Dispelling the Anthropic Shadow

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:

The fact that life has survived so long is evidence that the rate of
potentially omnicidal events is low...[this and the anthropic shadow effect] cancel out, so that overall the historical record provides evidence for a true rate close to the observed rate.

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?

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 no longer endorse this, see reply below:

I don't think this does away with the problem, because for decision making purposes the fact that a random event is extinction-causing or not is still relevant (thinking of the Supervolcano vs Martians case in the paper). I didn't see this addressed in the paper. Here's a scenario that hopefully illustrates the issue:

A game is set up where a ball will be drawn from a jar. If it comes out red then "extinction" occurs, the player loses immediately. If it comes out green then "survival" occurs, and the player continues to the next round. This is repeated (with the ball replaced every time) for an unknown number of rounds with the player unable to do anything.

Eventually, the game master decides to stop (for their own unknowable reasons), and offers the player two options:

1. Play one more round of drawing the ball from the jar and risking extinction if it comes out red
2. Take a fixed 10% chance of extinction

If they get through this round then they win the game.

The game is played in two formats:

1. Jack is offered the game as described above, where he can lose before getting to the decision point
2. Jill is offered a game where rounds before the decision point don't count, she can observe the colour of the ball but doesn't risk extinction. Only on the final round does she risk extinction

Let's say they both start with a prior that P(red) is 15%, and that the actual P(red) is 20%. Should they adopt different strategies?

The answer is yes:

1. For Jack, he will only end up at the decision point if he observes 0 red balls. Assuming a large number of rounds are played, if he naively applies Bayesian reasoning he will conclude P(red) is very close to 0 and choose option 1 (another round of picking a ball). This is clearly irrational, because it will always result in option 1 being chosen regardless of the true probability and of his prior^[1]. A better strategy is to stick with his prior if it is at all informative
2. For Jill, she will end up at the decision point regardless of whether she sees a red ball. Assuming a large number of practice rounds are played, in almost all worlds applying naive Bayesian reasoning will tell her P(red) is close to 20%, and she should pick option 2. In this case the decision is sensitive to the true probability, and she only loses out in the small proportion of worlds where she observes an unusually low number of red balls, so the naive Bayesian strategy seems rational

The point is that the population of Jacks that get the opportunity to make the decision is selected to be only those that receive evidence that imply a low probability, and this systematically biases the decision in a way that is predictable beforehand (such that having the information that this selection effect exists can change your optimal decision).

I think this is essentially the same objection raised by quila below, and is in the same vein as Jonas Moss's comment on Toby's post (I'm not 100% sure of this, I'm more confident that the above objection is basically right than that it's the same as these two others).

It's quite possible I'm missing something in the paper, since I didn't read it in that much detail and other people seem convinced by it. But I didn't see anything that would make a difference for this basic case of an error in decision making being caused by the anthropic shadow (and particularly I didn't see how observing a larger number of rounds makes a difference).

1. ^{^}

   A way to see that this is common-sense irrational is to suppose it's a coin flip instead of a ball being drawn, where it's very hard to imagine how you could physically bias a coin to 99% heads, so you would have a very strong prior against that. In this case if you saw 30 heads in a row (and you could see that it wasn't a two-headed coin) it would still seem stupid to take the risk of getting tails on the next round

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

FWIW, I think it's rarely a good idea to assume the validity of anything where anthropics plays an important role. Or decision theory (c.f. this). These are very much not settled areas.

This sometimes even applies when it's not obvious that anthropics is being invoked. I think Dissolving the Fermi Paradox and Grabby aliens both rely on pretty strong assumption about anthropics that are easy for readers to miss. (Tristan Cook does a good job of making the anthropics explicit, and exploring a wide range, in this post.)

summary of my comment: in anthropics problems where {what your meaning 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.

1. we're uncertain about rate of omnideath events.
   • simplifying premise: the rate is discretely either high or very low, and we start off with 50% credence on each
2. we're instantiated ≥1 times in either case, so our existence does not have any probability of ruling either case out.
3. 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 low, this has expected value equal to: prior(low rate) × {value-of-action per world, conditional on low rate} × {amount of worlds we're in, conditional on low rate}
   • if we act as if the rate is high, this has expected value equal to: prior(high rate) × {value-of-action per world, conditional on high rate} × {amount of worlds we're in, conditional on high rate}
4. (if we assume similar conditional 'value-of-action per world' in each), then acting as if the rate is low has higher EV (on those 50/50 priors), because the amount of worlds we're in is much higher if the rate of omnideath events is low.

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.)

1. prior: uncertain about rate of omnideath events.
   • (same simplifying premise)
2. i'm instantiated exactly once.
   • i'm statistically more probable to be instantiated exactly once if the rate is low.
     • though, a world with a low rate of omnideath events could still have one happen, in which case i wouldn't exist conditional on that world.
   • i'm statistically more probable to be instantiated exactly zero times if the rate is high.
     • though, a world with a high rate of omnideath events could still have one not happen, in which case i would exist conditional on that world.

3. (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 low, this has expected value equal to: prior(low rate) × {value-of-action in the sole world, conditional on low rate} × {statistical probability we are alive, conditional on low rate}

   • 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.)

4. (if we assume similar conditional 'value-of-action' in each sole world), then acting as if the rate is low has higher EV (on those 50/50 priors), because 'statistical probability we are alive' is much higher if the rate of omnideath events is low.

(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."

1. ^{^}

   (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') 

2. ^{^}

   (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.)

I thought this piece was going to be about the firm Anthropic . . . anyway, interesting subject, carry on!