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

Sascha Kurz; Stefan Napel

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

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arxiv 1503.02859 v2 pith:VE5EYELZ submitted 2015-03-10 math.OC cs.GT

Sascha Kurz , Stefan Napel This is my paper · ORCID

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keywords dimensionvotingchallengecouncilgamesintersectionrecordsystem

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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.

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