News from the world of maths: United Kingdom - Nil Points

It is one of my favourite times of year, and I'm not even European.

The Eurovision Song Contest to Australians is a strange mix of bad 80s music, songs about "joy", "love" and "unity", amazingly good-looking hosts, scantily dressed Eastern Europeans and reality TV winners from Western Europe.

But another reason I love it is because it is about politics and maths. For the first time in my life, living in the UK, I get a chance to vote for the winner and watch it live instead of having to ignore radio reports (of course it's all over the news) till the Sydney Sunday evening replay.

The voting of Eurovision is a complex interaction of politics and voting blocks. Each country votes in a popular vote, in which they cannot vote for themselves, and each country has equal voting power. Voting is often based on politics — Cyprus and Greece nearly always exchange votes — and I can remember the days when Ireland and the UK were similarly connected. On the other hand, France does not vote for the UK and the Balkan states have mixed allegiances.

Eurovision is a perfect example of what mathematicians call a complex system. This consists of a group of objects (countries) which interact with each other (by giving each other points for their songs), and this interaction can be tracked over time. A statistical analysis of the system can then give some insight in the nature of the interaction. For example, it can show whether certain countries form cliques that always vote similarly, or whether a country's voting is largely "in tune" with that of the whole group.

Some time ago a team of Oxford scientists performed statistical tests to see whether the voting behaviours of different countries are in some way related. In every statistical test you need a "control experiment" to compare your results to. Suppose, for example, that two countries always seem to vote the same way. Then, before you can deduce that their musical tastes are indeed related, you need to show that the two countries vote the same way significantly more often than would happen in a song contest in which the countries' voting is truly independent. To create such a control experiment, the team simulated a "random song contest", in which each country assigns its points randomly to 10 other countries. They then compared the results of all their tests to the random contest.

One such test involves seeing whether voting relationships between countries persists over time. If, for example, country A gives and/or receives points from another country B over a long period of time, then we can deduce that in some way the musical tastes of the two countries are related. Carrying out the same analysis between country A and all other countries in turn will show whether or not country A is "in tune" with the rest of Europe.

Another test observes the number of countries to which a given country A has awarded points and from which it has also received points. If a country has many such "reciprocal links", then one might deduce that its musical taste harmonises well with that of Europe in general.

The remaining tests were devised to identify cliques of countries whose voting behaviour is correlated. For example, the team checked to see whether two countries that have both received and/or awarded points to a third country are likely to give or receive points from each other.

And the results of the study? Well, you'll just have to read our Plus article United Kingdom - twelve points for more information on the statistical tests, and don't forget to vote!