This is a linkpost for Dispelling the Anthropic Shadow by Teruji Thomas.
Abstract:
There are some possible events that we could not possibly discover in our past. We could not discover an omnicidal catastrophe, an event so destructive that it permanently wiped out life on Earth. Had such a catastrophe occurred, we wouldn’t be here to find out. This space of unobservable histories has been called the anthropic shadow. Several authors claim that the anthropic shadow leads to an ‘observation selection bias’, analogous to survivorship bias, when we use the historical record to estimate catastrophic risks. I argue against this claim.
Upon a first read, I found this paper pretty persuasive; I'm at >80% that I'll later agree with it entirely, i.e. I'd agree that "the anthropic shadow effect" is not a real thing and earlier arguments in favor of it being a real thing were fatally flawed. This was a significant update for me on the issue.
Anthropic shadow effects are one of the topics discussed loosely in social settings among EAs (and in general open-minded nerdy people), often in a way that assumes the validity of the concept[1]. To the extent that the concept turns out to be completely not a thing — and for conceptual rather than empirical reasons — I'd find that an interesting sociological/cultural fact.
I also found this remarkably clear and definitive--a real update for me, to the point of coming with some actual relief! I'm afraid I wasn't aware of the existing posts by Toby Crisford and Jessica Taylor.
I suppose if there's a sociological fact here it's that EAs and people who are nerdy in similar sorts of ways, myself absolutely included, can be quick to assume a position is true because it sounds reasonable and seemingly thoughtful other people who have thought about the question more have endorsed it. I don't think this single-handedly demonstrates we're too quick; not everyone can dig into everything, so at least to some extent it makes sense to specialize and defer despite the fact this is bound to happen now and then.
Of course argument-checking is also something one can specialize in, and one thing about the EA community which I think is uncommon and great is hiring people like Teru to dig into its cultural background assumptions like this...
I'm having trouble understanding this. The part that comes closest to making sense to me is this summary:
Are they just applying https://en.wikipedia.org/wiki/Self-indication_assumption_doomsday_argument_rebuttal to anthropic shadow without using any of the relevant terms, or is it something else I can't quite get?
Also, how would they respond to the fine-tuning argument? That is, it seems like most planets (let's say 99.9%) cannot support life (eg because they're too close to their sun). It seems fantastically surprising that we find ourselves on a planet that does support life, but anthropics provides an easy way out of this apparent coincidence. That is, anthropics tells us that we overestimate the frequency of things that allow us to be alive. This seems like reverse anthropic shadow, where anthropic shadow is underestimating the frequency of things that cause us to be dead. So is the paper claiming that anthropics does change our estimates of the frequency of good things, but can't change our estimate of the frequency of bad things? Why would this be?
To answer the first question, no, the argument doesn’t rely on SIA. Let me know if the following is helpful.
Suppose your prior (perhaps after studying plate tectonics and so on, but not after considering the length of time that’s passed without an an extinction-inducing supervolcano) is that there’s probability “P(A)”=0.5 that risk of an extinction-inducing supervolcano at the end of each year is 1/2 and probability “P(B)”=0.5 that the risk is 1/10. Suppose that the world lasts at least 1 year and most 3 years regardless.
Let “A1” be the possible world in which the risk was 1/2 per year and we blew up at the end of year 1, “A2” be that in which the risk was 1/2 per year and we blew up at the end of year 2, and “A3” be that in which the risk was 1/2 per year and we never blew up, so that we got to exist for 3 years. Define B1, B2, B3 likewise for the risk=1/10 worlds.
Suppose there’s one “observer per year” before the extinction event and zero after, and let “Cnk”, with k<=n, be observer #k in world Cn (C can be A or B). So there are 12 possible observers: A11, A21, A22, A31, A32, A33, and likewise for the Bs.
If you are observer Cnk, your evidence is that you are observer #k. The question is what Pr(A|k) is; what probability you should assign to the annual risk being 1/2 given your evidence.
