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Which distribution would you use? Why the particular weights you've chosen and not slightly different ones?

I think you just have to make your distribution uninformative enough that reasonable differences in the weights don't change your overall conclusion. If they do, then I would concede that the solution to your specific question really is clueless. Otherwise, you can probably find a response.

come up with a probability distribution for the fraction of heads over 1,000,000 flips.

Rather than thinking of directly of appropriate distribution for the 1,000,000 flips, I'd think of a distribution to model itself. Then you can run simulations based on the distribution of $p$ to calculate the distribution of the fraction of 1000,000 flips. $p \in (0.5, 1.0]$ , and then we need to select a distribution for $p$ over that range.

There is no one correct probability distribution for p because any probability is just an expression of our belief, so you may use whatever probability distribution genuinely reflects your prior belief. A uniform distribution is a reasonable start. Perhaps you really are clueless about p, in which case, yes, there's a certain amount of subjectivity about your choice. But prior beliefs are always inherently subjective, because they simply describe your belief about the state of the world as you know it now. The fact you might have to select a distribution, or set of distributions with some weighted average, is merely an expression of your uncertainty. This in itself, I think, doesn't stop you from trying to estimate the result.

I think this expresses within Bayesian terms the philosophical idea that we can only make moral choices based on information available at the time; one can't be held morally responsible for mistakes made on the basis of the information we didn't have.

Perhaps you disagree with me that a uniform distribution is the best choice. You reason thus: "we have some idea about the properties of coins in general. It's difficult to make a coin that is 100% biased towards heads. So that seems unlikely". So we could pick a distribution that better reflects your prior belief. Perhaps a suitable choice might be $B e t a (2, 2)$ with a truncation at 0.5, which will give the greatest likelihood of $p$ just above 0.5, and a declining likelihood down to 1.0.

Maybe you and i just can't agree after all that there is still no consistent and reasonable prior choice you can make, and not even any compromise. And let's say we both run simulations using our own priors and find entirely different results and we can't agree on any suitable weighting between them. In that case, yes, I can see you have cluelessness. I don't think it follows that, if we went through the same process for estimating the longtermist moral worth of malaria bednet distribution, we must have intractable complex cluelessness about specific problems like malaria bednet distribution. I think I can admit that perhaps, right now, in our current belief state, we are genuinely clueless, but it seems that there is some work that can be done that might eliminate the cluelessness.

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Solving the moral cluelessness problem with Bayesian joint probability distributions

by ben.smith

Feb 28 20215 min read 13

11

PhilosophyCluelessnessMoral philosophy

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Solving the moral cluelessness problem with Bayesian joint probability distributions

Primer on cluelesness

The complex cluelessness problem

A "set point/Control Theory" solution

A general Bayesian joint probability solution

What am I missing?

13 comments

Hillary Greaves laid out a problem of "moral cluelessness" in her paper Cluelessness, http://users.ox.ac.uk/~mert2255/papers/cluelessness.pdf

Primer on cluelesness

There are some resources on this problem below, taken from the Oxford EA Fellowship materials:

(Edit: one text deprecated and redacted)

Hilary Greaves on Cluelessness, 80000 Hours podcast (25 min) https://80000hours.org/podcast/episodes/hilary-greaves-global-priorities-institute/

If you value future people, why do you consider short-term effects? (20 min) https://forum.effectivealtruism.org/posts/ajZ8AxhEtny7Hhbv7/if-you-value-future-people-why-do-you-consider-near-term

Simplifying cluelessness (30 min) https://philiptrammell.com/static/simplifying_cluelessness.pdf

Finally there's this half hour talk of Greaves presenting her ideas around cluelessness:

https://www.youtube.com/watch?v=fySZIYi2goY

The complex cluelessness problem

Greaves has the following worry about complex cluelessness:

The cases in question have the following structure:
For some pair of actions of interest A1, A2,
- (CC1) We have some reasons to think that the unforeseeable consequences of A1 would systematically tend to be substantially better than those of A2;
- (CC2) We have some reasons to think that the unforeseeable consequences of A2 would systematically tend to be substantially better than those of A1;
- (CC3) It is unclear how to weigh up these reasons against one another.

