Andrew Sprung compares voting to prayer:
I think that there's some similarity in this to the way some people who pray think about prayer -- if their thinking about a personal God is at all complicated. The act is intrinsically beneficial to the doer and therefore must have some nebulous impact on the universe. It's a participation in God's will -- not instead of trying to influence God, but in hopes that thinking correctly about what you want will somehow make it more likely to be what God wants too, and therefore more likely to happen. Somewhat sublimated superstition.
Maybe a vote is a prayer. It's certainly a gesture of faith. If I don't do it, who will? There's a mystery in participation.