For many years I've been interested in the "paradox" that your vote tends to never alter the outcome of an election, yet the outcome is in fact determined by the votes. I wrote a blog post about this and tried to explain it in terms of emergence, we as voters are just feeling what it's like to be just a tiny part of a much bigger system.
Then I tried to explain that "voter turnout" is in fact one of the most important metrics for an election, it determines the legitimacy and stability of the process. So therefore even though your vote won't determine the winner, it will contribute to voter turnout and thus is productive and useful.
http://www.kmeme.com/2010/10/why-you-should-vote.html
However I don't find my argument all that compelling, because even voter turnout is going to be approximately the same whether you vote or not.
In the post I bring up littering as something else where your tiny contribution adds up to be bigger result. I personally would never litter on purpose, yet I often skip voting because it seems like it doesn't make a difference. Is voting rational? How do you justify voting or not voting? My post was non-partisan so I'm soliciting non-partisan comments, trying to focus on the theory behind voting in general.
Thanks for the links. They seem to mostly be saying: the "pay off" for being the swing vote is gigantic, changing everyone's life, so even though the chance of being that vote is infinitesimal it's rational to go for the tiny chance of making a huge difference.
I'm sure this is valid reasoning, but it's disappointing to me if this is the whole story. It's like voting as lottery, that your vote essentially never matters except when it has this giant impact.
I think there is mapping problem here as well. Just as you can't map your vote onto one of the excess votes in a normal election, you can't map your vote onto that one winning vote in a close election. In each case it's a game of probabilities and fractional contributions only. But I can't sort it all out.