Tuesday, October 19, 2004

Polling and Prices

UPDATE: Visitors from Andrea Moro's 2004 Presidential Electoral College Predictions page probably want the explanation of my tradesports.com market based prediction. It is below, but so is other stuff. The direct explanation is here.

I have a friend, Andrea Moro (he's a guy) who has a pretty cool site, 2004 Election Predictions. What his site does is, automatically every hour on the hour, download the latest state polls from another website. His website then uses the error margins from these polls and calculates the probability that Bush wins the state. For instance, if a state has Bush up by 4 and a 4 point margin of error, then Bush is given a 97.5% chance of winning that state. If Bush is up by 2 with a 4 point margin, then Bush is given (I think) about an 80% chance of winning that state. The program then aggregates all of these individual state probabilities and comes up with a probability that Bush makes it to 270. His current probability (Tuesday October 19th, 7:30 PM CDT)is a 37% chance of a Bush win. Mostly this is due to the fact that the latest Survey USA Florida poll has Kerry by 1. If the Mason Dixon poll has Bush up (National Review's KerrySpot says it will have Bush up by 3) then Andrea's number will move up in a big way.

Andrea understands, of course, that his number assumes that the only problem with these polls is sampling error. That is, he assumes that every voter has an equal probability of being called by the poller. The sample gets skewed only due to pure chance and never because of bad polling methodology. Everyone (including Andrea) knows this is nonsense. The polls disagree with each other too much for this to be true.

So another possibility is looking at the state prices from Tradesports.com. Here, people trade real money for securities which pay $100 if Bush wins a given state. The problem 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 $60 and the Bush-Florida security sells for $65, then Bush has a 60% 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 .65*.60. 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. Given this assumption of perfectly correlated pricing errors, there is currently a 60% chance of Bush winning, the market price of Bush-Ohio.

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