A wonderful download available at the Atlas website (atlas-games.com/arm5/index.php) are the Debate rules adapted from Dynasties and Demagogues. I have never even looked at the original game, but after trying them out a few times I think the Debate rules are a true jewel. In a nutshell, Debate works like combat, but you inflict "political fatigue" instead of physical damage. The coolest part of it all is the wide choice of "maneuvers" that offer many interesting tactical options and add a lot of colour to the scene ("Smear Opponent", "Offer Compromise" and "Humurous Jab" are just a few).
I think it's a common misconception in rpgs that you need mechanics to resolve physical conflict, and you are better off without mechanics to resolve social conflict. I've never understood why it seems to be such a popular view. If two characters debate something, why should you make the debate ability of the players (and according to the Storyguide's call!) decide the matter? After all, when two characters are involved in an arm-wrestling match, you do not have the players arm-wrestle, right?
A good set of mechanical rules for debate allows you to give a fair, unbiased evaluation of the characters' strengths without having to resort to (too many) judgement calls. Also, from my experience, the debate rules above make for much more colourful debates than those I can get most players come up "freeform": subtle threats, distracting patter, lies, opponent smearing, dazzling rethoric, offers of compromise, tantrums (those are maneuvers too!)...
There was a great game from Australia ( from the 90's) that used a card deck for sword fights and for rhetorical "fights". One of the best systems I saw for this. Since a debate was like a fencing match.
I loved the original Dynasties book, but I've got an upcoming Ars game featuring arguments at the Tribunal about whether the Order should aid the King of France in his attempt to seek out the Holy Oil of Anointing. This debate dovetails into some treatise written by a PC about loosening the restrictions between the Order and the Nobility, and I was looking for a bit of Courtroom Drama to occur there.
Interesting. Different from the Arts and Achademe Dispatio (sp) rules. Since the average population is swayed by logical fallacies, like ad hominem attacks etc. I would use the Arts and Achademe rules for educated debates, but use this for say a Troubadour persuading some rabble to rise up against a tyrant.