The treaty of Nice, which came into force in February 2003, is unfair and irrational in the opinion of Życzkowski and Slomczyński. For instance, it gives Germany, which has a population in excess of 82 million, the same number of votes (29) in the European Parliament as Italy, which only has around 57 million inhabitants. Moreover, Poland receives 27 votes despite having a population of only 38 million. Moreover, the draft Constitution -- which calls for the Nice system to be replaced in 2009 -- seems to favour the largest and smallest countries in the EU at the expense of medium-sized countries such as Poland and Spain.

Życzkowski, a physicist, and Slomczyński, a mathematician, developed a voting scheme based on the so-called Penrose Law, which states that the voting weight of a country is directly proportional to the square root of its population. This approach was pioneered by the English psychiatrist and mathematician Lionel S Penrose, father of the scientists Roger and Oliver and the chess player Jonathan.

Życzkowski and Slomczyński calculated that all citizens would have the same voting power if new laws required the support of 62% of the total EU population in votes at the European Council. Such a system would also give more power to smaller countries while safeguarding the rights of larger states. Under the proposed system the number of votes that each country has in the European Council would be proportional to the square root of its population.

The Polish duo say their system is a compromise between the conflicting interests of the bigger states -- France, Germany, Italy and the UK -- that favour the draft Constitution and medium-sized countries such as Poland and Spain who prefer the Nice Treaty. Furthermore, the scheme could easily be extended to accommodate new member states in the future. “It is difficult to predict, however, to what extent politicians would be interested in accepting such a system,” Życzkowski told PhysicsWeb.