Social:Jagiellonian compromise

Short description: Electoral system for two-tier voting bodies

The Jagiellonian compromise is an electoral 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. The compromise was analysed by various authors({{{1}}}, {{{2}}}) 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 [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].

See also

• List of countries and dependencies by population
• Penrose method

References

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.
• Życzkowski, Karol; Słomczyński, Wojciech (2012). "Square Root Voting System, Optimal Threshold and $$ \uppi $$ π". Power, Voting, and Voting Power: 30 Years After. pp. 573–592. doi:10.1007/978-3-642-35929-3_30. ISBN 978-3-642-35928-6.