I get a strong feeling that you wanted from the start to find a result in favour of voting, and have simply been looking for a justification. To employ one of the LW mantras - if (under a given value system) it is rational to stay at home, would you truly want to believe that it is rational to stay at home?
Anyway, voting can be modellised fairly well as a tragedy of the commons; the resource being shared is "degree to which politicians are and feel controlled by the electorate", and each voter can eat a little of it in exchange for some free time. Most of the arguments about TotC also apply here; however, the nature voting does also create some more sophisticated scenarios, such as an organised minority of exceptionally disciplined voters.
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.