{"paper":{"title":"Counting Votes with Multisets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Bart Jacobs, Michael Johnson, Richard Buckland","submitted_at":"2026-05-29T08:58:26Z","abstract_excerpt":"A multiset is a 'set' in which elements may occur multiple times. These structures are ideal for expressing the outcome of an election, for instance of the form 60 'yes' and 40 'no'. Moreover, multisets are a useful datatype in vote counting algorithms. This will be illustrated in three different forms of vote counting, known as: 'instant-runoff', 'De Borda', and 'single transferrable vote'. The relevant abstract properties of multisets are: (1) they form a (free) commutative monoid, and (2) they form a functor, and (3) also a monad. This paper illustrates how such categorical properties can b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05218","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/2606.05218/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"}