Lognormal Jobs

I often meet people who think that because computer tech is improving exponentially, its social impact must also be exponential. So as soon as we see any substantial social impact, watch out, because a tsunami is about to hit. But it is quite plausible to have exponential tech gains translate into only linear social impact. All we need is a lognormal distribution, as in this diagram:


Imagine that each kind of jobs that humans do requires a particular level of computing power in order for computers to replace humans on that job. And imagine that these job power levels are distributed lognormally.

In this case an exponential growth in computing power will translate into a linear rate at which computers displace humans on jobs. Of course jobs may clump along this log-computing-power axis, giving rise to bursts and lulls in the rate at which computers displace jobs. But over the long run we could see a relatively steady rate of job displacement even with exponential tech gains. Which I’d say is roughly what we do see.

Added 3am: Many things are distributed lognormally.

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  • Matt M

    ‘But it is quite plausible to have exponential tech gains translate into only linear social impact. All we need is a lognormal distribution’

    Doesn’t follow. You haven’t made the case that the distribution could plausibly be lognormal. The existence of such a distribution is not sufficient to claim plausibility. In particular, since pretty much all human capabilities are distributed approximately normally, is seems odd that the automation threshold for jobs held by the human population would not also be normally distributed.

    (Addendum, your point about exponential growth resulting in normal gains would have been far more transparent if the horizontal axis in you diagram was linear)

    • sflicht

      Income distribution is approximately log normal (with a fat tail), AFAIK. Certainly not normal. To the extent that income proxies for marginal product (not 100% true but not 100% wrong), lognormal is not a crazy prior for automatizability of jobs.

      • Matt M

        And the plausibility argument is complete!

        That said, I don’t think marginal product is a good proxy for automatizability. It has nothing to do with the complexity of the task being performed, and more to do with the incremental value of marginal improvements in large enterprises.

    • Pngwn

      ‘ In particular, since pretty much all human capabilities are distributed approximately normally

      Citation needed… Nassim Taleb could (and did) write a book on how wrong that is.

      In any case, I don’t think that it was the author’s point that it MUST be lognormally distributed.

      Instead, I think the point was that a lognormal distribution explains the historical pattern, and is thus plausible. With that, I would agree.

      Lending credence to the claim is that fact that the computation of a job varies wildely. Cashiers are basically adding machines, whereas psychologists have to understand complex social and biological structures.

      The ease with which they are automated isn’t even in the same ballpark, which you wouldn’t see with a normal distribution.

      • Matt M

        I said approximately.

        Anyway, I just wanted to see some justification. Otherwise any growth pattern could ‘plausibly’ explain any other growth pattern, in which the content is a pure calculus existence result, and nothing to do with the phenomenon supposedly being explained.

      • Matt M

        To your second point, I agree that these two jobs have very different thresholds for automation. But I don’t see how any particular distribution of automation thresholds in the economy follows from that.

      • one of the dudes

        The normal-lognormal debate is interesting:

        Normal: physical characteristics (eg height), intelligence (as measured by things like GRE scores, although that might be somewhat die to test design)

        Lognormal: Income as proxy for the marginal product. This is very likely due to the network effects in the society rather than ability distribution.

      • arch1

        height at least (well, adult human female height at least:-) is not only normal but *also* lognormal, as noted in the article reference by the final URL.

  • free_agent

    It’s worse than that — a single increment of technology brings about industrialization, whose exponential growth rate is much higher than anything that preceded it.

    But there’s also the limitation on understanding; it’s likely that the limitation on self-driving vehicles isn’t computer power per se but our understanding of how to solve the problem. And the former can progress even faster than the latter. I recall an article (from 20 or 30 years ago) summarizing the progress in fluid mechanics simulations. It noted that while raw computer power had advanced dramatically (Moore’s Law), the improvements of algorithms (in terms of the amount of computer power needed to obtain a result) had been even faster.

  • RobotEnomics

    I like the logic behind this… but question using bank tellers, see for example Bessen, Learning by Doing – “One might expect such automation to decimate the ranks of bank tellers, but in fact the number of bank teller jobs did not decrease as the ATMs were rolled out (see Chart 1). Instead, two factors combined to preserve teller jobs.”

    • You are right, I should use a different example.

      • one of the dudes

        Rather than the absolute number of tellers the chart should show it relative to some underlying growth baseline (e.g. bank revenues or assets), which was crazy steep in finance after mid 80s.

