# 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 analyzed by various authors[2][3][4] and received attention in the popular press.[5] 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 ${\displaystyle q_{*}\approx 1/2+1/{\sqrt {\pi M}}}$.[6]