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orthonormal comments on The prior of a hypothesis does not depend on its complexity - Less Wrong
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Good post, but I object to the title. On average, more complex hypotheses must have lower prior probabilities, just for reasons of summability to 1.
I think a more proper title would be "The prior of a hypothesis is not a function of its complexity".
People sometimes casually use "is a function of" to mean "depends on", so "is not determined by its complexity" might be clearer.
Huh? All hypotheses of a given complexity don't have to sum to 1, because they aren't mutually exclusive.
The math of it isn't as neat as I'd like, but what I mean is that there are only finitely many hypotheses of each complexity, exponentially many as the complexity goes up, and that most of them differ from each other at some point, so ordinary summability criteria "almost" apply. I don't think that the number of epiphenomenal hypotheses could be enough to keep the average up.
A hypothesis has approximately the same complexity as its negation, so we have many pairs that sum to 1 each.