{
  "abstract": "Reporting the best of $M$ noisy, unbiased scores overstates the winner's value by up to $c\\sqrt{V}$, where $V$ is the total noise variance and the sharp constant $c$ depends on how the noise is dependent. It was known only at the two extremes, arbitrary dependence ($\\sqrt{(M-1)/M}$) and i.i.d. noise. We determine it for two classes in between: for independent, not identically distributed noise it is $\\sqrt{(M-1)/(2M)}$, and for pairwise nonnegatively correlated noise it is $(M-1)/M$; for uncorrelated noise this answers the maximum version of an open question about the expected range. Explicit finite constructions attain both. As a corollary, the bias of the cross-validation estimator is bounded sharply within each class. All theorems are formally verified in Lean 4. Across 448 language-model and classifier selection pipelines, designs with per-candidate items realize a median 0.75 of the independent-class ceiling. At a fixed item budget, scoring all candidates on shared items is markedly less optimistic than giving each candidate its own items.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31948",
  "author_total": 3,
  "authors": [
    {
      "name": "Ivan Viakhirev"
    },
    {
      "name": "Kirill Borodin"
    },
    {
      "name": "Grach Mkrtchian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/br3r3zsx1kym9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31948",
  "fulltext_url": null,
  "id": "br3r3zsx1kym9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31948",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Machine Learning and Data Classification"
    ]
  ],
  "openalex": "W7223691069",
  "pdf_url": "https://arxiv.org/pdf/2610.31948",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/br3r3zsx1kym9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31948",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31948"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Sharp Bounds on the Winner's Bias under Independent and Nonnegatively Correlated Noise",
  "title_text": "Sharp Bounds on the Winner's Bias under Independent and Nonnegatively Correlated Noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:25Z",
  "url": "https://research.draconitic.com/paper/br3r3zsx1kym9",
  "venue": "arXiv",
  "versions": []
}