I’ve been concentrating on using polls to predict the outcome of the Presidential election here, but another alternative is to let someone else do it for you – or lots of people, who are prepared to put their money where their mouth is. This is the appeal of prediction markets like Intrade.com: participants (who I call “Intraders”) effectively bet on the outcome, and the bet is backed not by the company, but by other Intraders. Their collective opinion on the likelihood of the different outcomes sets the market price, and if you think they’ve got it wrong you can put money on it.
Prediction markets for the 2008 election were recently discussed in electoralvote.com (referencing this discussion on electoralmap.net); his conclusion was that Intraders just follow the polls, and so you might as well just look at the polls directly. Is this the right conclusion?
I wasn’t entirely happy with the way the curve shown in the graph was chosen – I wanted a more direct way to show the relationship between polling and Intrade.com prices. So I’ve translated the market prices into a measure more amenable to calculation, which I call the Intrade.com PPF. First, I translate the prices into a Democratic victory probability by dividing the price for a Democratic market in each state by the sum of the prices for the Democratic and Republican markets in that state; this works around the fact that for various reasons these prices don’t quite add up to 100. Second, I feed this into Φ-1, the “percentage point function” of the normal distribution – so I’m assuming that Intraders are making a guess at the probability distribution of the eventual margin of victory, and that it’s normally distributed.
The advantage of manipulating the figures in this way is that we can then just fit a straight line to the numbers to see what that implies about what Intraders believe about the market.
I think the resulting graph shows that Intraders are strongly influenced by the polls, but that they are by no means the only influence on how they bet.
First, look at how far the points stray from the line. New Hampshire (NH) and California (CA) look about the same as far as the polls are concerned, but Intraders are much more confident of a Democratic victory in CA than they are in NH. This scatter is representative of all the non-polling data that the Intraders are bringing to bear in making their estimates.
Second, we can learn something from the line we’ve fitted. From where the line crosses the x-axis, we can conclude that Intraders think that Obama is going to lose a percentage point on average, nationally, compared to today’s polls. That’s not enough to lose the election, but it’s a significant shift; if it reflects a pro-Republican bias on the part of Intraders then there’s money to be made betting on Democrats there. And the slope of the line means they think the standard deviation of the difference between the polls and the final results will be around 15%.
Third, there’s an interesting S-shape visible in the graph. Our conversion from probabilties to PPF should have eliminated that, and left us with something closer to a straight line. I think this reflects psychological errors on the part of Intraders – they are happy to use guesswork when they polls even, follow the polls when they show wider margins, but when the polls show very wide margins they can’t quite buy it, and offer prices that would be more appropriate for a tighter race. I strongly suspect that this means one could make some money betting exactly according to the line fitting on this graph – ie betting on the Republicans for the points above the line, and on the Democrats for the points below it – and if I had money to spare I’d try it instead of writing about it here.