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What is the reasoning behind the "anthropic shadow" effect? 2019-09-03T13:21:37.913Z

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Comment by tobycrisford on Don’t Be Comforted by Failed Apocalypses · 2022-05-18T06:27:56.496Z · EA · GW

I can see that is a difference between the two cases. What I'm struggling to understand is why that leads to a different answer.

My understanding of the steps of the anthropic shadow argument (possibly flawed or incomplete) is something like this:

You are an observer -> We should expect observers to underestimate the frequency of catastrophic events on average, if they use the frequency of catastrophic events in their past -> You should revise your estimate of the frequency of catastrophic events upwards

But in the coin/tile case you could make an exactly analogous argument:

You see a blue tile -> We should expect people who see a blue tile to underestimate the frequency of heads on average, if they use the frequency of heads in their past -> You should revise your estimate of the frequency of heads upwards.

But in the coin/tile case, this argument is wrong, even though it appears intuitively plausible. If you do the full bayesian analysis, that argument leads you to the wrong answer. Why should we trust the argument of identical structure in the anthropic case?

Comment by tobycrisford on Don’t Be Comforted by Failed Apocalypses · 2022-05-17T18:52:58.889Z · EA · GW

In the tile case, the observers who see a blue tile are underestimating on average. If you see a blue tile, you then know that you belong to that group, who are underestimating on average. But that still should not change your estimate. That's weird and unintuitive, but true in the coin/tile case (unless I've got the maths badly wrong somewhere).

I get that there is a difference in the anthropic case. If you kill everyone with a red tile, then you're right, the observers on average will be biased, because it's only the observers with a blue tile who are left, and their estimates were biased to begin with. But what I don't understand is, why is finding out that you are alive any different to finding out that your tile is blue? Shouldn't the update be the same?

Comment by tobycrisford on Don’t Be Comforted by Failed Apocalypses · 2022-05-17T17:45:46.214Z · EA · GW

Thanks for your reply!

If 100 people do the experiment, the ones who end up with a blue tile will, on average, have fewer heads than they should, for exactly the same reason that most observers will live after comparitively fewer catastrophic events.

But in the coin case that still does not mean that seeing a blue tile should make you revise your naive estimate upwards. The naive estimate is still, in bayesian terms, the correct one.

I don't understand why the anthropic case is different.

Comment by tobycrisford on Don’t Be Comforted by Failed Apocalypses · 2022-05-17T14:22:39.520Z · EA · GW

I've never understood the bayesian logic of the anthropic shadow argument. I actually posted a question about this on the EA forum before, and didn't get a good answer. I'd appreciate it if someone could help me figure out what I'm missing. When I write down the causal diagram for this situation, I can't see how an anthropic shadow effect could be possible.

Section 2 of the linked paper shows that the probability of a catastrophic event having occurred in some time frame in the past given that we exist now: P(B_2|E), is smaller than its actual probability of occurring in that time frame, P. The two get more and more different the less likely we are to survive the catastrophic event (they call our probability of survival Q). It's easy to understand why that is true. It is more likely that we would exist now if the event did not occur than if it did occur. In the extreme case where we are certain to be wiped out by the event, then P(B_2|E) = 0.

This means that if you re-ran the history of the world thousands of times, the ones with observers around at our time would have fewer catastrophic events in their past, on average, than is suggested by P. I am completely happy with this.

But the paper then leaps from this observation to the conclusion that our naive estimate of the frequency of catastrophic events (i.e. our estimate of P) must be biased downwards. This is the point where I lose the chain of reasoning. Here is why.

What we care about here is not P(B_2|E). What we care about is our estimate of P itself. We would ideally like to calculate the posterior distribution of P, given both B_1,2 (the occurrence/non-occurrence of the event in the past), and our existence, E. The causal diagram here looks like this:

P -> B_2 -> E

This diagram means: P influences B_2 (the catastrophic event occurring), which influences E (our existence).  But P does not influence E except through B_2.

