Dunbar’s Function

The study of eu­daimonic com­mu­nity sizes be­gan with a seem­ingly silly method of calcu­la­tion: Robin Dun­bar calcu­lated the cor­re­la­tion be­tween the (logs of the) rel­a­tive vol­ume of the neo­cor­tex and ob­served group size in pri­mates, then ex­tended the graph out­ward to get the group size for a pri­mate with a hu­man-sized neo­cor­tex. You im­me­di­ately ask, “How much of the var­i­ance in pri­mate group size can you ex­plain like that, any­way?” and the an­swer is 76% of the var­i­ance among 36 pri­mate gen­era, which is re­spectable. Dun­bar came up with a group size of 148. Rounded to 150, and with the con­fi­dence in­ter­val of 100 to 230 tossed out the win­dow, this be­came known as “Dun­bar’s Num­ber”.

It’s prob­a­bly fair to say that a literal in­ter­pre­ta­tion of this num­ber is more or less bo­gus.

There was a bit more to it than that, of course. Dun­bar went look­ing for cor­rob­o­ra­tive ev­i­dence from stud­ies of cor­po­ra­tions, hunter-gath­erer tribes, and utopian com­mu­ni­ties. Hut­terite farm­ing com­mu­ni­ties, for ex­am­ple, had a rule that they must split at 150—with the ra­tio­nale ex­plic­itly given that it was im­pos­si­ble to con­trol be­hav­ior through peer pres­sure be­yond that point.

But 30-50 would be a typ­i­cal size for a co­he­sive hunter-gath­erer band; 150 is more the size of a cul­tural lineage of re­lated bands. Life With Alacrity has an ex­cel­lent se­ries on Dun­bar’s Num­ber which ex­hibits e.g. a his­togram of Ul­tima On­line guild sizes—with the peak at 60, not 150. LWA also cites fur­ther re­search by PARC’s Yee and Duch­e­neaut show­ing that max­i­mum in­ter­nal co­he­sive­ness, mea­sured in the in­ter­con­nect­ed­ness of group mem­bers, oc­curs at a World of War­craft guild size of 50. (Stop laugh­ing; you can get much more de­tailed data on or­ga­ni­za­tional dy­nam­ics if it all hap­pens in­side a com­puter server.)

And Dun­bar him­self did an­other re­gres­sion and found that a com­mu­nity of 150 pri­mates would have to spend 43% of its time on so­cial groom­ing, which Dun­bar in­ter­preted as sug­gest­ing that 150 was an up­per bound rather than an op­ti­mum, when groups were highly in­cen­tivized to stay to­gether. 150 peo­ple does sound like a lot of em­ploy­ees for a tight-knit startup, doesn’t it?

Also from Life With Alacrity:

A group of 3 is of­ten un­sta­ble, with one per­son feel­ing left out, or else one per­son con­trol­ling the oth­ers by be­ing the “split” vote. A group of 4 of­ten de­volves into two pairs… At 5 to 8 peo­ple, you can have a meet­ing where ev­ery­one can speak out about what the en­tire group is do­ing, and ev­ery­one feels highly em­pow­ered. How­ever, at 9 to 12 peo­ple this be­gins to break down —not enough “at­ten­tion” is given to ev­ery­one and meet­ings risk be­com­ing ei­ther too noisy, too bor­ing, too long, or some com­bi­na­tion thereof.

As you grow past 12 or so em­ploy­ees, you must start spe­cial­iz­ing and hav­ing de­part­ments and di­rect re­ports; how­ever, you are not quite large enough for this to be effi­cient, and thus much em­ployee time that you put to­ward man­age­ment tasks is wasted. Only as you ap­proach and pass 25 peo­ple does hav­ing sim­ple de­part­ments and man­agers be­gin to work again...

I’ve already noted the next chasm when you go be­yond 80 peo­ple, which I think is the point that Dun­bar’s Num­ber ac­tu­ally marks for a non-sur­vival ori­ented group. Even at this lower point, the noise level cre­ated by re­quired so­cial­iza­tion be­comes an is­sue, and fil­ter­ing be­comes es­sen­tial. As you ap­proach 150 this be­gins to be un­man­age­able...

