Ask someone who’s worked in a non-academia cognitive job for a while (like e.g. a tech company), at a company with more than a dozen people, and they’ll be like “lolwut obviously humans don’t factorize problems well, have you ever seen an actual company?”. I’d love to test this theory, please give feedback in the comments about your own work experience and thoughts on problem factorization.
What does “well” mean here? Like what would change your mind about this?
I have the opposite intuition from you: it’s clearly obvious that groups of people can accomplish things that individuals cannot; while there are inefficiencies from bureaucracy, those inefficiencies are regularly outweighed by the benefit having more people provides; and that benefit frequently comes from factorization (i.e. different parts of the company working on different bits of the same thing).
As one example: YCombinator companies have roughly linear correlation between exit value and number of employees, and basically all companies with $100MM+ exits have >100 employees. My impression is that there are very few companies with even $1MM revenue/employee (though I don’t have a data set easily available).
First: a group of 100 people can of course get more done over a month than an individual, by expending 100 times as many man-hours as the individual. (In fact, simple argument: anything an individual can do in a month a group of 100 can also do in a month by just having one group member do the thing independently. In practice this doesn’t always work because people get really stupid in groups and might not think to have one person do the thing independently, but I think the argument is still plenty strong.) The question is whether the group can get as much done without any individual person doing a very large chunk of the work; each person should only need to do a small/simple task. That’s the point of problem factorization.
Second: the relevant question is not whether there exist factorizable problems; they clearly exist. (Assembly lines are proof of existence.) The question is whether there do not exist unfactorizable problems—more precisely, whether alignment can be solved without running into a single subproblem which humans cannot factor without missing some crucial consideration.
For more info on the sort of things which drive my intuition here, see Coordination as a Scarce Resource. If I suddenly found out that none of the examples in that post actually happened, or that they were all extremely unusual, then I’d mainly be very confused, but that would be the sort of thing which would potentially end in changing my mind about this.
As one example: YCombinator companies have roughly linear correlation between exit value and number of employees, and basically all companies with $100MM+ exits have >100 employees. My impression is that there are very few companies with even $1MM revenue/employee (though I don’t have a data set easily available).
I don’t think this is especially relevant, but I disagree with this picture on two counts. First, I think valuation tends to cause hiring, not vice versa—for instance, in google the very large majority of employees do not work on search, and the non-search employees account for a tiny fraction of the company’s income (at least as of last time I checked, which was admittedly a while ago). Second, Instagram: IIRC the company had 13 employees when it was acquired by Facebook for $1B. I would guess that there are plenty of very small $100M companies, we just don’t hear about them as often because few people have friends who work at them and they don’t need to publicize to raise capital.
Thanks! The point about existence proofs is helpful.
After thinking about this more, I’m just kind of confused about the prompt: Aren’t big companies by definition working on problems that can be factored? Because if they weren’t, why would they hire additional people?
Very late reply, reading this for the 2022 year in review.
As one example: YCombinator companies have roughly linear correlation between exit value and number of employees, and basically all companies with $100MM+ exits have >100 employees. My impression is that there are very few companies with even $1MM revenue/employee (though I don’t have a data set easily available).
So there are at least two different models which both yield this observation.
The first is that there are few people who can reliably create $1MM / year of value for their company, and so companies that want to increase their revenue have no choice but to hire more people in order to increase their profits.
The second is that it is entirely possible for a small team of people to generate a money fountain which generates billions of dollars in net revenue. However, once you have such a money fountain, you can get even more money out of it by hiring more people, comparative advantage style (e.g. people to handle mandatory but low-required-skill jobs to give the money-fountain-builders more time to do their thing). At equilibrium, companies will hire employees until the marginal increase in profit is equal to the marginal cost of the employee.
