{
  "abstract": "It is known that completeness of the coalitional ($C$-)desirability relation in a simple game does not imply the existence of a weighted-majority representation. We show that weightedness is implied in an approximate sense. Call an $n$-player simple game $\\varepsilon$-weighted if, for some weight vector in the $(n-1)$-simplex, any losing coalition weight exceeds any winning coalition weight by at most $\\varepsilon$; let $\\varepsilon^{\\ast}$ be the smallest such $\\varepsilon$. We establish an upper bound on $\\varepsilon^{\\ast}$ in a general $C$-complete game, and deduce that, if all classes of equally desirable players become large asymptotically but the number of classes is bounded, then $\\varepsilon^{\\ast}=O(1/n_{\\min})$ for the minimal player class size $n_{\\min}$, and the bound is tight. Importantly, the minimal attainable fraction $δ$ of coalitions mislabeled by a weighting rule also tends to $0$ when $n_{\\min}\\rightarrow\\infty$ and the number of player classes is bounded, with $δ=O(1/\\sqrt{n_{\\min}})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08968",
  "author_total": 2,
  "authors": [
    {
      "name": "Ezra Einy"
    },
    {
      "name": "Ori Haimanko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/emscqf8ngxh6s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08968",
  "fulltext_url": null,
  "id": "emscqf8ngxh6s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08968",
  "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.GT"
    ],
    [
      "arxiv",
      "econ.TH"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2002|Game Theory and Voting Systems"
    ]
  ],
  "openalex": "W7220979139",
  "pdf_url": "https://arxiv.org/pdf/2610.08968",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/emscqf8ngxh6s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.08968",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08968"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Large player classes and approximately weighted voting",
  "title_text": "Large player classes and approximately weighted voting",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/emscqf8ngxh6s",
  "venue": "arXiv",
  "versions": []
}