The article does focus on the long-tail of intensity and quality of both pleasure and pain rather than frequency. That said, it discusses the Lognormal World as a general principle, which would also predict that the frequency of pain or pleasure would follow a long-tail in addition to their intensity and quality.
This is backed up by the previous article “Cluster Headache Frequency Follows a Long-Tail Distribution”, where we analyzed a survey about Cluster Headache frequency among sufferers, and showed it followed a long-tail (with statistics like “The bottom 80% accounts for 17% of incidents and the bottom 90% accounts for 30% of incidents”, and values ranging from 1 Cluster Headache a year all the way to more than 1,000). We should collect data on e.g. kidney stone, migraine, etc. frequency per individual to see if they also follow a long-tail. Given the general pattern, we suspect they probably do.
Thanks. I was actually asking about a different frequency distribution. You’re talking about the frequency of extreme pain among people with extreme pain which has no bearing on the quote above. I’m talking about the frequency of extreme pain experiences among all pain experiences (i. e. is extreme pain it lmuch less prevalent). Hence the example about mild discomfort.
The short answer is—extreme pain is vastly more common than is generally believed. Statistics such as 20% of people in the USA experience chronic pain, with 8% experiencing high-impact chronic pain (interferes with most aspects of life). If indeed we live in Lognormal World, we can expect that the median person will probably have relatively low acquaintance with extreme suffering (until old age), but that the people in the top 10% of sufferers will have 10X the amount, and people in the 99% will have 100X the amount. If we take a person-neutral point of view (i.e. Empty or Open Individualism) and care about “moments of experience” it does not really matter who gets to experience it, at least not morally. There are no diminishing returns per person when it comes to the negative value of suffering (once adaptation has been taken into account).
As with other long-tails, it may seem hard to believe that ”...the bulk of suffering is concentrated in a small percentage of experiences...”. But so it is hard to imagine that there are billionaires out there if all one knows about is the income of one’s family and small circle of friends. Millionaires are rare, but not that rare (about 3% of the population), and we have that in the case of income the bulk of capital is concentrated in a small percent of people (e.g. ~20% of the population controlling ~80% of the wealth, and the top 1% controlling ~45% of it).
Likewise, the research presented here would suggest that in the case of suffering there are “suffering billionaires” out there, and that they account for a much larger % of total suffering than we intuitively would imagine.
Related; I think people do directly make choices that hint at this. Examples would include spending large numbers of resources on drugs and sex on the positive side, and (I’d expect) large numbers of resources to avoid torture / short-duration-but-painful situations.
Listening to the Feeling Good podcast, one common thing is that many people in America have deep fears of becoming homeless, and work very hard to avoid that specific outcome. Much of this is irrational, but some quite justified.
To the second half of your comment, I agree that extreme suffering can be very extreme and I think this is an important contribution. Maybe we have a misunderstanding about what ‘the bulk’ of suffering refers to. To me it means something like 75-99% and to you it means something like 45% as stated above? I should also clarify that by frequency I mean the product of ‘how many people have it’, ‘how often’ and ‘for how long’.
“the people in the top 10% of sufferers will have 10X the amount, and people in the 99% [I assume you mean top 1%?] will have 100X the amount”
I’m confused, you seem to be suggesting that every level of pain accounts for the _same_ amount of total suffering here.
To elaborate, you seem to be saying that at any level of pain, 10x worse pain is also 10x less frequent. That’s a power law with exponent 1. I.e. the levels of pain have an extreme distribution, but the frequencies do too (mild pains are extremely common). I’m not saying you’re wrong—just that I’ve seen also seems consistent with extreme pain being less than 10% of the total. I’m excited to see more data :)
Hi! Thank you for elaborating on what your question is :)
“Bulk” is indeed a very ambiguous term. Would you say 80% is “the bulk”? And 20% is “a small percentage”? If so we would be in agreement. If not, it is more of a wording issue than a matter of substance, I think.
