Jagiellonian compromise

Template:Short description Template:Use dmy dates Template:Use British English Oxford spelling The Jagiellonian compromise is an electoral system for two-tier voting bodies originally proposed in 2004Template:Sfn for the Council of the European Union as a way of achieving "one person, one vote" within the union. The compromise, proposed by two authors from the Jagiellonian University, was analysed by various authorsTemplate:Sfnm 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 $j$ with population $N_j$ is proportional to $\sqrt{N_j}$. Jagiellonian Compromise is based on a single criterion only. Decision of the Council of the union of $M$ member states is taken if the sum of the weights of states voting in favour of a given proposal exceeds the qualified majority quota $q$ equal to

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

For a generic distribution of population among $M$ states of the union, the optimal threshold $q_{*}$ decreases with $M$ as $q_{*}\approx 1/2+1/\sqrt{\pi M}$. The number $\pi$ appears in an expression related to voting theory as a consequence of an averaging over the Dirichlet distribution.Template:Sfn

See also

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

References

Bibliography

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