I don't mean "Exchange letters between the characters".
There is an Oratory skill for each character, like jousting or leadership or swordsmanship. Diplomats (and courtiers?) use it. It would be largely skill dependent, in the same way that a Duel is skill dependent (I assume).
And yes, it should generally have teeth, and not just be some random thing.
Baron Sourface says that my idea/religion/whatever stinks, and so do I. Rather than challenging him to a duel, I challenge him to a public debate. If he accepts, we both get options regarding how we go about the thing. Maybe options that impact how much prestige/honour loss/gain is involved. "Go for blood, insult his heritage and family" would have more impact than "Keep it on topic, just debate the subject at hand".
