Exactly. So the question is, which set of rules, of the two you contrast, is more appropriately applied to the situation of birth order of an intelligent species? Here's a way to set up the rules where the Carter hypothesis seems at first to be correct, in the absence of any other information. Imagine one morning you wake up and are visited by an alien time traveller. The time traveller tells you that he has observed the extinction of a million intelligent species on a million worlds. He amuses himself by picking lives completely at random, and paying them a visit, and he chose you. And he mentions, by the way, that of course by these rules, 90% of the time he is talking to someone whose species does not outnumber that individual's birth order by more than a factor of 10. Why would you not conclude that your chances of being in that group are 90%, if you know nothing that distinguishes the species in question? You may have a hard time sleeping that night as you ponder the Carter catastrophe.

But you wake up feeling better, because it has occurred to you that he did not tell you the 90% figure applied to the subgroup of beings who were in around the 10 billionth in birth order! And indeed, there's no way to know that the 90% figure would apply to that subgroup without more information. (Bringing us back to Fram's original point.) So you ask yourself, what more information do I have? And you begin to wonder if the 90% overall average goes up or down among the 10 billionth beings from species similar to your own....