Ben wrote on ExI:
However, exchangeability likely does NOT imply Chaitin randomness....
I think you're right about that, though I confess my understanding of
Chaitin randomness is still sketchy.
My understanding is that exchangeability in the de Finneti sense implies
only the sort of randomness defined by the more conventional axiom of
randomness, which I sent to you and a few others in private email this
morning:
"Axiom of Randomness: the limiting relative frequency of each attribute in
a collective C is the same in any infinite subsequence of C which is
determined by a place selection."
(http://plato.stanford.edu/entries/probability-interpret/)
This is only the ordinary frequentist view of randomness.
De Finneti viewed exchangeability as a reduction of the objectivist notion
of independence, i.e., on his view we can and should reduce the allegedly
metaphysical notions of 'objective probability' and 'independence' to his
equivalent notions of 'subjective probability' and 'exchangeability'.
Nothing there as far as I know about the sort of maximum-entropy
randomness that I think incompressible Chaitin-random sequences are
thought to be.
-gts
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