In my post I suggested there are two separate motivations for voting:
1) Picking the winner. Essentially no one does this in big elections, but yes there is that tiny chance. I didn't go into this motivation. Thinking about it now I suspect using a lottery-like mentality a lot of people do vote for this reason: they just might be the one.
2) Adding to voter turnout, thus making the election legitimate. Everyone who votes does this, but it's only by a tiny amount. This I would equate to "not littering" in that you are unambiguously helping but only incrementally. This I think is in fact the stronger reason for voting, but still your contribution is very tiny.
In the end I'm down to "civic duty" and "it's the right thing to do" and stuff like that as far as the best reason to vote. Maybe the lesson is it's good large chunk of people are NOT rational, because I do maintain as turnout goes down, the results get worse, as far as what people "really" want.
Now I didn't mention social pressure either. There was a swiss study where voter turnout didn't go up when vote-by-mail was made an option. The supposition being people no longer felt the pressure to make an appearance at the polls to be a good citizen, they could just surreptitiously not vote in the privacy of their own home.
http://www.mitpressjournals.org/doi/abs/10.1162/jeea_a_00015?journalCode=jeea
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.