"I believe X to be like me" => "whatever I decide, X will decide also" seems tenuous without some proof of likeness that is beyond any guarantee possible in humans...

Maybe you could aspire to such determinism in a proven-correct software system running on proven-robust hardware.

Well, yeah, this is primarily a theory for AIs dealing with other AIs.

You could possibly talk about human applications if you knew that the N of you had the same training as rationalists, or if you assigned probabilities to the others having such training.