*This means if we condition on B_2, the fact we exist now should have no further impact on our estimate of P* 

To sum up my confusion: The distribution of (P|B_2,E) should be equivalent to the distribution of (P|B_2). I.e., there is no anthropic shadow effect.

In my original EA forum question I took the messy anthropics out of it and imagined flipping a biased coin hundreds of times and painting a blue tile red with probability 1-Q (extinction) if we ever get a head. If we looked at the results of this experiment, we could estimate the bias of the coin by simply counting the number of heads. The colour of the tile is irrelevant. And we should go with the naive estimate, even though it is again true that people who see a blue tile will have fewer heads on average than is suggested by the bias of the coin

What this observation about the tile frequencies misses is that the tile is more likely to be blue when the probability of heads is smaller (or we are more likely to exist if P is smaller), and we should take that into account too.

Overall it seems like our naive estimate of P based on the frequency of the catastrophic event in our past is totally fine when all things are considered.

I'm struggling at the moment to see why the anthropic case should be different to the coin case.

Comment by tobycrisford on Is the reasoning of the Repugnant Conclusion valid? · 2022-05-11T07:19:52.044Z · EA · GW

"I would say exactly the same for this. If these people are being freshly created, then I don't see the harm in treating them as identical."

I think you missed my point. How can 1,000 people be identical to 2,000 people? Let me give a more concrete example. Suppose again we have 3 possible outcomes:

(A) (Status quo): 1 person exists at high welfare +X

(B): Original person has welfare reduced to X - 2, 1000 new people are created at welfare +X

(C): Original person has welfare reduced only to X - , 2000 new people are created, 1000 at welfare , and 1000 at welfare X + .

And you are forced to choose between (B) and (C).

How do you pick? I think you want to say 1000 of the potential new people are "effectively real", but which 1000 are "effectively real" in scenario (C)? Is it the 1000 at welfare ? Is it the 1000 at welfare X+? Is it some mix of the two?

If you take the first route, (B) is strongly preferred, but if you take the second, then (C) would be preferred.  There's ambiguity here which needs to be sorted out.

"Then, supposedly no one is effectively real. But actually, I'm not sure this is a problem. More thinking will be required here to see whether I am right or wrong."

Thank you for finding and expressing my objection for me! This does seem like a fairly major problem to me.

"Sorry, but this is quite incorrect. The people in (C) would want to move to (B)."

No, they wouldn't, because the people in (B) are different to the people in (C). You can assert that you treat them the same, but you can't assert that they are the same. The (B) scenario with different people and the (B) scenario with the same people are both distinct, possible, outcomes, and your theory needs to handle them both. It can give the same answer to both, that's fine, but part of the set up of my hypothetical scenario is that the people are different.

"Isn't the very idea of reducing people to their welfare impersonal?"

Not necessarily. So called "person affecting" theories say that an act can only be wrong if it makes things worse for someone. That's an example of a theory based on welfare which is not impersonal. Your intuitive justification for your theory seemed to have a similar flavour to this, but if we want to avoid the non-identity problem, we need to reject this appealing sounding principle. It is possible to make things worse even though there is no one who it is worse for. Your 'effectively real' modification does this, I just think it reduces the intuitive appeal of the argument you gave.

Comment by tobycrisford on The COILS Framework for Decision Analysis: A Shortened Intro+Pitch · 2022-05-10T17:00:48.195Z · EA · GW

Where would unintended consequences fit into this?

E.g. if someone says:

"This plan would cause X, which is good. (Co) X would not occur without this plan, (I) We will be able to carry out the plan by doing Y, (L) the plan will cause X to occur, and (S) X is morally good."

And I reply:

"This plan will also cause Z, which is morally bad, and outweights the benefit of X"

Which of the 4 categories of claim am I attacking? Is it 'implementation'?

