{
  "annotation_id": "ce8f00b9-1ab1-4d8e-815f-114e537a19a9",
  "date_created": "2026-03-02T18:01:14.522000Z",
  "date_modified": "2026-03-02T18:01:14.522000Z",
  "file_hash": "f05110b89e4d54c3d6a351432b10b62b356059f1d05296666baf6094cc891ac4",
  "private": false,
  "record": {
    "abstract": "Systems of indirect voting based on the principle of qualified majority can\nbe analysed using the methods of game theory. In particular, this applies to\nthe voting system in the Council of the European Union, which was recently a\nsubject of a vivid political discussion. The a priori voting power of a voter\nmeasures his potential influence over the decisions of the voting body under a\ngiven decision rule. We investigate a system based on the law of Penrose, in\nwhich each representative in the voting body receives the number of votes (the\nvoting weight) proportional to the square root of the population he or she\nrepresents. Here we demonstrate that for a generic distribution of the\npopulation there exists an optimal quota for which the voting power of any\nstate is proportional to its weight. The optimal quota is shown to decrease\nwith the number of voting countries.",
    "arxiv_id": "physics/0610271",
    "authors": [
      "Wojciech Slomczynski",
      "Karol Zyczkowski"
    ],
    "categories": [
      "physics.soc-ph"
    ],
    "journal_ref": "Acta Physica Polonica B37, 3133-3143 (2006)",
    "title": "Penrose voting system and optimal quota",
    "url": "https://arxiv.org/abs/physics/0610271"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8b0826c9-53eb-4686-af1e-b941f537b541",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}