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drnickbone comments on Of all the SIA-doomsdays in the all the worlds... - Less Wrong
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You are assuming a uniform distribution across the sample space. That assumption seems to be hanging in mid-air: there is absolutely nothing supporting it.
Not assuming. Defining. The measure on the sample space that I was referring to when I said "first 10^-50" is the probability distribution on the sample space. No other measure of the sample space has even been mentioned. I really was not saying anything that's not totally tautological.
Edit: Or are you referring back to the Doomsday argument and suggesting that you are not, a priori, a randomly selected human?
That's not what people usually mean when they say things like "the first 1% of the sample space". When they want to talk about the probability distribution on the sample space they tend to say "the first 1% of the population".
How do you know what the probability distribution in the sample space is, anyway?
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.