{"paper":{"title":"On Covering Codes and Upper Bounds for the Dimension of Simple Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA"],"primary_cat":"cs.GT","authors_text":"Martin Olsen","submitted_at":"2016-09-16T09:21:33Z","abstract_excerpt":"Consider a situation with $n$ agents or players where some of the players form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not (losing). A simple game can be viewed as a monotone boolean function. The dimension of a simple game is the smallest positive integer $d$ such that the simple game can be expressed as the intersection of $d$ threshold functions where each threshold function uses a threshold and $n$ weights. Taylor and Zwicker have shown that $d$ is bounded from above by the number"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04960","kind":"arxiv","version":1},"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"}