She then uses donating bednets to poor countries as an example of this. By donating bednets, we can save lives at scale. Saving lives could increase the fertility rate, eventually leading to a higher population. There are good reasons to think that a higher population is net-negative for the long-term, or could even constitute an existential threat (CC1). On the other hand, it's entirely possible that saving lives in the short term could improve humanity's long term prospects (CC2) - perhaps a higher population now will lead to a larger number of people throughout the rest of the universe's history enjoying their lives, or perhaps the diminished human tragedy in our own century (because of lives saved) could lead to a more stable and better-educated world that better prepares for existential risk. But as I lay out below, I don't know why this would lead us to CC3.

A "set point/Control Theory" solution

This solution applies to the specific example but doesn't address the general problem.

Many dynamic systems have a way of restoring equilibria that are out of balance. In nature, overpopulation of a species in an ecosystem leads to famine, which leads to a decrease in population, and so overall, the long-run species population may not change.

For human overpopulation, if overpopulation becomes a serious problem, lower population growth now is likely to lead to fewer efforts to constrain population in the future. Conversely, higher population growth now is likely to lead to more efforts to constrain population in the future. Thus, by saving lives now (the short term), we might create a problem that is solved in the medium term, with no long-run consequences.

It may be that many processes tend towards equilibria. The key problem for a longtermist in valuing the long-term danger of an intervention may be its effect on existential risk in the next few hundred years, and medium-term consequences should be evaluated in that context.

A general Bayesian joint probability solution

Hillary Greaves gives this solution in her paper, I believe:

Just as orthodox subjective Bayesianism holds, here as elsewhere, rationality requires that an agent have well-defined credences. Thus, insofar as we are rational, each of us will simply settle, by whatever means, on her own credence function for the relevant possibilities. And once we have done that, subjective c-betterness is simply a matter of expected value with respect to whatever those credences happen to be. In this model, the subjective c-betterness facts may well vary from one agent to another (even in the absence of any differences in the evidence held by the agents in question), but there is nothing else distinctive of ‘cluelessness’ cases; in particular, (2) there is no obstacle to consequences guiding actions, and (3) there is no rational basis for decision discomfort.

To solve the malaria net problem, we can calculate the probability of things like:

Short-run fertility meaningfully impacts long-run fertility
Likely increase in fertility due to the malaria net intervention
Each million of population increase will increase existential risk by x.
Fewer deaths will yield some level of improved well-being and community resilience; the additional resilience and well-being improves long-run global education and decision-making around existential risk, lowering existential risk by x
...and so on

Then, we consider two scenarios:

Donate bednets
Do not donate bednets

For each scenario:

Calculate the joint probability of existential risk and other long-term consequences under each of these scenarios, given these propositions. We don't need a full model of existential risk; it's enough to start with an estimate of the relationship between existential risk and relevant variables like population increase, global education, etc.
Weight the estimated value of each action by the joint probability.
Select the action with the highest estimated value based on the joint probability.

What am I missing?

Greaves seems to anticipate this response, as above, and goes on to say:

The alternative line I will explore here begins from the suggestion that in the situations we are considering, instead of having some single and completely precise (real-valued) credence function, agents are rationally required to have imprecise credences: that is, to be in a credal state that is represented by a many-membered set of probability functions (call this set the agent’s ‘representor’).21 Intuitively, the idea here is that when the evidence fails conclusively to recommend any particular credence function above certain others, agents are rationally required to remain neutral between the credence functions in question: to include all such equally-recommended credence functions in their representor.

I am very confused by this turn of reasoning. I don't think I understand what she means by credence function, and imprecise credences. But I don't really understand the problem of imprecise credence, or why this is necessarily related to a 'many-membered set of probability functions'. For our malaria bednets question, we still have one probability function (you might think of that as aggregate well-being across the history of the universe, which will for our purposes can be reduced to existential risk or probability humanity becomes extinct within the next 500 years). We simply

Take the probability distributions of each thing we are uncertain about
Find the joint probability distribution for each of those things under each of our scenarios
Compare the joint probability distributions to find the action with the highest expected value

and we're done! I don't see how the problem of a whole set of probability functions is inevitable, or even how we anticipate it might be a problem here.

Can anyone shed light on this?

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MaximeCdSMar 1 202110

Hey!

I think Hilary Greaves does a great job at explaining what cluelessness in non-jargon terms in her most recent appearance on 80K podcast.

