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Jagiellonian Compromise
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Jagiellonian Compromise : ウィキペディア英語版
Jagiellonian Compromise

The Jagiellonian Compromise is a voting system for two tier voting bodies originally proposed in 2004
for the Council of the European Union as a way of achieving "one person, one vote" within the Union.
==Reaction and explanation==
The Compromise was analyzed by various authors〔
〕〔Pukelsheim, Friedrich. ''Putting citizens first: Representation and power in the European Union'' in ''Institutional Design and Voting Power in the European Union'' ed. M. Cichocki, Ashgate, Farnham 2010, pp. 235-254〕〔E. Ratzer. '' On the “Jagiellonian compromise” – voting in the European Union'',
http://www.inference.phy.cam.ac.uk/ear23/voting/voting.pdf〕 and received attention in the popular press. The system is based on the square root law of Penrose, which implies that ''a priori'' voting power defined by the Penrose–Banzhaf index of a member of a voting body is inversely proportional to the square root of its size. Hence the number of votes obtained by a representative of a state j with population
N_j is proportional to \sqrt .
Jagiellonian Compromise is based on a single criterion only. Decision of the Council of the Union of M Member States is taken if the sum of the weights of States voting in favour of a given proposal exceeds the qualified majority quota q equal to
:q = \frac12 \cdot\left(1 + \frac}}\right)
For a generic distribution of population among M States of the Union
the optimal threshold q_
* decreases with M
as q_
* \approx 1/2 +1/\sqrt .

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