{
  "abstract": "Consider $k$ independent Bernoulli populations, each sampled $n$ times, and select the $t$ populations with the largest success counts, breaking ties uniformly. Classical monotonicity reduces the worst case over the preference zone with separation $δ$ to the slippage family with levels $p$ and $p+δ$, leaving only its absolute location $p\\in[0,1-δ]$ undetermined. A Gaussian approximation suggests the symmetric center $p_{\\mathrm c}=(1-δ)/2$, and the exact two-population problem is uniquely centered there for every $n\\ge2$. For fixed $k,t$ and $δ\\in(0,1)$, we prove that exact eventual centering holds precisely when $k=2t$. When $k\\ne2t$, the least-favorable location $p_{n,k,t}^*$ satisfies \\[ p_{n,k,t}^*-p_{\\mathrm c} =(k-2t)C_δn^{-1/2}e^{-nΓ_δ}\\{1+o(1)\\}, \\] where $C_δ$ and $Γ_δ$ are explicit and positive. In either case, the least-favorable location is eventually unique. The proof writes incorrect selection as a union of pairwise misrankings and applies inclusion--exclusion, yielding a bipartite graph expansion. A single misranking has its exact maximum at the symmetric center and determines the central curvature; two-edge intersections sharing one population determine the central slope through their multiplicity imbalance; all remaining graphs have higher large-deviation rates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03466",
  "author_total": 2,
  "authors": [
    {
      "name": "Yinhao Wu"
    },
    {
      "name": "Pinyuen Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5mkj01rrg1yz9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03466",
  "fulltext_url": null,
  "id": "5mkj01rrg1yz9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03466",
  "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",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7208791888",
  "pdf_url": "https://arxiv.org/pdf/2609.03466",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5mkj01rrg1yz9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03466",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03466"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Least-Favorable Location for Binomial Top-$t$ Selection",
  "title_text": "Least-Favorable Location for Binomial Top-t Selection",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:42Z",
  "url": "https://research.draconitic.com/paper/5mkj01rrg1yz9",
  "venue": "arXiv",
  "versions": []
}