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An upper bound on the dimension of the voting system of the European Union Council under the Lisbon rules
The voting rules of the European Council (EU) under the Treaty of Lisbon
became effective on 1 November 2014. Kurz \& Napel (2015) showed that the
dimension of this voting system is between and . The lower bound
actually sets a new world record for the dimension of the real-world voting
bodies. In this article, by finding a new way to represent the union of two
weighted games as an intersection of certain weighted games (Theorem 1), we
greatly reduce the upper bound to just . We also consider what
will happen to our upper bound and Kurz \& Napel's lower bound if the United
Kingdom is no longer a member of the European Union Council