TL;DR I don’t think this post provides an argument that we should interpret pleasure/pain scales as logarithmic. What’s more, whether or not this is true is not necessary for post’s practical claim - which is roughly that “the best/worst things are much better/worse than most people think”.
Thanks for writing this up; sorry not to have got around to it sooner.
I think there are two claims that need be to carefully distinguished.
(A) that the relationship between actual and reported pleasure(/pain) is not linear but instead follows some other relationship, e.g. a logarithmic function where a 1-unit increase in self-reported pleasure represents a ten-fold increase in actual pleasure.
(B) whether the best/worst experiences that some people have are many times more intense than other people (who haven’t had those experiences) assume they are.
I point this out because you say
the best way to interpret pleasure and pain scales is by thinking of them as logarithmic compressions of what is truly a long-tail. The most intense pains are orders of magnitude more awful than mild pains (and symmetrically for pleasure). [...]
Since the bulk of suffering is concentrated in a small percentage of experiences, focusing our efforts on preventing cases of intense suffering likely dominates most utilitarian calculations.
The idea, I take it, is that if we thought the relationship between self-reported and actual pleasure(/pain) was linear, but it turns out it was logarithmic, then the best(/worse) experiences are much better(/worse) that we expected they were because we’d be using the wrong scale.
However, I don’t think you’ve provided (any?) evidence that (A) is true (or that it’s true but we thought it was false). What’s more, (B) is actually quite plausible by itself and you can claim (B) is true without needing (A) to be true.
Let me unpack this a bit.
(A) is a claim about how people choose to use self-reported scales. The idea is that people have experiences of a certain intensity they can distinguish for themselves in cardinal units, e.g. you can tell (roughly) how many perceivable increments of pleasure one experience gives you vs the next. A further question is how people choose to report these intensities when people give them a scale, say a 0-10 scale.
This reporting could be linear, logarithmic, etc. Indeed, people could choose to report anyway they want to. It seems most likely people use a linear reporting function because that’s the helpful way to use language to convey how you feel to the person asking you how you feel. I won’t get stuck into this here, but I say more about it in my PhD thesis at chapter 4, section 4.
Hence, on your pleasure/pain scales when you contrast ‘intuitive’ to ‘long-tailed’ scales, what I think you mean is that the intuitive scale is really ‘reported’ pleasure and the ‘long-tailed’ scale is ‘actual’ pleasure i.e. your claim is that there is a logarithmic relationship between reported and actual pleasure. I note you don’t provide evidence that people generally use scales this way. Regarding the stings scale, that just is a logarithmic scale by construction, where going from a 1 to 2 on the scale represent a 10 times increase in actual pain. That doesn’t show we have to report pleasure using log scales, or that we do, just that the guy who constructed that scale chose to build it that way. In fact, we can only use log pleasure/pain scales if we can somehow measure pain/pleasure on an arithmetic scale in the first place, and then convert from those numbers to a log scale, which requires that people are able to construct arithmetic pleasure/pain scales anyway.
(You might wonder if people can know, on an arithmetic scale, how much pleasure/pain they feel. However, if people really have no idea about this, then it follows they can’t intelligibly report their pleasure/pain at all, whatever scale they are using.)
Regarding (B), note that claims such as “the worst stings are 1000x worse than the average person expects they are” can be true without it needing to be the case that people have misunderstood how other people tend to use pleasure/pain scale. For instance, I could alternatively claim that the relationship between reported pleasure/pain and actual pain is linear, but that people’s predictions are just misinformed—e.g. torture is actually more worse than they thought. For comparison, if I claim “the heaviest building in the world weighs 1000x more than most people think it weighs” I don’t need to say anything about the relationship between reports of perceived weight and actual weight.
Hence, if you want to claim “experiences X and Y are much better/worse than we thought”, just claim that without getting into distracting stuff about reported vs actual scale use!
(P.S. The Fechner-Weber stuff is a red-herring: that’s about the relationship between increases in an objective quantity and in subjective perceptions of increases in that quantity. That’s different from talking about the relationship between a reported subjective quantity and the actually experienced subjective quantity. Plausibly the former relationship is logarithmic, but one shouldn’t directly infer from that that the latter relationship is logarithmic too).
Thank for commenting. First of all I agree that the claims of (A) and (B) do need to be distinguished, and I admit I didn’t make that conceptual distinction very clear in the article. I agree that the most important takeaway from the piece is (B), and I also think that this alone is already enough to challenge EA’s prioritization methods (i.e. ultra-painful experiences are completely flying under the radar from the point of view of QALYs and similar metrics; reducing the incidence of cluster headaches, migraines, kidney stones, etc. could be an extremely cost-effective EA objective).
With that said, I would claim that (1) the article does actually provide evidence for (A), (2) taking this seriously clarifies a lot of puzzling facts about experience and how it is reported, and (3) understanding that pain and pleasure follows a long-tail (most likely a log-normal distribution) gives us a new principled way to approach cause prioritization.
