In 2010 I attended a meeting on Quantum Coherence and Decoherence in Benasque, Spain. I've reproduced part of my original blog post on the meeting below.
Here are the slides for my talk today at Benasque: On the origin of probability in quantum mechanics.
At the end I took a poll of the workshop participants and found that over half agreed with the following statement. About 20 percent were strongly opposed. Note this is a meeting on quantum coherence and decoherence, so there are a lot of practical types here, including experimentalists.
It is plausible (but of course unproven) that unitary evolution of a pure state in a closed system can reproduce, for semi-classical creatures inside the system, all of the phenomenology of the Copenhagen interpretation.
As one insightful participant pointed out while I was taking the poll, this is really a mathematical question (if not entirely well-posed), not a physics question.
My recent paper with Roman Buniy: Macroscopic Superpositions in Isolated Systems answers the mathematical question about the dynamics of complex isolated systems under Schrodinger evolution. I had forgotten entirely about the poll in the intervening years (I only came across the blog post by accident recently), but the question persisted... Only in 2020 did I realize that von Neumann's Quantum Ergodic Theorem   can be used to prove the result.
Added from comments:
There are really multiple issues here. Theorists will differ in their opinions on the following questions:
1. (largely mathematical): Does the phenomenology of pure state evolution in a closed system (e.g., the universe) reproduce Copenhagen for observers in the system?
This is a question about dynamical evolution: of the system as a whole, and of various interacting subsystems. It's not a philosophical question and, in my opinion, it is what theorists should focus on first. Although complicated, it is still reasonably well-posed from a mathematical perspective, at least as far as foundational physics questions go.
I believe the evidence is strong that the answer to #1 is Yes, although the issue of the Born rule lingers (too complicated to discuss here, but see various papers I have written on the topic, along with other people like Deutsch, Zurek, etc.). It is clear from Weinberg's writing that he and I agree that the answer is Yes, modulo the Born rule.
Define this position to be
Y* := "Yes, possibly modulo Born"
There are some theorists who do not agree with Y* (see the survey results above), but they are mostly people who have not thought it through carefully, in my opinion. I don't know of any explicit arguments for how Y* fails, and our recent results applying the vN QET strengthen my confidence in Y*.
I believe (based on published remarks or from my personal interactions) that the following theorists have opinions that are Y* or stronger: Schwinger, DeWitt, Wheeler, Deutsch, Hawking, Feynman, Gell-Mann, Zeh, Hartle, Weinberg, Zurek, Guth, Preskill, Page, Cooper (BCS), Coleman, Misner, Arkani-Hamed, etc.
But there is a generational issue, with many older (some now deceased!) theorists being reticent about expressing Y* even if they believe it. This is shifting over time and, for example, a poll of younger string theorists or quantum cosmologists would likely find a strong majority expressing Y*.
[ Social conformity and groupthink are among the obstacles preventing broader understanding of question #1. That is, in part, why I have listed specific high profile individuals as having reached the unconventional but correct view! ]
2. Does this make you confident that the other branches really "exist"? They are "real"?
Here we get into philosophical questions and you will get a range of answers.
Many of the Y* theorists (including me) might say:
a. MW is the only logically complete version of QM we have. Copenhagen is not well-defined and inadequate for cosmology (cf density perturbations from inflation and galaxy formation).
b. I find the existence of the other branches rather extravagant, and I leave open the possibility that there might be some more fundamental modification of QM that changes everything. But I have no idea what that model looks like and there are strong constraints on its properties from Bell, causality, etc. Even a small amount of nonlinearity in the Schrodinger equation leads to lots of causality violation, etc. etc.
c. I believe that any practical experiment that tries to check whether unitary evolution always holds (i.e., the other branches are *in principle accessible*) will always find it to be the case. In particular this means we will realize and manipulate more and more complicated superposition states over time, and this raises the question of why you and I cannot be in a superposition state right now...
Note it is possible that only one single decoherent branch of the universal wavefunction is actually realized by Nature ("is real"), and that quantum randomness is an illusion. Hartle and Gell-Mann were sort of hedging this way in some of their last papers on this topic. But remember Gell-Mann even hedged about the reality of quarks before they were directly observed in deep inelastic scattering.
An aspect to this problem that few theorists appreciate is that a quantum theory of gravity is, at the global level, "timeless": it should be a theory of quantum amplitudes describing an entire spacetime geometry and quantum trajectories of other degrees of freedom on that manifold. As such the many branches of the universal wavefunction are realized "all at once" and concepts like observers must be emergent -- they cannot be fundamental aspects of the theory itself.
Most of the action in quantum gravity (i.e., strings or loop qg) has been "local" in nature: what are the stringy excitations, compactification, local vacua, etc. The global wavefunction of the universe was already considered by Wheeler and DeWitt but there are still lots of unresolved issues.