The question here is which is the correct / best interpretation of quantum mechanics.
The key word in this is interpretation. The actual predictions of what we should actually observe are the same for all the various interpretations of quantum mechanics - this should be no surprise, because we are not discussing the actual mathematics of quantum mechanics, nor its predictions.
We are in fact discussing the unobservable aspects of quantum mechanics. If I perceive a random quantum event, is there also a counterpart of me that perceives the other outcome of that event? Quantum mechanics inherently describes the world in terms of a combination of both outcomes. We perceive just one. But is there another me perceiving the other outcome? There's no way to experimentally see the answer to that, and that's why there is debate.
To my mind the whole debate is about a confabulation. What makes us think that we have any data to decide whether we should think this way or that way about all these options that we can't see? We inherently don't have any information about this. Frankly the best we can do is suggest we shouldn't be adding arbitrary ideas on top of the part that we can check. If QM seems to describe what we see, and could also perfectly well describe some other things that might exist, but which we can't see, well, we might just as well say the best answer we have is given by QM, and leave it at that.
Then we can start to rank the 'interpretations'. The Copenhagen interpretation suggests there's a priveliged branch in some way, which is the one we actually perceive. Why should there be? This priveliged branch idea is adding something that we don't need to add.
And that's really the picture for all the 'interpretations'. All we know for sure is that QM appears to be a good model for what we can see. We may as well as assume it does just as well for those things we can't see.
Many worlds is pretty much that view.
he Copenhagen interpretation suggests there's a priveliged branch in some way, which is the one we actually perceive. Why should there be? This priveliged branch idea is adding something that we don't need to add.
MWI adds a privileged basis that is also unnecessary.
Many worlds is pretty much that view.
MWI adds a universal quantum state that is not , and cannot be, observed.
The subject has already been raised in this thread, but in a clumsy fashion. So here is a fresh new thread, where we can discuss, calmly and objectively, the pros and cons of the "Oxford" version of the Many Worlds interpretation of quantum mechanics.
This version of MWI is distinguished by two propositions. First, there is no definite number of "worlds" or "branches". They have a fuzzy, vague, approximate, definition-dependent existence. Second, the probability law of quantum mechanics (the Born rule) is to be obtained, not by counting the frequencies of events in the multiverse, but by an analysis of rational behavior in the multiverse. Normally, a prescription for rational behavior is obtained by maximizing expected utility, a quantity which is calculated by averaging "probability x utility" for each possible outcome of an action. In the Oxford school's "decision-theoretic" derivation of the Born rule, we somehow start with a ranking of actions that is deemed rational, then we "divide out" by the utilities, and obtain probabilities that were implicit in the original ranking.
I reject the two propositions. "Worlds" or "branches" can't be vague if they are to correspond to observed reality, because vagueness results from an object being dependent on observer definition, and the local portion of reality does not owe its existence to how we define anything; and the upside-down decision-theoretic derivation, if it ever works, must implicitly smuggle in the premises of probability theory in order to obtain its original rationality ranking.
Some references:
"Decoherence and Ontology: or, How I Learned to Stop Worrying and Love FAPP" by David Wallace. In this paper, Wallace says, for example, that the question "how many branches are there?" "does not... make sense", that the question "how many branches are there in which it is sunny?" is "a question which has no answer", "it is a non-question to ask how many [worlds]", etc.
"Quantum Probability from Decision Theory?" by Barnum et al. This is a rebuttal of the original argument (due to David Deutsch) that the Born rule can be justified by an analysis of multiverse rationality.