{
  "annotation_id": "a99c689b-35a6-4672-adcb-285447a8d7c2",
  "date_created": "2026-03-02T18:01:18.086000Z",
  "date_modified": "2026-03-02T18:01:18.086000Z",
  "file_hash": "8086e8efe081d57f1e10da41d4910aa440fb81bb090fc13e03e146b645de144b",
  "private": false,
  "record": {
    "abstract": "We investigate systems of indirect voting based on the law of Penrose, in\nwhich each representative in the voting body receives the number of votes\n(voting weight) proportional to the square root of the population he or she\nrepresents. For a generic population distribution the quota required for the\nqualified majority can be set in such a way that the voting power of any state\nis proportional to its weight. For a specific distribution of population the\noptimal quota has to be computed numerically. We analyse a toy voting model for\nwhich the optimal quota can be estimated analytically as a function of the\nnumber of members of the voting body. This result, combined with the normal\napproximation technique, allows us to design a simple, efficient, and flexible\nvoting system which can be easily adopted for varying weights and number of\nplayers.",
    "arxiv_id": "physics/0701338",
    "authors": [
      "Wojciech Slomczynski",
      "Karol Zyczkowski"
    ],
    "categories": [
      "physics.soc-ph"
    ],
    "journal_ref": "Homo Oeconomicus 24, 381 - 399 (2007)",
    "title": "From a toy model to the double square root voting system",
    "url": "https://arxiv.org/abs/physics/0701338"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2a50812f-fe4b-4cb1-b374-98e71a886575",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}