I'd argue that can't be deemed representative democracy at all. You wouldn't be approving, even implicitly, of government action- you'd be palming off your choice to someone else. Gay marriage or no gay marriage? Joe Lieberman can decide for me, after considering the choice best for himself. That's not going to work.
How the hell is that any different than palming off your choice to a group of people that happen to rally around a flag you happen to like the design of?
I like gay marriage. The Democrats promise to bring in gay marriage. I will vote for them to allow them to do so.
I like Joe Lieberman. I will vote for Joe Lieberman. He will decide whether I like gay marriage, after consulting with his lobbyists.
Dissent is important because of people like you on both sides of the political spectrum who insist that it has to be 'my party, right or wrong' and will follow lockstep with their party regardless of the shit they step in or the cliffs they walk off of.
I'm not saying that at all. I'm saying "my party should pass policy". The Democrats are often wrong, as are the Greens (far less so, actually), and I disagree with them when they're wrong. But if I were an elected Democrat (or Green), I wouldn't obstruct party policy that I disagree with*, because members of a party should never obstruct party objectives. Otherwise nothing can be done, ever.
* Unless it was a conscience vote or the policy was so wrong I felt I had to resign. Those are the options- always vote in favour, or resign.