If we assume (using numbers from the article) that a vote costs $20 (an hour of our time), the odds are 1 to 10 million, and the payoff is $7.7 trillion (even though it's the country getting the benefit, not the voter) then the Kelly criterion* implies that it's only rational to vote if your net worth is more than $200 million. Somebody making $20 an hour probably isn't worth $200 million, and so even if voting did have a positive expected value, it's not a rational strategy.
TL,DR: There is more to betting strategy than expected valve, and no rational gambler takes a bet with 1/10 million odds for $20.
(It's also worth considering a la Hofstadter/Yudkowsky that something like your decision process is instantiated in other people like you -- if you decide not to vote, many of them won't either, even with no causal link.)
-- Its astonishing that there is nothing in this regarding the US Debt. eg http://www.kpcb.com/insights/usa-inc-full-report [1]
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[1] Summary> http://www.businessinsider.com/mary-meeker-usa-inc-february-...
I love how he concludes that voting is rational. I'd never thought to multiply the, potentially massive, cost of the candidate I disfavor getting elected, multiply it by the tiny chance my vote makes the difference, and compare the result to the amount of money I make in an hour. He admits his cost figures are fudged, but in principle, it works out.
Since I spotted this on the front page, it seems to have been nuked by mods. Perhaps that's for the better, but I'd be much more interested in discussing politics if everyone could handle it with the restrained style and tone in this article. Interesting link.