{"paper":{"title":"Balancing Notions of Equity: Trade-offs Between Fair Portfolio Sizes and Achievable Guarantees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jai Moondra, Mohit Singh, Swati Gupta","submitted_at":"2023-11-06T16:15:38Z","abstract_excerpt":"Motivated by fairness concerns, we study the `portfolio problem': given an optimization problem with set $D$ of feasible solutions, a class $\\mathbf{C}$ of fairness objective functions on $D$, and an approximation factor $\\alpha \\ge 1$, a set $X \\subseteq D$ of feasible solutions is an $\\alpha$-approximate portfolio if for each objective $f \\in \\mathbf{C}$, there is an $\\alpha$-approximation for $f$ in $X$. Choosing the classes of top-$k$ norms, ordered norms, and symmetric monotonic norms as our equity objectives, we study the trade-off between the size $|X|$ of the portfolio and its approxim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03230","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.03230/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}