Dunbar's Number Is Quadratic (2020) | Hacker News Reader

Dunbar's Number Is Quadratic (2020)

generativist.falsifiable.com

76 pointsBluestein40 comments

Instead of viewing Dunbar's number as a law, I view it as a sometimes useful, mental model. This article is about how Dunbar's number, as a mental model, breaks down when applied to social media. It makes a strong case for that.

Like all mental models, Dunbar's number is not perfect. However, readers who stop after the introduction of this article may be left thinking it's not useful at all.

I find it very useful in helping leaders in early-stage organizations that are growing fast recognize why the tools & techniques they've used to get to 30-80 people are breaking down as they approach 100-150 people. It helps frame why new tools & techniques for organization and communication are required.

Dunbar told me it grows by approximately tripling. And yes, when you cross a Dunbar bound the old tools and techniques fail in surprising ways.

45-50

150

450/500

1500

5000

I've looked a bit at military history and it is interesting to see how consistent they generally are. They'll have a squad of about 10, though the variance can be up to 50%, grouped into companies of ~100, grouped into legions of ~1000, into armies of ~10,000. It wasn't until the 20th Century that armies could become really huge. But the most all-purpose and independent units tended to be in the 100-150 range. Big enough to have enough people to do everything you typically need to do with adequate redundancy. Dunbar's numbers are good enough rules-of-thumb. Some people have better social memories and so will have larger Dunbar number capabilities, just as others have smaller.

In the bc era Chinese armies routinely had 50000 warhorses let alone ground-pounding infantry. Your data is ... incomplete. I would recommend looking a bit more at military history, quite a bit more.

Anecdotal, I have been using 10, 20, 50, 100, 200, 500,... as the 'break points' where organizational structures need a rethink. So far, it has worked for me. These also match the lines on a log graph.

I wonder if there is a maximum or plateau, beyond which it doesn't matter. is there a difference between 30 million and 300 million, 3 billion to 30 billion?

Ah! We are entering "paperclip factory" territory here, with your question ... :)

> is there a difference between 30 million and 300 million, 3 billion to 30 billion?

In organizational terms? That is, terms of how you would go about organizing or operating ...

... I would humbly only go as far as saying this: I feel there has to be (some) upper limit beyond which any "structure" other than a "self-organizing" structure will collapse or be unmanageable.-

PS. DAOs (which, sadly, seem (?) to be on the wane), were at (some) end of that spectrum, methinks ...

Most, if not all, human structures are self organizing by definition. They simply differ in their stability depending on scale and conditions.

I wonder if the stability of DAOs benefit or are hindered with scale. It may be implementation specific as well.

The Sci-fi part of my brain finds parallels in feudalism, which used delegation and strict hierarchy to deal with the span of control issue.

> It may be implementation specific as well.

I would posit it is. Totally.-

PS. For all we know, the first thing a superhumanly intelligent AGI might do is "forcibly-self-organize" us into a DAO, doing away with the political system. I, for one, would welcome that :)

> The Sci-fi part of my brain finds parallels in feudalism

Elsethread - when talking abou how the Mongols almost overtook Europe - the claim was made that - to a point - part of the reason the hordes had to stop is that "descentralized" (as opposed to centralized clan-leader-ruled) feudal structures made it hard to make advances.-

... so feudalism came up, as a somewhat advanced form of decentralization. Which was neat.-

Yep, I’ve seen the tripling rule in scale-ups and it was brutal as it kicked in, each time. At a certain point we began to anticipate it.

That feels at least directionally correct. And it even goes up from there. An organization with a few thousand people is quite different from a 20-30K one.

I'm not sure about the math and exact numbers (which probably vary depending upon the situation anyway) but it's pretty clear that things are quite different at different scale points.

(And, should it hold, we get to cities: 100K people, 300K people, 1M people, are different cities to live in - qua size ...

... and different organizations, of course.-

Leaves me wondering - among many things - what the "largest qua payroll" organization worldwide might be.-

US Dept. of Defense, Chinese PLA, Indian railways. Walmart, Saudi Aramco come to mind.-

It's complicated by the fact that larger organizations/cities/etc. can be effectively agglomerations of smaller entities with tighter or looser coupling. But, yes, in general.

You can see some of this in your examples.

US DoD is, of course, actually part of the US government but relatively few DoD employees ever really interact with people in other US government branches. Ditto with Walmart store employees and the "mothership."

Entirely good point.-

Voting for a position at the government of my ~3M people city is completely different from voting for a position at the government of my ~300M people country.

Logically, it makes sense that the situation keeps changing. But it still feels weird. How many different kinds of relationship are we capable of?

> How many different kinds of relationship are we capable of?

Kinds? (qualitative) ...