Any Bayesian, whether following SIA or SSA (or anything else), agrees that
Pr(A|k) = Pr(k|A)Pr(A)/Pr(k),
where Pr(.) is the credence an observer should have for an event according to a given anthropic principle. The anthropic principles disagree about the values of these credences, but here the disagreements cancel out. Note that we do not necessarily have Pr(A)=P(A): in particular, if the prior P(.) assigns equal probability to two worlds, SIA will recommend assigning higher credence Pr(.) to the one with more observers, e.g. by giving an answer of Pr(coin landed heads) = 1/3 in the sleeping beauty problem, where on this notation P(coin landed heads) = 1/2.
On SSA, your place among the observers is in effect generated first by randomizing among the worlds according to your prior and then by randomizing among the observers in the chosen world. So Pr(A)=0.5, and
Pr(1|A) = 1/2 + 1/4*1/2 + 1/4*1/3 = 17/24
(since Pr(n=1|A)=1/2, in which case k=1 for sure; Pr(n=2|A)=1/4, in which case k=1 with probability 1/2; and Pr(n=3|A)=1/4, in which case k=1 with probability 1/3);
Pr(2|A) = 1/4*1/2 + 1/4*1/3 = 5/24; and
Pr(3|A) = 1/4*1/3 = 2/24.
For simplicity we can focus on the k=2 case, since that’s the case analogous to people like us, in the middle of an extended history. Going through the same calculation for the B worlds gives Pr(2|B) = 63/200, so Pr(2) = 0.5*5/24 + 0.5*63/200 = 157/600.
So Pr(A|2) = 125/314 ≈ 0.4.
On SIA, your place among the observers is generated by randomizing among the observers, giving proportionally more weight to observers in worlds with proportionally higher prior probability, so that the probability of being observer Cnk is
1/12*Pr(Cn) / [sum over possible observers, labeled “Dmj”, of (1/12*Pr(Dm))].
This works out to Pr(2|A) = 2/7 [6 possible observers given A, but the one in the n=1 world “counts for double” since that world is twice as likely than the n=2 or =3 worlds a priori];
Pr(A) = 175/446 [less than 1/2 since there are fewer observers in expectation when the risk of early extinction is higher], and
Pr(2) = 140/446, so
Pr(A|2) = 5/14 ≈ 0.36.
So in both cases you update on the fact that a supervolcano did not occur at the end of year 1, from assigning probability 0.5 to the event that the underlying risk is 1/2 to assigning some lower probability to this event.
But I said that the disagreements canceled out, and here it seems that they don’t cancel out! This is because the anthropic principles disagree about Pr(A|2) for a reason other than the evidence provided by the lack of a supervolcano at the end of year 1: namely the possible existence of year 3. How to update on the fact that you’re in year 2 when you “could have been” in year 3 gets into doomsday argument issues, which the principles do disagree on. I included year 3 in the example because I worried it might seem fishy to make the example all about a 2-period setting where, in period 2, the question is just “what was the underlying probability we would make it here”, with no bearing on what probability we should assign to making it to the next period. But since this is really the example that isolates the anthropic shadow consideration, observe that if we simplify things so that the world lasts at most 2 years (and there 6 possible observers), SSA gives
Pr(2|A) = 1/4, Pr(A) = 1/2, Pr(2) = 4/5 -> Pr(A|2) = 5/14.
and SIA gives
Pr(2|A) = 1/3, Pr(A) = 15/34, Pr(2) = 14/34 -> Pr(A|2) = 5/14.
____________________________
An anthropic principle that would assign a different value to Pr(A|2)--for the extreme case of sustaining the “anthropic shadow”, a principle that would assign Pr(A|2)=Pr(A)=1/2--would be one in which your place among the observers is generated by
This is more in the spirit of SSA than SIA, but it is not SSA, and I don't think anyone endorses it. SSA randomizes over worlds and then over observers within each world, so that observing that you’re late in time is indeed evidence that “most worlds last late”.
Thank you, this is helpful.
