1. Let E be the number of electoral votes in your state. We estimate the probability that these are necessary for an electoral college win by computing the proportion of the 10,000 simulations for which the electoral vote margin based on all the other states is less than E, plus 1/2 the proportion of simulations for which the margin based on all other states equals E. (This last part assumes implicitly that we have no idea who would win in the event of an electoral vote tie.) [Footnote: We ignored the splitting of Nebraska’s and Maine’s electoral votes, which retrospectively turned out to be a mistake in 2008, when Obama won an electoral vote from one of Nebraska’s districts.]
2. We estimate the probability that your vote is decisive, if your state’s electoral votes are necessary, by working with the subset of the 10,000 simulations for which the electoral vote margin based on all the other states is less than or equal to E. We compute the mean M and standard deviation S of the vote margin among that subset of simulations and then compute the probability of an exact tie as the density at 0 of the Student-t distribution with 4 degrees of freedom (df), mean M, and scale S.
The product of two probabilities above gives the probability of a decisive vote in the state.
This gives the following results for the 2008 presidential election, where they estimate that you had less than one chance in a hundred billion of deciding the election in DC, but better than a one in ten million chance in New Mexico. (For reference, 131 million people voted in the election.)
Is this basically correct?
(I guess you also have to adjust for your confidence that you are voting for the better candidate. Maybe if you think you're outside the top ~20% in "voting skill"—ability to pick the best candidate—you should abstain. See also.)
I would assum they have the math right but not really sure why anyone cares. It's a bit like the Voter's Paradox. In and of it self it points to an interesting phenomena to investivate but really doesn't provide guidance for what someone should do.
I do find it odd that the probabilities are so low given the total votes you mention, and adding you also have 51 electoral blocks and some 530-odd electoral votes that matter. Seems like perhaps someone is missing the forest for the trees.
I would make an observation on your closing thought. I think if one ... (read more)