Agree that the adverse effects that I dedicate a large part of the post to do not speak to the question of whether impact actually follows a power-law distribution. They are just arguments against thinking about impact in that way.I think I acknowledge that repeatedly in the post, but can see now that the title makes it sound like I focus mainly on the “Empirical problem”.
“I think that after you sort through this kind of consideration you would be able to recover some version of the power law claim basically intact”—I wonder if our disagreement on that is traceable and resolvable, or whether it stems from some pretty fundamental intuitions which it’s hard to argue about sensibly?
ex ante vs. ex post: Interesting that you raise that! I’ve talked to a few people about the ideas in the essay, and I think something like your argument here was the most common response. I think I remain more persuaded by the claim that impact is not power law distributed at all, even ex post and not just because we don’t have the means to predict ex ante. But I agree that the case for a power law distribution is harder to defend ex ante (because of all the uncertainty) than ex post, and my confidence in doubting the claim is stronger for ex ante impact evaluations than it is for ex post evaluations.
True and good point that I basically ignored the benefits of power-law thinking. I’ll consider whether I think my thoughts on these benefits can fit somewhere in the essay, and will update it accordingly if I find an appropriate fit. Thanks for pointing this out!
Your conclusion sounds largely agreeable to me (though I imagine we would disagree when asked to specify how large the “tail-upsides” are that people should look for in a cautious manner).
I’m definitely a little surprised to hear that you don’t think that impact is power-law distributed at all, even ex post. I wonder if it’s worth trying to get numerical about this, rather than talk qualitatively about “whether impact is power-law distributed”. Because really it’s the quantitative ratios that matter rather than the exact nature of the distribution out in the tails (e.g. I doubt the essential disagreement here is about whether it’s a power law vs a lognormal).
If you restrict to people who are broadly trying to do good with their work (at least a little bit), I’d be interested if you would offer guesses about the ratios (ex post) in impact comparing someone at the 90th centile to e.g. someone at the 50th centile; someone at the 99th centile; someone at the 99.99th centile. (I think it’s kind of hard to produce numbers for these things because of course there’s massive amounts of uncertainty, but my guess is that these four points would be spread out by somewhere between 2 and 4 orders of magnitude.)
And how much spread do we need to get here in order to justify a lot of attention going into looking for tail-upsides? Of course the exact amount of effort that’s appropriate will vary with what you think of these tails, but if you think that some of your options might be twice as good (in expectation) than others, that’s already enough to justify a lot of attention trying to make sure you find the good ones.
Notes on why I tend to expect something like a power law:
Some of my reason is looking at (what I understand of) the historical distribution of impact. It’s certainly a bit flatter than a naive analysis would suggest after accounting for a bunch of the credit-sharing issues, selection effects in what we hear about, etc.; but I still think it will go like something along these lines.
Some of my reason is looking at distributions for some related things (like job productivity for jobs of various levels of complexity).
Some of my reason is having looked into the generating mechanisms for power laws and thinking that this looks like the type of place that they come up. (But this isn’t super informative about numerically how thick the tails should be.)
Appreciate the attempt to make headway on the disagreement!
I feel pretty lost when trying to quantify impact at these percentiles. Taking concerns about naive attribution of impact into consideration, I don’t even really know where to start to try to come up with numbers here. I just notice that I have a strong intuition, backed up by something that seems to me like a plausible claim: given that myriad actors always contribute to any outcome, it is hard to imagine that there is one (or a very few) individual(s) that does all of the heavy lifting...
“And how much spread do we need to get here in order to justify a lot of attention going into looking for tail-upsides?”
—Also a good question. I think my answer would be: it depends on the situation and how much up- or downsides come along with looking for tail-upsides. If we’re cautious about the possible adverse effects of impact maximizing mindsets, I agree that it’s often sensible to look for tail-upsides even if they would “only” allow us to double impact. Then there are some situations/problems where I believe the collective rationality mindset, which looks for “how should I and my fellows behave in order to succeed as a community” rather than “how should I act now to maximize the impact I can have as a relatively direct/traceable outcome from my own action?”
I just notice that I have a strong intuition, backed up by something that seems to me like a plausible claim: given that myriad actors always contribute to any outcome, it is hard to imagine that there is one (or a very few) individual(s) that does all of the heavy lifting...
I want to note that this property isn’t a consequence of a power-law distribution. (It’s true of some power laws but not others, depending on the exponent.) I think you’re right about this in most cases (though in some domains like theoretical physics I think it’s more plausible that most of the heavy lifting gets done by a few people).
But even if there aren’t a small number of individuals doing all the heavy lifting, it can still be the case that some people are doing far more than others. For example think of income distribution: it definitely isn’t the case that just a few people earn most of the money, but it definitely is the case that some people earn far more than others. If you were advising someone on how to make as much money as possible, you wouldn’t tell them to chase after the possibility that they could be in the 0.0001%, but you would want them to have an awareness of the shape of the distribution, and some idea of how to find high-paying industries; and if you were advising a lot of people you’d probably want to talk about circumstances in which founding a company would make sense.
Similar reframes might acknowledge that some efforts help facilitate large benefits, while also acknowledging all do-gooding efforts are ultimately co-dependent, not simply additive*? I like the aims of both of you, including here and here, to capture both insights.
(*I’m sceptical of the simplification that “some people are doing far more than others”. Building on Owen’s example, any impact of ‘heavy lifting’ theoretical physicists seems unavoidably co-dependent on people birthing and raising them, food and medical systems keeping them alive, research systems making their research doable/credible/usable, people not misusing their research to make atomic weapons, etc. This echos the points made in the ‘conceptual problem’ part of the post)
Thanks for that thoughtful comment!
