A lot of people think it's irrational to vote if your vote isn't going to have an effect on the outcome. I live in an extremely blue district of a slightly red county in a very blue state. In local and statewide elections, my vote has so little an effect that it's not worth voting if the only point of voting is for my one vote to have an effect on the outcome. New York is overwhelmingly going to continue to support Senators Schumer and Clinton, and they tend to vote Democratic in governor elections except when there's a very moderate Republican like George Pataki on the ballot. County-wide races are closer, and so is the U.S. House district, which was almost a toss-up in 2006. Things were even more one-sided when I lived in Rhode Island.
But it simply isn't true that voting is only worth doing if you're going to be the deciding vote. There are other reasons people give for voting, some better than others. One that often occurs to me when it seems hopeless for my candidate is that if everyone voting for the other side thought it wasn't worth voting because the outcome is assured then my candidate might have a chance. Other reasons include that it helps you psychologically to feel like you're contributing and that it's simply your obligation to do what you can to influence things for the better even if what you can isn't by itself going to make the difference in who wins the election.
Any of those responses would be sufficient by itself, except perhaps the psychological benefit one (at least if that involves self-deception, and if it doesn't then it's not a distinct reason but depends on one of the others). I think there's an even better reason to vote, and I think it might actually be what motivates me most, but I hadn't actually thought about it in these terms until today. It takes a page from Calvinist responses to the objection that if the future is already determined then there's no point in praying.
Calvinists come in several varieties, but the most common sort of Calvinist (which isn't the same as being the most noticed kind on the internet) is compatibilist about human freedom and divine predetermination. If God has a plan that includes everything I'm going to do, everything every other person is going to do, and an outcome for every prayer I ever pray, then is it worth praying? My prayer isn't going to change anything, after all. Of course, my prayer would also be in this plan, and if I didn't pray then a different outcome may well have been in the works. Compatibilists about divine predetermination and human action are going to insist that God works through our choices and doesn't just force things outside our control. Our prayers are part of how God's plan works itself out as history unfolds.
One thing Calvinist sometimes say is that praying is not so much for the outcome but for us. God wants us to pray because of what God will do in us because we pray. I don't want to deny that, but it's certainly not the emphasis in scripture on reasons to pray. The emphasis seems to be on two things. One is that prayer does affect things. It doesn't change them, because the future can't be changed anymore than the past or present can. If the future is a certain way then it can't be changed. Even open theists don't think the future can be changed. Why should someone who thinks there's a definite future think it can be changed? But for the reasons in the previous paragraph, the future can be influenced. It can be caused by things in the present, and I can be part of that process of bringing it about. A compatibilist should have no trouble saying that sort of thing.
But there's another reason in scripture for why we should pray, even though God has worked out the end from the beginning, and this one (unlike the previous one) does have some relevance for voting. God wants us to communicate our dependence on him and to express our desires to him. He wants us to see him as the Father who cares for us and meets our needs and our wishes, provided that our wishes are righteous and as long as there isn't some other reason beyond our ken for why God wouldn't grant a particular wish (as there may well be). As Jesus points out, what father when presented with a request from a child for bread or fish will give a snake? God wants to bestow good things on his children and delights when we come to him with requests, for the same reasons a giving parent delights in such things. Given that, it's a privilege to call him Father, which is why it's a big deal that Jesus starts out the Lord's prayer with "our Father". Those who don't avail themselves of that title in addressing him are missing out on something great. Those who don't address him at all are missing out on even more.
The same dynamic plays out in a smaller way with voting. I'm privilege to live in a country that seeks my opinion on who should occupy certain offices. Even if my vote doesn't have an effect in putting someone in office, it's a privilege to be able to contribute my thoughts in the process of the communal decision that an election involves. I don't believe voting is a moral right. But I think I'd be wasting an opportunity to express my opinion if I didn't vote, and wasting a privilege is at least unfortunate (and I would even argue that it's immoral). This seems to me to be a much better reason to vote than any of the more common ones that I hear, even if most of them are good enough reasons.