One idea I had for diplomacy is to have a triangular battlemap where the corners represent logos, ethos, and pathos, but I'm not really sure what to do beyond that. Should there be some kind of elemental rock paper scissors going on? Or people are just weak to certain types of arguments? As much as I like the idea of making a complicated system for arguments, I'm sure someone else has done it better and I don't know how to find it.

There is Dungeons and Discourse, based on this and this comic. One version here and another here.