{"paper":{"title":"Algebraic Voting Theory & Representations of $S_m \\wr S_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Erin McNicholas, H\\'el\\`ene Barcelo, Kathryn Nyman, Megan Bernstein, Sarah Bockting-Conrad, Shira Viel","submitted_at":"2018-07-06T00:56:56Z","abstract_excerpt":"We consider the problem of selecting an $n$-member committee made up of one of $m$ candidates from each of $n$ distinct departments. Using an algebraic approach, we analyze positional voting procedures, including the Borda count, as $\\mathbb{Q}S_m \\wr S_n$-module homomorphisms. In particular, we decompose the spaces of voter preferences and election results into simple $\\mathbb{Q}S_m \\wr S_n$-submodules and apply Schur's Lemma to determine the structure of the information lost in the voting process. We conclude with a voting paradox result, showing that for sufficiently different weighting vec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03743","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":""},"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"}