{"paper":{"title":"Power of the Crowd","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Athanasios Batakis, Dorian Le Peutrec, Pierre Debs","submitted_at":"2021-12-15T11:11:34Z","abstract_excerpt":"Consider an Galton Watson tree of height $m$: each leaf has one of $k$ opinions or not. In other words, for $i \\in \\{1, . . . , k\\}$, $x$ at generation $m$ thinks $i$ with probability $p_i$ and nothing with probability $p_0$. Moreover the opinions are independently distributed for each leaf. Opinions spread along the tree based on a specific rule: the majority wins! In this paper, we study the asymptotic behavior of the distribution of the opinion of the root when $m \\to +\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.08042","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/2112.08042/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"}