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Originally Posted by Chuck
If all I knew was that there were going to be a finite number of humans and I was one of them then I'd have to say that there's a 90% chance that I'm in the last 90%. But I have made other observations. As stated in the problem, I know that the population is increasing geometrically. With the possibility of truly vast numbers of new people being added, how is it possible for anyone to seriously think that he's now probably in the last 90%?
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Yes, this is also my position on this-- that we are applying additional information that can compromise the idea that we are in the last 90% born. I feel that one can never use the number of people that have lived in the same argument as one that asserts we are 90% likely to be in the last 90%. So it's true that anyone can conclude they are 90% likely to be in the last 90% in the absence of all information, but they cannot look at how many people have been born (be it 10 or 20 billion or whatever it is), as then they are no longer acting in the absence of all information.
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It would be different if the earth really had standing room only or a killer asteroid were already spotted. But as it is, the same geometric progression that suggests that most of the people who will ever live will be in the last few generations also suggests that we aren't in those generations.
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The Carter hypothesis would require that the exponential phase is quite likely to be coming to a close, on the grounds that any random person is likely to be born near the close of such a phase, not near its inception. But as soon as we look at how many people have been born, so where we are in that exponential process, we can no longer use that argument because there can be correlations that we are simply unaware of that spoil the Carter argument. In other words, if you have no information that can interact with correlations, then you have a truly random sample, but as soon as you use information that might involve correlations, even if you don't know what the correlations are, you can no longer assume your sample is random. That's also the conclusion from the "envelope puzzle" described in a thread spawned by this one, I forget its title. (I never reached rapprochement with Grant on this issue, I wonder what his opinion is at this point.)