I just remembered, there was a study that proofed the concept of the duality you mentioned. They measured the brain waves(i don't remember how) of people while making decisions. Pressing one of two buttons in this case i think. And it's exactly like you say, the decider acts at least half a second(could be more, but not less.) before the perceiver(or the person in that case?) thought now he makes the decision. Even when they thougt they do it by chance(in their mind rapidly switching between the buttons, and then just smash one of them) the scientists could always tell beforehand which button they will press.

Maybe i find it.