The TradeSports data

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The table itself is in this node

Analysis

The two big assumptions here are that the outcomes for the various "states" (we think of D.C. as a state) are independent Bernoulli trials, and that the TradeSports quotes are reasonable proxies for the means of these trials. Neither is a particularly believable assumption, but it's the best I can do. Also, no attempt is made to account for non-winner-takes-all outcomes in ME, NE, or CO, nor for the vagaries of faithless electors.

Total EVs up for grabs

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Dynamic program for the PDF over EVs

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The PDF and CDF

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The mean Bush-advantage

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Other parameters of the distribution. Probability of Bush loss/tie/win is 41.7%, 1.5%, 56.8%

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Log plot of the PDF

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The binomial distribution with the same mean, for comparison

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Plot of the PDF, with the binomial distribution for comparison

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Plot of the CDF

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Quintiles

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Hmm... the CDF is shockingly linear between 20% and 80%. Is there a simple explanation for that?

The following revised dynamic program computes a PDF for a given subset of the states.

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The PDF of the lose/tie/win variable for a given subset of the states with a given bias

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The entropy of a PDF, in bits

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The entropy of the lose/tie/win variable for a given subset of the states with a given bias

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The entropy of the election

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The conditional entropy over the states l given the result for state n

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The conditional entropies for the various states, as percentages of the total entropy

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The states sorted by the conditional entropies

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The upper levels of the decision tree of the lose/tie/win variable

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Created by Mathematica (November 1, 2004)