Dimension of the Lisbon Voting Rules in the EU Council: A Challenge and New World Record
8 Pages Posted: 10 Mar 2015
Date Written: March 10, 2015
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 13368 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.
Keywords: simple games, weighted games, dimension, real-world voting systems, set covering problem, computational challenges
JEL Classification: C71, C63, D72
Suggested Citation: Suggested Citation