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Will_Sawin comments on Techniques for probability estimates - Less Wrong
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This provides an excellent demonstration of E.T. Jaynes's point that making something more random really means making it more complicated.
The point isn't to make it more random, the point is to make it more trustworthy. You can participate in the process and be confident that the result is random without having to put any trust in the other participants.
Regardless, your original language claiming it made it more random was correct, because it does make it more hard-to-predict-but-with-clear-symmetry, aka random.