Because the xkcd odds are computed based on the completely bogus assumption that Obama and McCain win or lose states independently.

When we get to election day, the states become pretty independent; but until that day, there are very strong correlations between the results in different states.

Thank you. I actually did this same simulation (I have the Python code if you want it), and got about 80% for Obama -- this was a couple of weeks back.

I sent it around and people rightly pointed out that the states are definitely not independent. The most interesting thing you can do with this is figure out what the implied dependence is.

Huh, what?

First: early voting has already started in some states, second: there is always a correlation between how states vote, because they're based on how the candidates have performed.

Suppose there are only three states.

Suppose that all states have an 80% probability of voting for Obama.

If they are independent, the odds of an Obama win are .8 * 8 * .8 + 3 * .8 * .8 * .2=.896

However, suppose the states are maximally DEPENDENT-- they always vote the same way. Then, the odds of an Obama win are exactly .8

The effect will be much stronger with more states, hence the gigantic difference between XKCD's result, and intrade's odds on an obama vs mccain win. In the limit of an infinite number of states, 51% odds in each + independence would give Obama a 100% chance of winning!

Things are much more complex, but this is basically the point cperciva was making. It is almost certainly true that the states are not independent. For example, the odds in Ohio are factoring in the chance of some gigantic gaffe or a terrorist strike or whatever, that would change the vote everywhere.

I really hope Munroe's right, and that Obama wins, but I think that 91% is too high. An October surprise could drive a large move, which would make the states very highly correlated. This is much like what often occurs in the stock market. Individual stocks might be only mildly correlated (0.1 - 0.4) in general, but in a crash (or rally) the correlations converge upon 1. Elections are full of last-minute "crashes" and "rallies".

My market on an Obama win is 70-74. I'm including the very serious possibility of election tampering favoring the Republicans, as many allege occurred in 2004, as well as (alas) the Bradley effect. It's difficult to place probabilities on unprecedented, infrequent events, and this is an unprecedented presidential election, not only because Obama is black-- that's only a small component-- but because he's an entirely different kind of political candidate than we've seen in the past, and because we're frankly in a very different country in 2008 than we were in during 2000 or '04.

Well - the 68% is not really a percentage: it's the price of a contract which will pay 100 to the owner if Obama wins. It's the market's consensus of what the probability is, so yeah it's a percentage. Given that the state-by-state percentages are also contracts, it seems that somebody with a little bit of time on their hands, and some programming smarts, could make a little money doing some arbitrage between the state contracts and the overall contract.

Because markets are imperfect.

"It is based on Intrade.net state-by-state prediction market odds..."

When betting state-by-state, people think Obama is doing better than when they bet nationally.

http://en.wikipedia.org/wiki/Monte_Carlo_method

I bet there's some money to be made on prediction market arbitrage if you know what you're doing.

Also: http://www.fivethirtyeight.com/2008/09/intrade-betting-is-su...