Back from that thread, with a quote lifted from there:
Quote:
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Originally Posted by Ken G
Quote:
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Originally Posted by grant hutchison
Concentrating on a subset of repeated trials with (birth-number = ten billion) for Carter is, to my way of thinking, missing the point in the same way as concentrating on a subset with (y=$10): that's not the way the world works, and the overall truth of the prediction comes out only when the full range of values is explored.
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I agree completely with this-- you are making my argument precisely. The last part of your sentence is exactly why Carter is wrong to say that there is only a 5% chance humanity will outlive its 200 billionth member! Because the first number, 5%, cannot be used in concert with the 10 billion to come up with 200 billion. |
I disagree. I successfully used both bits of information in your envelopes puzzle to come up with a betting strategy which is successful over repeated trials. The fair price is struck if the buyer offers a price equal to the value revealed in the first envelope,
whatever that price may be.
Carter uses his bits of information to come up with a probabilistic betting strategy which is successful over repeated trials (5% are wrong, 95% are right). This success is attained if the "bettor" bets on a total population equal to 20 times his birth number,
whatever that birth number may be.
Both approaches go
around any concern about the shape of the distribution. (And of course both approaches can also
immediately be improved if we are provided with additional information about the distribution.)
By singling out an inappropriate subset of cases which share a
specific value (of revealed content, of birth number) I think you're actually creating an apparent problem that doesn't exist if the whole picture is observed.
Grant Hutchison