It is not necessary to invoke Many Worlds in order to perform a straight forward statistical prediction. If using such a devise makes one's computations easier, fine; but, the Many Worlds concept only has credence if one feels compelled to grant a tangible ("real") existence to the Wave Function.
The Wave Function is far easier to understand if we treated it as a mathematical representation. The idea that a wave function "collapses" and can only do so if observed by a consciousness is pure fantasy; the function is resolved (meaning probability = 1.0) occurs with any encounter with another particle or force field. Feynman's Path Integral precisely describes any such encounter. The wave function is re-initiated after the encounter based on the phase state changes resulting from the encounter.
Physics was never really the deterministic process so worshipped by Einstein. It was always a statistically probabilistic set of occurrences that was undetectable at the macro-level. QM merely made our system of approximations apparent. Newton showed that where enough atoms gather together, they will act as one predictably in accordance with macro-physics. So, why are quantum physicists driven to mysticism to explain mathematics found everywhere in our daily lives?
The wave function is a probability distribution function like any other. It is an algorithm that describes the accumulative effect of our predictive error until the next encounter or "measurement." It is not a phase-space state of a particle anymore than the other mathematical symbols used in the Path Integral equation. Why does the function "collapse" when we observe the particle? Because at the QM level, we cannot observe without disturbing the particle's phase-space states. Thus, the wave function must reset based on this disturbance.
What seems to unnerve so many is our inability to measure at once all the relevant states of a particle. But that's true at the macro-level as well. In order to measure my automobile speed, I must travel some distance; but, in so doing I have smeared my location over that distance. We can make both measurements close enough together so it doesn't matter for a car. In QM, however, it matters! That's all.
Entanglement is not spooky communications at distance, and it is not determined by some unknown local variable. The classic case is merely our lack of knowledge about what is happening inside this "cat's box." We know that when two electrons are entangled, one spins up and the other spins down. We simply don't know which. later, at some distance of separation, we find that one spins down and simultaneously find the other spins up. All we did was open the box to see if the cat was dead yet.
Sean Carroll is far less prone to bait the lay reader with flights of fancy; his ontological themes remain grounded in "observable" reality. He also appreciates the need to explain that the English words used by scientists mean different things when talking physics. At another extreme is the mathematically rigorous and startling interpretations of Roger Penrose; no doubt, his ground-breaking postulates have spawned hundreds of science/math careers. It is the broad range of authoritative differences in interpretation that make the study of physics so exiting and revealing.
The novice is probably best served by starting with the currently accepted Core Theory. Need a starting point? Wikipedia continues to build a depth of offerings to get you started. Also, consider the Feynman Lectures on YouTube. From there one can appreciate how and why such theories as Many World gain traction.
It remains undisputed, however, that the mathematical logic of the Core Theory is astonishingly accurate and prescient. The Copenhagen Interpretation adherents, while still the largest single group among practicing physicists, represent an every-decreasing minority view among at least a dozen other viable interpretations. So, the oft spoken truism still applies: "Shut up and compute." -- Mermin