Comment by tobycrisford on Is the reasoning of the Repugnant Conclusion valid? · 2022-05-07T14:08:54.308Z · EA · GW

You can assert that you consider the 1000 people in (B) and (C) to be identical, for the purposes of applying your theory. That does avoid the non-identity problem in this case. But the fact is that they are not the same people. They have different hopes, dreams, personalities, memories, genders, etc.

By treating these different people as equivalent, your theory has become more impersonal.  This means you can no longer appeal to one of the main arguments you gave to support it: that your recommendations always align with the answer you'd get if you asked the people in the population whether they'd like to move from one situation to the other. The people in (B) would not want to move to (C), and vice versa, because that would mean they no longer exist. But your theory now gives a strong recommendation for one over the other anyway.

There are also technical problems with how you'd actually apply this logic to more complicated situations where the number of future people differs. Suppose that 1000 extra people are created in (B), but 2000 extra people are created in (C), with varying levels of welfare. How do you apply your theory then? You now need 1000 of the 2000 people in (C) to be considered 'effectively real', to continue avoiding non-identity problem like conclusions, but which 1000? How do you pick? Different choices of the way you decide to pick will give you very different answers, and again your theory is becoming more impersonal, and losing more of its initial intuitive appeal.

Another problem is what to do under uncertainty. What if instead of a forced choice between (B) and (C), the choice is between:

0.1% chance of (A), 99.9% chance of (B)

0.1000001% chance of (A), 99.9% chance of (C).

Intuitively, the recommendations here should not be very different to the original example. The first choice should still be strongly preferred. But are the 1000 people still considered 'effectively real' in your theory, in order to allow you to reach that conclusion? Why? They're not guaranteed to exist, and actually, your real preferred option, (A), is more likely to happen with the second choice.

Maybe it's possible to resolve all these complications, but I think you're still a long way from that at the moment. And I think the theory will look a lot less intuitively appealing once you're finished.

I'd be interested to read what the final form of the theory looks like if you do accomplish this, although I still don't think I'm going to be convinced by a theory which will lead you to be predictably in conflict with your future self, even if you and your future self both follow the theory. I can see how that property can let you evade the repugnant conclusion logic while still sort of  being transitive. But I think that property is just as undesirable to me as non-transitiveness would be.

Comment by tobycrisford on Is the reasoning of the Repugnant Conclusion valid? · 2022-05-04T22:09:49.794Z · EA · GW

"We minimise our loss of welfare according to the methodology and pick B, the 'least worst' option."

But (B) doesn't minimise our loss of welfare. In B we have welfare X-2, and in C we have welfare X - , so wouldn't your methodology tell us to pick (C)? And this is intuitively clearly wrong in this case. It's telling us not tmake a negligible sacrifice to our welfare now in order to improve the lives of future generations, which is the same problematic conclusion that the non-identity problem gives to certain theories of population ethics.

I'm interested in how your approach would tell us to pick (B), because I still don't understand that?

I won't reply to your other comment just to keep the thread in one place from now on (my fault for adding a P.S, so trying to fix the mistake). But in short, yes, I disagree, and I think that these flaws are unfortunately severe and intractable. The 'forcing' scenario I imagined is more like the real world than the unforced decisions. For most of us making decisions, the fact that people will exist in the future is inevitable, and we have to think about how we can influence their welfare. We are therefore in a situation like (2), where we are going to move from (A) to either (B) or (C) and we just get to pick which of (B) or (C) it will be. Similarly, figuring out how to incorporate uncertainty is also fundamental, because all real world decisions are made under uncertainty.

Comment by tobycrisford on Is the reasoning of the Repugnant Conclusion valid? · 2022-05-03T16:46:10.279Z · EA · GW

I understood your rejection of the total ordering on populations, and as I say, this is an idea that others have tried to apply to this problem before.

