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In recent years, enlargement of the European Union has brought with itrenewed discussion of voting arrangements in the Council of the EU. Duringthese negotiations, the Polish government proposed a voting scheme that giveseach country a voting weight proportional to the square root of its population,and sets a quota according to an optimality condition ("JagiellonianCompromise"). In this paper, the optimal quota is found exactly for the currentpopulation data from the 27 EU member states, and it is found that rounding ofthe voting weights can be used to improve the voting scheme.

Square root voting in the Council of the European Union: Rounding effects and the Jagiellonian Compromise