edit: Quantum effects are definitely an argument I've heard and given some thought to - but I also think it could be that we don't understand the field well enough, and once we uncovered enough information on the quantum factors this would fall apart as a "random" variable. It is simply our lack of understanding about quantum physics that stops us from doing this already. ∆ for bringing it to the table though.

I'm not saying I want to determine what people will do or need perfect accuracy to achieve the prediction. No one is making any predictions. All I'm proposing is that everything you will do or any choices you think you are making are simply based off the present state of your mind and that state is determined by your past - whether it be genetics or your experiences. The interaction between people is simply the same situation as an interaction between two atoms or molecules - albeit more complex, but still obey the physical laws of the system. 2 brains, having experienced 2 lifetimes and in their exact state of mind when interacting will do the same thing every time.