Of course one can say it is futile to reason about that. But if one does could perhaps reveal a wrong understanding of the MWI. Or it could clarfy how far one can extend this interpretation.
Sean Carroll states in Why the Many-Worlds Formulation of Quantum Mechanics Is Probably Correct
So nothing stops us from writing down a state of the form (spin is up ; apparatus says “up”) + (spin is down ; apparatus says “down”). (2) The plus sign here is crucial. This is not a state representing one alternative or the other, as in the textbook view; it’s a superposition of both possibilities. In this kind of state, the spin of the particle is entangled with the readout of the apparatus. … Once our quantum superposition involves macroscopic systems with many degrees of freedom that become entangled with an even-larger environment, the different terms in that superposition proceed to evolve completely independently of each other. It is as if they have become distinct worlds — because they have.
Because the many-worlds don‘t interact we will never be able to proof their reality experimentally. But not denying them could produce strange thoughts as in the following story:
He has bought rail tickets with seat reservation for tomorrow. Before that he‘ and he‘‘ measure the spin of a particle. He‘ measures „spin up“ and he‘‘ measures „spin down“. They know they are in different worlds now which don‘t interact with each other but nevertheless share the same memory. In the evening having not a particular preference he‘ choses red- and he‘‘ white wine. The next morning he‘ and he‘‘ enter the train and sit down on their reserved seat. He‘ wonders if he‘‘ thinks about of him‘. Then his‘ train starts while his‘‘ is delayd.
Please forgive me for writing down such a trivial if not stupid story. What is wrong with it in the context of the many-worlds interpretation.
EDIT How do we interpret the following scenario which increases the complexity?: After the measurement was performed his sister dials his number. To whom does she talk, to him' or to him''? If she talks to him' then for reason of consistency she will always have contact to him' in the future. If so, is the decision randomly selected? Is something wrong with this scenario?