{
  "abstract": "Fairness audits with several sensitive attributes are often performed one coordinate at a time. This can miss purely intersectional disparities: a score may be independent of each sensitive coordinate while depending on their joint profile. We study distributional demographic parity for a real-valued score using one-dimensional Wasserstein geometry. We distinguish two complementary constructions. Conditional and sequential audits characterize joint parity through their zero sets, but their positive values do not generally decompose a fixed joint Wasserstein disparity. By contrast, full-cell conditional quantile functions define a Hilbert-valued random variable whose variance is the joint disparity. Conditional expectations of this quantile process induce a monotone information game: every reveal order yields an exact martingale decomposition of the same joint disparity, while Shapley values provide an order-free attribution across sensitive attributes. Under independent sensitive attributes, the game reduces to a Hoeffding-ANOVA decomposition and Shapley splits each interaction energy equally among its members; under dependence, orthogonality is lost and explicit formulas reveal suppression and redundancy effects that marginal audits can hide. We give fixed-grid estimators and permutation calibration, and illustrate the framework on synthetic examples and ACSIncome. The resulting framework separates three questions that are often conflated: whether joint distributional parity holds, how a fixed joint disparity decomposes along an information path, and how that disparity can be attributed across sensitive coordinates without privileging an ordering.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19252",
  "author_total": 3,
  "authors": [
    {
      "name": "Agathe Fernandes Machado"
    },
    {
      "name": "Charlotte Jamotton"
    },
    {
      "name": "Arthur Charpentier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5xask55yzhs8z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19252",
  "fulltext_url": null,
  "id": "5xask55yzhs8z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19252",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "3311|Ethics and Social Impacts of AI"
    ]
  ],
  "openalex": "W7221873556",
  "pdf_url": "https://arxiv.org/pdf/2610.19252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5xask55yzhs8z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:42Z",
      "native_id": "2610.19252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19252"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Multi-Sensitive Distributional Fairness: Joint Wasserstein Audits and Shapley Allocation",
  "title_text": "Multi-Sensitive Distributional Fairness: Joint Wasserstein Audits and Shapley Allocation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:42Z",
  "url": "https://research.draconitic.com/paper/5xask55yzhs8z",
  "venue": "arXiv",
  "versions": []
}