Agree that the adverse effects that I dedicate a large part of the post to do not speak to the question of whether impact actually follows a power-law distribution. They are just arguments against thinking about impact in that way. I think I acknowledge that repeatedly in the post, but can see now that the title makes it sound like I focus mainly on the “Empirical problem”.
“I think that after you sort through this kind of consideration you would be able to recover some version of the power law claim basically intact”—I wonder if our disagreement on that is traceable and resolvable, or whether it stems from some pretty fundamental intuitions which it’s hard to argue about sensibly?
ex ante vs. ex post: Interesting that you raise that! I’ve talked to a few people about the ideas in the essay, and I think something like your argument here was the most common response. I think I remain more persuaded by the claim that impact is not power law distributed at all, even ex post and not just because we don’t have the means to predict ex ante. But I agree that the case for a power law distribution is harder to defend ex ante (because of all the uncertainty) than ex post, and my confidence in doubting the claim is stronger for ex ante impact evaluations than it is for ex post evaluations.
True and good point that I basically ignored the benefits of power-law thinking. I’ll consider whether I think my thoughts on these benefits can fit somewhere in the essay, and will update it accordingly if I find an appropriate fit. Thanks for pointing this out!
Your conclusion sounds largely agreeable to me (though I imagine we would disagree when asked to specify how large the “tail-upsides” are that people should look for in a cautious manner).
I’m definitely a little surprised to hear that you don’t think that impact is power-law distributed at all, even ex post. I wonder if it’s worth trying to get numerical about this, rather than talk qualitatively about “whether impact is power-law distributed”. Because really it’s the quantitative ratios that matter rather than the exact nature of the distribution out in the tails (e.g. I doubt the essential disagreement here is about whether it’s a power law vs a lognormal).
If you restrict to people who are broadly trying to do good with their work (at least a little bit), I’d be interested if you would offer guesses about the ratios (ex post) in impact comparing someone at the 90th centile to e.g. someone at the 50th centile; someone at the 99th centile; someone at the 99.99th centile. (I think it’s kind of hard to produce numbers for these things because of course there’s massive amounts of uncertainty, but my guess is that these four points would be spread out by somewhere between 2 and 4 orders of magnitude.)
And how much spread do we need to get here in order to justify a lot of attention going into looking for tail-upsides? Of course the exact amount of effort that’s appropriate will vary with what you think of these tails, but if you think that some of your options might be twice as good (in expectation) than others, that’s already enough to justify a lot of attention trying to make sure you find the good ones.
Notes on why I tend to expect something like a power law:
Some of my reason is looking at (what I understand of) the historical distribution of impact. It’s certainly a bit flatter than a naive analysis would suggest after accounting for a bunch of the credit-sharing issues, selection effects in what we hear about, etc.; but I still think it will go like something along these lines.
Some of my reason is looking at distributions for some related things (like job productivity for jobs of various levels of complexity).
Some of my reason is having looked into the generating mechanisms for power laws and thinking that this looks like the type of place that they come up. (But this isn’t super informative about numerically how thick the tails should be.)
Appreciate the attempt to make headway on the disagreement!
I feel pretty lost when trying to quantify impact at these percentiles. Taking concerns about naive attribution of impact into consideration, I don’t even really know where to start to try to come up with numbers here. I just notice that I have a strong intuition, backed up by something that seems to me like a plausible claim: given that myriad actors always contribute to any outcome, it is hard to imagine that there is one (or a very few) individual(s) that does all of the heavy lifting...
“And how much spread do we need to get here in order to justify a lot of attention going into looking for tail-upsides?” —Also a good question. I think my answer would be: it depends on the situation and how much up- or downsides come along with looking for tail-upsides. If we’re cautious about the possible adverse effects of impact maximizing mindsets, I agree that it’s often sensible to look for tail-upsides even if they would “only” allow us to double impact. Then there are some situations/problems where I believe the collective rationality mindset, which looks for “how should I and my fellows behave in order to succeed as a community” rather than “how should I act now to maximize the impact I can have as a relatively direct/traceable outcome from my own action?”
Re:
I want to note that this property isn’t a consequence of a power-law distribution. (It’s true of some power laws but not others, depending on the exponent.) I think you’re right about this in most cases (though in some domains like theoretical physics I think it’s more plausible that most of the heavy lifting gets done by a few people).
But even if there aren’t a small number of individuals doing all the heavy lifting, it can still be the case that some people are doing far more than others. For example think of income distribution: it definitely isn’t the case that just a few people earn most of the money, but it definitely is the case that some people earn far more than others. If you were advising someone on how to make as much money as possible, you wouldn’t tell them to chase after the possibility that they could be in the 0.0001%, but you would want them to have an awareness of the shape of the distribution, and some idea of how to find high-paying industries; and if you were advising a lot of people you’d probably want to talk about circumstances in which founding a company would make sense.
Perhaps we could promote the questions:
‘How can I help facilitate the most good?’, or
‘How can I support the most good?’
and not the question:
‘How can I do the most good?’
Similar reframes might acknowledge that some efforts help facilitate large benefits, while also acknowledging all do-gooding efforts are ultimately co-dependent, not simply additive*? I like the aims of both of you, including here and here, to capture both insights.
(*I’m sceptical of the simplification that “some people are doing far more than others”. Building on Owen’s example, any impact of ‘heavy lifting’ theoretical physicists seems unavoidably co-dependent on people birthing and raising them, food and medical systems keeping them alive, research systems making their research doable/credible/usable, people not misusing their research to make atomic weapons, etc. This echos the points made in the ‘conceptual problem’ part of the post)