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My argument for that is essentially structured as a dissolution of "existence", an answer to the question "Why do I think I exist?" instead of "Why do I exist?". Whatever facts are related to one's feeling of existence — all the neurological processes that lead to one's lips moving and saying "I think therefore I am", and the physical processes underlying all of that — would still be true as subjunctive facts about a hypothetical mathematical structure. A brain doesn't have some special existence-detector that goes off if it's in the "real" universe; rather, everything that causes us to think we exist would be just as true about a subjunctive.
This seems like a genuinely satisfying dissolution to me — "Why does anything exist?" honestly doesn't feel intractably mysterious to me anymore — but even ignoring that argument and starting only with Occam's Razor, the Level IV Multiverse is much more probable than this particular universe. Even so, specific rational evidence for it would be nice; I'm still working on figuring out what qualify as such.
There may be some. First, it would anthropically explain why this universe's laws and constants appear to be well-suited to complex structures including observers. There doesn't have to be any The Universe that happens to be fine-tuned for us; instead, tautologically, we only find ourselves existing in universes in which we can exist. Similarly, according to Tegmark, physical geometries with three non-compactified spatial dimensions and one time dimension are uniquely well-suited to observers, so we find ourselves in a structure with those qualities.
Anyway, yeah, I think there are some good reasons to believe (or at least investigate) it, plus some things that still confuse me (which I've mentioned elsewhere in this thread and in the last section of my post about it), including the aforementioned "infinite ethics problem of awesome magnitude".
Measure doesn't help if each action has all possible consequences: you'd just end up with the consequences of all actions having the same measure! Measure helps with managing (reasoning about) infinite collections of consequences, but there still must be non-trivial and "mathematically crisp" dependence between actions and consequences.
There is also a set of world-histories satisfying (drop ball) which is distinct from the set of world-histories satisfying NOT(drop ball). Of course, by throwing this piece of world model out the window, and only allowing to compensate for its absence with measures, you do make measures indispensable. The problem with what you were saying is in the connotation, of measure somehow being the magical world-modeling juice, which it's not. (That is, I don't necessarily disagree, but don't want this particular solution of using measure to be seen as directly answering the question of predictability, since it can be understood as a curiosity-stopping mysterious answer by someone insufficiently careful.)
It's not a generally valid solution (there are solutions that don't use measures), though it's a great solution for most purposes. It's just that using measures is not a necessary condition for consequentialist decision-making, and I found that thinking in terms of measures is misleading for the purposes of understanding the nature of control.
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