To start with, I'm not in any way suggesting replacing the current debate format with something else, only adding a new feature (just wanted to clear that up right away). I don't know about anyone else, but it seems that so little gets resolved in many discussions on this site. Everyone states his or her opinion back and forth a few times, perhaps phrased differently each time, and then the thread ends. Part of the problem, it seems to me, is that it's so easy to lose focus when there are so many hands in the pot. Someone's failing to get the context of a discussion, or someone else has some other issue that he just has to get out there that might only be tangentially related to the discussion, and things get sidetracked.
Or how about this: show of hands of how many people here have had a debate opponent just about pinned down on a specific issue, then someone else comes in and makes a wild comment that draws in a whole flurry of responses from others, and the person you had initially caged just quietly slinks away amid the clamor.
Another problem with multiple free-for-all formats (which, again, I'm not asking to do away with, because such formats have their advantages, too) is that posters in that kind of environment tend feel a pressure to make their posts noticeable among the din rather than terribly thoughtful. It tends to promote schnazziness and snarkiness over reflection and digestion (there are exceptions of course, but they seem painfully rare).
But by allowing some threads where there are only two members discussing an issue (having previously consented to do so), you may find the intellectual quality of the discussion to substantially elevated. The issue I think would likely be discussed more thoroughly, and there wouldn't be as much pressure to "score points". You may even see something radical, like two opponents actually agreeing on certain points after they've had a chance to consider the subject in a somewhat less combative debating environment. Who knows, posts in a debate like that might even find themselves worthy of being quoted outside of

.
Another advantage: It would provide a better incentive to good behavior in the rest of the forum, as those unable to exercise self-control may very well find themselves shut out of (and hence, unable to disrupt) some of the most interesting discussions on the board.
So, to the two Powers That Be, do you think this idea would be at least worth trying out for a spell to see if it bears any fruit?