AFAIK, in physics this property is called indempotence: the choice is determined by the state of mind at the time of the choice and not by history that led to that state. Theoretically many different histories can lead to this state, or the history may not exist at all, if mind was created in this state 5 minutes ago, in all these cases the subsequent behavior will be the same.
Theoretically, yes. (Good point!) But the number of variables is large enough that I think you can discard the many different histories as well as the non-existent history.
