In quantum mechanics, particles like electrons can be observed in one of two spin states: up or down. The theory, however, doesn’t require the state to be completely determined before we look at it. Any given electron doesn’t have to be in one of those spin eigenstates; it can be in a superposition of spin up and spin down. It’s like Schroedinger’s cat being in a superposition of alive and dead, but less dramatic. For instance, a particular electron may be in a state which has a probability of 60% of being in an up state and 40% of being in the down state. Once measured it will definitely be one or the other, but if you repeat the process with many electrons prepared in the same state, you’ll end up with a 60:40 ratio in what you observe.
There’s a very interesting company on the internet called Intrade, which runs an operation which provides a marketplace for buying and selling shares of current events. If you think Obama will win the election, you can buy a share of “Barack Obama to win 2008 US Presidential Election”, and if he wins you’ll get $10 a share. If he doesn’t win the person who sold you the share gets to keep whatever you paid him for the share. Sales are done via the usual bid/ask process. Thus the share price (right now $6.01 a share) represents the probability for the event to happen. As of this writing it’s 60.1% Obama and 36.9% McCain. It doesn’t quite add up to 100%, mostly reflecting the possibility that Obama or McCain may not make it to the election due to death, disease, scandal, or whatever other reason. Exchange fees also account for some fraction of the gap.
You could say the election is in a linear superposition of the Obama and McCain states, and trading exchanges in some sense give you information about the wavefunction of the election. On November 4 the observation will be made and the function will (probably) collapse to the Obama or the McCain eigenstate. Until then we can get a sense of the time evolution of the wavefunction by tracking the share prices. If so, the prices for Obama and McCain should correlate inversely. Let me plot the share prices since July 1 for each. Each data point represents the closing price for a particular day. We expect to see Obama = 100 – McCain. Obama is on the y axis, McCain on the x.
We actually see Obama = 87.5 – (0.728)McCain, with a correlation coefficient of 0.859. Given that politics is a lot more complicated than two sharp spin eigenvalues, it’s not so bad.
What does all this mean? Nothing much. We could already have guessed that one candidate’s gain is the other candidate’s loss. But there is that wiggle room at the right and left of the graph that asks for an explanation. If McCain is certain to lose, Obama should have more than an 87% chance of winning, and vice versa. It’s these nonsensical gaps in theory that can lead to discovery – or the conclusion that the data source is simply flawed. The uncertainty in the slope and intercepts are quite small (0.046 and 1.526 respectively), so the error is very likely systematic rather than fuzziness in the data.
Any suggestions? Is there some interesting effect that causes the wiggle room, or is market trading just not equipped to describe the situation adequately near the margins?