But the approach others have tried to take is to use the lack of a precise "better than" relation to evade the logic of the repugnant conclusion arguments, while still ultimately concluding that population Z is worse than population A. If you only conclude that Z is not worse than A, and A is not worse than Z (i.e. we should be indifferent about taking actions which transform us from world A to world Z), then a lot of people would still find that repugnant!

Or are you saying that your theory tells us not to transform ourselves to world Z? Because we should only ever do anything that will make things actually better?

If so, how would your approach handle uncertainty? What probability of a world Z should we be willing to risk in order to improve a small amount of real welfare?

And there's another way in which your approach still contains some form of the repugnant conclusion. If a population stopped dealing in hypotheticals and actually started taking actions, so that these imaginary people became real, then you could imagine a population going through all the steps of the repugnant conclusion argument process, thinking they were making improvements on the status quo each time, and finding themselves ultimately ending up at Z. In fact it can happen in just two steps, if the population of B is made large enough, with small enough welfare.

I find something a bit strange about it being different when happening in reality to when happening in our heads. You could imagine people thinking

"Should we create a large population B at small positive welfare?"

"Sure, it increases positive imaginary welfare and does nothing to real welfare"

"But once we've done that, they will then be real, and so then we might want to boost their welfare at the expense of our own. We'll end up with a huge population of people with lives barely worth living, that seems quite repugnant."

"It is repugnant, we shouldn't prioritise imaginary welfare over real welfare. Those people don't exist."

"But if we create them they will exist, so then we will end up deciding to move towards world Z. We should take action now to stop ourselves being able to do that in future."

I find this situation of people being in conflict with their future selves quite strange. It seems irrational to me!

Comment by tobycrisford on Is the reasoning of the Repugnant Conclusion valid? · 2022-05-03T16:37:29.768Z · EA · GW

It sounds like I have misunderstood how to apply your methodology. I would like to understand it though. How would it apply to the following case?

Status quo (A): 1 person exists at very high welfare +X

Possible new situation (B): Original person has welfare reduced to X - 2 , 1000 people are created with very high welfare +X

Possible new situation (C): Original person has welfare X - , 1000 people are created with small positive welfare .

I'd like to understand how your theory would answer two cases: (1) We get to choose between all of A,B,C.  (2) We are forced to choose between (B) and (C), because we know that the world is about to instantaneously transform into one of them.

This is how I had understood your theory to be applied:

  • Neither (B) nor (C) are better than (A), because an instanataneous change from (A) to (B) or (C) would reduce real welfare (of the one already existing person).
  • (A) is not better than (B) or (C) because to change (B) or (C) to (A) would cause 1000 people to disappear (which is a lot of negative real welfare).
  • (B) and (C) are neither better or worse than each other, because an instantaneous change of one to the other would involve the loss of 1000 existing people (negative real welfare) which is only compensated by the creation of imaginary people (positive imaginary welfare). It's important here that the 1000 people in (B) and (C) are not the same people. This is the non-identity problem.

 From your reply it sounds like you're coming up with a different answer when comparing (B) to (C), because both ways round the 1000 people are always considered imaginary, as they don't literally exist in the status quo? Is that right?

If so, that still seems like it gives a non-sensical answer in this case, because it would then say that (C) is better than (B) (real welfare is reduced by less), when it seems obvious that (B) is actually better? This is an even worse version of the flaw you've already highlighted, because the existing person you're prioritising over the imaginary people is already at a welfare well above the 0 level.

If I've got something wrong and your methodology can explain the intuitively obvious answer that (B) is better than (C), and should be chosen in example (2) (regardless of their comparison to A), then I would be interested to understand how that works.

Comment by tobycrisford on Is the reasoning of the Repugnant Conclusion valid? · 2022-04-24T11:38:02.987Z · EA · GW

P.S. Thinking about this a bit more, doesn't this approach fail to give sensible answers to the non-identity problem as well? Almost all decisions we make about the future will change not just the welfare of future people, but which future people exist. That means every decision you could take will reduce real welfare, and so under this approach no decision can be be better than any other, which seems like a problem!

