{"paper":{"title":"On Hierarchies of Fairness Notions in Cake Cutting: From Proportionality to Super Envy-Freeness","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Alexandros Psomas, Arnav Mehra","submitted_at":"2025-06-15T19:32:38Z","abstract_excerpt":"We consider the classic cake-cutting problem of producing fair allocations for $n$ agents, in the Robertson-Webb query model. In this model, it is known that: (i) proportional allocations can be computed using $O(n \\log n)$ queries, and this is optimal for deterministic protocols; (ii) envy-free allocations (a subset of proportional allocations) can be computed using $O\\left( n^{n^{n^{n^{n^{n}}}}} \\right)$ queries, and the best known lower bound is $\\Omega(n^2)$; (iii) perfect allocations (a subset of envy-free allocations) cannot be computed using a bounded (in $n$) number of queries.\n  In th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.12950","kind":"arxiv","version":1},"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/2506.12950/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"}