Dimension of the Lisbon voting rules in the EU Council: a challenge and new world record

The Lisbon voting system of the Council of the European Union, which became effective in November 2014, 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.