[supercat]

One major problem with this sort of calculation is that it presumes the 50 state outcomes are independent when they clearly aren't; many events which would affect any state outcome are likely to affect many.

Consider, for example, a "contest" with three states (Freedonia, Pottsylvania, and Wackyland) and two candidates (Alex and Bob). Alex has a 66.7% chance of winning in Fredonia, and a 66.7% chance of winning in Pottsylvania. He only has a 33.3% chance of winning in Wackyland. What is the probability of his winning at least two states?

If the events were independent, the probability would be 16/27 [8/27 of Alex winning the first two and not the third; 2/27 of his winning the first and third making and not the second; 2/27 of the winning second and third and not the first; 4/27 of winning all three].

If the events are not independent, though, the probability can range anywhere from 1/3 to 2/3. To see why, imagine that a die will be rolled at midnight on June 22. Consider the following two scenarios:

1. Freedonia votes for Alex if the die roll is 1-4. Pottsylvania votes for Alex if the die roll is 3-6. Wackyland votes for Alex if the roll is 3-4. In this case, the only way Alex wins is with a roll of 3-4, probability 1/3.
2. Freedonia votes for Alex if the die roll is 1-4. Pottsylvania votes for Alex if the die roll is 2-5. Wackyland votes for Alex if the roll is 1 or 5. In this case, Alex will win if the die roll is anything other than six, probability 5/6.

As you can see, innterdependence of events can make a huge difference in the probabilities of combinations of events occurring.

[Rome2000]

Wackyland

Thats down the road from Stoopidsville.

[Political Junkie Too]

But why isn't that accounted for in a 50-node symmetrical decision tree? All possible combinations would be accounted for, with their probabilities of occuring taken into account.

I still can't get it in my head why each state's electoral vote winner isn't considered an independent event. It's not like the voters of one state wait to see how another state voted before voting themselves. Are you suggesting that there is some event that ties the outcomes of separate states together into one dependent outcome?

-PJ