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. The compromise was analysed by various authors^[2] and received attention in the popular press.^[3] 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 ${\sqrt {N_{j}}}$ . 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={\frac {1}{2}}\cdot \left(1+{\frac {\sqrt {\sum _{i=1}^{M}N_{i}}}{\sum _{i=1}^{M}{\sqrt {N_{i}}}}}\right)

For a generic distribution of population among $M$ states of the union, the optimal threshold $q_{*}$ decreases with $M$ as $q_{*}\approx 1/2+1/{\sqrt {\pi M}}$ .^[4]

References

Footnotes

^ Słomczyński & Życzkowski 2004.
^ Kirsch 2010; Pukelsheim 2010; Ratzer 2006.
^ Highfield, Roger (14 July 2004). "The EU Constitution Is 'Unfair', According to Game Theorists". The Telegraph. London. Retrieved 30 August 2017.
^ 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 (eds.). 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 (eds.). 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" (PDF). Cambridge, England: University of Cambridge. Retrieved 30 August 2017. {{cite journal}}: Cite journal requires |journal= (help)
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. arXiv:1104.5213. doi:10.1007/978-3-642-35929-3_30. ISBN 978-3-642-35928-6. S2CID 118756505.

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