The one who makes his arguements clear and concise to the on lookers. If he just gets the last word, what has he accomplished? Nothing just the end.

There's no mathematically quantifiable way to tell who won an argument. You'd have to judge by the content. My own interpretation:

When person A is still producing reasonable arguments (backed up by reliable evidence and logically acceptable), while person B has degenerated into mindless insults and is unable/unwilling to adequately reply to A's arguments, I would call it a pretty clear win by A. Which party left the debate first is immaterial; the winning party could well have left because they were sick of the other guy's idiotic nonarguments.

When A and B were both producing reasonable arguments, then B suddenly disappears, that often means B realised they couldn't make any more reasonable arguments and hence shrank away. Not an absolute though.

When both sides are mindlessly mudslinging each other, I'd say both sides lose :P

And I think there are times when there is no win or loss, e.g. when the two parties start off with very different viewpoints, and after some discussion they amiably agree to disagree, or they settle for a shared perspective.

The creator of the debate wins. All he has to do is ban the opposition ;)

I guess it really isn't the most down votes, but is what the audience thought of the debate. Therefore there will be voting.

The winner is clearly the one with the most down-votes. This person accomplished their objective.