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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1509.07567","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-24T23:21:43Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"26cf8573090d2a6fa255a33ede6256b1b853c1d7bdee2c9ba181c844245ee556","abstract_canon_sha256":"4f3cf43755fb1aada4237da5abba649ece83f9e73016e79aa4f82695c57dbbe7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:02.458094Z","signature_b64":"eCMmuyMwm6o7Cjs3xDzQrMnMPfb5Uz35Wo6W/TY9cRMTLZrLMOBb+fYANXyGaVF07YoLXHgAVzfCKv6E0/hbDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec03498b2b8b9866acc16794322d1085c2197cc727b3b01d148f58ccf5a645b6","last_reissued_at":"2026-05-18T01:32:02.457720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:02.457720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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