Non-trivial probability distributions for priors and Occam's razor

Is this point novel?

Compare Rob Zahra's April 2009 comment.

A Proof of Occam's Razor

There is a problem - length isn't the only way to order hypotheses. If there was some other method of ordering that fulfilled the right conditions (even just some obvious function of length, e.g. length char value of the first letter), it could be used instead to order hypotheses, which would then be decreasing in probability on that* parameter instead. You could give bonus points for mentioning the Flying Spaghetti Monster if you wanted, and it would be a perfectly fine ordering.

This is certainly an interesting line of investigation, and as far as I know it's still unsolved. There's still some things that need to be proven to get to an Occam-like distribution, which I mentioned the last time this came up.

Specifically, I haven't seen any good justification for the assumption about there being a finite number of correct hypotheses (or any variant on this assumption; there's lots to choose from), since there could be hypothesis-schemas that generate infinite numbers of true hypotheses. A full analysis of this question would probably have to account for those, in a way that assigns all the hypotheses from a particular schema complexity of the schema. I also haven't seen anyone argue from "prior probabilities decrease monotonically" to "prior probabilities decrease exponentially"; it seems natural since the size of the space of hypotheses of length n increases exponentially with n, but I don't know how to prove that they don't instead decrease faster or slower than exponentially, or what other assumptions may be necessary.

People are definitely aware of this in the literature, but still, congratulations on re-deriving it (and consider reading more of the literature if this stuff interests you). Another version: at most n hypothesis can have probability greater than 1/n. This doesn't even reference description length.

I vaguely remember a similar point being made by Jaynes in PT:TLoS

I must be missing something. Your argument makes no sense at all to me. It is very simple to construct a countable set of hypotheses of various lengths, all of which have prior probability exactly 1/2. The hypotheses denote events in a universe consisting of an infinite sequence of coin flips, for example.

Furthermore, I must be misreading your definition of h(n), because as I read it, h(n) goes to 1 as n goes to infinity. I.e. it becomes overwhelmingly likely that at least one shorter-than-n hypothesis is correct.