Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 $7$ 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.

4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn