{"paper":{"title":"Proportionality from Sampled Approvals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.GT","authors_text":"Gregory Kehne","submitted_at":"2026-06-09T05:50:09Z","abstract_excerpt":"How much voter input is necessary in order to ensure representation in multiwinner elections? If voters are randomly selected from an underlying population, how many draws are necessary to find a proportional committee of $k$ candidates, with high probability?\n  Sample-based adaptations of standard multiwinner voting rules that satisfy the justified representation (JR) proportionality axiom use $\\tilde O(k^5 \\log \\frac{m}{\\delta})$ sampled approval ballots over $m$ candidates, where $\\delta$ is a probability of failure and $\\tilde O$ suppresses $\\mathrm{polylog}(k)$ factors. We present a rule "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10446","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/2606.10446/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"}