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 ${\displaystyle j}$ 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 ${\displaystyle q_{*}\approx 1/2+1/{\sqrt {\pi M}}}$.^[4]

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