As an ice-breaker for people who are not naturally gregarious, you may find that the passionate arguments are abbreviated to "Mumble, red.". "Oh, I'm green. Do you like Scarecrow?"

Or even:
A - "Red."
B - "Green and Scarecrow".
A - "Lion."
A&B - "OK."

I think that enabling the quality of argument to affect whether or not the change is made would affect this, rather than making it wholly random. How that would be determined is a different matter. It could be the number of arguments that one person can come up with for their case, that the other person accepts as legitimate. This is partly subjective of course; someone arguing that green is good because sprouts are green may encounter vociferous resistance to the validity of their argument.