I thought I would re-post this excellent discussion of the many-worlds interpretation by David Yerle:
Why I Believe in the Many-Worlds Interpretation
I agree with him 100%, and he says it better than I ever could. The crux of the argument is this: it depends on the book you’re reading, but as a practical matter there are typically 4 postulates of quantum mechanics (about the primacy of the wavefunction, Schrödinger’s equation, measurements being Hermitian operators, and wave function collapse). Many worlds is what you get when you reject the unmotivated “wave function collapse” postulate. It is a simpler theory in terms of axioms, so obeys Occam’s razor. If multiple universes bother you, think of how much it bothered people in the 1600’s to contemplate multiple suns (much less multiple galaxies!)
Many Worlds Theory 
“It is a simpler theory in terms of axioms, so obeys Occam’s razor.”
Old Bill is rolling over in his graves. Occam’s razor does not reduce axioms, but entities.
I am unaware of any official definition of what “entity” is or how that differs from an “axiom”. Philosophy isn’t like science; every philosopher defines the terms differently than any other. All that matters is MY definition, which is to say that an axiom IS an entity. Which is to say that TO ME, less axioms is more elegant than less “entities” whatever that means. If I take your criticism seriously then I’d have to doubt the existence of trillions of stars, since a single star (our sun) is much simpler.
Yerle’s post leaves me with the same questions about the Many Worlds Interpretation. First, what about the probabilities of the transition between different worlds or states? For instance, suppose that the result of an observation is state A with probability 1/4 and state B with probability 3/4. One way to get there is to have one copy of state A and three copies of state B, with equal transition probabilities for each copy. Plainly the probabilities remain unexplained. Second, the probabilities sound like ordinary probabilities, like shuffling a deck of cards and not knowing which card is on top. But QM probabilities are not ordinary probabilities. Something else that remains unexplained.
Edit: I left out a sentence after the statements about copies. I meant to say something like this, “But the claim is nothing like that.”
(1) “First, what about the probabilities of the transition between different worlds or states?” Zero; you can’t transition between different universes.
(2) In the second case, you bring up the “measurement problem” which has remained an area of research for years now, and still is not 100% settled. What are the probabilities referring to? You’re correct in saying that one explanation is that there are three worlds of one kind, and one of another. But that doesn’t account for Born’s rule (that the probability is identically the square of the modulus of the inner product of the initial and final state vectors). Which is to say, it’s rather technical. However, your comment “But QM probabilities are not ordinary probabilities” is not quite right. If you believe in the many worlds interpretation, then the probabilities CAN be interpreted classically, and then there’s nothing weird about the probabilities at all. See for example my initial work on the subject: http://arxiv.org/abs/0806.3970
In my opinion, the only reason quantum mechanical probabilities are “weird” is that people jump through hoops and make up all kinds of nonsense in order to AVOID the simplest and most elegant interpretation, which is just that there are many universes.
Thanks for your quick responses, Matthew. 🙂
“(1) “First, what about the probabilities of the transition between different worlds or states?” Zero; you can’t transition between different universes.”
Here is what I was trying to say. Say that I start in state A, and in a very short time either make a certain observation (state B) or not (state C). OC, I cannot make a transition between states B and C, but don’t I make one between state A and either state B or state C?
“If you believe in the many worlds interpretation, then the probabilities CAN be interpreted classically, and then there’s nothing weird about the probabilities at all. See for example my initial work on the subject: http://arxiv.org/abs/0806.3970”
Thanks for the reference. 🙂
Min