I thought about that too, if he passes 6 times (and I've passed 6 times) I know that he has at least 6 (and he knows I have 10 or 12), so I pass a 7th time, and he passes a 7th time too. So now I know he can't have 6 therefore he has 8.
This, however isn't the quickest way so it would probably fail if your partner is optimizing.
This, however isn't the quickest way so it would probably fail if your partner is optimizing.