Anyone who hasn't seen it should read Peter Norvig's Election FAQ, particularly the section "Is it rational to vote?" [1]
Short version: "Yes. Voting for president is one of the most cost-effective actions any patriotic American can take."
Slightly longer version: "The value of not voting is that you save an hour of your time. The value of voting is the probability that your vote will decide the election (1 in 10 million if you live in a swing state) times the cost difference (potentially $6 trillion). That means the expected value of your vote is $600,000."
But the value of your vote isn't actually 1 in # of votes. It's actually P(your state undecided) x P(nation undecided without your state) x (Value of your candidate winning - Value of other candidate winning).
For example, say your state has 10 million voters and the election is a statistical dead heat (i.e., each voter has a probability of p=0.5 for voting for candidate A vs B). Then P(your state undecided without your vote) = (5 million choose 10 million) x pow(2^-10 million) ~= 1/(sqrt(2 pi) 2.5 million) = 1.6e-7.
And that's assuming the best case where your state's voters could go either way. The probabilities become exponentially smaller (literally: exp(-n^2)) if your state actually has political leanings.
I'm also not sure how we could even approach a $6 trillion gap under plausible assumptions. Does anyone really believe that the gap between each candidate is $6 trillion (note: total economy is $15B) or $20k/person?
If you take compound interest and the legacy for generations to come into consideration, the difference from decisions made today between the candidates would easily surpass $6 trillion, and possibly while you're still alive. Besides, things like education, over time, have far more intangible and invaluable implications than a figure could ever show.
This also assumes that $OTHER_CANDIDATE would not have done something similar, which I don't think is correct. The war in Afghanistan was a virtual certainty, regardless of who was president.
1. It is 1 in 10 million if you live in a swing state.
2. You expect $6 trillion, that figure is incorrect as mseebach2 points out.
3. The probability of winning the state lottery might be 1 in 10 million. So I'm far better off buying a lottery ticket, since in the improbable event of winning I would actually make money, in contrast to hoping that the improbable event of my vote tipping the balance and creating a stronger economy would improve my income (the contrary might be true).
Nonsense, only in California are there more than 10 million voters. In Virginia, there are 3.8M, 1.9M per party. If the candidates are 2% apart, there's about a 1/100K chance of casting a deciding vote.
Short version: "Yes. Voting for president is one of the most cost-effective actions any patriotic American can take."
Slightly longer version: "The value of not voting is that you save an hour of your time. The value of voting is the probability that your vote will decide the election (1 in 10 million if you live in a swing state) times the cost difference (potentially $6 trillion). That means the expected value of your vote is $600,000."
[1] http://norvig.com/election-faq-2012.html#rational