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JoshuaZ comments on Stupid Questions Open Thread - Less Wrong Discussion
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I think 1) should probably be split into two arguments, then. One of them is that Many World is strictly simpler (by any mathematical formalization of Occam's Razor.) The other one is that collapse postulates are problematic (which could itself be split into sub-arguments, but that's probably unnecessary).
Grouping those makes no sense. They can stand (or fall) independently, they aren't really connected to each other, and they look at the problem from different angles.
The claim in parentheses isn't obvious to me and seems to be probably wrong. If one replaced any with "many" or "most" it seems more reasonable. Why do you assert this applies to any formalization?
Kolmogorov Complexity/Solmanoff Induction and Minimum Message Length have been proven equivalent in their most-developed forms. Essentially, correct mathematical formalizations of Occam's Razor are all the same thing.
This is a pretty unhelpful way of justifying this sort of thing. Kolmogorv complexity doesn't give a unique result. What programming system one uses as one's basis can change things up to a constant. So simply looking at the fact that Solomonoff induction is equivalent to a lot of formulations isn't really that helpful for this purpose.
Moreover, there are other formalizations of Occam's razor which are not formally equivalent to Solomonoff induction. PAC learning is one natural example.
The whole point is superfluous, because nobody is going to sit around and formally write out the axioms of these competing theories. It may be a correct argument, but it's not necessarily convincing.