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({{{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 ${\displaystyle j}$ 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

${\displaystyle q=\frac{1}{2}\cdot (1+\frac{\sqrt{{\displaystyle \sum _{i=1}^M}{N}_i}}{{\displaystyle \sum _{i=1}^M}\sqrt{N_i}})}$

For a generic distribution of population among ${\displaystyle M}$ States of the Union, the optimal threshold ${\displaystyle q_{*}}$ decreases with ${\displaystyle M}$ as ${\displaystyle q_{*}\approx 1/2+1/\sqrt{\pi M}}$.^[3]

• List of countries and dependencies by population
• Penrose method

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