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Dependent Variables in Political Prediction Markets
There's a great example of the mathematics of dependent and independent variables over at InTrade right now. The betting company has just launched a CLINTON.LIFELINE contract, which reflects her chances of winning all three of the Ohio, Texas, and Pennsylvania primaries. At the moment, it's trading at 11.2%.
Clinton's chances of winning Ohio, according to InTrade are 55.1%; her chances in Texas are 29.4%; and her chances in Pennsylvania (which doesn't happen until April 22) are 22%. If all these three probabilities were independent of each other, her chances of winning all three would be just 3.6%. On the other hand, at the other end of the spectrum one can imagine a world in which if Clinton won the most improbable state (Pennsylvania), she'd be bound to win the more probable states of Ohio and Texas. In that case, the chances of her winning all three states would be 22%.
As it is, the Lifeline contract is trading right in the middle of those two points, implying that the three states are different, but not completely different. Which makes sense to me. Of course, this contract will only really trade independently until March 4: after that, it will either expire at zero, or else trade exactly in line with DEM.PENN.CLINTON.
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