> Using the traders' probabilities, I ran Monte Carlo
> simulations of the election (over one million runs).
> Bush won 43.5% of these mock elections.
I suspected that. :)
As a statistician, I use Monte Carlo simulations
extensively, but unfortunately, they seem relatively
useless in this case.
Using a Monte Carlo simulation assumes an independence
of the probabilities in each state - quite the opposite
of their actual high correlation. As an example, suppose
you started your simulation with Delaware (14.7%), and
Bush won one run. That would hardly affect the outcome
of the rest of that run (it probably puts the final
most likely result at about 50-50).
But in the real world, Bush winning Delaware means that
he wins a landslide (he would certain win Florida, Ohio,
Missouri, Nevada, not to mention New Hampshire, New
Mexico, Wisconsin, Iowa, Oregon, and Pennsylvania).
If you (somehow) could look into the future and see that
Bush will win Vermont, wouldn't you want to bet all you
could at (today's) even money odds? I sure would.
Don't let me discourage you. I enjoy seeing the results
of your runs, but your methodology would not pass any
scrutiny for statistical validity. Sorry.
Yes -- treating these probabilities as independent is a necessary, but unjustified, presupposition of the Monte Carlo simulation I ran. So, the point you make -- which has been made on previous threads of this sort -- is correct. The problem, however, is not with Monte Carlo simulations per se. An analytic solution is similarly compromised by our ignorance of the conditional probabilities. In any event, don't worry: I'm not discouraged by your valid point.