Good catch that the numbers I provided would suggest a power law that just keeps going (e.g. similar to St. Petersburg paradox?). If we use the Cluster Headache dataset, the numbers are:
50% percentile experiences 70 CH/year
80% percentile experiences 365 CH/year
90% percentile experiences 730 CH/year
98% percentile experiences 2190 CH/year
So at least in this case the 90th percentile does get 10X the amount of the 50th percentile. But the 98th and 99th percentile is not as high as 100X, and more like 20 to 50x. So not quite the numbers I used as an example, but also not too far off.
I should also clarify that by frequency I mean the product of ‘how many people have it’, ‘how often’ and ‘for how long’.
Here is the main idea: In Lognormal World, you would see a lognormal distribution for “amount of suffering per person”, “peak suffering per person”, “how long suffering above a certain threshold lasts for each person”, etc.
To illustrate this point, let’s say that each person’s hedonic tone per each second of their life is distributed along a lognormal with an exponent that is a Gaussian with mean x and sd of y. We would then also have that x, across different people, is distributed along a Gaussian with a mean of z and sd of t. Now, if you want to get the global distribution of suffering per second across people, you would need to convolve two Gaussians on the logarithmic pain scale (which represent the exponents of the lognormal distributions). Since convolving two Gaussians gives you another Gaussian, we would then have that the global distribution of suffering per second is also a lognormal distribution! So both at the individual, and the global scale the lognormal long-tails will be present. Now, for you to appreciate the “bulk” of the suffering, you would need to look at the individuals who have the largest means for the normal distribution in the exponent (x in this case). Hence why looking at one’s own individual % of time in extreme pain does not provide a good idea of how much of it there is in the wild across people (especially if one is close to the median; i.e. a pretty happy person).
Your 4 cluster headache groups contribute about equally to the total number of cluster headaches if you multiply group size by # of CH’s. (The top 2% actually contribute a bit less). That’s my entire point. I’m not sure if you disagree?
I would disagree for the following reason. For a group to contribute equally it needs to have both its average and its size be such that when you multiply them you get the same value. While it is true that people at the 50% percentile get 1⁄10 of the people at the 90% (and ~1/50 of the 99%), these do not define groups. What we need to look at instead is the cumulative distribution function:
The bottom 50% accounts for 3.17% of incidents
The bottom 90% accounts for 30% of incidents
The bottom 95% accounts for 43% of incidents
What I am getting at is that for a given percentile, the contribution from the group “this percentile and lower” will be a lot smaller than the value at that percentile multiplied by the fraction of the participants below that level. This is because the distribution is very skewed, so for any given percentile the values below it quickly decrease.
Another way of looking at this is by assuming that each percentile has a corresponding value (in the example “number of CHs per year”) proportional to the rarity of that percentile or above. For simplicity, let’s say we have a step function where each time we divide the group by half we get twice the value for those right above the cut-off:
0 to 50% have 1/year
50 to 75% have 2/year
75 to 87.5% have 4/year
and so on...
Here each group contributes equally (size * # of CH is the same for each group). Counter-intuitively, this does not imply that extremes account for a small amount. On the contrary, it implies that the average is infinite (cf. St. Petersburg paradox): even though you will have that for any given percentile, the average below it is always finite (e.g. between 0 and 40% it’s 1/year), the average (and total contribution) above that percentile is always infinite. In this idealized case, it will always be the case that “the bulk is concentrated on a tiny percentile” (and indeed you can make that percentile as small as you want and still get infinitely more above it than below it).
The empirical distribution is not so skewed that we need to worry about infinity. But we do need to worry about the 57% accounted for by the top 5%.
That fair, I made a mathematical error there. The cluster headache math convinces me that a large chunk of total suffering goes to few people there due to lopsided frequencies. Do you have other examples? I particularly felt that the relative frequency of extreme compared to less extreme pain wasn’t well supported.
