Humans are bad at small numbers. Your vote does indeed matter. But it only matters 10^-8 of a presidency. With littering you're probably anchored to 1 piece of litter, so 1 matters. But in voting you're probably anchored to 1 presidency, rather than, say, 1 dollar. Noting, of course, that on the order of 10^10 dollars get spent per presidential race, so your vote is about $100.
In a typical election with a greater-than-one vote differential, it doesn't seem like your vote matters at all to the outcome. In the specific sense that if you had not voted, the outcome would have been identical. So I guess that is something to resolve, do you deserve fractional "credit" for the win, even if the win differential was by millions of votes?
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.