I'm entertaining a third category of uncertainty - what player-characters know? As follows
- I generally take persuasion to require something to be on offer in exchange for some action (or inaction)
- Successful persuasion could then mean any or all of
- The PC knows what they would need to offer
- The NPC is clear on what action is wanted in exchange
- The NPC knows that the PCs offer is good (else its deception, not persuasion!)
- The NPC is willing to accept less (and possibly in the case of failure, demand more)
Nothing there needs to amount to mind control - the NPC isn't forced by persuasion to do the action - and there is still plenty of room for uncertainty. To put it another way, the NPC's decision may be deterministic, but the facts in play between the parties remain stochastic.
Were that how it worked, then it could as well be symmetrical. A PC gets to decide, but they base their decision on the facts in play which are established stochastically. That could go something like this
- Queen Meg (NPC) wants to persuade PCs. "Please, do as I desire in this matter!"
- DM makes a check or perhaps its a contest, but let's say Meg prevails. PCs are required to say what it would take to go along with the persuasion (what needs to be on offer). We can take it that PCs must play in good faith and are privy to their own thought processes, so this must be genuine: if what they ask for is given, they really will do the thing. "We would, were we only to have the means to sustain our families in our absence, perhaps 500 gp?" (Or "Apologies your Queeness, there's no way we can do that.")
- Given Meg's success (or as a result of further checks) the DM makes clear the degree of comfort that Meg's offer will be good (gives the party accurate or perhaps inaccurate - given deception - clues as to that.) "Look, here is a bag of coin that you can verify with your own eyes to contain 500 gp, and I will escrow it with Doctor Quine who you well know you can trust."
In the past I have seen much social interaction cut straight to the point of decision. The check is taken to be - does PC mind control NPC to do X? That can be nuanced by supposing there are some Xs that the NPC will on no account do, but we are still focusing the check on establishing the decision. What Parlay introduces is focusing the check on facts surrounding the decision. What will you do? What would make you do X?
The decision remains up to the PCs, but if they have hand-on-heart said they would please Queen Meg in the matter, were they given 500 gp, then they are either employing deception (which Meg might see through) or they are sincere. Given the latter, there doesn't seem any reason why they should choose not to please Meg: seeing as they said they would do so in the given circumstance. They could prevaricate, and that can play out as it should. They might lie, and again there is no issue. We could gain scope for symmetry - NPC to PC and PC to NPC - without making social skills mind control for any side.