I’m not sure I understand the second question. I would have thought both updates are in the same direction: the fact that we’ve survived on Earth a long time tells us that this is a planet hospitable to life, both in terms of its life-friendly atmosphere/etc and in terms of the rarity of supervolcanoes.
We can say, on anthropic grounds, that it would be confused to think other planets are hospitable on the basis of Earth’s long and growing track record. But as time goes on, we get more evidence that we really are on a life-friendly planet, and haven’t just had a long string of luck on a life-hostile planet.
The anthropic shadow argument was an argument along the lines, “no, we shouldn’t get ever more convinced we’re on a life-friendly planet over time (just on the evidence that we’re still around). It is actually plausible that we’ve just had a lucky streak that’s about to break—and this lack of update is in some way because no one is around to observe anything in the worlds that blow up”.
Habryka referred me to https://forum.effectivealtruism.org/posts/A47EWTS6oBKLqxBpw/against-anthropic-shadow , whose "Possible Solution 2" is what I was thinking of. It looks like anthropic shadow holds if you think there are many planets (which seems true) and you are willing to accept weird things about reference classes (which seems like the price of admissions to anthropics). I appreciate the paper you linked for helping me distinguish between the claim that anthropic shadow is transparently true without weird assumptions, vs. the weaker claim in Possible Solution 2 that it might be true with about as much weirdness as all the other anthropic paradoxes.
Is this article different than these other existing critiques of Anthropic shadow arguments?
https://forum.effectivealtruism.org/posts/A47EWTS6oBKLqxBpw/against-anthropic-shadow
https://www.lesswrong.com/posts/EScmxJAHeJY5cjzAj/ssa-rejects-anthropic-shadow-too
They both are a lot clearer to me (in-particular, they both make their assumptions about anthropic reasoning explicit), though that might just be a preference for the LessWrong/EA Forum style instead of academic philosophy.
I haven't digested the full paper yet, but based on the summary pasted below, this is precisely the claim I was trying to argue for in the "Against Anthropic Shadow" post of mine that you have linked.
It looks like this claim has been fleshed out in a lot more detail here though, and I'm looking forward to reading it properly!
In the post you linked I also went on quite a long digression trying to figure out if it was possible to rescue Anthropic Shadow by appealing to the fact that there might be large numbers of other worlds containing life (this plausibly weakens the strength of evidence provided by A, which may then stop the cancellation in C). I decided it technically was possible, but only if you take a strange approach to anthropic reasoning, with a strange and difficult-to-define observer reference class.
Possibly focusing so much on this digression was a mistake though, since the summary above is really pointing to the important flaw in the original argument!
I can't believe Toby's initial post only had 28 Karma, it's excellent, crazytown....
I think a proper account of this wants to explain why there appear to be arguments which argue for an anthropic shadow effect, and why there appear to be arguments which argue against an anthropic shadow effect, and how to reconcile them.
In my view, Teru Thomas's paper is the first piece which succeeds in doing that.
(My historical position is like "I always found anthropic shadow arguments fishy, but didn't bottom that concern out". I found Toby Crisford's post helpful in highlighting what might be a reason not to expect anthropic shadow effects, but it left things feeling gnarly so I wasn't confident in it -- again, without investing a great deal of time in trying to straighten it out. I missed Jessica Taylor's post, but looking at it now I think I would have felt similarly to Toby Crisford's analysis.)
summary of my comment: in anthropics problems where {what your sense of of 'probability' yields} is unclear, instead of focusing on 'what the probability is', focus on fully comprehending the situation and then derive what action you prefer to take.[1]
imv this is making a common mistake ("conflating logical and indexical uncertainty"). here's what i think the correct reasoning is. it can be done without ever updating our probability about what the rate is.
i write two versions of this for two cases:
case 1, where something like many-worlds is true, in which case as long as the rate of omnideath events is below ~100%, there will always be observers like you.
case 2, where there is only one small world, in which case if the rate of an omnideath event occurring at least once were high there might be 'no observers' or 'no instantiated copies of you'.
