What is The Probability Your Vote will Make a Difference?Economic Inquiry (2009)
One of the reasonable motivations for voting is that one vote can make a difference, as Edlin, Gelman, and Kaplan  showed. In a presidential election, the probability that your vote is decisive is equal to the probability that your state is necessary for an electoral college win, times the probability the vote in your state is tied in that event. We computed these probabilities a week before the 2008 presidential election, using state-by-state election forecasts based on the latest polls. The states where a single vote was most likely to matter are New Mexico, Virginia, New Hampshire, and Colorado, where your vote had an approximate 1 in 10 million chance of determining the national election outcome. On average, a voter in America had a 1 in 60 million chance of being decisive in the presidential election.
Citation InformationAndrew Gelman, Nate Silver and Aaron S. Edlin. "What is The Probability Your Vote will Make a Difference?" Economic Inquiry (2009)
Available at: http://works.bepress.com/aaron_edlin/70/