],"include":[87],"Copeland":[89],"set":[90,94,98,107,112],"Smith":[93],"Schwartz":[97],"von":[100],"Neumann\u2010Morgenstern":[101],"stable":[102],"Banks":[106],"Slater":[111],".":[113],"We":[114],"investigate":[115],"relationships":[117],"between":[118],"completely":[122],"characterize":[123],"their":[124],"computational":[125],"complexity,":[126],"allows":[128],"us":[129],"to":[130],"obtain":[131],"hardness":[132],"results":[133],"for":[134],"entire":[135],"classes":[136],"social":[138],"(\u00a9":[141],"2009":[142],"WILEY\u2010VCH":[143],"Verlag":[144],"GmbH":[145],"&":[146],"Co.":[147],"KGaA,":[148],"Weinheim)":[149]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}