{
  "abstract": "Let $C(m,n)$ denote the probability that, among $n$ independent uniformly random permutations of $m$ labels, there exists a label that precedes every other label in a strict majority of the permutations. We prove that $C(m,n)>C(m,n+2)$ for $m \\ge 3$ and odd $n \\ge 1$, and that $C(m,n)>C(m+1,n)$ for $m \\ge 2$ and odd $n \\ge 3$. These results establish Kelly's two monotonicity conjectures for odd electorates. The proofs use integral representations involving probabilities associated with sums of independent Bernoulli random variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29904",
  "author_total": 2,
  "authors": [
    {
      "name": "Seick Kim"
    },
    {
      "name": "Hocheol Shin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fqrddaym9g3mt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29904",
  "fulltext_url": null,
  "id": "fqrddaym9g3mt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29904",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2002|Game Theory and Voting Systems"
    ]
  ],
  "openalex": "W7223198196",
  "pdf_url": "https://arxiv.org/pdf/2610.29904",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fqrddaym9g3mt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29904",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29904"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Kelly's conjectures on Condorcet winner probabilities for odd electorates",
  "title_text": "Kelly's conjectures on Condorcet winner probabilities for odd electorates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/fqrddaym9g3mt",
  "venue": "arXiv",
  "versions": []
}