Wait! I've had a revelation. The reason that Carter's 95% confidence is in general not correct is the correlation between 10 billion and the actual "average" number of intelligent beings in any species. I've said that already. The only way Carter works is if there is no such correlation,and although you may not agree with that statement right now, perhaps you will when I point out that there is a way to eliminate that correlation, and that is if the population distribution is scale free. This gibes with your last point about being able to rescale the numbers, so that's why I think this might be a useful insight to this discussion. So what kind of distribution is scale free? A power law! So Carter only works if populations are distributed according to a power law. So it's not the Gaussian distribution, it's power laws, that are special. So that's good news and bad news for Carter. The good news is, there are a lot of distributions in life that do come out power laws. The bad news is, they always break down at some point. If the true population-distribution power law is too small, then you have zero population expectation, and if it's too large, then you have infinite population expectation. You have to introduce a scale to avoid these problems, and as soon as you do, bingo, the correlation appears and Carter breaks down. I maintain that your intuition is correct, but it's working under the unrevealed assumption of a scale-free population distribution, which in practice is not possible. But if you can resuscitate the scale-free idea, then you have resuscitated Carter. Otherwise, RIP.