Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Penrose voting system and optimal quota   Systems of indirect voting based on the principle of qualified majority can
be analysed using the methods of game theory. In particular, this applies to
the voting system in the Council of the European Union, which was recently a
subject of a vivid political discussion. The a priori voting power of a voter
measures his potential influence over the decisions of the voting body under a
given decision rule. We investigate a system based on the law of Penrose, in
which each representative in the voting body receives the number of votes (the
voting weight) proportional to the square root of the population he or she
represents. Here we demonstrate that for a generic distribution of the
population there exists an optimal quota for which the voting power of any
state is proportional to its weight. The optimal quota is shown to decrease
with the number of voting countries.

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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
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The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys