Here's a REIGN social combat system you can fit on a playing card.You use Inspire or Fascinate or Intimidate or whatever seems relevant to the type of argument you're making. Each person involved has a "goal track." If you hit ten on your goal track you've achieved your goal. 

Defensive dice gobble with no timing requirement -- so countering smears is pretty efficient but won't advance your goals. When you achieve your goal, you can't achieve anything further. You can stay in the conflict to defend yourself against others' goals, or tear down their progress on their own track, but you can't start a new track. If you can push someone else's goal track into negatives, they're out of it, they won't persuade anyone.

Completed goals let you do one of two things. (1) Add a die to a relevant Company roll. (2) Paint an individual with a reputation. Reputation works just like a Mission -- influencing rolls until it's replaced with a different one. Reputations made in private can be changed in private, but a public reputation can only be changed in public.

Example 1: Fink and Swine are arguing before the king, each claiming he should be Earl of Sty. Fink's goal is "convince my followers to fight hard for Sty." Swine has the same goal. Neither interferes with the other, both argue well and each walks away with partisans amped up to fight, each side utterly ignoring the other side's logic. When they clash, each army has a +1d.

Example 2: Goth and Vandal are tearing into one another verbally at the duchess' ball. Vandal's goal is "Make Goth feel sexually inadequate." Goth's goal is "Make Vandal realize he can't treat me like this." Vandal has a hell of a vocabulary. Not only does he quickly hit 10 on his track, he beats Goth's goal back to -1 afterwards and swaggers away. Now Goth has the reputation "Sexually inadequate" and every time he tries to convince a woman that he's OK, he takes a -1d to his pool. (On the other time, every time he tries to convince you it's all right to leave him alone with your daughter, he gets a +1d bonus.)

Example 3: Bree decides to cheer Goth up. Her goal is, "Make Goth feel like a REAL man" and the methods she uses are exceptionally persuasive -- not least because Goth isn't resisting. She hits 10 on her track, lickety-split, and now Goth has a +1d bonus when convincing women he delivers more male than UPS, but a -1d bonus for seeming erotically harmless.

Might need a bit of paint and some limits on how many bonuses to Company rolls you can stack, and maybe everyone should have the option of starting with a reputation, but it looks functional.