i try to show these are actually symmetrical.
finally i show symmetry to a case 3, where our priors are 50/50 between two worlds, in one of which we certainly (rather than probably) would not exist; we do not need to update our priors (in response to our existence), even in that case, to choose what to do.
case 1: where something like many-worlds is true.
note that there is no step here where the probability is updated away from 50/50.
probability is the name we give to a variable in an algorithm, and this above algorithm goes through all the relevant steps without using that term. to focus on 'what the probability becomes' is just a question of definitions: for instance, if defined as {more copies of me in a conditional = (by definition) 'higher probability' assigned to that conditional}, then that sense of probability would 'assign more to a low rate' (a restatement of the end of step 4).
onto case 2: single world
(i expect the symmetry to be unintuitive. i imagine a reader having had a thought process like this:
"if i imagine a counterfactual where the likelihood of omnideath events per some unit of time is high, then because [in this case 2] there is only one world, it could be the case that my conditionals look like this: 'there is one copy of me if the rate is low, but none at all if the rate is high'. that would be probabilistic evidence against the possibility it's high, right? because i'm conditioning on my existence, which i know for sure occurs at least once already." (and i see this indicated in another commenter's, "I also went on quite a long digression trying to figure out if it was possible to rescue Anthropic Shadow by appealing to the fact that there might be large numbers of other worlds containing life")
i don't know if i can make the symmetry intuitive, so i may have to abandon some readers here.)
(again then going right to the EV calculation):
we could act as if the rate is low, or act as if it is high. these have different ramifications:
if we act as if the rate is high, this has expected value equal to: prior(high rate) × {value-of-action in the sole world, conditional on high rate} × {statistical probability we are alive, conditional on high rate}
(these probabilities are conditional on either rate already being true, i.e p(alive|some-rate), but we're not updating the probabilities of either rate themselves. this would violate bayes' formula if we conditioned on 'alive', but we're intentionally avoiding that here.
in a sense we're avoiding it to rescue the symmetry of these three cases. i suspect {not conditioning on one's own existence, rather preferring to act as if one does exist per EV calc} could help with other anthropics problems too.)
(i notice i could use the same sentences with only a few changes from case 1, so maybe this symmetry will be intuitive)
(to be clear, in reality our prior might not be 50/50 (/fully uncertain); e.g., maybe we're looking at the equations of physics and we see that it looks like there should be chain reactions which destroy the universe happening frequently, but which are never 100% likely; or maybe we instead see that they suggest world-destroying chain reactions are impossible.)
main takeaway: in anthropics problems where {what your sense of of 'probability' yields} is unclear, instead of focusing on 'what the probability is', focus on fully comprehending the situation and then derive what action you prefer to take.
(case 3) i'll close with a further, more fundamental-feeling insight: this symmetry holds even when we consider a rate of 100% rather than just 'high'. as in, you can run that through this same structure and it will give you the correct output.
the human worded version of that looks like, "i am a fixed mathematical function. if there are no copies of me in the world[2], then the output of this very function is irrelevant to what happens in the world. if there are copies of me in the world, then it is relevant / directly corresponds to what effects those copies have. therefore, because i am a mathematical function which cares about what happens in worlds (as opposed to what the very function itself does), i will choose my outputs as if there are copies of me in the world, even though there is a 50% chance that there are none."
(as in the 'sleeping beauty problem', once you have all the relevant variables, you can run simulations / predict what choice you'd prefer to take (such as if offered to bet that the day is tuesday) without ever 'assigning a probability')
(note: 'the world' is underdefined here, 'the real world' is not a fundamental mathematical entity that can be pointed to in any formal systems we know of, though we can fix this by having the paragraph, instead of referring to 'the world', refer to some specific function which the one in question is uncertain about whether itself is contained in it.
we seem to conceptualize the 'world' we are in as some particular 'real world' and not just some abstract mathematical function of infinitely many. i encourage thinking more about this, though it's unrelated to the main topic of this comment.)