{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/ordinal-maximin-share-approximation-for-goods","title":"Ordinal Maximin Share Approximation for Goods","arxiv_id":"2109.01925","date":"2021-09-04","proceeding":null,"authors":["Hadi Hosseini","Andrew Searns","Erel Segal-Halevi"],"abstract":"In fair division of indivisible goods, $\\ell$-out-of-$d$ maximin share (MMS) is the value that an agent can guarantee by partitioning the goods into $d$ bundles and choosing the $\\ell$ least preferred bundles. Most existing works aim to guarantee to all agents a constant fraction of their 1-out-of-$n$ MMS. But this guarantee is sensitive to small perturbation in agents' cardinal valuations. We consider a more robust approximation notion, which depends only on the agents' \\emph{ordinal} rankings of bundles. We prove the existence of $\\ell$-out-of-$\\lfloor(\\ell+\\frac{1}{2})n\\rfloor$ MMS allocations of goods for any integer $\\ell\\geq 1$, and present a polynomial-time algorithm that finds a $1$-out-of-$\\lceil\\frac{3n}{2}\\rceil$ MMS allocation when $\\ell = 1$. We further develop an algorithm that provides a weaker ordinal approximation to MMS for any $\\ell > 1$.","url_abs":"https://arxiv.org/abs/2109.01925v3","url_pdf":"https://arxiv.org/pdf/2109.01925v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"ordinal-maximin-share-approximation-for-goods","repo_url":"https://github.com/erelsgl/ordinal-maximin-share","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2109.01925","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2109.01925"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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