## election

With the day of the referendum on the UK voting system drawing nearer, Tony Crilly uses a toy example to compare the first past the post, AV and Condorcet voting systems, and revisits a famous mathematical theorem which shows that there is nothing obvious about voting.

When you try to put democracy into action you quickly run into tricky maths problems. This is what happened to Andrew Duff, rapporteur for the European Constitutional Affairs Committee, who was charged with finding a fair way of allocating seats of the European Parliament to Member States. Wisely, he went to ask the experts: last year he approached mathematicians at the University of Cambridge to help come up with a solution. A committee of mathematicians from all over Europe was promptly formed and today it has published its recommendation.

Tonight, in the final televised debate ahead of the election, the three main party leaders will talk about the economy, the recession, public sector debt, spending or cuts, and more. All will use statistics to back up their points or to pull apart their opponents' arguments. But how can we work out whether to believe the figures and what do they really mean?

One advantage of the UK voting system is that nobody could possibly fail to understand how it works. However, the disadvantages are well-known. Differently sized constituencies mean that the party in government doesn't necessarily have the largest share of the vote. The first-past-the-post system turns the election into a two-horse race, which leaves swathes of the population un-represented, forces tactical voting, and turns election campaigns into mud-slinging contests.

There are many alternative voting systems, but is there a perfect one? The answer, in a mathematical sense, is no.

This may seem like an odd question — after all, he’s won — but it opens up some deep philosophical issues surrounding probability. **David Spiegelhalter** investigates how probability can be defined.

**Steven J. Brams**proposes an alternative voting system that could help make things more democratic.