I was impressed by Pierre-Antoine Kremp’s open-source poll aggregator and election forecaster (all in R and Stan with an automatic data feed!) so I wrote to Kremp:
I was thinking it could be fun to compute probability of decisive vote by state, as in this paper. This can be done with some not difficult but not trivial manipulations of your simulations. Attached is some code from several years ago. I’ll have to remember exactly what all the steps were but I don’t think it will be hard to figure this all out. Are you interested in doing this? It would be fun, and we could get it out there right away.
And he did it! We went back and forth a bit on the graphs and he ended up with this map:
Best places to be a voter, in terms of Pr(decisive) are New Hampshire and Colorado (in either state the probability that your vote determines the election is 1 in a million); Nevada, Wisconsin, or Pennsylvania (1 in 2 million), Michigan, New Mexico, North Carolina, or Florida (1 in 3 million), or Maine (1 in 5 million). At the bottom of the list are a bunch of states like Maryland, Vermont, Idaho, Wyoming, and Oklahoma where you can forget about your vote making any difference in the electoral college.
(That said, I’d recommend voting for president even in those non-swing states because your vote can still determine who will win in the popular vote, or it might be enough to cause a change in the rounded popular vote, for example changing the outcome from 50-50 (to the nearest percentage point) to 51-49. Or enough to make the vote margin in 2016 exceed Obama’s margin over Romney in 2012. Any of these can affect perceptions of legitimacy and mandates, which could be a big deal in the election’s aftermath.)
We also made a graph similar to the one from our paper from the 2008 election, decomposing the probability of decisive vote as:
Pr (your vote is decisive) = Pr (your state’s electoral votes are necessary for the winning candidate) * Pr (the vote in your state is tied | your state’s electoral votes are necessary)
We ignore the thing with Maine and Nebraska possibly splitting their electoral votes, and we assign DC’s 3 votes to the Democrats.
Here’s the graph showing Pr (your state’s electoral votes are necessary) vs. Pr (the vote in your state is tied | your state’s electoral votes are necessary):
The diagonals are iso-lines for constant Pr(decisive), so you see the swing states on the upper right of the graph and the less close states on the left, in the 1-in-a-billion range and below.
Despite these probabilities being low, I do think it can be rational to vote, for the reasons discussed in this paper (or more briefly here, or even more briefly in my article scheduled to appear today in Slate); see also my comment here for clarification of some common points of confusion on this issue.
P.S. By the way, and speaking of reproducible research, I’m really glad that I had the code that I used to those calculations back in 2008, and also that I’d written it up as a paper. It would’ve been a bit of work to reconstruct the calculations with only the code or only the written description. But with both available, it was a piece of cake.