Jagiellonian Compromise

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 j with population Nj is proportional to Nj. 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=12⋅(1+∑i=1MNi∑i=1MNi)

For a generic distribution of population among M States of the Union, the optimal threshold q* decreases with M as q*≈1/2+1/πM.[3]

## See also

* List of countries and dependencies by population
* Penrose method

## References

### Notes

1. ↑ Słomczyński & Życzkowski 2004.
2. ↑ Highfield, Roger (14 July 2004). "The EU Constitution is 'Unfair', According to Game Theorists". The Telegraph (London). https://www.telegraph.co.uk/news/science/science-news/3325470/The-EU-constitution-is-unfair-according-to-game-theorists.html. Retrieved 30 August 2017.
3. ↑ Życzkowski & Słomczyński 2012.

### 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. `{{cite arXiv}}`: Invalid `|ref=harv` (help)
Życzkowski, Karol; Słomczyński, Wojciech (2012). "Square Root Voting System, Optimal Threshold and π". arXiv:1104.5213. `{{cite arXiv}}`: Invalid `|ref=harv` (help)CS1 maint: missing class (link)

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