ABSTRACT
This chapter proposes a complete voting system based on the Penrose square-root law. The representative voting system based on the Penrose square-root law and the appropriate choice of optimal quota may be used as a reference point while analysing the rules established by politicians. The square-root voting system was proposed independently in the European Union (EU) context without any relation to the Penrose square-root law. Voting rules implemented by various political or economic bodies may be studied with the help of tools that have been developed over many decades in game theory. The majority of experts agree that both the voting system established by the Treaty of Nice and the Treaty Establishing a Constitution for Europe have obvious drawbacks. The Jagiellonian Compromise, which allocates voting power according to the square root of population, restores some of the power to medium-sized countries that would be taken away by the Constitution.