LWA sug­gests that com­mu­nity satis­fac­tion has two peaks, one at size ~7 for sim­ple groups, and one at ~60 for com­plex groups; and that any com­mu­nity has to frac­tion, one way or an­other, by the time it ap­proaches Dun­bar’s Num­ber.

One of the pri­mary prin­ci­ples of evolu­tion­ary psy­chol­ogy is that “Our mod­ern skulls house a stone age mind” (saith Tooby and Cos­mides). You can in­ter­pret all sorts of angst as the fric­tion of a stone age mind rub­bing against a mod­ern world that isn’t like the hunter-gath­erer en­vi­ron­ment the brain evolved to han­dle.

We may not di­rectly in­ter­act with most of the other six billion peo­ple in the world, but we still live in a world much larger than Dun­bar’s Num­ber.

Or to say it with ap­pro­pri­ate gen­er­al­ity: tak­ing our cur­rent brain size and mind de­sign as the in­put, we live in a world much larger than Dun­bar’s Func­tion for minds of our type.

Con­sider some of the con­se­quences:

If you work in a large com­pany, you prob­a­bly don’t know your tribal chief on any per­sonal level, and may not even be able to get ac­cess to him. For ev­ery rule within your com­pany, you may not know the per­son who de­cided on that rule, and have no re­al­is­tic way to talk to them about the effects of that rule on you. Large amounts of the or­ga­ni­za­tional struc­ture of your life are be­yond your abil­ity to con­trol, or even talk about with the con­trol­lers; di­rec­tives that have ma­jor effects on you, may be handed down from a level you can’t reach.

If you live in a large coun­try, you prob­a­bly don’t know your Pres­i­dent or Prime Minister on a per­sonal level, and may not even be able to get a few hours’ chat; you live un­der laws and reg­u­la­tions that you didn’t make, and you can’t talk to the peo­ple who made them.

This is a non-an­ces­tral con­di­tion. Even chil­dren, while they may live un­der the dic­ta­to­rial rule of their par­ents, can at least per­son­ally meet and talk to their tyrants. You could ex­pect this un­nat­u­ral (that is, non-EEA) con­di­tion to cre­ate some amount of anomie.

Though it’s a side is­sue, what’s even more… in­ter­est­ing.… is the way that our brains sim­ply haven’t up­dated to their diminished power in a su­per-Dun­bar­ian world. We just go on de­bat­ing poli­tics, fev­er­ishly ap­ply­ing our valuable brain time to find­ing bet­ter ways to run the world, with just the same fer­vent in­ten­sity that would be ap­pro­pri­ate if we were in a small tribe where we could per­suade peo­ple to change things.

If peo­ple don’t like be­ing part of large or­ga­ni­za­tions and coun­tries, why do they stick around? Be­cause of an­other non-an­ces­tral con­di­tion—you can’t just gather your more sen­si­ble friends, leave the band, and gather nuts and berries some­where else. If I had to cite two non-reg­u­la­tory bar­ri­ers at work, it would be (a) the cost of cap­i­tal equip­ment, and (b) the sur­round­ing web of con­tacts and con­tracts—a web of in­stalled re­la­tion­ships not eas­ily du­pli­cated by a new com­pany.

I sus­pect that this is a ma­jor part of where the stereo­type of Tech­nol­ogy as the Ma­chine Death-Force comes from—that along with the pro­fes­sional spe­cial­iza­tion and the ex­pen­sive tools, you end up in so­cial struc­tures over which you have much less con­trol. Some of the fear of cre­at­ing a pow­er­ful AI “even if Friendly” may come from that stereo­typ­i­cal anomie—that you’re cre­at­ing a stronger Ma­chine Death-Force to reg­u­late your life.

But we already live in a world, right now, where peo­ple are less in con­trol of their so­cial des­tinies than they would be in a hunter-gath­erer band, be­cause it’s harder to talk to the tribal chief or (if that fails) leave un­pleas­ant re­stric­tions and start your own coun­try. There is an op­por­tu­nity for progress here.