Comment by tobycrisford on Is the reasoning of the Repugnant Conclusion valid? · 2022-04-24T11:16:49.051Z · EA · GW

This is an interesting approach. The idea that we can avoid the repugnant conclusion by saying that B is not better than A, and neither is A better than B, is I think similar to how Parfit himself thought we might be able to avoid the repugnant conclusion: https://onlinelibrary.wiley.com/doi/epdf/10.1111/theo.12097

He used the term "evaluative imprecision" to describe this. Here's a quote from the paper:

"Precisely equal is a transitive relation. If X and Y are precisely equally good, and Y and Z are precisely equally good, X and Z must be precisely equally good. But if X and Y are imprecisely equally good, so that neither is worse than the other, these imprecise relations are not transitive. Even if X is not worse than Y, which is not worse than Z, X may be worse than Z."

It's easy to see how evaluative imprecision could  help us to avoid the repugnant conclusion.

But I don't think your approach actually achieves what is described in this quote, unless I'm missing something? It only refutes the repugnant conclusion in an extremely weak sense. Although Z is not better than A in your example, it is also not worse than A. That still seems quite repugnant!

Doesn't your logic explaining that neither A or B are worse than each other also apply to A and Z?

Comment by tobycrisford on An uncomfortable thought experiment for anti-speciesist non-vegans · 2022-04-19T16:16:11.322Z · EA · GW

I think this point of view makes a lot of sense, and is the most reasonable way an anti-speciesist can defend not being fully vegan.

But I'd be interested to hear more about what the very strong 'instrumental' reasons are for humans not subjugating humans, and why they don't apply to humans subjugating non-humans?

(Edit: I'm vegan, but my stance on it has softened a bit since being won round by the total utilitarian view)

Comment by tobycrisford on How does the simulation hypothesis deal with the 'problem of the dust'? · 2022-03-10T20:52:45.646Z · EA · GW

This is a very interesting and weird problem. It feels like the solution should have something to do with the computational complexity of the mapping? E.g. is it a mapping that could be calculated in polynomial or exponential time? If the mapping function is as expensive to compute as just simulating the brain in the first place, then the dust hasn't really done any of the computational work.

Another way of looking at this: if you do take the dust argument seriously, why do you even need the dust at all? The mapping from dust to mental states exists in the space of mathematical functions, but so does the mapping from time straight to mental states, with no dust involved.

I guess the big question here is when does a sentient observer contained inside a mathematical function "exist"? What needs to happen in the physical universe for them to have experiences? That's a really puzzling and interesting question.

Comment by tobycrisford on [deleted post] 2022-01-07T13:01:02.360Z

"deciding, based on reason, that Exposure A is certain to have no effect on Outcome X, and then repeatedly running RCTs for the effect of exposure A on Outcome X to obtain a range of p values"

If the p-values have been calculated correctly and you run enough RCTS, then we already know what the outcome of this experiment will be: p<0.05 will occur 5% of the time, p<0.01 will occur 1% of the time, etc for all values of p between 0 and 1.

The other way round is more interesting, it will tell you what the "power" of your test was (https://en.wikipedia.org/wiki/Power_of_a_test), but that strongly depends on the size of the effect of B on X, as well as the sample size in your study. You'll probably miss something if you pick a single B and X pair to represent your entire field.

I think the point is that any p-value threshold is arbitrary. The one you should use depends on context. It should depend on how much you care about false positives vs false negatives in that particular case, and on your priors. Also maybe we should just stop using p-values and switch to using likelihood ratios instead. Both of these changes might be useful things to advocate for, but I wouldn't have thought changing one arbitrary threshold to another arbitrary threshold is likely to be very useful.

