Follow the logic of what you stated, “The result is not because of free will, it is a result of free will (choosing to take the placebo). You’re talking about the after effects of free will.”
Yes, I was pointing out that they are after effects of free will.
Maybe I didn’t understand what you were saying. The placebo example doesn’t prove free will. I would ask you in your example, what about those that take the placebo and don’t get better-does that mean they don’t have free will?