the OOM of variation in āground truthā come from alpha and n, not xmin
alpha, we could talk all day, but the model is not extremely sensitive to it
on the other hand, if you say letās have more OOMs in the possible values of ground truth, following the power law, that means jacking n up
and when you jack n up you have even more opportunities for errors to be crazy big, and this effect dominates (at least thatās what I read from the OP) and the curse becomes worse
now if we change alpha and n at the same time, idk
my honest opinion is that numbers are just one way to process information, and using them for this is so out of distribution that itās essentially meaningless (as it is when discussing p(doom) and stuff like that)
The difference between the most vs least spooky X-risks is way more than a 100X difference.
I think I would agree with this, if I had to put a number.
What I mean in my comment is, with this model, if you say okay letās pick a bigger n so that we see bigger differences in OOMs, then you are also introducing more points of failure in the estimation, and that effect dominates.
Do you have an a priori reason to discard this? Besides the conclusion being wacky, which is a good reason to discard a model anyways.