Note that as remarked above, this argument assumes that the prior probability for N is flat, or 50% for N1 and 50% for N2 in the absence of any information about X. On the other hand, it is possible to conclude, given X, that N2 is more likely than N1, if a different prior is used for N. More precisely, Bayes' theorem tells us that P(N|X)=P(X|N)P(N)/P(X), and the conservative application of the Copernican principle tells us only how to calculate P(X|N). Taking P(X) to be flat, we still have to make an assumption about the prior probability P(N) that the total number of humans is N. If we conclude that N2 is much more likely than N1 (for example, because producing a larger population takes more time, increasing the chance that a low-probability but cataclysmic natural event will take place in that time), then P(X|N) can become more heavily weighted towards the bigger value of N. A further, more detailed discussion, as well as relevant distributions P(N), are given below in the Rebuttals section.