Square root voting system, optimal threshold and \pi
Abstract
The problem of designing an optimal weighted voting system for the twotier 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 onedimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2011
 DOI:
 10.48550/arXiv.1104.5213
 arXiv:
 arXiv:1104.5213
 Bibcode:
 2011arXiv1104.5213Z
 Keywords:

 Physics  Physics and Society
 EPrint:
 revised version, 21 pages in latex