As far as I understand it, cluelessness arises because, as we don't have sufficient evidence, we're very unsure about what our credence should be, to the point they feel -or maybe just are- arbitrary. In this case, you could still just carry out the expected value calculation and opt to do the most choice worthy action as you suggest. However, it seems unsatisfying because the credence function you use is arbitrary. Indeed, given your level of evidence, you could very well have opted for another set of beliefs that would have lead you to act differently.

Thus, one might argue that in order to be rational in this type of predicament, you have to consider several probability functions that are consistent with the evidence you have. In other words, you are required to have "imprecise credences" because you cannot determine in a principled manner which probability function you should use.

As Hilary Greaves herself points out in the podcast I mentioned above, if you're not troubled by this, and you're by yourself, you can just compute the expected value, but issues can arise when you try to coordinate with other agents that have different arbitrary beliefs. This is why it might be important to take cluelessness seriously.

I hope this helps!

ben.smithMar 4 20211

Her choice to use multiple, independent probability functions itself seems arbitrary to me, although I've done more reading since posting the above and have started to understand why there is a predicament.

Instead of multiple independent probability functions, you could start with a set of probability distributions for each of the items you are uncertain about, and then calculate the joint probability distribution by combining all of those distributions. That'll give you a single probability density function on which you can base your decision.

If you start with a set of several probability functions, with each representing a set of beliefs, then calculating their joint probability would require sampling randomly from each function according to some distribution specifying how likely each of the functions are. It can be done, with the proviso that you must have a probability distribution specifying the relative likelihood of each of the functions in your set.

However, I do worry the same problem arises in this approach in a different form. If you really do have no information about the probability of some event, then in Bayesian terms, your prior probability distribution is one that is completely uninformative. You might need to use an improper prior, and in that case, they can be difficult to update on in some circumstances. I think these are a Bayesian, mathematical representation of what Greaves calls an "imprecise credence".

But I think the good news is that many times, your priors are not so imprecise that you can't assign some probability distribution, even if it is incredibly vague. So there may end up not being too many problems where we can't calculate expected long-term consequences for actions.

I do remain worrying, with Greaves, that GiveWell's approach of assessing direct impact for each of its potential causes is woefully insufficient. Instead, we need to calculate out the very long term impact of each cause, and because of the value of the long-term future, anything that affects the probability of existential risk, even by an infinitesimal amount, will dominate the expected value of our intervention.

And I worry that this sort of approach could end up being extremely counterintuitive. It might lead us to the conclusion that promoting fertility by any means necessary is positive, or equally likely, to the conclusion that controlling and reducing fertility by any means necessary is positive. These things could lead us to want to implement extremely coercive measures, like banning abortion or mandating abortion depending on what we want the population size to be. Individual autonomy seems to fade away because it just doesn't have comparable value. Individual autonomy could only be saved if we think it would lead to a safer and more stable society in the long run, and that's extremely unclear.

And I think I reach the same conclusion that I think Greaves has, that one of the most valuable things you can do right now is to estimate some of the various contingencies, in order to lower the uncertainty and imprecision on various probability estimates. That'll raise the expected value of your choice because it is much less likely to be the wrong one.

MaximeCdSMar 10 20219

Her choice to use multiple, independent probability functions itself seems arbitrary to me,...

I'm not sure what makes you think that. Prof. Greaves does state that rational agents may be required "to include all such equally-recommended credence functions in their representor". This feels a lot less arbitrary that deciding to pick a single prior among all those available and decide to compute the expected value of your actions based on it.

Instead of multiple independent probability functions, you could start with a set of probability distributions for each of the items you are uncertain about, and then calculate the joint probability distribution by combining all of those distributions. That'll give you a single probability density function on which you can base your decision.

I agree that you could do that, but it seems even more arbitrary! If you think that choosing a set of probability functions was arbitrary, then having a meta-probability distribution over your probability distributions seems even more arbitrary, unless I'm missing something. It doesn't seem to me like the kind of situations where going meta helps: intuitively, if someone is very unsure about what prior to use in the first place, they should also probably be unsure about coming up with a second-order probability distribution over their set of priors .

You might need to use an improper prior, and in that case, they can be difficult to update on in some circumstances. I think these are a Bayesian, mathematical representation of what Greaves calls an "imprecise credence".

