Dimension of the European Union Council according to the Lisbon Treaty

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Kurz, Sascha ; Napel, Stefan:
Dimension of the European Union Council according to the Lisbon Treaty.
2015
Veranstaltung: 2nd German Day on Computational Game Theory , 10.-11.02.2015 , Berlin, Deutschland.
(Veranstaltungsbeitrag: Workshop , Vortrag )

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Abstract

In this talk we prove that the voting system of the European Union Council according to the Lisbon Treaty can not be represented as the intersection of five or fewer weighted games, i.e., its dimension is at least six, which makes it the current record holder within the class of real-world voting systems. Using (heuristic) discrete optimization techniques we compute a representation as the intersection of a few thousand weighted games. The exact determination of the dimension of the present EU voting system is introduced as a challenging computational problem. The Boolean dimension is determined to be exactly three.