... exactly like a Duel.
The options that I suggested were off the top of my head. Food for thought, if you will.
I haven't dueled in ages, so I'm hazy on the mechanics, but IIRC, you and your adversary have to be in the same region, and someone issues a duel, and the other accepts [side note, there should be a small negative impact for refusing a duel - or debate]
Once both parties are involved, they each get options about how to fight. Aggressive, neutral, defensive, etc. I don't remember what they are, maybe its on the wiki.
Debate could work similarly. I pick a tone - aggressive, neutral, defensive, and can choose 'scope' or something similar. If I want to really stick it to him I'll throw out all kind of wild accusations and imply that he/she is a bastard. Or I'll pick the option to stay on topic and discuss the subject matter.
Then the system does some code magic, and picks a winner, throws in some flavor text based on both character's tone and scope, and hands out honour/prestige gain/loss. Finished.