I think I have the answer that will clear a lot of this up. As we've discussed, the Carter conjecture requires using no information, or the probabilities could change. But you do have to use one bit of information to make it fly-- you have to know what your birth number is, say 10 billionth. But beware, as soon as you input any information it will change the odds, even if you are not sure how. Ultimately, the validity of the Carter argument therefore relies on an unjustifiable assumption about how the total population numbers of intelligent species are distributed.

Let me clarify. Lets assume we have an immortal alien, keeping a census on all intelligent populations in our galaxy, from the beginning. No matter how the populations are distributed, only 5% of those beings will live in the first 5% of their populations. But is this still true of the subclass of 10 billionth born? Very likely not! For example, what if the total number of an intelligent species is a random number evenly distributed from 1 to a trillion. Then it is clear that if we restrict to the subclass of 10-billionth borns, we have populations that range evenly from 10 billion to a trillion. Hence in that model, the 10 billionth born has about an 80% chance of being in the first 5%! The answer depends on the population distributions. So the Carter conjecture is internally inconsistent-- you are not allowed to use both your birth number and the 5% chance of being in the first 5% in the same calculation! The only time this would be valid is if the population distribution worked out such that 10 billionth borns really did work out to be in the first 5% of their populations in 5% of all species, which would require an amazing coincidence and we certainly have no reason to expect it.

So here's what I'm saying. It is correct (modulo all the other difficulties about counting) to say "as a randomly chosen life, I have only a 5% chance of being in the first 5% of my species". What you can not say is "as the 10 billionth born, this means there's only a 5% chance our species will outnumber 200 billion". You can't use the number from the second sentence in concert with the number in the first sentence, because you would definitely expect the information in the second sentence to screw up the truth of the first sentence, even if you don't know how!