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Last Updated: Wednesday, 7 July, 2004, 11:13 GMT 12:13 UK
Maths tweak required for EU voting
EU flags, AP
Voting in Europe can be a complex thing

They claim suggested changes to voting rules for the EU Council of Ministers, the senior decision-making body in the union, will give the citizens of the largest countries a disproportionate influence over policy-making.

The new system is contained in the draft EU constitution recently agreed by Europe's leaders. It will come into force in 2009.

Current voting rules are based on the Treaty of Nice, which was signed in February 2001. They stipulate that each country's representative on the council should have a certain number of votes, called the country's voting weight.

Even these are not wholly fair, say Wojciech Slomczynski and his colleague Karol Zyczkowski, from Jagiellonian University in Krakow.

Heavyweight nations

For example, Germany, with over 80 million people, has 29 votes. Italy has the same number of votes, even though its population is only roughly two-thirds that of Germany; while Poland with just 38 million people gets 27 votes.

Bar chart displaying voting weights, BBC
Total number of votes: 321
Qualified Majority: 232 (72.3%)
Nice Treaty came into force in Feb 2004
In its original guise, the draft European Constitution, aiming to change the Nice system later this decade, proposed a simpler system in which a decision would go through if two criteria were met.

Firstly, at least half the EU's member states would have to agree; and second, this majority should represent at least 60% of the entire EU population.

It was felt this system would favour the traditional big players Germany, France and the UK - at the expense of some medium-sized nations, such as Poland and Spain.

Slomczynski said it was needlessly complicated as well.

He argues that each country's voting power should more closely match its population size, and points to a mathematical idea to achieve this that has existed for many years.

Finding balance

"This idea was originated by Lionel Penrose, a British mathematician in the mid 40s. His work was about the distribution of votes in the UN General Assembly and he invented what we now call the Penrose Square Root Law," Slomczynski told the BBC's Science in Action programme.

"It tells us that the influence of each citizen of the EU upon the outcome of the voting of the Council will be the same if the voting power of a given member state in the Council is proportional to the square root of its population," Slomczynski added.

Slomczynski and Zyczkowski believe the hotly disputed qualified majority figure should be set at 62% of the population.

They say rigorous mathematical arguments show this quota to be optimal - the voting power of each citizen in every European country would then be exactly the same.

"There's a very important difference between voting weights and voting powers. If a given party has in a parliament 55% of votes, it has full power, so the quantities are different. But if we establish this threshold of qualified majority in the case of the EU Council at 62%, then those two countries are just equal," said Slomczynski.

As it stands, however, Europe's leaders have gone for a settlement put forward by the Irish.

Their new plan says measures must have the backing of at least 55% of EU states, representing at least 65% of the total population, in order to pass.

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