{"paper":{"title":"Majority Digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"J\\\"org Endrullis, Lawrence S. Moss, Tri Lai","submitted_at":"2015-09-24T23:21:43Z","abstract_excerpt":"A majority digraph is a finite simple digraph $G=(V,\\to)$ such that there exist finite sets $A_v$ for the vertices $v\\in V$ with the following property: $u\\to v$ if and only if \"more than half of the $A_u$ are $A_v$\". That is, $u\\to v$ if and only if $ |A_u \\cap A_v | > \\frac{1}{2} \\cdot |A_u|$. We characterize the majority digraphs as the digraphs with the property that every directed cycle has a reversal. If we change $\\frac{1}{2}$ to any real number $\\alpha\\in (0,1)$, we obtain the same class of digraphs. We apply the characterization result to obtain a result on the logic of assertions \"mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07567","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"}