However if you switch to continuous probabilities your estimate of the character of the coin will change.
No. If the distribution is symmetrical, then the probability density at .5 will be unchanged after a single coin toss.
these two statements contradict each other.
No they don't. He was saying that his estimate of the probability that the coin is unbiased (or approximately unbiased) does not change, but that the probability that the coin is weighted towards heads increased at the expense of the probability that the coin is weighted towards tails (or vice-versa, depending on the outcome of the first toss), which is correct.
If the distribution is symmetrical, then the probability density at .5 will be unchanged after a single coin toss.
In the continuous-distribution world the probability density at exactly 0.5 is infinitesimally small. And the probability density at 0.5 plus-minus epsilon will change.
No they don't.
Yes, they do. We're talking about expected values of coin tosses now, not about the probabilities of the coin being biased.
This is a thread for rationality-related or LW-related jokes and humor. Please post jokes (new or old) in the comments.
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Q: Why are Chromebooks good Bayesians?
A: Because they frequently update!
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A super-intelligent AI walks out of a box...
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Q: Why did the psychopathic utilitarian push a fat man in front of a trolley?
A: Just for fun.