Voting for the Other Side

Does anyone else ever get the sense that one of the major distinctions between a "liberal" voter and a "conservative" voter is that the former justifies his vote based on what he thinks other people believe whereas the later is more likely to argue he votes on what he believes?
I feel like this comes up a lot in conversations on issues like gay rights and abortion: "Why should I (usually meaning you) impose my beliefs on someone else by voting against gay marrage? Why should I force someone to live according to my morality?"
Well, it seems to me that the best answer to this is honest democracy. The way the game is supposed to work is that we all vote for what we believe will be best for the country. The group that has the most votes wins the game. If we start casting our votes for things we don't believe in, then we are, in effect, surrendering our suffrage. This was precisely the kind of thing that led the founding fathers to not give slaves full representation and that led English politicians in the 17th Century to restrict voting rights only to land owners. The fear was that slaves or servants would vote in their master's best interest rather than in their own. In our paradoxically world, the opposite seems to be the case. Rather than those with less power surrendering their votes to those with more power, those in the majority are being asked to surrender their wills over to the minority.
If you vote pro-choice or pro-gay marriage, you are essentially saying that you think these things are a good thing for the country, that we should have more of them, and that you want your children to live in a country that has more of it. You are saying that the future survival of the nation depends on redefining marriage and the ability to kill your own offspring. If you vote against gay marriage and abortion, it doesn't have to be some kind of moral indictment or condemnation of persons. It means that you don't think those are the best direction for the country, that you think the future of this country will do best with uninterrupted, government-sponsored heterosexual reproduction.