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Originally Posted by BioSci
Yes, but to then add the aspect of only looking at pre-selected values of M no longer matches the Carter situation.
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I see it as
precisely the Carter situation. The "pre-selected value" of M is our own birth number, the scale for the predicted continued longevity of humanity that leads to the "catastrophe". In my game, the selection of M is the same as the selection of "you", out of the N humans that will live. It is
identical to the Carter argument, phrased in terms of birth number (which is the only valid way to phrase it without assuming strange things about exponential growth that never hold in any system).
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The Carter hypothesis does not select a given "M" and so this argument does not apply.
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See above.
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The fact that "the plainly obvious statement that 90% of beings live in the last 90% of any set from which they are generically chosen" is the power of the Carter hypothesis when simply combined with an exponential population curve and assumption that all known species have a finite existence.
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But that "combination" with an exponential curve is kind of ridiculous anyway. There are hosts of systems that undergo temporary exponential growth, then settle into some other pattern. To use that predictively is to be ignorant of a vast fraction of reality.
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That is the strength of the argument - that a statistical estimate can be made with so little input. It is also the weakness of the argument because it requires one to ignore any additional knowledge.
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The argument falls completely flat even in the absence of any additional knowledge. It makes assumptions that are unjustified, and its own assumptions are its weakness.
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Well, it certainly is important to include knowledge into an probability calculation if such knowledge is available to improve the validity and reliability of the calculation.
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Agreed, this is normally part of the value of using probability. But it doesn't "change the probability", it merely changes the inputs we choose to include. The calculation is always purely our own choosing, it has no "reality" to it, and so cannot "change" in some absolute kind of way.
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Certainly, one's calculation is only as good as the assumptions that went into the calculation. If knowledge is available but not used, then any such calculation is limited by the assumptions that were used (are the dice loaded?)
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Yes, I agree.
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If you chose not to use any other information to help describe the likely population distribution (and have a value of M as a result of an essentially random selection {not-pre-selected} from a finite population), then the Carter estimate is the best you can do
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No, you cannot even do that well, it's just wrong probability to apply it to classes of similar M.