Doesn't always work though. I 'gave in' most the time but still just got a pat on the back and they left.
The problem is sometimes the other PC will disagree with you .. but also be wrong. If you agree with them then you lose some side quest or treasure or whatever. If you disagree it goes to RPS which you might loss anyway and still miss out but also piss off the other PC. Honestly I think the only way you can do it is to give them both the agreeable personality.