Thank you!
The article does focus on the long-tail of intensity and quality of both pleasure and pain rather than frequency. That said, it discusses the Lognormal World as a general principle, which would also predict that the frequency of pain or pleasure would follow a long-tail in addition to their intensity and quality.
This is backed up by the previous article “Cluster Headache Frequency Follows a Long-Tail Distribution”, where we analyzed a survey about Cluster Headache frequency among sufferers, and showed it followed a long-tail (with statistics like “The bottom 80% accounts for 17% of incidents and the bottom 90% accounts for 30% of incidents”, and values ranging from 1 Cluster Headache a year all the way to more than 1,000). We should collect data on e.g. kidney stone, migraine, etc. frequency per individual to see if they also follow a long-tail. Given the general pattern, we suspect they probably do.
Thanks. I was actually asking about a different frequency distribution. You’re talking about the frequency of extreme pain among people with extreme pain which has no bearing on the quote above. I’m talking about the frequency of extreme pain experiences among all pain experiences (i. e. is extreme pain it lmuch less prevalent). Hence the example about mild discomfort.
The short answer is—extreme pain is vastly more common than is generally believed. Statistics such as 20% of people in the USA experience chronic pain, with 8% experiencing high-impact chronic pain (interferes with most aspects of life). If indeed we live in Lognormal World, we can expect that the median person will probably have relatively low acquaintance with extreme suffering (until old age), but that the people in the top 10% of sufferers will have 10X the amount, and people in the 99% will have 100X the amount. If we take a person-neutral point of view (i.e. Empty or Open Individualism) and care about “moments of experience” it does not really matter who gets to experience it, at least not morally. There are no diminishing returns per person when it comes to the negative value of suffering (once adaptation has been taken into account).
As with other long-tails, it may seem hard to believe that ”...the bulk of suffering is concentrated in a small percentage of experiences...”. But so it is hard to imagine that there are billionaires out there if all one knows about is the income of one’s family and small circle of friends. Millionaires are rare, but not that rare (about 3% of the population), and we have that in the case of income the bulk of capital is concentrated in a small percent of people (e.g. ~20% of the population controlling ~80% of the wealth, and the top 1% controlling ~45% of it).
Likewise, the research presented here would suggest that in the case of suffering there are “suffering billionaires” out there, and that they account for a much larger % of total suffering than we intuitively would imagine.
Related; I think people do directly make choices that hint at this. Examples would include spending large numbers of resources on drugs and sex on the positive side, and (I’d expect) large numbers of resources to avoid torture / short-duration-but-painful situations.
Listening to the Feeling Good podcast, one common thing is that many people in America have deep fears of becoming homeless, and work very hard to avoid that specific outcome. Much of this is irrational, but some quite justified.
To the second half of your comment, I agree that extreme suffering can be very extreme and I think this is an important contribution. Maybe we have a misunderstanding about what ‘the bulk’ of suffering refers to. To me it means something like 75-99% and to you it means something like 45% as stated above? I should also clarify that by frequency I mean the product of ‘how many people have it’, ‘how often’ and ‘for how long’.
“the people in the top 10% of sufferers will have 10X the amount, and people in the 99% [I assume you mean top 1%?] will have 100X the amount”
I’m confused, you seem to be suggesting that every level of pain accounts for the _same_ amount of total suffering here.
To elaborate, you seem to be saying that at any level of pain, 10x worse pain is also 10x less frequent. That’s a power law with exponent 1. I.e. the levels of pain have an extreme distribution, but the frequencies do too (mild pains are extremely common). I’m not saying you’re wrong—just that I’ve seen also seems consistent with extreme pain being less than 10% of the total. I’m excited to see more data :)
Hi! Thank you for elaborating on what your question is :)
“Bulk” is indeed a very ambiguous term. Would you say 80% is “the bulk”? And 20% is “a small percentage”? If so we would be in agreement. If not, it is more of a wording issue than a matter of substance, I think.
