That argument only works for SSA if type 1 and type 2 planets exist in parallel.
I was talking about a model where either every planet in the multiverse is type 1, or every planet in the multiverse is type 2.
But extinction vs non-extinction is sampled separately on each planet.
Then SSA gives you an anthropic shadow.
(If your reference class is “all observers” you still get an update towards type 2, but it’s weaker than for SIA. If your reference class is “post-nuclear-weapons observers”, then SSA doesn’t update at all.)
Suppose there are 100 planets and in type 1, 99 are destroyed, and in type 2, 10 are destroyed. Suppose your reference class is “all observers”. Then, conditional on type 1, you’re about 0.5% likely to observe being post cold war, and conditional on type 2, you’re about 45% likely to observe being post cold war. These likelihoods are proportional to the SSA posteriors (due to equal priors).
Under SIA, you start with a ~19:10 ratio in favor of type 2 (in the subjective a priori). The likelihood ratios are the same as with SSA so the posteriors are equally weighted towards type 2. So the updates are of equal magnitude in odds space under SSA and SIA.
If your reference class is “post nuclear weapons observers” then I agree that SSA doesn’t update at all. SIA also doesn’t update but starts with a 90:1 prior in favor of type 2. I think this is an odd choice of reference class, and constructing your reference class to depend on your time index nullifies the doomsday argument, which is supposed to be an implication of SSA. I think choices of reference class like this will have odd reflective behavior because e.g. further cold wars in the future will be updated on by default.
Then, conditional on type 1, you’re about 0.5% likely to observe being post cold war, and conditional on type 2, you’re about 45% likely to observe being post cold war.
I would have thought:
p(post cold war | type-1) = 1⁄101 ~= 1%.
p(post cold war | type-2) = 10⁄110 ~= 9%.
I don’t think this makes a substantive difference to the rest of your comment, though.
Under SIA, you start with a ~19:10 ratio in favor of type 2 (in the subjective a priori). The likelihood ratios are the same as with SSA so the posteriors are equally weighted towards type 2. So the updates are of equal magnitude in odds space under SSA and SIA.
Oh, I see. I think I agree that you can see SIA and SSA as equivalent updating procedures with different priors.
Nevertheless, SSA will systematically assign higher probabilities (than SIA) to latent high probabilities of disaster, even after observing themselves to be in worlds where the disasters didn’t happen (at least if the multiverse + reference class is in a goldilocks zone of size and inclusivity). I think that’s what the anthropic’s shadow is about. If your main point is that the action is in the prior (rather than the update) and you don’t dispute people’s posteriors, then I think that’s something to flag clearly. (Again — I apologise if you did something like this in some part of the post I didn’t read!)
I think this is an odd choice of reference class, and constructing your reference class to depend on your time index nullifies the doomsday argument, which is supposed to be an implication of SSA. I think choices of reference class like this will have odd reflective behavior because e.g. further cold wars in the future will be updated on by default.
I agree it’s very strange. I always thought SSA’s underspecified reference classes were pretty suspicious. But I do think that e.g. Bostrom’s past writings often do flag that the doomsday argument only works with certain reference classes, and often talks about reference classes that depend on time-indices.
Type-2 worlds have a 10% chance of being destroyed, not a 90% chance. So P(post cold war | type 2) = 90 / 190.
If your main point is that the action is in the prior (rather than the update) and you don’t dispute people’s posteriors, then I think that’s something to flag clearly.
My point is that the difference between SSA and SIA is in the prior. I dispute anthropic shadow posteriors since both SSA and SIA posteriors overwhelmingly believe type 2, but anthropic shadow arguers say you can’t update towards type 2 using the evidence of being post cold war at all.
That argument only works for SSA if type 1 and type 2 planets exist in parallel.
I was talking about a model where either every planet in the multiverse is type 1, or every planet in the multiverse is type 2.
But extinction vs non-extinction is sampled separately on each planet.
Then SSA gives you an anthropic shadow.
(If your reference class is “all observers” you still get an update towards type 2, but it’s weaker than for SIA. If your reference class is “post-nuclear-weapons observers”, then SSA doesn’t update at all.)
Suppose there are 100 planets and in type 1, 99 are destroyed, and in type 2, 10 are destroyed. Suppose your reference class is “all observers”. Then, conditional on type 1, you’re about 0.5% likely to observe being post cold war, and conditional on type 2, you’re about 45% likely to observe being post cold war. These likelihoods are proportional to the SSA posteriors (due to equal priors).
Under SIA, you start with a ~19:10 ratio in favor of type 2 (in the subjective a priori). The likelihood ratios are the same as with SSA so the posteriors are equally weighted towards type 2. So the updates are of equal magnitude in odds space under SSA and SIA.
If your reference class is “post nuclear weapons observers” then I agree that SSA doesn’t update at all. SIA also doesn’t update but starts with a 90:1 prior in favor of type 2. I think this is an odd choice of reference class, and constructing your reference class to depend on your time index nullifies the doomsday argument, which is supposed to be an implication of SSA. I think choices of reference class like this will have odd reflective behavior because e.g. further cold wars in the future will be updated on by default.
I would have thought:
p(post cold war | type-1) = 1⁄101 ~= 1%.
p(post cold war | type-2) = 10⁄110 ~= 9%.
I don’t think this makes a substantive difference to the rest of your comment, though.
Oh, I see. I think I agree that you can see SIA and SSA as equivalent updating procedures with different priors.
Nevertheless, SSA will systematically assign higher probabilities (than SIA) to latent high probabilities of disaster, even after observing themselves to be in worlds where the disasters didn’t happen (at least if the multiverse + reference class is in a goldilocks zone of size and inclusivity). I think that’s what the anthropic’s shadow is about. If your main point is that the action is in the prior (rather than the update) and you don’t dispute people’s posteriors, then I think that’s something to flag clearly. (Again — I apologise if you did something like this in some part of the post I didn’t read!)
I agree it’s very strange. I always thought SSA’s underspecified reference classes were pretty suspicious. But I do think that e.g. Bostrom’s past writings often do flag that the doomsday argument only works with certain reference classes, and often talks about reference classes that depend on time-indices.
Type-2 worlds have a 10% chance of being destroyed, not a 90% chance. So P(post cold war | type 2) = 90 / 190.
My point is that the difference between SSA and SIA is in the prior. I dispute anthropic shadow posteriors since both SSA and SIA posteriors overwhelmingly believe type 2, but anthropic shadow arguers say you can’t update towards type 2 using the evidence of being post cold war at all.