I understand the fact that the pain scales of stings and cluster headaches are *by construction* logarithmic. But you have to understand that such a scale would only ever be “filled to the top” if experiences actually differed in intensity also by the same amount. The article (and presentation, which I strongly recommend you watch) explain that all of the following are consistent with the pain scales (as reported!) are actually logarithmic:
(a) the characteristic distribution of neural activity is log-normal, and under the modest assumption that intensity of experience is roughly proportional (or at least polynomially proportional) to intensity of experience, that entails the distribution of intensity is also log-normal.
(b) the above can be further understood as a kind of “neuronal weather” (see the “avalanches” metaphor in the video presentation)
(c) the predictions of the log-normal world are held by the data, and in particular:
(c1) there are few categories of experiences that capture most of the extremely good and extremely bad sensations
(c2) there is consistency in the deference judgements of the quality of experience (as seen in the deference graph), and importantly
(c3) The ratio of “1st worst or best experience vs. 2nd worst or best experience” fits a log-normal distribution and it does not fit a normal distribution.
For the above reasons, bringing up the Fechner-Weber is not, I would claim, a red-herring. Rather, I think it ties together the whole argument. Here is why:
I understand that Fechner-Weber’s law maps physical intensity to subjective intensity, and that valence is not externally driven a lot of the time. But you may have missed the argument I’m making here. And that is that in one interpretation of the law, a pre-conscious process does a log transform on the intensity of the input and that by the time we are aware of it, what we become aware of are the linear differences in our experience. In the alternate interpretation of the law, which I propose, the senses (within the window of adaptation) translate the intensity of the input into an equivalent intensity of experience. And the reason *why* we can only detect multiplicative differences in the input *is because* we can only notice consciously multiplicative differences in the intensity of experience. Do you see what I am saying? In this account, the fact that people would naturally and spontaneously use a logarithmic scale to report their level of pain is a simple implication of the fact that you can only definitively tell that “the pain got worse” when it got 10% worse and not when it became 1 unit worse (which soon becomes hard to notice when you talk about experiences with e.g. 1000 pain units per second).
In other words, the scales are logarithmic because we can only notice with confidence multiplicative increments in the intensity of experience. And while this is fine and does not seem to have strong implications on the lower end of the scale, it very quickly escalates, to the point where by the time you are in 7⁄10 pain you live in a world with orders of magnitude more pain units per second than you did when you were in 2⁄10 pain.
Finally, you really need the logarithmic scales to make room for the ultra-intense levels of pleasure and pain that I highlighted in the “existence of extremes” section. If people reported their pain on a linear scale, they would quickly run into the problem that they cannot describe even something as painful as a broken bone, let along something like a cluster headache.
TL;DR I don’t think this post provides an argument that we should interpret pleasure/pain scales as logarithmic. What’s more, whether or not this is true is not necessary for post’s practical claim - which is roughly that “the best/worst things are much better/worse than most people think”.
Thanks for writing this up; sorry not to have got around to it sooner.
I think there are two claims that need be to carefully distinguished.
(A) that the relationship between actual and reported pleasure(/pain) is not linear but instead follows some other relationship, e.g. a logarithmic function where a 1-unit increase in self-reported pleasure represents a ten-fold increase in actual pleasure.
(B) whether the best/worst experiences that some people have are many times more intense than other people (who haven’t had those experiences) assume they are.
I point this out because you say
The idea, I take it, is that if we thought the relationship between self-reported and actual pleasure(/pain) was linear, but it turns out it was logarithmic, then the best(/worse) experiences are much better(/worse) that we expected they were because we’d be using the wrong scale.
However, I don’t think you’ve provided (any?) evidence that (A) is true (or that it’s true but we thought it was false). What’s more, (B) is actually quite plausible by itself and you can claim (B) is true without needing (A) to be true.
Let me unpack this a bit.
(A) is a claim about how people choose to use self-reported scales. The idea is that people have experiences of a certain intensity they can distinguish for themselves in cardinal units, e.g. you can tell (roughly) how many perceivable increments of pleasure one experience gives you vs the next. A further question is how people choose to report these intensities when people give them a scale, say a 0-10 scale.
This reporting could be linear, logarithmic, etc. Indeed, people could choose to report anyway they want to. It seems most likely people use a linear reporting function because that’s the helpful way to use language to convey how you feel to the person asking you how you feel. I won’t get stuck into this here, but I say more about it in my PhD thesis at chapter 4, section 4.
Hence, on your pleasure/pain scales when you contrast ‘intuitive’ to ‘long-tailed’ scales, what I think you mean is that the intuitive scale is really ‘reported’ pleasure and the ‘long-tailed’ scale is ‘actual’ pleasure i.e. your claim is that there is a logarithmic relationship between reported and actual pleasure. I note you don’t provide evidence that people generally use scales this way. Regarding the stings scale, that just is a logarithmic scale by construction, where going from a 1 to 2 on the scale represent a 10 times increase in actual pain. That doesn’t show we have to report pleasure using log scales, or that we do, just that the guy who constructed that scale chose to build it that way. In fact, we can only use log pleasure/pain scales if we can somehow measure pain/pleasure on an arithmetic scale in the first place, and then convert from those numbers to a log scale, which requires that people are able to construct arithmetic pleasure/pain scales anyway.
