Greg Mankiw, an economist at Harvard has posted to his blog, an application of Bayes rule to the 2008 Presidential Election. He finds election probabilities from the website Intrade and defines the necessary variables as follows:

“Let A be the event that a candidate wins the general election, and B be the event that a candidate wins his or her party’s nomination. Tradesports gives us the betting market’s view of P(A) and P(B). It is a safe assumption that P(B / A) = 1, that is, a candidate can win only if nominated. We can then use Bayes theorem to compute P(A / B), the probability that the candidate will win the general election conditional on being nominated.”

Mankiw calculated the conditional probabilities at the time of his post, in November of 2006, so I have updated the calculations to show the current probabilities.

According to Intrade, the current probabilities of the three main candidates to win their respective party nominations (as of 3/29/08) are as follows:

Obama: 80.1%

Clinton: 18.5%

McCain: 95.4% (His nomination has yet to be formally announced)

The current probabilities of Presidential election (as of 3/29/08) are as follows:

Obama: 47.9%

Clinton: 11.9%

McCain: 39.7%

Given these numbers we can now determine the conditional probabilities P(A/B) by taking P(B/A)*P(A) and dividing it by P(B)

These above numbers give the following conditional probabilities (the probability that the candidate will win the general election conditional on being nominated):

Obama: 59.8%

Clinton: 64.3%

McCain: 41.6%

According to the market, it seems that even though Obama is more likely to end up President than Clinton, Clinton is more likely to win the general election if she is nominated. So although it may seem as if Clinton is a long shot to win the Presidential election right now, if she can win the Democratic nomination, her odds greatly improve. Either way, it is clear from this analysis that with a little over seven months to go until the election, the markets are very much undecided as to our next president.