Square root system

Square root system

A system invented by the British mathematician Lionel Penrose to allocate seats or votes in legislatures. 

The system was proposed to be used in the EU by the Swedish government in 2003 and by the Polish government during the negotiations of the so-called Reform Treaty. 

The system would distribute votes in the Council according to the square root of a state's population. 

This system would give e.g. allocate two votes to Denmark, 3 to Sweden, 6 to Poland and 9 to Germany. Under the system until 1 November 2014, Germany has 29 votes, Poland 27, Sweden 10 and Denmark 7.

The first rejected and then approved Lisbon Treaty provided for the so-called double majority where member states also vote with the exact size of their population from 1 November 2014, when the most important vote is taken according to the number of citizens with Germany having a population of 80, 5 million.