Comment by tobycrisford on Reasons and Persons: Watch theories eat themselves · 2022-01-02T17:01:09.361Z · EA · GW

From my memory of Reasons+Persons, Parfit does say that common-sense morality being collectively directly self-defeating refutes common-sense morality, but he doesn't think that consequentialism being indirectly self-defeating refutes consequentialism. This is because it isn't an aim of consequentialism that people have consequentialist temperaments, or even that they believe in consequentialism, and because any theory will be indirectly self-defeating in some circumstances (the satan thought experiment proves that).

I really like this summary, but just wanted to point this out, because the objections to common-sense morality and consequentialism were conflated in your take-away, while I think Parfit thought they were different. He claimed that his arguments refuted common-sense morality, but I don't think he made that claim about consequentialism.

Maybe this distinction comes under the category of questions you don't care about that much though, which is fair enough!

Comment by tobycrisford on Saving Average Utilitarianism from Tarsney - Self-Indication Assumption cancels solipsistic swamping. · 2021-05-16T18:58:25.619Z · EA · GW

I think this is a really interesting observation.

But I don't think it's fair to say that average utilitarianism  "avoids the repugnant conclusion".

If the world contains only a million individuals whose lives are worse than not existing (-100 utils each), and you are considering between two options: (i) creating a million new individuals who are very happy (50 utils each) or (ii) creating N new individuals whose lives are barely worth living (x utils each), then for any x, however small, there is some N where (ii) is preferred, even under average utilitarianism.

There are many serious problems with average utilitarianism, not least that it doesn't remove the repugnant conclusion anyway . So although I think this refutation of solipsistic swamping makes sense and is interesting, I don't think it increases my credence in average utilitarianism very much.

Comment by tobycrisford on Incompatibility of moral realism and time discounting · 2020-12-16T08:41:25.225Z · EA · GW

This is a beautiful thought experiment, and a really interesting argument. I wonder if saying that it shows an incompatibility between moral realism and time discounting is too strong though? Maybe it only shows an incompatibility between time discounting and consequentialism?

Under non-consequentialist moral theories, it is possible for different moral agents to be given conflicting aims. For example, some people believe that we have a special obligation towards our own families. Suppose that in your example, Anna and Christoph are moving towards their respective siblings, and we neglect relativistic effects. In that case, both Anna and Christoph might agree that it is right for Anna to take the carrot, and  that it is also right for Christoph to take the carrot, even though these aims conflict. This is not inconsistent with moral realism.

Similarly, in the relativistic case, we could imagine believing in the moral rule that "everyone should be concerned with utility in their own inertial frame", together with some time discounting principle. Both Anna and Christoph would believe in the true statements "Anna should take the carrot" and "Christoph should take the carrot". They would acknowledge that their aims conflict, but that is not inconsistent with moral realism.

I think the analogy here is quite strong, because you could imagine a time discounter defending their point of view by saying we have stronger obligations to those closer to us in time, in the same way that we might have stronger obligations towards those closer to us in space, or genetically.

On the other hand, when you consider General Relativity, there are no global inertial frames, so it's interesting to imagine how a steelmanned time discounter would adapt the "everyone should be concerned with utility in their own inertial frame" principle to be consistent with General Relativity. Maybe anything they try would have some weird consequences.

Comment by tobycrisford on What are some low-information priors that you find practically useful for thinking about the world? · 2020-08-28T14:16:39.547Z · EA · GW

I think I disagree with your claim that I'm implicitly assuming independence of the ball colourings.

I start by looking for the maximum entropy distribution within all possible probability distributions over the 2^100 possible colourings. Most of these probability distributions do not have the property that balls are coloured independently. For example, if the distribution was a 50% probability of all balls being red, and 50% probability of all balls being blue, then learning the colour of a single ball would immediately tell you the colour of all of the others.

But it just so happens that for the probability distribution which maximises the entropy, the ball colourings do turn out to be independent. If you adopt the maximum entropy distribution as your prior, then learning the colour of one tells you nothing about the others. This is an output of the calculation, rather than an assumption.