My crackpot quantitative model is that the speed with which a team can create value in a single domain scales with approximately the square root of the number of people on the team (i.e. a team of 100 will create 10x as much value as a single person). Low sample size but this has been the case in the handful of (mostly programming) projects I’ve been a part of as the number of people on the team fluctuates, at least for n between 1 and 100 on each project (including a project that started with 1, then grew to ~60, then dropped back down to 5).
Sure, I think everyone agrees that marginal returns to labor diminish with the number of employees. John’s claim though was that returns are non-positive, and that seems empirically false.
What does “well” mean here? Like what would change your mind about this?
I have the opposite intuition from you: it’s clearly obvious that groups of people can accomplish things that individuals cannot; while there are inefficiencies from bureaucracy, those inefficiencies are regularly outweighed by the benefit having more people provides; and that benefit frequently comes from factorization (i.e. different parts of the company working on different bits of the same thing).
As one example: YCombinator companies have roughly linear correlation between exit value and number of employees, and basically all companies with $100MM+ exits have >100 employees. My impression is that there are very few companies with even $1MM revenue/employee (though I don’t have a data set easily available).
Two key points here.
First: a group of 100 people can of course get more done over a month than an individual, by expending 100 times as many man-hours as the individual. (In fact, simple argument: anything an individual can do in a month a group of 100 can also do in a month by just having one group member do the thing independently. In practice this doesn’t always work because people get really stupid in groups and might not think to have one person do the thing independently, but I think the argument is still plenty strong.) The question is whether the group can get as much done without any individual person doing a very large chunk of the work; each person should only need to do a small/simple task. That’s the point of problem factorization.
Second: the relevant question is not whether there exist factorizable problems; they clearly exist. (Assembly lines are proof of existence.) The question is whether there do not exist unfactorizable problems—more precisely, whether alignment can be solved without running into a single subproblem which humans cannot factor without missing some crucial consideration.
For more info on the sort of things which drive my intuition here, see Coordination as a Scarce Resource. If I suddenly found out that none of the examples in that post actually happened, or that they were all extremely unusual, then I’d mainly be very confused, but that would be the sort of thing which would potentially end in changing my mind about this.
I don’t think this is especially relevant, but I disagree with this picture on two counts. First, I think valuation tends to cause hiring, not vice versa—for instance, in google the very large majority of employees do not work on search, and the non-search employees account for a tiny fraction of the company’s income (at least as of last time I checked, which was admittedly a while ago). Second, Instagram: IIRC the company had 13 employees when it was acquired by Facebook for $1B. I would guess that there are plenty of very small $100M companies, we just don’t hear about them as often because few people have friends who work at them and they don’t need to publicize to raise capital.
Thanks! The point about existence proofs is helpful.
After thinking about this more, I’m just kind of confused about the prompt: Aren’t big companies by definition working on problems that can be factored? Because if they weren’t, why would they hire additional people?
Very late reply, reading this for the 2022 year in review.
So there are at least two different models which both yield this observation.
The first is that there are few people who can reliably create $1MM / year of value for their company, and so companies that want to increase their revenue have no choice but to hire more people in order to increase their profits.
The second is that it is entirely possible for a small team of people to generate a money fountain which generates billions of dollars in net revenue. However, once you have such a money fountain, you can get even more money out of it by hiring more people, comparative advantage style (e.g. people to handle mandatory but low-required-skill jobs to give the money-fountain-builders more time to do their thing). At equilibrium, companies will hire employees until the marginal increase in profit is equal to the marginal cost of the employee.
My crackpot quantitative model is that the speed with which a team can create value in a single domain scales with approximately the square root of the number of people on the team (i.e. a team of 100 will create 10x as much value as a single person). Low sample size but this has been the case in the handful of (mostly programming) projects I’ve been a part of as the number of people on the team fluctuates, at least for n between 1 and 100 on each project (including a project that started with 1, then grew to ~60, then dropped back down to 5).
Sure, I think everyone agrees that marginal returns to labor diminish with the number of employees. John’s claim though was that returns are non-positive, and that seems empirically false.