... I think you very much upped the ante there :)

I'd posit a (cheap, easy) guess: Infinite.-

PS. Of course, taking the "cheap" way out in thinking about this of assuming each one-on-one relationship (not to mention one-to-many, and many-to-one and many-to-many, like mentioned upthread) to be a unique "kind", is an easy way out: As many types of relationships as people, because no two people are alike, and so is their relationship. Heck, considering each of the individuals (themselves) involved, might subjectively experience a different relationship, there's even a "two to each pair" pairing of relationship types to participants, to be considered ...

Now, when, IMHO it gets interesting is if we - a bit more rigoroulsy - attempt a "taxonomy" of relationship "types".-

(And, then, again, I am sure anthropology has studied and catalogued those to death ...)

As a start: https://en.wikipedia.org/wiki/List_of_largest_employers

Thou hittest the nail right on the head :)

PS. Foxconn. Of course.-

PSS. The "tripling" rule seems to hold. 1/1.5MM seems to be a "grouping", peaking at around 3MM on average. 3MM. That is large for an organization ...

This matches my experience.

There are very clearly differences in how organizations have to be operated as they grow. And one byproduct of that is a person who may be a fantastic fit for an organization of size x may no longer be a good fit for an organization of size 5x or 10x.

> a person who may be a fantastic fit for an organization of size x may no longer be a good fit for an organization of size 5x or 10x.

Interesting, in that you might even have to "backpedal" (rehire) as growth happens.-

Of course, people leave organizations for many reasons. But a ton of people who like being in a small (however you care to define) growing organization don't have as good a place in a larger, more process-heavy one with more narrowly-defined roles and responsibilities.

> I view it as a sometimes useful, mental model.

It's very nearly always useful. Many of the worst problems we have in the world around us arise because, it turns out, people just don't scale.

> people just don't scale.

Which, if I may, applies both in the sense that groups of people "handle" differently, and differently vis-a-vis group size, and in the sense that we seem to have an innate inability as humans to deal with exponential, non-linear, "network" phenomena.-

> It helps frame why new tools & techniques for organization and communication are required.

Quite useful in that context, as you say, like a mental model.-

PS. Interesting that the "threshold" seems to be somewhere between 80 transitioning to 100 (ballparking, of course).-

Well, there is a transition at something around 20, and another transition at larger numbers too (no idea where exactly, but 500 is above the transition).

I find it interesting that everybody focus on the transition at 100. (Except for educators, that are completely aware of the 20 one.)

Would be interesting to know what people in the strategy department of the US military know about this topic.

Certainly you can look at the sizes of various units in the US Army.

https://www.defense.gov/Multimedia/Experience/Military-Units...

Of course, they have various considerations that may not apply more generally.

Group size as a variable must have been studied to death from the military, HR and OR angles ...

20 is totally a "thing".-

PS. Manywhere, average classroom size is 30ish ...

Dunbar's number isn't quadratic any more than the table of elements is quadratic. We can make fairly good approximations of how two elements will interact with each other just by knowing properties of the elements themselves.

The analogy fails to describe people given that major past issues can color relationships, but it doesn't seem reasonable to think that the number of such major issues will grow linearly with tribe size, this those will also be sub quadratic (I am proposing that as tribe size doubles, the number of people you love/hate due to past shared experiences less than doubles).

> I am proposing that as tribe size doubles, the number of people you love/hate due to past shared experiences less than doubles).

You'd be surprised. More I know, more I like me dog, as someone said :)

One of my uncles was a politician and he was not just acquainted with some thousands of people, he talked with them and remembered everything, and even when meeting someone new outside his constituency was quite likely to know some friends or relatives. Would one call that a profesional Dunbar number!

That is just a gift some people have.-

PS. Romans, used a professional "nomenclator", that would follow you around helping you remember these things.-

I don't see how this shows Dunbar's number is quadratic any more than storing 150 integers in an array from which you may need to multiply random pairs later. Computing all 22,500* pairs would be quadratic, but I don't see (or have overlooked) a justification for this in the article.

Feasibly, if your whole 150 person village had a meeting, you'd want all pairs. But then you'd also want all triplets, quartets, etc which I believe is exponential.

*Technically 22,350, as you don't need self pairs

> But then you'd also want all triplets, quartets, etc which I believe is exponential.

This sounds like a "so-and-so acts different towards bar in front of baz" scenario.-

The critical observation is that that information can be stored as part of the information of "so-and-so", since there are only a handful of exact "bar" and "baz" values (a few more are added via categories) per root person.

> That is, you know 150 people when you can competently predict how any two of them would interact in paired-off social circumstances without you.

There is shockingly little justification for a core tenant of this piece. Which I suppose is fitting, since the origin of Dunbar's number is also shockingly thin on science...

> the origin of Dunbar's number is also shockingly thin on science...

Now that's an interesting angle. I'd be curious to know more, since Dunbar's often quoted.-

(2020)

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