Tactical manoeuvres: making votes count in elections

On Monday a cross-party group of politicians attempted to derail the UKIP train by labelling them racists. This move is almost certainly not going to reduce UKIP support, as calling UKIP supporters racist is unlikely to woo them to your cause, but that is the current thinking.

If politicians cannot stop UKIP coming to power, perhaps the electorate can? In elections past, there were regular attempts to use tactical voting to get a preferable outcome for themselves, and was even in the run up to the 2010 election. European elections are run differently.

European elections are unique in the British voting calendar for being done by proportional representation (PR) – except in Northern Ireland, where they are done by a similar system called Single Transferable Vote – and as such are not well understood by people used to the more common First Past the Post system of local and general elections.

In its purest form, PR is very simple: if a party gets 35 per cent of the vote, they get 35 per cent of the seats in the assembly. There is a complicating factor: there are a set number of seats in the assembly (in the case of the European elections, between three and ten per region) so getting a few more votes probably won't make any difference.

This is how it works: Imagine that each party is sitting at a table, and they each have a stack of poker chips, one for each person who voted for them. Party A, with the largest stack, has the most votes, so gets the first seat in the assembly. This party then splits their stack into two equal piles and we look at who has the highest stack again. It could be that Party A now has the two largest stacks, and so it gets another seat in the assembly, and it splits its chips into three equal piles, or Party B now has the highest stack in which case it gets the next seat and its pile is split into two. This continues until all the seats are filled.

We see that if, say, there are five seats in the EU region then any party with more than a sixth of the vote will get a seat, as otherwise the other parties need to have five piles of chips, all bigger than this pile, and that’s too many chips. With UKIP polling at around 30 per cent, considerably more than the 18 per cent that represents one in six, they will get a seat regardless of what the other voters do.

We normally think this is a good thing. Making a voting system resistant to tactical voting is considered a benefit of the system, not a problem. But, if people want to keep UKIP out, what can they do to minimise the number of seats UKIP gains using tactical voting?

Small parties, collecting a few per cent of the vote, don't help to defeat a party at all. To protest a protest vote, one needs to go with the largest parties. The latest poll by the Sunday Times puts UKIP on 31, Conservatives 19, Labour 28, Lib Dems 9, Greens 8, with Other on 5, so let's assume that this is how people would want to vote in East Midlands with its five MEPs. In this case, UKIP, Labour and Conservative all get a seat each, and then we have to split our piles, and we see that UKIP and Labour each get another one. However, if everyone who voted for someone else put their vote into Conservatives and Labour, we could have something like UKIP 31, Conservative and Labour 32, and this means that Conservative and Labour pick up those second seats. If everybody who would vote for anyone other than UKIP/Con/Lab switched their vote to Conservative, however, we would see UKIP 31, Con 41 and Lab 28, and so UKIP picks up a second seat again. If they shifted their support to Labour then Labour would pick up both of the other two seats, but it would take everyone, and 4 per cent not voting tactically would be enough to let UKIP in.

Even with complete knowledge of how everyone wants to vote, it is very hard to co-ordinate such a campaign to shift votes in such a complicated way. But it should be difficult to tactically vote to get rid of someone you don't like against the wishes of a substantial minority of people. If UKIP is the most popular party in May, it will get a large number of seats, and the electorate can’t stop it.

Dr David Craven is a Birmingham Fellow in the School of Mathematics, at the University of Birmingham.