Tuesday, March 09, 2004

Mathematics of the electoral college: part I 

This is the first in what will be a series of posts on the mathematics of the electoral college. Over at Tradesports.com they have odds on Bush winning individual states in November. If we make the (admittedly vastly oversimplifying) assumption that Bush's wins/losses in individual states are independent events, with a bit of thought it's possible to convert these into odds that Bush will win a majority of votes in the electoral college.

One way to do this would be to run a simulation of millions of elections, deciding each state based on the Tradesports odds and keeping track of the number of Bush wins. This would give a good approximate answer. But there's actually a mathematical way to find the exact odds. For those interested in the math involved, here are the details. For the rest, the summary:

chance Kerry wins the election: 31%
chance Kerry wins assuming he wins Ohio: 44%
chance Kerry wins assuming he wins Florida: 49%
chance Kerry wins assuming he wins neither Ohio nor Florida: 14%

Are these numbers too low? Probably. In the real world, wins in one state are positively correlated with wins in other states. If Kerry were to win Ohio, for example, that's probably an indication he performed well nationally, picking up a lot of other swing states and putting his chances at much better than 44%. So the 44% and 49% figures shouldn't be taken too seriously. I don't think the 31% is that far off, though; Tradesports puts Kerry's chances at 37%. And the 14% may even be too high.

The implication is clear: we need either Ohio or Florida! Despite the recent polls showing Kerry ahead in Florida, my guess is that Ohio will be easier to win.
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