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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 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 ${\displaystyle j}$ with population ${\displaystyle N_{j}}$ is proportional to ${\displaystyle {\sqrt {N_{j}}}}$. Jagiellonian Compromise is based on a single criterion only. Decision of the Council of the union of ${\displaystyle M}$ member states is taken if the sum of the weights of states voting in favour of a given proposal exceeds the qualified majority quota ${\displaystyle q}$ equal to

${\displaystyle q={\frac {1}{2}}\cdot \left(1+{\frac {\sqrt {\sum _{i=1}^{M}N_{i}}}{\sum _{i=1}^{M}{\sqrt {N_{i}}}}}\right)}$

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

See also

• List of countries and dependencies by population
• Penrose method
• Jagiellonian University

References

Footnotes

1. Słomczyński & Życzkowski 2004.
2. Kirsch 2010; Pukelsheim 2010; Ratzer 2006.
3. Highfield, Roger (14 July 2004). "The EU Constitution Is 'Unfair', According to Game Theorists". The Telegraph. London. Retrieved 30 August 2017.
4. 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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