Social:Jagiellonian Compromise

From HandWiki
Revision as of 11:00, 23 October 2022 by Unex (talk | contribs) (fix)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

The Jagiellonian Compromise is an electoral system for two-tier voting bodies originally proposed in 2004[1] 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 analysed by various authors({{{1}}}, {{{2}}}) and received attention in the popular press.[2] 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 [math]\displaystyle{ j }[/math] with population [math]\displaystyle{ N_j }[/math] is proportional to [math]\displaystyle{ \sqrt{N_j} }[/math]. Jagiellonian Compromise is based on a single criterion only. Decision of the Council of the Union of [math]\displaystyle{ M }[/math] Member States is taken if the sum of the weights of States voting in favour of a given proposal exceeds the qualified majority quota [math]\displaystyle{ q }[/math] equal to

[math]\displaystyle{ q = \frac12 \cdot\left(1 + \frac{\sqrt{\sum_{i=1}^M N_i}}{\sum_{i=1}^M \sqrt{N_i}}\right) }[/math]

For a generic distribution of population among [math]\displaystyle{ M }[/math] States of the Union, the optimal threshold [math]\displaystyle{ q_* }[/math] decreases with [math]\displaystyle{ M }[/math] as [math]\displaystyle{ q_* \approx 1/2 +1/\sqrt{\pi M} }[/math].[3]

See also

References

Notes

Bibliography

Kirsch, Werner (2010). "The Distribution of Power in the Council of Ministers of the European Union". in Cichocki, Marek A.; Życzkowski, Karol. Institutional Design and Voting Power in the European Union. Farnham, England: Ashgate Publishing. pp. 93ff. ISBN 978-1-4094-9995-4. 
Pukelsheim, Friedrich (2010). "Putting Citizens First: Representation and Power in the European Union". in Cichocki, Marek A.; Życzkowski, Karol. Institutional Design and Voting Power in the European Union. Farnham, England: Ashgate Publishing. pp. 235–254. ISBN 978-1-4094-9995-4. 
Ratzer, Edward (2006). On the 'Jagiellonian Compromise': Voting in the European Union. Cambridge, England: University of Cambridge. http://www.inference.phy.cam.ac.uk/ear23/voting/voting.pdf. Retrieved 30 August 2017. 
Słomczyński, Wojciech; Życzkowski, Karol (2004). "Voting in the European Union: The Square Root System of Penrose and a Critical Point". arXiv:cond-mat/0405396.CS1 maint: ref=harv (link)
Życzkowski, Karol; Słomczyński, Wojciech (2012). "Square Root Voting System, Optimal Threshold and π". arXiv:1104.5213.CS1 maint: ref=harv (link)