I was not trying to imply that the probability distribution on the sample space was known, simply that whatever it is, the probability of being in the first 10^-50 of it is 10^-50. The entire point of the doomsday argument (and much of Bayesian statistics, for that matter) is that if the probability distribution on the sample space is not known, you can use your data point to update your priors over them.
If no other measure on the sample space has been mentioned, they aren’t likely to be referring to anything else. Anyway, it’s what I was referring to.
You don’t, but whatever it is, you have a 10^-50 chance of being in the first 10^-50 of it.
Then I don’t understand what was the point of your original comment.
I said: “If you have no idea of what sample space looks like, that chance isn’t “pretty small”, it’s unknown.”
Your example where you happen to know not just the sample space but actually the probability distribution seems entirely irrelevant.
I was not trying to imply that the probability distribution on the sample space was known, simply that whatever it is, the probability of being in the first 10^-50 of it is 10^-50. The entire point of the doomsday argument (and much of Bayesian statistics, for that matter) is that if the probability distribution on the sample space is not known, you can use your data point to update your priors over them.