Another prob­lem with our over­sized world is the illu­sion of in­creased com­pe­ti­tion. There’s that fa­mous sur­vey which showed that Har­vard stu­dents would rather make $50,000 if their peers were mak­ing $25,000 than make $100,000 if their peers were re­ceiv­ing $200,000—and worse, they weren’t nec­es­sar­ily wrong about what would make them happy. With a fixed in­come, you’re un­hap­pier at the low end of a high-class neigh­bor­hood than the high end of a mid­dle-class neigh­bor­hood.

But in a “neigh­bor­hood” the size of Earth—well, you’re ac­tu­ally quite un­likely to run into ei­ther Bill Gates or An­gelina Jolie on any given day. But the me­dia re­lentlessly bom­bards you with sto­ries about the in­ter­est­ing peo­ple who are much richer than you or much more at­trac­tive, as if they ac­tu­ally con­sti­tuted a large frac­tion of the world. (This is a com­bi­na­tion of bi­ased availa­bil­ity, and a difficulty in dis­count­ing tiny frac­tions.)

Now you could say that our he­do­nic rel­a­tivism is one of the least pleas­ant as­pects of hu­man na­ture. And I might agree with you about that. But I tend to think that deep changes of brain de­sign and emo­tional ar­chi­tec­ture should be taken slowly, and so it makes sense to look at the en­vi­ron­ment too.

If you lived in a world the size of a hunter-gath­erer band, then it would be eas­ier to find some­thing im­por­tant at which to be the best—or do some­thing that gen­uinely struck you as im­por­tant, with­out be­com­ing lost in a vast crowd of oth­ers with similar ideas.

The eu­daimonic size of a com­mu­nity as a func­tion of the com­po­nent minds’ in­tel­li­gence might be given by the de­gree to which those minds find it nat­u­ral to spe­cial­ize—the num­ber of differ­ent pro­fes­sions that you can ex­cel at, with­out hav­ing to in­vent pro­fes­sions just to ex­cel at. Be­ing the best at Go is one thing, if many peo­ple know about Go and play it. Be­ing the best at “play­ing ten­nis us­ing a foot­ball” is eas­ier to achieve, but it also seems a tad… ar­tifi­cial.

Call a spe­cial­iza­tion “nat­u­ral” if it will arise with­out an over­sup­ply of po­ten­tial en­trants. New­ton could spe­cial­ize in “physics”, but to­day it would not be pos­si­ble to spe­cial­ize in “physics”—even if you were the only po­ten­tial physi­cist in the world, you couldn’t achieve ex­per­tise in all the physics known to mod­ern-day hu­man­ity. You’d have to pick, say, quan­tum field the­ory, or some par­tic­u­lar ap­proach to QFT. But not QFT over left-handed bib­ble-braids with cher­ries on top; that’s what hap­pens when there are a thou­sand other work­ers in your field and ev­ery­one is des­per­ate for some way to differ­en­ti­ate them­selves.

When you look at it that way, then there must be much more than 50 nat­u­ral spe­cial­iza­tions in the mod­ern world—but still much less than six billion. By the same logic as the origi­nal Dun­bar’s Num­ber, if there are so many differ­ent pro­fes­sional spe­cialties that no one per­son has heard of them all, then you won’t know who to con­sult about any given topic.

But if peo­ple keep get­ting smarter and learn­ing more—ex­pand­ing the num­ber of re­la­tion­ships they can track, main­tain­ing them more effi­ciently—and nat­u­rally spe­cial­iz­ing fur­ther as more knowl­edge is dis­cov­ered and we be­come able to con­cep­tu­al­ize more com­plex ar­eas of study—and if the pop­u­la­tion growth rate stays un­der the rate of in­crease of Dun­bar’s Func­tion—then even­tu­ally there could be a sin­gle com­mu­nity of sen­tients, and it re­ally would be a sin­gle com­mu­nity.

Part of The Fun The­ory Sequence

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