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 [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

• List of countries and dependencies by population
• Penrose method

References

Notes

Bibliography

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