I do not think that's what Prof. Greaves mean when she says "imprecise credence". This article for the Stanford Encyclopedia of Philosophy explains the meaning of that phrase for philosophers. It also explains what a representor is in a better way that I did.

But I think the good news is that many times, your priors are not so imprecise that you can't assign some probability distribution, even if it is incredibly vague. So there may end up not being too many problems where we can't calculate expected long-term consequences for actions.

I think Prof. Greaves and Philip Trammel would disagree with that, which is why they're talking about cluelessness. For instance, Phil writes:

Perhaps there is some sense in which my credences should be sharp (see e.g. Elga (2010)), but the inescapable fact is that they are not. There are obviously some objects that do not have expected values for the act of giving to Malaria Consortium. The mug on my desk right now is one of them. Upon immediately encountering the above problem, my brain is like the mug: just another object that does not have an expected value for the act of giving to Malaria Consortium. Nor is there any reason to think that an expected value must “really be there”, deep down, lurking in my subconscious. Lots of theorists, going back at least to Knight’s (1921) famous distinction between “risk” and “uncertainty”, have recognized this.

Hope this helps.

ben.smithMar 12 20211

> Hope this helps.

It does, thanks--at least, we're clarifying where the disagreements are.

If you think that choosing a set of probability functions was arbitrary, then having a meta-probability distribution over your probability distributions seems even more arbitrary, unless I'm missing something. It doesn't seem to me like the kind of situations where going meta helps: intuitively, if someone is very unsure about what prior to use in the first place, they should also probably be unsure about coming up with a second-order probability distribution over their set of priors .

All you need to do to come up with that meta-probability distribution is to have some information about the relative value of each item in your set of probability functions. If our conclusion for a particular dilemma turns on a disagreement between virtue ethics, utilitarian ethics, and deontological ethics, this is a difficult problem that people will disagree strongly on. But can you even agree that these each bound, say, to be between 1% and 99% likely to be the correct moral theory? If so, you have a slightly informative prior and there is a possibility you can make progress. If we really have completely no idea, then I agree, the situation really is entirely clueless. But I think with extended consideration, many reasonable people might be able to come to an agreement.

Upon immediately encountering the above problem, my brain is like the mug: just another object that does not have an expected value for the act of giving to Malaria Consortium. Nor is there any reason to think that an expected value must “really be there”, deep down, lurking in my subconscious.

I agree with this. If the question is, "can anyone, at any moment in time, give a sensible probability distribution for any question", then I agree the answer is "no".

But with some time, I think you can assign a sensible probability distribution to many difficult-to-estimate things that are not completely arbitrary nor completely uninformative. So, specifically, while I can't tell you right now about the expected long-run value for giving to Malaria Consortium, I think I might be able to spend a year or so understanding the relationship between giving to Malaria Consortium and long-run aggregate sentient happiness, and that might help me to come up with a reasonable estimate of the distribution of values.

We'd still be left with a case where, very counterintuitively, the actual act of saving lives is mostly only incidental to the real value of giving to Malaria Consortium, but it seems to me we can probably find a value estimate.

About this, Greaves (2016) says,

averting child deaths has longer-run effects on population size: both because the children in question will (statistically) themselves go on to have children, and because a reduction in the child mortality rate has systematic, although difficult to estimate, effects on the near-future fertility rate. Assuming for the sake of argument that the net effect of averting child deaths is to increase population size, the arguments concerning whether this is a positive, neutral or a negative thing are complex.

And I wholeheartedly agree, but it doesn't follow from the fact you can't immediately form an opinion about it that you can't, with much research, make an informed estimate that has better than an entirely indeterminate or undefined value.

EDIT: I haven't heard Greaves' most recent podcast on the topic, so I'll check that out and see if I can make any progress there.

EDIT 2: I read the transcript to the podcast that you suggested, and I don't think it really changes my confidence that estimating a Bayesian joint probability distribution could get you past cluelessness.

