{"id":"https://openalex.org/W4415428066","doi":"https://doi.org/10.3233/faia251236","title":"District-Limited Bribery in Multidistrict Apportionment Elections with Threshold","display_name":"District-Limited Bribery in Multidistrict Apportionment Elections with Threshold","publication_year":2025,"publication_date":"2025-10-21","ids":{"openalex":"https://openalex.org/W4415428066","doi":"https://doi.org/10.3233/faia251236"},"language":null,"primary_location":{"id":"doi:10.3233/faia251236","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia251236","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.3233/faia251236","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075022050","display_name":"Joanna Kaczmarek","orcid":"https://orcid.org/0000-0001-6652-6433"},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Joanna Kaczmarek","raw_affiliation_strings":["Institut f\u00fcr Informatik, MNF, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, D\u00fcsseldorf, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6652-6433","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, MNF, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, D\u00fcsseldorf, Germany","institution_ids":["https://openalex.org/I44260953"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050661976","display_name":"J\u00f6rg Rothe","orcid":"https://orcid.org/0000-0002-0589-3616"},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J\u00f6rg Rothe","raw_affiliation_strings":["Institut f\u00fcr Informatik, MNF, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, D\u00fcsseldorf, Germany"],"raw_orcid":"https://orcid.org/0000-0002-0589-3616","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, MNF, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, D\u00fcsseldorf, Germany","institution_ids":["https://openalex.org/I44260953"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079453635","display_name":"Tessa Seeger","orcid":"https://orcid.org/0000-0003-2604-264X"},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tessa Seeger","raw_affiliation_strings":["Institut f\u00fcr Informatik, MNF, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, D\u00fcsseldorf, Germany"],"raw_orcid":"https://orcid.org/0000-0003-2604-264X","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, MNF, Heinrich-Heine-Universit\u00e4t D\u00fcsseldorf, D\u00fcsseldorf, Germany","institution_ids":["https://openalex.org/I44260953"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I44260953"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.58780632,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T11770","display_name":"Fiscal Policy and Economic Growth","score":0.9677000045776367,"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/T11770","display_name":"Fiscal Policy and Economic Growth","score":0.9677000045776367,"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/T11461","display_name":"Local Government Finance and Decentralization","score":0.9631999731063843,"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"}},{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9585999846458435,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/apportionment","display_name":"Apportionment","score":0.9348999857902527},{"id":"https://openalex.org/keywords/parliament","display_name":"Parliament","score":0.7303000092506409},{"id":"https://openalex.org/keywords/general-election","display_name":"General election","score":0.6195999979972839},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5238999724388123},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.37040001153945923},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.2881999909877777}],"concepts":[{"id":"https://openalex.org/C2778337684","wikidata":"https://www.wikidata.org/wiki/Q3173700","display_name":"Apportionment","level":2,"score":0.9348999857902527},{"id":"https://openalex.org/C2781440851","wikidata":"https://www.wikidata.org/wiki/Q35749","display_name":"Parliament","level":3,"score":0.7303000092506409},{"id":"https://openalex.org/C59742305","wikidata":"https://www.wikidata.org/wiki/Q1076105","display_name":"General election","level":3,"score":0.6195999979972839},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5238999724388123},{"id":"https://openalex.org/C190253527","wikidata":"https://www.wikidata.org/wiki/Q295354","display_name":"Law and economics","level":1,"score":0.39079999923706055},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.37040001153945923},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.3610999882221222},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.31769999861717224},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.29789999127388},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.2881999909877777},{"id":"https://openalex.org/C2992889544","wikidata":"https://www.wikidata.org/wiki/Q5356385","display_name":"Electoral reform","level":4,"score":0.26980000734329224},{"id":"https://openalex.org/C119588120","wikidata":"https://www.wikidata.org/wiki/Q13365595","display_name":"Proportional representation","level":4,"score":0.26809999346733093},{"id":"https://openalex.org/C141141315","wikidata":"https://www.wikidata.org/wiki/Q2379942","display_name":"Guard (computer science)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C2778698365","wikidata":"https://www.wikidata.org/wiki/Q2100614","display_name":"General assembly","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.2599000036716461},{"id":"https://openalex.org/C100001284","wikidata":"https://www.wikidata.org/wiki/Q2248246","display_name":"Public economics","level":1,"score":0.2574999928474426}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3233/faia251236","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia251236","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.3233/faia251236","is_oa":true,"landing_page_url":"https://doi.org/10.3233/faia251236","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"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":{"Apportionment":[0],"methods":[1,185],"allocate":[2],"a":[3,9,57,62,71,95,102,111,142,164],"fixed":[4],"number":[5,59,91],"of":[6,60,80,92,126,202],"seats":[7,69,93],"in":[8,30,70,157],"parliament":[10],"to":[11,66,88,135,149],"parties":[12],"based":[13],"on":[14],"their":[15],"vote":[16],"counts.":[17],"In":[18],"many":[19,48],"countries,":[20],"parliamentary":[21],"elections":[22,29,43],"are":[23],"organized":[24],"by":[25,98],"first":[26],"holding":[27],"separate":[28],"several":[31],"districts":[32],"and":[33,181,190,199],"then":[34],"putting":[35],"the":[36,78,90,119,124,130,139,154,174,178,187],"single":[37],"results":[38],"together.":[39],"We":[40,160,194],"call":[41],"such":[42,74],"multidistrict":[44],"apportionment":[45,192],"elections.":[46],"Moreover,":[47],"countries":[49],"have":[50],"an":[51,84],"additional":[52],"general":[53,112,165],"electoral":[54,113,166],"threshold,":[55,114,167],"i.e.,":[56],"minimum":[58],"votes":[61,155],"party":[63,97],"must":[64,133],"receive":[65],"win":[67],"any":[68],"parliament.":[72],"For":[73],"methods,":[75],"we":[76,106],"study":[77,196],"complexity":[79,125,198],"bribery":[81],"problems":[82,175],"where":[83],"external":[85,131],"agent":[86,132],"seeks":[87],"increase":[89],"for":[94,118,145,152,177],"distinguished":[96],"bribing":[99],"voters":[100],"within":[101],"given":[103],"budget.":[104],"Specifically,":[105],"investigate":[107],"how":[108],"adding":[109,163],"either":[110],"or":[115,121,169],"district":[116,171],"limits":[117],"budget,":[120],"both":[122],"influences":[123],"bribery.":[127],"District":[128],"limits\u2014which":[129],"adhere":[134],"while":[136],"still":[137],"respecting":[138],"overall":[140],"budget\u2014denote":[141],"maximum":[143],"budget":[144],"each":[146,148],"district,":[147],"be":[150],"spent":[151],"changing":[153],"only":[156],"that":[158,162],"district.":[159],"show":[161],"with":[168],"without":[170],"limits,":[172],"makes":[173],"NP-complete":[176],"largest-remainder":[179],"method":[180],"all":[182],"divisor":[183],"sequence":[184],"(including":[186],"prominent":[188],"D\u2019Hondt":[189],"Sainte-Lagu\u00eb":[191],"methods).":[193],"also":[195],"parameterized":[197],"domain":[200],"restrictions":[201],"these":[203],"problems.":[204]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-24T00:00:00"}