Good catch that the numbers I provided would suggest a power law that just keeps going (e.g. similar to St. Petersburg paradox?). If we use the Cluster Headache dataset, the numbers are:
50% percentile experiences 70 CH/year
80% percentile experiences 365 CH/year
90% percentile experiences 730 CH/year
98% percentile experiences 2190 CH/year
So at least in this case the 90th percentile does get 10X the amount of the 50th percentile. But the 98th and 99th percentile is not as high as 100X, and more like 20 to 50x. So not quite the numbers I used as an example, but also not too far off.
Here is the main idea: In Lognormal World, you would see a lognormal distribution for “amount of suffering per person”, “peak suffering per person”, “how long suffering above a certain threshold lasts for each person”, etc.
To illustrate this point, let’s say that each person’s hedonic tone per each second of their life is distributed along a lognormal with an exponent that is a Gaussian with mean x and sd of y. We would then also have that x, across different people, is distributed along a Gaussian with a mean of z and sd of t. Now, if you want to get the global distribution of suffering per second across people, you would need to convolve two Gaussians on the logarithmic pain scale (which represent the exponents of the lognormal distributions). Since convolving two Gaussians gives you another Gaussian, we would then have that the global distribution of suffering per second is also a lognormal distribution! So both at the individual, and the global scale the lognormal long-tails will be present. Now, for you to appreciate the “bulk” of the suffering, you would need to look at the individuals who have the largest means for the normal distribution in the exponent (x in this case). Hence why looking at one’s own individual % of time in extreme pain does not provide a good idea of how much of it there is in the wild across people (especially if one is close to the median; i.e. a pretty happy person).
Your 4 cluster headache groups contribute about equally to the total number of cluster headaches if you multiply group size by # of CH’s. (The top 2% actually contribute a bit less). That’s my entire point. I’m not sure if you disagree?
Hey Soeren!
I would disagree for the following reason. For a group to contribute equally it needs to have both its average and its size be such that when you multiply them you get the same value. While it is true that people at the 50% percentile get 1⁄10 of the people at the 90% (and ~1/50 of the 99%), these do not define groups. What we need to look at instead is the cumulative distribution function:
The bottom 50% accounts for 3.17% of incidents
The bottom 90% accounts for 30% of incidents
The bottom 95% accounts for 43% of incidents
What I am getting at is that for a given percentile, the contribution from the group “this percentile and lower” will be a lot smaller than the value at that percentile multiplied by the fraction of the participants below that level. This is because the distribution is very skewed, so for any given percentile the values below it quickly decrease.
Another way of looking at this is by assuming that each percentile has a corresponding value (in the example “number of CHs per year”) proportional to the rarity of that percentile or above. For simplicity, let’s say we have a step function where each time we divide the group by half we get twice the value for those right above the cut-off:
0 to 50% have 1/year
50 to 75% have 2/year
75 to 87.5% have 4/year
and so on...
Here each group contributes equally (size * # of CH is the same for each group). Counter-intuitively, this does not imply that extremes account for a small amount. On the contrary, it implies that the average is infinite (cf. St. Petersburg paradox): even though you will have that for any given percentile, the average below it is always finite (e.g. between 0 and 40% it’s 1/year), the average (and total contribution) above that percentile is always infinite. In this idealized case, it will always be the case that “the bulk is concentrated on a tiny percentile” (and indeed you can make that percentile as small as you want and still get infinitely more above it than below it).
The empirical distribution is not so skewed that we need to worry about infinity. But we do need to worry about the 57% accounted for by the top 5%.
That fair, I made a mathematical error there. The cluster headache math convinces me that a large chunk of total suffering goes to few people there due to lopsided frequencies. Do you have other examples? I particularly felt that the relative frequency of extreme compared to less extreme pain wasn’t well supported.