Only one vote matters. In the United States, the vote that gives a presidential candidate the majority in the state that tips the electoral college decides it all. Nevertheless, about 122 million US voters went to the polls for the 2008 Presidential election.
If the only benefit you get from voting is your candidate winning, this behavior is totally irrational. Voters spend precious time and effort traveling to the polls or arranging for mail-in ballots, with very small odds that this will make any difference in the final outcome. Of course, the simplest explanation is that this argument is wrong and voting can be rational, but you could also say that voting is self-expression.
In a recent paper (gated), Douglas VanDerwerken
takes a slightly different approach. He estimates a one in 2.5 million chance that his vote will matter this year, given that he lives in North Carolina (a competitive state in 2008, and likely in 2012 too).* But then he points out that, "Even if your vote does not have an effect on the election, it can certainly have an effect on you." His broader message is that:
Statistics is not divorced from subjectivity, nor from morality. What you decide depends on your moral axioms.
We can use statistics to inform our objective calculations, and our subjective intuitions, but decision-making is not a "plug and chug" process. In summarizing data, the statistician makes important decisions about how to abstract away from reality and what message to send. When that information as inputs for further decision-making--which always involves trade-offs--the statistician bears some responsibility for the outcome. Once again we are reminded that statistics is a rhetorical practice. (See also here and here.)
*Full disclosure: Doug teaches the lab section of a Duke statistics course in which I am currently enrolled.