{"paper":{"title":"Coarse-graining and the Blackwell order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"David Wolpert, Eckehard Olbrich, Johannes Rauh, J\\\"urgen Jost, Nils Bertschinger, Pradeep Kr. Banerjee","submitted_at":"2017-01-26T07:50:20Z","abstract_excerpt":"Suppose we have a pair of information channels, $\\kappa_{1},\\kappa_{2}$, with a common input. The Blackwell order is a partial order over channels that compares $\\kappa_{1}$ and $\\kappa_{2}$ by the maximal expected utility an agent can obtain when decisions are based on the channel outputs. Equivalently, $\\kappa_{1}$ is said to be Blackwell-inferior to $\\kappa_{2}$ if and only if $\\kappa_{1}$ can be constructed by garbling the output of $\\kappa_{2}$. A related partial order stipulates that $\\kappa_{2}$ is more capable than $\\kappa_{1}$ if the mutual information between the input and output is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07602","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}