[EDIT: I think the SIA doomsday argument works after all, and my objection to it was based on framing the problem in a misguided way. Feel free to ignore this post or skip to the resolution at the end.]

ORIGINAL POST:

Katja Grace has developed a kind of doomsday argument from SIA combined with the Great Filter. It has been discussed by Robin Hanson, Carl Shulman, and Nick Bostrom. The basic idea is that if the filter comes late, there are more civilizations with organisms like us than if the filter comes early, and more organisms in positions like ours means a higher expected number of (non-fake) experiences that match ours. (I'll ignore simulation-argument possibilities in this post.)

I used to agree with this reasoning. But now I'm not sure, and here's why. Your subjective experience, broadly construed, includes knowledge of a lot of Earth's history and current state, including when life evolved, which creatures evolved, the Earth's mass and distance from the sun, the chemical composition of the soil and atmosphere, and so on. The information that you know about your planet is sufficient to uniquely locate you within the observable universe. Sure, there might be exact copies of you in vastly distant Hubble volumes, and there might be many approximate copies of Earth in somewhat nearer Hubble volumes. But within any reasonable radius, probably what you know about Earth requires that your subjective experiences (if veridical) could only take place on Earth, not on any other planet in our Hubble volume.

If so, then whether there are lots of human-level extraterrestrials (ETs) or none doesn't matter anthropically, because none of those ETs within any reasonable radius could contain your exact experiences. No matter how hard or easy the emergence of human-like life is in general, it can happen on Earth, and your subjective experiences can only exist on Earth (or some planet almost identical to Earth).

A better way to think about SIA is that it favors hypotheses containing more copies of our Hubble volume within the larger universe. Within a given Hubble volume, there can be at most one location where organisms veridically perceive what we perceive.

Katja's blog post on the SIA doomsday draws orange boxes with humans waving their hands. She has us update on knowing we're in the human-level stage, i.e., that we're one of those orange boxes. But we know much more: We know that we're a particular one of those boxes, which is easily distinguished from the others based on what we observe about the world. So any hypothesis that contains us at all will have the same number of boxes containing us (namely, just one box). Hence, no anthropic update.

Am I missing something? :)

RESOLUTION:

The problem with my argument was that I compared the hypothesis "filter is early and you exist on Earth" against "filter is late and you exist on Earth". If the hypotheses already say that you exist on Earth, then there's no more anthropic work to be done. But the heart of the anthropic question is whether an early or late filter predicts that you exist on Earth at all.

Here's an oversimplified example. Suppose that the hypothesis of "early filter" tells us that there are four planets, exactly one of which contains life. "Late filter" says there are four planets, all of which contain life. Suppose for convenience that if life exists on Earth at all, you will exist on Earth. Then P(you exist | early filter) = 1/4 while P(you exist | late filter) = 1. This is where the doomsday update comes from.