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jpaulson comments on Applications of logical uncertainty - Less Wrong
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Why not start with a probability distribution over (the finite list of) objects of size at most N, and see what happens when N becomes large?
It really depends on what distribution you want to define though. I don't think there's an obvious "correct" answer.
Here is the Haskell typeclass for doing this, if it helps: https://hackage.haskell.org/package/QuickCheck-2.1.0.1/docs/Test-QuickCheck-Arbitrary.html
Because there is no defined "size N", except perhaps for nodes in the tree representation of the inductive type.