(You might wonder if people can know, on an arithmetic scale, how much pleasure/pain they feel. However, if people really have no idea about this, then it follows they can’t intelligibly report their pleasure/pain at all, whatever scale they are using.)
Regarding (B), note that claims such as “the worst stings are 1000x worse than the average person expects they are” can be true without it needing to be the case that people have misunderstood how other people tend to use pleasure/pain scale. For instance, I could alternatively claim that the relationship between reported pleasure/pain and actual pain is linear, but that people’s predictions are just misinformed—e.g. torture is actually more worse than they thought. For comparison, if I claim “the heaviest building in the world weighs 1000x more than most people think it weighs” I don’t need to say anything about the relationship between reports of perceived weight and actual weight.
Hence, if you want to claim “experiences X and Y are much better/worse than we thought”, just claim that without getting into distracting stuff about reported vs actual scale use!
(P.S. The Fechner-Weber stuff is a red-herring: that’s about the relationship between increases in an objective quantity and in subjective perceptions of increases in that quantity. That’s different from talking about the relationship between a reported subjective quantity and the actually experienced subjective quantity. Plausibly the former relationship is logarithmic, but one shouldn’t directly infer from that that the latter relationship is logarithmic too).
Hey Michael,
Thank for commenting. First of all I agree that the claims of (A) and (B) do need to be distinguished, and I admit I didn’t make that conceptual distinction very clear in the article. I agree that the most important takeaway from the piece is (B), and I also think that this alone is already enough to challenge EA’s prioritization methods (i.e. ultra-painful experiences are completely flying under the radar from the point of view of QALYs and similar metrics; reducing the incidence of cluster headaches, migraines, kidney stones, etc. could be an extremely cost-effective EA objective).
With that said, I would claim that (1) the article does actually provide evidence for (A), (2) taking this seriously clarifies a lot of puzzling facts about experience and how it is reported, and (3) understanding that pain and pleasure follows a long-tail (most likely a log-normal distribution) gives us a new principled way to approach cause prioritization.
I understand the fact that the pain scales of stings and cluster headaches are *by construction* logarithmic. But you have to understand that such a scale would only ever be “filled to the top” if experiences actually differed in intensity also by the same amount. The article (and presentation, which I strongly recommend you watch) explain that all of the following are consistent with the pain scales (as reported!) are actually logarithmic:
(a) the characteristic distribution of neural activity is log-normal, and under the modest assumption that intensity of experience is roughly proportional (or at least polynomially proportional) to intensity of experience, that entails the distribution of intensity is also log-normal.
(b) the above can be further understood as a kind of “neuronal weather” (see the “avalanches” metaphor in the video presentation)
(c) the predictions of the log-normal world are held by the data, and in particular:
(c1) there are few categories of experiences that capture most of the extremely good and extremely bad sensations
(c2) there is consistency in the deference judgements of the quality of experience (as seen in the deference graph), and importantly
(c3) The ratio of “1st worst or best experience vs. 2nd worst or best experience” fits a log-normal distribution and it does not fit a normal distribution.
For the above reasons, bringing up the Fechner-Weber is not, I would claim, a red-herring. Rather, I think it ties together the whole argument. Here is why:
I understand that Fechner-Weber’s law maps physical intensity to subjective intensity, and that valence is not externally driven a lot of the time. But you may have missed the argument I’m making here. And that is that in one interpretation of the law, a pre-conscious process does a log transform on the intensity of the input and that by the time we are aware of it, what we become aware of are the linear differences in our experience. In the alternate interpretation of the law, which I propose, the senses (within the window of adaptation) translate the intensity of the input into an equivalent intensity of experience. And the reason *why* we can only detect multiplicative differences in the input *is because* we can only notice consciously multiplicative differences in the intensity of experience. Do you see what I am saying? In this account, the fact that people would naturally and spontaneously use a logarithmic scale to report their level of pain is a simple implication of the fact that you can only definitively tell that “the pain got worse” when it got 10% worse and not when it became 1 unit worse (which soon becomes hard to notice when you talk about experiences with e.g. 1000 pain units per second).
In other words, the scales are logarithmic because we can only notice with confidence multiplicative increments in the intensity of experience. And while this is fine and does not seem to have strong implications on the lower end of the scale, it very quickly escalates, to the point where by the time you are in 7⁄10 pain you live in a world with orders of magnitude more pain units per second than you did when you were in 2⁄10 pain.
Finally, you really need the logarithmic scales to make room for the ultra-intense levels of pleasure and pain that I highlighted in the “existence of extremes” section. If people reported their pain on a linear scale, they would quickly run into the problem that they cannot describe even something as painful as a broken bone, let along something like a cluster headache.