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AlephNeil comments on On Branching vs Probability - Less Wrong
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The many worlds interpretation is not just splitting so that it can be deterministic.
Imagine in your example that someone wanted to know if it was random or splitting. They point a telescope through the fifth dimension, and see an identical universe, except with the opposite event. Someone suggests that maybe it's mostly probabilistic, but there's a split at the end. The person then manages to look closely enough to distinguish the next twenty or so universes. They're told that it just branches further than they thought before.
This is what it is with quantum physics. We know there's multiple universes because we can test for them. Any quantum theory requires a configuration space for all the relevant particles. The only question is if it has one giant configuration space for the whole universe, or has little configuration spaces, which otherwise already follow all the laws of the giant one, that randomly split and combine.
My motivation for suggesting that "MWI is what you get when you mistakenly try to conceive of a quantum theory as deterministic" is the following:
First, imagine we have a simple deterministic universe like the Life universe. Forget about quantum theory for now, and suppose that we're going to build a simulation of a "Coin universe" within the Life universe. Suppose we decide to do it by simulating all branches at once, and 'tagging them' somehow to indicate their relative probabilities. Then the "tags" will be epiphenomenal, and 'from the inside' the beings will experience a universe where "Theory 1" is true. In other words, the probabilities we assign won't affect the experiences of the simulated beings.
Now, I want to say that this branching simulation is "what you get when you mistakenly try to model the coin universe as a deterministic universe".
OK, now let's replace the coin universe with a universe where quantum mechanics is the 'theory of everything'. Now we could simulate it within the Life universe by deterministically modelling the entire wavefunction, and that might even be the only way of doing so, but it isn't clear to me that this wouldn't cause some or all of the information about probabilities to become "epiphenomenal" in the same way as before. As Steane says:
Hanson's ingenious concept of "Mangled Worlds" might be exactly what I need to reassure myself that a deterministic simulation of the entire wavefunction would 'feel the same from the inside' as a genuine quantum universe. Armok_Gob was right to mention it. But then I'm just an "interested layperson", and no physicists or philosophers of physics besides Hanson himself ever seem to mention Mangled Worlds, so I'm not quite sure what to make of it.