So you can easily imagine that getting just a little bit of extra information would massively change your credences. And there, it might be that here’s why we feel so uncomfortable with making what feels like a high-stakes decision on the basis of really non-robust credences, is because what we really want to do is some third thing that wasn’t given to us on the menu of options. We want to do more thinking or more research first, and then decide the first-order question afterwards.
Hilary Greaves: So that’s a line of thought that was investigated by Amanda Askell in a piece that she wrote on cluelessness. I think that’s a pretty plausible hypothesis too. I do feel like it doesn’t really… It’s not really going to make the problem go away because it feels like for some of the subject matters we’re talking about, even given all the evidence gathering I could do in my lifetime, it’s patently obvious that the situation is not going to be resolved.

My reaction to that (beyond I should read Askell's piece) is that I disagree with Greaves that a lifetime of research could resolve the subject matter for something like giving to Malaria Consortium. I think it's quite possible one could make enough progress to arrive at an informative probability distribution. And perhaps it only says "across the probability distribution, there's a 52% likelihood that giving to x charity is good and a 48% probability that it's bad", but actually, if the expected value is pretty high, it's still strong impetus to give to x charity.

I still reach the problem where we've arrived at a framework where our choices for short-term interventions are probably going to be dominated by their long-run effects, and that's extremely counterintuitive, but at least I have some indication.

Milan GriffesMar 12 20213

I remain partial to the path forward I proposed here: Doing good while clueless

ben.smithMar 13 20211

Thanks! That was helpful, and my initial gut reaction is I entirely agree :-)

Have you had an opportunity to see how Hillary Greaves might react to this line of thinking? If I had to hazard a guess I imagine she'd be fairly sympathetic to the view you expressed.

kirchner.janMar 12 20213

Interesting! Thank you for writing this, this is something I was also wondering about while reading for the Warwick EA fellowship. My intuition is also that in the case of a "many-membered set of probability functions", I'd define a prior over those and then compute an expected value as if nothing happened. I acknowledge that there is substantial (or even overwhelming) uncertainty sometimes and I can understand the impulse of wanting a separate conceptual handle for that. But it's still "decision making under uncertainty" and should therefore be subsumable under Bayesianism.

I feel similar to ben.smith that I might be completely missing something. But I also wonder if this confusion might just be an echo of the age-old Bayesianism vs Frequentism debate, where people have different intuition about whether priors over probability distributions are a-ok.

ben.smithMar 12 202113

There is an argument from intuition that carry some force by Schoenfield (2012) that we can't use a probability function:

(1) It is permissible to be insensitive to mild evidential sweetening.
(2) If we are insensitive to mild evidential sweetening, our attitudes cannot be represented by a probability function.
(3) It is permissible to have attitudes that are not representable by a probability function. (1, 2)
...
You are a confused detective trying to figure out whether Smith or Jones committed the crime. You have an enormous body of evidence that to evaluate. Here is some of it: You know that 68 out of the 103 eyewitnesses claim that Smith did it but Jones' footprints were found at the crime scene. Smith has an alibi, and Jones doesn't. But Jones has a clear record while Smith has committed crimes in the past. The gun that killed the victim belonged to Smith. But the lie detector, which is accurate 71% percent of time, suggests that Jones did it. After you have gotten all of this evidence, you have no idea who committed the crime. You are no more confident that Jones committed the crime than that Smith committed the crime, nor are you more confident that Smith committed the crime than that Jones committed the
crime.
...
Now imagine that, after considering all of this evidence, you learn a new fact: it turns out that there were actually 69 eyewitnesses (rather than 68) testifying that Smith did it. Does this make it the case that you should now be more confident in S than J? That, if you had to choose right now who to send to jail, it should be Smith? I think not.
...
In our case, you are insensitive to evidential sweetening with respect to S since you are no more confident in S than ~S (i.e. J), and no more confident in ~S (i.e. J) than S. The extra eyewitness supports S more than it supports ~S, and yet despite learning about the extra eyewitness, you are no more confident in S than you are in ~S (i.e. J).

Intuitively, this sounds right. And if you went from this problem trying to understand solve the crime on intuition, you might really have no idea. Reading the passage, it sounds mind-boggling.

On the other hand, if you applied some reasoning and study, you might be able to come up with some probability estimates. You could identify the conditioning of P(Smith did it|an eyewitness says Smith did it), including a probability distribution on that probability itself, if you like. You can identify how to combine evidence from multiple witnesses, i.e., P(Smith did it|eyewitness 1 says Smith did it) & P(Smith did it|eyewitness 2 says Smith did it), and so on up to 68 and 69. You can estimate the independence of eyewitnesses, and from that work out how to properly combine evidence from multiple eyewitnesses.

