{"id":"https://openalex.org/W2951743867","doi":"https://doi.org/10.1017/s0021900200009530","title":"The Probability of the Alabama Paradox","display_name":"The Probability of the Alabama Paradox","publication_year":2012,"publication_date":"2012-09-01","ids":{"openalex":"https://openalex.org/W2951743867","doi":"https://doi.org/10.1017/s0021900200009530","mag":"2951743867"},"language":"en","primary_location":{"id":"doi:10.1017/s0021900200009530","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0021900200009530","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B312B82C536CE2FA71229D35C7A00D1A/S0021900200009530a.pdf/div-class-title-the-probability-of-the-alabama-paradox-div.pdf","source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B312B82C536CE2FA71229D35C7A00D1A/S0021900200009530a.pdf/div-class-title-the-probability-of-the-alabama-paradox-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022615833","display_name":"Svante Janson","orcid":"https://orcid.org/0000-0002-9680-2790"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Svante Janson","raw_affiliation_strings":["Uppsala University"],"affiliations":[{"raw_affiliation_string":"Uppsala University","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031800301","display_name":"Svante Linusson","orcid":"https://orcid.org/0000-0001-6339-2230"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Svante Linusson","raw_affiliation_strings":["KTH - Royal Institute of Technology"],"affiliations":[{"raw_affiliation_string":"KTH - Royal Institute of Technology","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022615833","https://openalex.org/A5031800301"],"corresponding_institution_ids":["https://openalex.org/I123387679","https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28425901,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"03","first_page":"773","last_page":"794"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13187","display_name":"Diffusion and Search Dynamics","score":0.9833999872207642,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9807999730110168,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8254916667938232},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.7148168683052063},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5941100120544434},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.45458850264549255},{"id":"https://openalex.org/keywords/parliament","display_name":"Parliament","score":0.4136420786380768},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33575570583343506},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.1836237907409668},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10428321361541748},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.055820196866989136}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8254916667938232},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.7148168683052063},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5941100120544434},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.45458850264549255},{"id":"https://openalex.org/C2781440851","wikidata":"https://www.wikidata.org/wiki/Q35749","display_name":"Parliament","level":3,"score":0.4136420786380768},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33575570583343506},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.1836237907409668},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10428321361541748},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.055820196866989136},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0021900200009530","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0021900200009530","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B312B82C536CE2FA71229D35C7A00D1A/S0021900200009530a.pdf/div-class-title-the-probability-of-the-alabama-paradox-div.pdf","source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1017/s0021900200009530","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0021900200009530","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B312B82C536CE2FA71229D35C7A00D1A/S0021900200009530a.pdf/div-class-title-the-probability-of-the-alabama-paradox-div.pdf","source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5699999928474426,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320936","display_name":"Royal Swedish Academy of Sciences","ror":"https://ror.org/00j62qv07"},{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2951743867.pdf","grobid_xml":"https://content.openalex.org/works/W2951743867.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2802739963","https://openalex.org/W2950333486"],"related_works":["https://openalex.org/W2023822311","https://openalex.org/W4252661029","https://openalex.org/W2375791221","https://openalex.org/W2254312451","https://openalex.org/W4365503523","https://openalex.org/W2097613883","https://openalex.org/W589623597","https://openalex.org/W4312908577","https://openalex.org/W2569479847","https://openalex.org/W2322759334"],"abstract_inverted_index":{"Hamilton's":[0],"method":[1,7],"is":[2,40,113],"a":[3,17,56,95],"natural":[4],"and":[5,121],"common":[6],"to":[8,27,69],"distribute":[9],"seats":[10,67],"proportionally":[11],"between":[12],"states":[13,105],"(or":[14],"parties)":[15],"in":[16,30,42,44],"parliament.":[18],"In":[19,48],"the":[20,32,35,60,64,72,77,88,91,101,110],"USA":[21],"it":[22,39],"has":[23],"been":[24],"abandoned":[25],"due":[26],"some":[28],"drawbacks,":[29],"particular":[31],"possibility":[33],"of":[34,66,84,87,97,104],"Alabama":[36,73,111],"paradox,":[37],"but":[38],"still":[41],"use":[43],"many":[45],"other":[46],"countries.":[47],"this":[49],"paper":[50],"we":[51,93],"give,":[52],"under":[53],"certain":[54],"assumptions,":[55],"closed":[57],"formula":[58,92],"for":[59],"asymptotic":[61],"probability,":[62],"as":[63],"number":[65,96,103],"tends":[68],"infinity,":[70],"that":[71,106],"paradox":[74,112],"occurs":[75],"given":[76],"vector":[78],"p":[79,82],"1":[80,118],",\u2026,":[81],"m":[83],"relative":[85],"sizes":[86],"states.":[89],"From":[90],"deduce":[94],"consequences.":[98],"For":[99],"example,":[100],"expected":[102],"will":[107],"suffer":[108],"from":[109],"asymptotically":[114],"bounded":[115],"above":[116],"by":[117],"/":[119],"e":[120],"on":[122],"average":[123],"approximately":[124],"0.123.":[125]},"counts_by_year":[],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-10-10T00:00:00"}
