## Faites vos jeux

Since the election was called I’ve been looking at a number of statistical sources who try to predict the outcome. I’ve been concentrating on sites where lots of individual opinions are aggregated, rather than looking for individual wizards. The three I’ve been regularly checking are:

1. Betfair, an exchange where people set their own odds for bets – in effect, a place which allows customers to be bookmakers. The markets fluctuate in real time as new bets are offered, and therefore it’s a very sensitive minute-by-minute guide to the latest feelings in the electoral-betting marketplace.

2. Sporting index. This is a spread-betting site, in which the sheer weight of money determines what the range of outcomes is on any given bet. If the offer on Tory seats is, say, 320-325, you can either bet that they’ll win fewer than 320 or more than 325. The company makes its money from the range in the middle, and this is, remarkably often, where the result tends to be. Spread betting has been shown to be more accurate than polling when it comes to predicting election results.

3. UK polling report, which collects and summarises opinion polls. Note that the usual question ‘how are you going to vote?’ is different from ‘who do you think will win?’ so these three sources aren’t measuring the exact same thing. (‘If you were voting today for whom would you vote?’ is a subtly different question too. The measure of voting intention tends to rate the Tories about a per centage point higher than the question of whom you prefer today.)

Anyway, I’ve been following all these for two weeks, planning to pass on their wisdoms, but there hasn’t been much to pass on, because the numbers have hardly moved. Two days before the election was called, the betting exchanges were offering to pay £59 on a successful £100 bet on a Tory ruling majority; £215 on no overall control; and £1450 on a Labour ruling majority. The spread on Sporting Index was, as it has consistently been, more bullish about the Tories: the money thought the Tories would win between 334 and 339 seats, ie would have a majority of between 18 and 28 seats. I was tempted to make a small bet on a hung Parliament, and on the Tories underperforming 334 seats, but not tempted enough to actually do anything about it.

Nothing much changed in these figures for two weeks. The odds on a Tory majority wobbled slightly downwards, and the odds on a hung Parliament wobbled slightly up; the Tory seats number headed downwards too. In all cases, the movement was small. On the morning of the first debate, 15 April, you would win £77 for your correct pro-Tory bet; £164 for no overall control; £1700 for Labour. The Tory seat spread was 327-332, i.e. a majority of 4 to 14 seats. At the same time, the opinion polls were suggesting a hung Parliament, with the Tories short by about 20 seats. So things had been fairly static.

But the debate has completely changed these numbers. The Tories aren’t the money favourites any more. They and the hung Parliament have effectively changed places. That £100 would now earn £172 if the Tories win, £73 for no overall control, and £2700 for Labour. Even the Tory-favouring spread betting is suggesting 307-312 seats, ie a Tory minority of 36-26. The polls suggest a hung Parliament with Labour the biggest party, 39 seats short of a majority.

Wow! Inside the two big parties, quite a few people are going to be doing a lot of Told You So – remember, one of the big parties’ main reasons for not having these debates was the advantage it would give the Lib Dems. The insiders’ view, I gather, is that this effect will not linger, once the Great British Public has its attention drawn to the Lib Dems policies on Europe and immigration (they’re in favour). At things currently stand, though, the numbers and not just the commentariat suggest that the debate has changed the election.

The information exchange I look at is Intrade. They offer contracts on each of the main parties winning the largest number of seats, and on each of the main parties winning an overall majority. One can figure out from the prices at which these contracts are trading what the probability is of there being a hung parliament in which a particular party has the largest number of seats.

For example, the contract that pays out if the Tories win the largest number of seats is currently trading at 0.76, and the contract that pays out if the Tories have an overall majority is trading at 0.34. So the probability that there’ll be a hung parliament in which the Tories have the largest number of seats is 0.42 (= 0.76 – 0.34), or 42%.

Applying the same logic to the other two parties we get a 19% probability of a hung parliament in which Labour have the largets number of seats, and a 3% probability of a hung parliament with the LibDems having the largest number.

That gives a 64% (= 42% + 19% + 3%) probability of a hung parliament.

The contract which pays out if there is, in fact, a hung parliament is trading at 0.62; the slight discrepancy isn’t material.

One can have some more fun with this (if fun is quite the word). If there is a 64% probability of a hung parliament, and a 42% probability of a hung parliament in which the Tories have the largest number of seats, then the probability that the Tories have the largest number of seats, given that there is a hung parliament, is 67% (= 42% / 64%).

Likewise, the probability of Labour having the largest number of seats, given that there is a hung parliament, is 29%, and for the LibDems the probability is 4%.

Now, as anyone who’s played with the BBC’s swingometer thingy knows, the most recent polls are suggesting the freaky situation of a hung parliament in which Labour comes third in the popular vote, but gains the largest number of seats. The swingometer shows that a LibDem surge hurts the Tories much more than it does Labour. But the Intrade markets are saying the most likely outcome is a hung parliament in which the Tories hold the largest number of seats.

Perhaps that’s because the Intrade markets are assuming the LibDem surge will ebb somewhat, which would put the Tories back in the lead both in terms of seats and the popular vote. Certainly that seems to be the conventional wisdom. What will be interesting to watch is whether prices on Intrade start indicating that the LibDem surge is more than a passing fancy.