And it might turn out that you don't update as a result of the extra eyewitness, under some circumstances. Perhaps you know the eyewitnesses aren't independent; they're all card-carrying members of the "We hate Smith" club. In that case it simply turns out that the extra eye-witness is irrelevant to the problem; it doesn't qualify as evidence, so it it doesn't mean you're insensitive to "mild evidential sweetening".

I think a lot of the problem here is that these authors are discussing what one could do when one sits down for the first time and tries to grapple with a problem. In those cases there's so many undefined features of the problem that it really does seem impossible and you really are clueless.

But that's not the same as saying that, with sufficient time, you can't put probability distributions to everything that's relevant and try to work out the joint probability.

----

Schoenfield, M. Chilling out on epistemic rationality. Philos Stud 158, 197–219 (2012).

MaxRaMar 13 20212

While browsing types of uncertainties, I stumbled upon the idea of state space uncertainty and conscious unawareness, which sounds similar to your explanation of cluelessness and which might be another helpful angle for people with a more Bayesian perspective.

There are, in the real world, unforeseen contingencies: eventualities that even the educated decision maker will fail to foresee. For instance, the recent tsunami and subsequent nuclear meltdown in Japan are events that most agents would have omitted from their decision models. If a decision maker is aware of the possibility that they may not be aware of all relevant contingencies—a state that Walker and Dietz (2011) call ‘conscious unawareness’ —then they face state space uncertainty.

https://link.springer.com/article/10.1007/s10670-013-9518-4

ben.smithMar 14 20214

A good point.

There are things you can do to correct for this sort of thing-for instance, go one level more meta, estimate the probability of unforeseen consequences in general, or within the class of problems that your specific problem fits into.

We couldn't have predicted the fukushima disaster, but perhaps we can predict related things with some degree of certainty - the average cost and death toll of earthquakes worldwide, for instance. In fact, this is a fairly well explored space, since insurers have to understand the risk of earthquakes.

The ongoing pandemic is a harder example - the rarer the black swan, the more difficult it is to predict. But even then, prior to the 2020 pandemic, the WHO had estimated the amortized costs of pandemics as in the order of 1% of global GDP annually (averaged over years when there are and aren't pandemics), which seems like a reasonable approximation.

I don't know how much of a realistic solution that would be in practice.

MichaelStJulesMar 13 20212

This is a great example, thanks for sharing!

MichaelStJulesMar 13 20217

I think the example Ben cites in his reply is very illustrative.

You might feel that you can't justify your one specific choice of prior over another prior, so that particular choice is arbitrary, and then what you should do could depend on this arbitrary choice, whereas an equally reasonable prior would recommend a different decision. Someone else could have exactly the same information as you, but due to a different psychology, or just different patterns of neurons firing, come up with a different prior that ends up recommending a different decision. Choosing one prior over another without reason seems like a whim or a bias, and potentially especially prone to systematic error.

It seems bad if we're basing how to do the most good on whims and biases.

If you're lucky enough to have only finitely many equally reasonable priors, then I think it does make sense to just use a uniform meta-prior over them, i.e. just take their average. This doesn't seem to work with infinitely many priors, since you could use different parametrizations to represent the same continuous family of distributions, with a different uniform distribution and therefore average for each parametrization. You'd have to justify your choice of parametrization!

As another example, imagine you have a coin that someone (who is trustworthy) has told you is biased towards heads, but they haven't given you any hint how much, and you want to come up with a probability distribution for the fraction of heads over 1,000,000 flips. So, you want a distribution over the interval [0, 1]. Which distribution would you use? Say you give me a probability density function . Why not $(1 - p) f (x) + p$ for some $p \in (0, 1)$ ? Why not $\frac{1}{\int_{0}^{1} f (x^{p}) d x} f (x^{p})$ for some $p > 0$ ? If $f$ is a weighted average of multiple distributions, why not apply one of these transformations to one of the component distributions and choose the resulting weighted average instead? Why the particular weights you've chosen and not slightly different ones?

ben.smithMar 14 20213

Which distribution would you use? Why the particular weights you've chosen and not slightly different ones?

come up with a probability distribution for the fraction of heads over 1,000,000 flips.