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All results of the experiment will be experienced by a future version of you.
No, this is definitely the Vertiginous Question. The "mechanism" that puts you in a certain branch is the same one puts you in a certain body. Are you also going to demand that neuroscientists answer the Vertiginous question before they can say that other people exist?
That "postulate" already exists if you believe in consciousness in the first place.
Literally the opposite: empiricism requires objectivey, trying to insist that only the things that you personally subjectively experience counts is as far from that as you can get.