I think I agree with your last paragraph, although there are some real problems here that I don't know how to solve. Why should we expect any of our existing knowledge to be a good guide to what we will observe in future? It has been a good guide in the past, but so what? 99 red balls apparently doesn't tell us that the 100th will likely be red, for certain seemingly reasonable choices of prior.

I guess what I was trying to say in my first comment is that the maximum entropy principle is not a solution to the problem of induction, or even an approximate solution. Ultimately, I don't think anyone knows how to choose priors in a properly principled way. But I'd very much like to be corrected on this.

Comment by tobycrisford on What are some low-information priors that you find practically useful for thinking about the world? · 2020-08-28T11:49:49.762Z · EA · GW

I think I disagree that that is the right maximum entropy prior in my ball example.

You know that you are drawing balls without replacement from a bag containing 100 balls, which can only be coloured blue or red. The maximum entropy prior given this information is that every one of the 2^100 possible colourings {Ball 1, Ball 2, Ball 3, ...} -> {Red, Blue} is equally likely (i.e. from the start the probability that all balls are red is 1 over 2^100).

I think the model you describe is only the correct approach if you make an additional assumption that all balls were coloured using an identical procedure, and were assigned to red or blue with some unknown, but constant, probability p. But that is an additional assumption. The assumption that the unknown p is the same for each ball is actually a very strong assumption.

If you want to adopt the maximum entropy prior consistent with the information I gave in the set-up of the problem, you'd adopt a prior where each of the 2^100 possible colourings are equally likely.

I think this is the right way to think about it anyway.

The re-paremetrisation example is very nice though, I wasn't aware of that before.

Comment by tobycrisford on What are some low-information priors that you find practically useful for thinking about the world? · 2020-08-26T19:57:28.300Z · EA · GW

The maximum entropy principle can give implausible results sometimes though. If you have a bag containing 100 balls which you know can only be coloured red or blue, and you adopt a maximum entropy prior over the possible ball colourings, then if you randomly drew 99 balls from the bag and they were all red, you'd conclude that the next ball is red with probability 50/50. This is because in the maximum entropy prior, the ball colourings are independent. But this feels wrong in this context. I'd want to put the probability on the 100th ball being red much higher.

Comment by tobycrisford on What is the reasoning behind the "anthropic shadow" effect? · 2019-09-06T10:39:43.654Z · EA · GW

Thank you for your answer!


I think I agree that there is a difference between the extinction example and the coin example, to do with the observer bias, which seems important. I'm still not sure how to articulate this difference properly though, and why it should make the conclusion different. It is true that you have perfect knowledge of Q, N, and the final state marker in the coin example, but you do in the (idealized) extinction scenario that I described as well. In the extinction case I supposed that we knew Q, N, and the fact that we haven't yet gone extinct (which is the analogue of a blue marker).


The real difference I suppose is that in the extinction scenario we could never have seen the analogue of the red marker, because we would never have existed if that had been the outcome. But why does this change anything?


I think you're right that we could modify the coin example to make it closer to the extinction example, by introducing amnesia, or even just saying that you are killed if both coins ever land heads together. But to sum up why I started talking about a coin example with no observer selection effects present:


In the absence of a complete consistent formalism for dealing with observer effects, the argument of the 'anthropic shadow' paper still appears to carry some force, when it says that the naive estimates of observers will be underestimates on average, and that therefore, as observers, we should revise our naive estimates up by an appropriate amount. However, an argument with identical structure gives the wrong answer in the coin example, where everything is understood and we can clearly see what the right answer actually is. The naive estimates of people who see blue will be underestimates on average, but that does not mean, in this case, that if we see blue we should revise our naive estimates up. In this case the naive estimate is the correct bayesian one. This should cast doubt on arguments which take this form, including the anthropic shadow argument, unless we can properly explain why they apply in one case but not the other, and that's what I am uncertain how to do.


Thank you for sharing the Nature paper. I will check it out!