ABSTRACT. The new voting system of the Council of the European Union cannot be represented as the intersection of six or fewer weighted games, i.e., its dimension is at least 7. This sets a new record for real-world voting bodies. A heuristic combination of different discrete optimization methods yields a representation as the intersection of 13 368 weighted games. Determination of the exact dimension is posed as a challenge to the community. The system's Boolean dimension is proven to be 3.
Quite recently, it has been shown that the voting system of the Council of the European Union under its Treaty of Lisbon rules has a dimension between 7 and 13 368 REF .
Dimension of the Lisbon voting rules in the EU Council: a challenge and new world record
ArXiv
ArXiv
Computer Science Mathematics Geography