Of course, in all of these derivations, only unitary evolution occurs, and in the end you get something ontological - i.e. branch weights. — tom

I think you may have misunderstood my comments on the Born rule (or I could have expressed them better) - I certainly agree that it should be derivable in principle from the ontology of QM. Anyway, I've just read through Carroll's blog post on his and Seben's derivation and it makes sense to me.

Basically the Born probabilities are explained in terms of self-locating uncertainty just after a measurement has been taken and decoherence has occurred. For branches with equal amplitudes, we should be indifferent about the branch we find ourselves on and so assign them equal probabilities. Whereas (as Zurek shows) branches with unequal amplitudes can be mathematically reduced to many more branches with equal amplitudes (which, as it happens, will be in proportion to the square of the amplitude). So that seems like an intuitive result.

Quantum states are fundamental to QM. The Schrodinger equation describes how the quantum state of a quantum system changes with time. — Andrew M

We're going around in circles. These quantum states are inherently probabilistic. That's the issue here, you want to say that they are not, but it's inherent to the way that states are assigned to the active energy of an active system, due to uncertainty, that these states are probabilistic. That is why they are epistemological rather than ontological, the epistemology has not overcome uncertainty to enable such an active system to be represented as states.

Anyway, I've just read through Carroll's blog post on his and Seben's derivation and it makes sense to me. — Andrew M

The Carroll / Seben derivation does seem to hinge on just a different purported version of 'rationality' to Wallace's derivation via decision theory, and an equally disputable one:

ESP: The credence one should assign to being any one of several observers having identical experiences is independent of features of the environment that aren’t affecting the observers. — Carroll

I appreciate this is the simple version of the supposed principle (Epistemic Separability Principle). It does seem open to pretty obvious objections. I wouldn't bet the house on 'credence' just as I wouldn't bet it on the definitions of rationality in decision theory. For instance, how can one know what is and isn't 'affecting' the observers? The supposed derivation certainly comes in for criticism from various quarters. I'm just expressing sceptical doubt, not disagreement, here.

For instance, how can one know what is and isn't 'affecting' the observers? — mcdoodle

The ESP seems to me just a version of a common-sense principle that we apply in everyday life. Suppose we are predicting whether it will rain this afternoon. We look at local factors and ignore irrelevant or remote factors.

There are also strong constraints in play, such as speed-of-light limits and isolation between branches.

The ESP seems to me just a version of a common-sense principle that we apply in everyday life. Suppose we are predicting whether it will rain this afternoon. We look at local factors and ignore irrelevant or remote factors. — Andrew M

Well, to invoke 'common sense' seems quite a weird thing to do,in the context of many worlds and the quantum universe. Some of the anti-many-worlds view is based on 'common sense', and advocates of many worlds give such common sense, when they disagree with it, short shrift. See earlier in this thread.

Obviously these things aren't however, deal-breakers in any way. This is another, like the David Wallace, attempt to derive the Born rule from what you call 'the ontology of QM'. (I see that the very enterprise of 'wanting to derive' is a disputed idea among the critics of many-worlds)

The maths still works, whatever words we bracket it within.