You could also use the law of total probability to calculate this:

P(president) = P(nomination) * P(president | nomination)
P(president | nomination) = P(president) / P(nomination)

It’s certainly a simpler calculation, but it’s also nice to go through the bets and their ratios to be more explicit about how you could actually take a market position on on electability. Also, if you do use the law of total probability, you have to remember to use the offer price for your long position, and the bid price for your short position, so in this example:

11 / 25 = 44%
12.5 / 20 = 62.5%

Gives us the same electability range of 44%–62.5%

I’ve been pretty into this idea for a while, witness this January 2008 email to some friends:

With Super PACs having raised hundreds of millions of dollars, and betting volumes in the low single-digit millions of dollars, it wouldn’t surprise me at all if someone were manipulating odds already

N.B. Neteller was an e-wallet system that used to allow US residents to transfer money into Intrade and other gambling accounts, but no longer does

Here’s what the tree looks like if we don’t provide priors:

This tree predicts more genders correctly, with an overall accuracy rate of 85%, but its performance is very lopsided: it predicts that 98% of the actual males are male, but only 41% of the actual females are female.

Here’s what the full unpruned tree looks like:

The code to generate this tree and then prune it is in the GitHub repo

Note there are some subtle differences between the correlation coefficient and the slope of the regression line. The correlation coefficient represents how closely the variables follow a linear relationship, while the regression slope represents how much of a change we expect to see in the dependent variable when we increase the independent variable by a value of 1.

Recommended further reading:

http://stats.stackexchange.com/questions/32464/how-does-the-correlation-coefficient-differ-from-regression-slope