Besides how to debate properly, as well as how to think regarding situations which put you on the spot, which I think we all need to learn.
Zikara, the judges are there to keep the debates from having no clear victor, which makes them slightly less pointless.
Also, I don't think I mentioned this but I meant to. The teams would have certain cycles to go through, like in the National Forensics League. There would be opening statements, rebuttals, crossfires, summaries, final crossfires, and final statements. Of course we don't need to make it that way, but we could make them have a time limit to finish the debate, like "Here are the teams, you have three days before the judges announce their nominations for victor". 2/3 majority is the way I would do it.