Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Square root voting system, optimal threshold and \pi   The problem of designing an optimal weighted voting system for the two-tier
voting, applicable in the case of the Council of Ministers of the European
Union (EU), is investigated. Various arguments in favour of the square root
voting system, where the voting weights of member states are proportional to
the square root of their population are discussed and a link between this
solution and the random walk in the one-dimensional lattice is established. It
is known that the voting power of every member state is approximately equal to
its voting weight, if the threshold q for the qualified majority in the voting
body is optimally chosen. We analyze the square root voting system for a
generic 'union' of M states and derive in this case an explicit approximate
formula for the level of the optimal threshold: q \simeq 1/2+1/\sqrt{{\pi} M}.
The prefactor 1/\sqrt{{\pi}} appears here as a result of averaging over the
ensemble of unions with random populations.

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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th