This is probably the wrong place to ask, but I'm confused by one point in the DA.

For reference, here's Wikipedia's current version:

Denoting by N the total number of humans who were ever or will ever be born, the Copernican principle suggests that humans are equally likely (along with the other N − 1 humans) to find themselves at any position n of the total population N, so humans assume that our fractional position f = n/N is uniformly distributed on the interval [0, 1] prior to learning our absolute position.

f is uniformly distributed on (0, 1) even after learning of the absolute position n. That is, for example, there is a 95% chance that f is in the interval (0.05, 1), that is f > 0.05. In other words we could assume that we could be 95% certain that we would be within the last 95% of all the humans ever to be born. If we know our absolute position n, this implies[dubious – discuss] an upper bound for N obtained by rearranging n/N > 0.05 to give N < 20n.

My question is: What is supposed to be special about the interval (0.05, 1)?

If I instead choose the interval (0, 0.95), then I end up 95% certain that I'm within the first 95% of all humans ever to be born. If I choose (0.025, 0.975), then I end up 95% certain that I'm within the middle 95% of all humans ever to be born. If I choose the union of the intervals (0, 0.475) & (0.525, 1), then I end up 95% certain that I'm within the 95% of humans closer to either the beginning or the end.

As far as I can tell, I could have chosen any interval or any union of intervals containing X% of humanity and then reasonably declared myself X% likely to be in that set. And sure enough, I'll be right X% of the time if I make all those claims or a representative sample of them.

I guess another way to put my question is: Is there some reason - other than drama - that makes it special for us to zero in on the final 95% as our hypothesis of interest? And if there isn't a special-making reason, then shouldn't we discount the evidential weight of the DA in proportion to how much we arbitrarily zero in on our hypothesis, thereby canceling out the DA?

Yes, yes, given that there's so much literature on the topic, I'm probably missing some key insight into how the DA works. Please enlighten.