Sunday, October 24, 2004

Using data

Welcome visitors from Andrea Moro's 2004 Presidential Electoral College Predictions page. Check out the rest of my blog.

At people trade real money for securities which pay $100 if Bush wins a given state. The difficulty with using these numbers is that there is no obvious way to proceed to a probability that Bush wins the election. It is easy to say if the Bush-Ohio security sells for $55 and the Bush-Florida security sells for $65, then Bush has a 55% chance of winning Ohio and a 65% chance of winning Florida according to the market. The problem is figuring out the joint probability of winning both (or more generally the probability of winning a combination that adds to 270). If sampling error is the only problem, we know that this is uncorrelated across states. With uncorrelated errors, the problem is easy. The probability that Bush wins both Florida and Ohio is simply .55*.65. With prices, there is no reason to believe that pricing error is uncorrelated across states. If Kerry wins Florida, whatever caused the market to get it wrong will plausibly also cause Kerry to win Ohio.

So I've come up with another statistic based on perfectly correlated pricing errors. That is, if Bush wins a state priced at x, he also wins every state priced greater than x. This assumption implies there is a pivotal state which causes Bush to go over 270 and the price of this state is the probability that Bush wins. To check on the
current value of this variable, check out Andrea Moro's 2004 Presidential Electoral College Predictions.

(For the more technically minded, assume a random variable x is drawn from a uniform [0,1] distribution. If stateprice > x, assume Bush wins the state, otherwise Kerry does. Certainly, this forumlation ensures that each state price is also the probability of Bush winning that state. Perfectly correlated pricing error in this context means there is one x drawn, not one x drawn for each state. Given this, if
stateprice1 > stateprice2 > x, then Bush wins both states. Thus one needs to rank the states by price and find the pivotal state. If x is drawn less than the price of the pivotal state, Bush wins. Otherwise, Kerry wins.)

UPDATE: Ray Fair had this idea first. If you go to the Intrade website:
and click "R. Fair, Yale, ..." near the upper right hand corner of the page,
you will get a paper of Fair's that uses the same assumption about ranking
the states which he argues seems like a very good approximation.