{"paper":{"title":"Three Candidate Plurality is Stablest for Correlations at most 1/10","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.PR","authors_text":"Steven Heilman","submitted_at":"2023-06-05T23:45:30Z","abstract_excerpt":"We prove the three candidate Plurality is Stablest Conjecture of Khot-Kindler-Mossel-O'Donnell from 2005 for correlations $\\rho$ satisfying $-1/43<\\rho<1/10$: the Plurality function is the most noise stable three candidate election method with small influences, when the corrupted votes have correlation $-1/43<\\rho<1/10$ with the original votes. The previous best result of this type only achieved positive correlations at most $10^{-10^{10}}$. Our result follows by solving the three set Standard Simplex Conjecture of Isaksson-Mossel from 2011 for all correlations $-1/43<\\rho<1/10$.\n  The Gaussia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.03312","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.03312/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}