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gwern comments on Statisticsish Question - Less Wrong
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Comments (13)
This sounds like Bernouilli's urn. If you have N papers/balls, only one of which is Yes, then on every draw, your expectation is 1/N, right? and as you keep drawing, N gets smaller by 1 every turn.
In other words, as we keep drawing without hitting Yes, the odds of hitting Yes keep changing and getting more: 1/N, 1/N-1, 1/N-1-1, 1/N-1-1-1...
But in Laplace's Law, every day that goes by with the sun rising, N gets bigger since here N is the number of days that have passed, not how many days are left to go; the odds that the sun won't rise keep changing and getting less, 1/N, 1/N+1, 1/N+1+1, 1/N+1+1+1...
Unless I am missing something, Laplace's law is not like your papers-in-hat/Bernouilli-urn example.
The difference is that in that case you know the exact number of balls of each type, in this case you do not. The difference between Bernoulli and Laplace is not whether N gets bigger or smaller, but whether the number of balls is known or has to be inferred.
Yes that is exactly the paradox I was having.
(edit):
Actually, Manfred seems to have solved the issue.