I see that your approach is to restrict to the human in the "restaurant". But here's the problem with doing that. There's only one 10 billionth born, let's say it's you. You're either in the corner, or you're not. But whether you are or not, on what are you going to base your conclusion that there was a 5% that you would be? What criterion can you use other than looking at the other 10 billionth borns in their own similar intelligent species? Let me go through the steps of Carter's argument. First all, we assert that you and I have only a 5% chance of being in the first 5% of humans. We've talked about potential difficulties with that, but those are irrelevant compared to this more central issue, so let's assume that this much is true. OK, now we do some research and find we are the 10 billionth born. The last step is to combine these tidbits as if the second did not alter the first, and conclude that there is only a 5% chance that humans will outnumber 200 billion. That is the wrong step. A probability is a fraction out of many trials that are equally likely. It is fine if those trials are idealized, they don't ever have to actually take place. But what is the set of trials that you are using to say that there is a 5% chance humanity will outnumber 200 billion, if it is not the trials represented by all the species in the "restaurant"? I can't see any basis for using a 5% probability in concert with a 200 billion total population. Can you explain any way whereby you have a set of (idealized) populations distributed such that 5% are more than 200 billlion and 95% are less? And if you can't, what does a 5% probability mean?