{"paper":{"title":"An upper bound on the dimension of the voting system of the European Union Council under the Lisbon rules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Tuen Wai Ng, Wai Shun Cheung, Yuming Chen","submitted_at":"2019-07-23T06:23:24Z","abstract_excerpt":"The voting rules of the European Council (EU) under the Treaty of Lisbon became effective on 1 November 2014. Kurz \\& Napel (2015) showed that the dimension of this voting system is between $7$ and $13,368$. The lower bound $7$ actually sets a new world record for the dimension of the real-world voting bodies. In this article, by finding a new way to represent the union of two weighted games as an intersection of certain weighted games (Theorem 1), we greatly reduce the upper bound $13,368$ to just $25$. We also consider what will happen to our upper bound and Kurz \\& Napel's lower bound if th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09711","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"}