  • arch1

    Robin, thanks for the pointer to the article*. You might want to add that your (rough) conclusion only follows here because the variability of the distribution isn’t small (if it’s small, lognormal becomes nearly identical to normal; e.g. distribution of heights of women). And that it only applies to the LHS of the distribution.

    *It makes a surprisingly persuasive case for the importance of the lognormal distribution. I found it fascinating that the authors, asked to find examples of data that fit the normal but not the lognormal model, *couldn’t find any* that were based on original measurements. The only such data they found “…consisted of differences, sums, means, or other functions of original measurements.”

  • arch1

    Sorry, another nit – unless I’m misunderstanding, the rate of job displacement grows (roughly) linearly with time, thus the number of displaced jobs grows quadratically. This doesn’t come across real clearly as you’ve described it (though the graph helps).

    • The fraction of all the original jobs does grow quadratically, but since workers reallocate to the remaining jobs, the % of workers whose jobs are displaced should stay pretty constant in the middle of the distribution. And the profits earned by displacing workers should also stay a constant %.

      • arch1

        I see the point you’re making now, thanks for the clarification.

  • Paul Christiano

    Some people make sloppy arguments for everything, but the usual case for discontinuous change isn’t exponential growth in computing hardware. It’s that all of the human jobs require broadly similar levels of hardware. For example, perception and motor control already use a large fraction of human brains, and so if computing hardware is the main issue then it may not be long between automating those functions (completely) and automating everything the brain does. More generally, you might think that most human jobs now use a significant part (say > 1%) of human brains.

    You can still argue against this view in many ways, especially: (1) many jobs can be automated with much less hardware than used by the human brain, especially given that humans weren’t under selection pressure to accomplish these tasks with minimal hardware, and (2) software may be the main driver of automation, and the software for some human jobs may be much harder than others. But it’s a different argument.

    • You could argue that the total distribution is a mixture of a wide spread due to jobs that don’t use remotely all of a human brain and a narrow spread due to jobs that use most of a human brain. Then my claim holds while the current tech level is many sigmas below the mean of the narrow part, but then the rate of job displacement might suddenly grow as the tech level gets near to the mean of the narrow part. But my guess is that most jobs don’t use most of a human brain, so most of the action is in the wide part of the mixture.

      • Paul Christiano

        I think that much of human brains (say >5%) are devoted to motor coordination and perception. So a task that exploited all of these faculties would use much of a brain. Presumably you can’t get by with that much less than a full human brain, since evolution was under some pressure to give us smaller/cheaper brains. This suggests that many tasks must be in the narrow part, namely the tasks that humans performed in the evolutionary environment.

        Is your position that each particular motor control task uses a small part of the brain, and that we only need so much brain so that we can do a wide variety of different motor tasks? I think that this is not that plausible on a neuroscience perspective. Or is your position that jobs in the real world are much easier than the kind of motor/perception tasks that occur in nature?

        In any case, it seems like we should at least have a significant probability (say >20%) that many “use” a significant fraction of the human brain (say >5%). If this is the case then employed humans will eventually be concentrated in those jobs (plausibly they already are), and we will see a rapid flurry of automation over the course of ~a decade.

        (Of course, as I mentioned, one could argue against the hardware-bottleneck story. But under the hardware bottleneck story it seems like we should at least put significant mass on a flurry of automation soon.)

      • “Or is your position that jobs in the real world are much easier than the kind of motor/perception tasks that occur in nature?” This; real job requirements are spread across a wide range. When jobs require more than humans have, they just don’t get done. When they require much less than humans have, they are far from the postulated narrow clump. Not clear why there should be many jobs right at the borderline.

      • Paul Christiano

        If difficulty and value are correlated (for example because there are many ways to make a job harder + more useful, or to make it easier + less useful), then you may expect clumping at the more difficult end. This looks very plausible, though obviously the conclusions depend on details.

  • fozzy

    The phrase “linear social impact” is fuzzy. If you only mean “linear displacement of jobs” then ok. But if you mean linear sum total social impact then we must also argue that linear displacement of jobs generate linear macrosocial impact. But that can be doubted. When the displaced reach some X % of population there might be quick and farreaching political change. (Or are you implicitly assuming all/most displaced will all get new jobs somehow?)

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