{"id":"https://openalex.org/W2582748216","doi":"https://doi.org/10.3390/e19100527","title":"Coarse-Graining and the Blackwell Order","display_name":"Coarse-Graining and the Blackwell Order","publication_year":2017,"publication_date":"2017-10-06","ids":{"openalex":"https://openalex.org/W2582748216","doi":"https://doi.org/10.3390/e19100527","mag":"2582748216"},"language":"en","primary_location":{"id":"doi:10.3390/e19100527","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19100527","pdf_url":"https://www.mdpi.com/1099-4300/19/10/527/pdf?version=1507537417","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/19/10/527/pdf?version=1507537417","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053941878","display_name":"Johannes Rauh","orcid":"https://orcid.org/0000-0001-6411-7775"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Johannes Rauh","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany","institution_ids":["https://openalex.org/I4210119712","https://openalex.org/I4210091327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111805479","display_name":"Pradeep Banerjee","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pradeep Banerjee","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany","institution_ids":["https://openalex.org/I4210119712","https://openalex.org/I4210091327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074755166","display_name":"Eckehard Olbrich","orcid":"https://orcid.org/0000-0002-3987-1271"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Eckehard Olbrich","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany","institution_ids":["https://openalex.org/I4210119712","https://openalex.org/I4210091327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072990982","display_name":"J\u00fcrgen Jost","orcid":"https://orcid.org/0000-0001-5258-6590"},"institutions":[{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"J\u00fcrgen Jost","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany","institution_ids":["https://openalex.org/I4210119712","https://openalex.org/I4210091327"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017316523","display_name":"Nils Bertschinger","orcid":"https://orcid.org/0000-0002-6699-9596"},"institutions":[{"id":"https://openalex.org/I2801628138","display_name":"Frankfurt Institute for Advanced Studies","ror":"https://ror.org/05vmv8m79","country_code":"DE","type":"facility","lineage":["https://openalex.org/I2801628138"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Nils Bertschinger","raw_affiliation_strings":["Frankfurt Institute for Advanced Studies, 60438 Frankfurt, Germany"],"affiliations":[{"raw_affiliation_string":"Frankfurt Institute for Advanced Studies, 60438 Frankfurt, Germany","institution_ids":["https://openalex.org/I2801628138"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073514351","display_name":"David H. Wolpert","orcid":"https://orcid.org/0000-0003-3105-2869"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]},{"id":"https://openalex.org/I1308548392","display_name":"Santa Fe Institute","ror":"https://ror.org/01arysc35","country_code":"US","type":"funder","lineage":["https://openalex.org/I1308548392"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Wolpert","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA 02139, USA","Santa Fe Institute, Santa Fe, NM 87501, USA"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Santa Fe Institute, Santa Fe, NM 87501, USA","institution_ids":["https://openalex.org/I1308548392"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5053941878"],"corresponding_institution_ids":["https://openalex.org/I4210091327","https://openalex.org/I4210119712"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.7497,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.86403801,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"10","first_page":"527","last_page":"527"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9193000197410583,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.9193000197410583,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/granularity","display_name":"Granularity","score":0.6980332136154175},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.6585564613342285},{"id":"https://openalex.org/keywords/intuition","display_name":"Intuition","score":0.5763251781463623},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5354213118553162},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4647592306137085},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44732189178466797},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4468897581100464},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4153577983379364},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.38379016518592834},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.11981832981109619},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.11849462985992432}],"concepts":[{"id":"https://openalex.org/C177774035","wikidata":"https://www.wikidata.org/wiki/Q1246948","display_name":"Granularity","level":2,"score":0.6980332136154175},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.6585564613342285},{"id":"https://openalex.org/C132010649","wikidata":"https://www.wikidata.org/wiki/Q189222","display_name":"Intuition","level":2,"score":0.5763251781463623},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5354213118553162},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4647592306137085},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44732189178466797},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4468897581100464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4153577983379364},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.38379016518592834},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.11981832981109619},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.11849462985992432},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e19100527","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19100527","pdf_url":"https://www.mdpi.com/1099-4300/19/10/527/pdf?version=1507537417","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1701.07602","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1701.07602","pdf_url":"https://arxiv.org/pdf/1701.07602","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:doaj.org/article:a81d9e79f00f449f9fa30a390cf33aa9","is_oa":true,"landing_page_url":"https://doaj.org/article/a81d9e79f00f449f9fa30a390cf33aa9","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 19, Iss 10, p 527 (2017)","raw_type":"article"},{"id":"pmh:oai:edoc.mpg.de:741461","is_oa":false,"landing_page_url":"http://edoc.mpg.de/741461","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, v.19 (2017)","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.3390/e19100527","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e19100527","pdf_url":"https://www.mdpi.com/1099-4300/19/10/527/pdf?version=1507537417","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2582748216.pdf","grobid_xml":"https://content.openalex.org/works/W2582748216.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1505771370","https://openalex.org/W1585991211","https://openalex.org/W2050495532","https://openalex.org/W2057989917","https://openalex.org/W2081988641","https://openalex.org/W2094458162","https://openalex.org/W2140084608","https://openalex.org/W2574238296","https://openalex.org/W2585967819","https://openalex.org/W3102073019","https://openalex.org/W3105841952"],"related_works":["https://openalex.org/W2931688134","https://openalex.org/W2377919138","https://openalex.org/W2378857091","https://openalex.org/W2999756192","https://openalex.org/W103652678","https://openalex.org/W4226090359","https://openalex.org/W2059697060","https://openalex.org/W4382701072","https://openalex.org/W4256502920","https://openalex.org/W2491314273"],"abstract_inverted_index":{"Suppose":[0],"we":[1],"have":[2],"a":[3,15,22,160,163],"pair":[4],"of":[5,75,155,166,168,180,221],"information":[6,96,207,222],"channels,":[7],"\u03ba":[8,11,29,32,52,60,66,76,85,91,105,109,128,134,147,156],"1":[9,30,53,67,92,110,129,148],",":[10,13],"2":[12,33,61,77,86,106,135,157],"with":[14],"common":[16],"input.":[17],"The":[18],"Blackwell":[19],"order":[20,24,82],"is":[21,54,87,102,119,130,149,162,189,193],"partial":[23,81],"over":[25,114],"channels":[26],"that":[27,84,141,176,202],"compares":[28],"and":[31,63,100,208],"by":[34,71,151],"the":[35,48,73,94,98,153,169,177,181,186,195,200,219],"maximal":[36],"expected":[37,178],"utility":[38,183],"an":[39],"agent":[40],"can":[41,68,204],"obtain":[42],"when":[43,146],"decisions":[44],"are":[45,125],"based":[46],"on":[47],"channel":[49,118,170,188],"outputs.":[50],"Equivalently,":[51],"said":[55],"to":[56,59,210],"be":[57,69],"Blackwell-inferior":[58,117],"if":[62,65,93],"only":[64,205],"constructed":[70,150],"garbling":[72],"output":[74,101],".":[78,158],"A":[79,116],"related":[80],"stipulates":[83],"more":[88],"capable":[89,132],"than":[90,107,133,191],"mutual":[95],"between":[97],"input":[99],"larger":[103,190],"for":[104,108,111,185,194],"any":[112],"distribution":[113],"inputs.":[115,171],"necessarily":[120],"less":[121,131],"capable.":[122],"However,":[123],"examples":[124],"known":[126],"where":[127],"but":[136],"not":[137],"Blackwell-inferior.":[138],"We":[139,213],"show":[140],"this":[142],"may":[143],"even":[144],"happen":[145],"coarse-graining":[152,161,203],"inputs":[154],"Such":[159],"special":[164],"kind":[165],"\u201cpre-garbling\u201d":[167],"This":[172,198],"example":[173],"directly":[174],"establishes":[175],"value":[179],"shared":[182],"function":[184],"coarse-grained":[187],"it":[192],"non-coarse-grained":[196],"channel.":[197],"contradicts":[199],"intuition":[201],"destroy":[206],"lead":[209],"inferior":[211],"channels.":[212],"also":[214],"discuss":[215],"our":[216],"results":[217],"in":[218],"context":[220],"decompositions.":[223]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}