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arXiv · 1907.09711

An upper bound on the dimension of the voting system of the European Union Council under the Lisbon rules

Yuming Chen·Wai Shun Cheung·Tuen Wai Ng
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Abstract

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 $7$ and $13,368$. The lower bound $7$ 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 $13,368$ to just $25$. 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.

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Yuming Chen, Wai Shun Cheung, Tuen Wai Ng. 2019-07-23. An upper bound on the dimension of the voting system of the European Union Council under the Lisbon rules. https://arxiv.org/abs/1907.09711

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