Dunbar’s number revisited

British anthropologist Robin Dunbar postulated in the 1990s that, given our brain size, human beings can only maintain 150 stable relationships.

A new study has taken a look at modern and traditional societies, and has concluded that the number is actually 132. But there is another limitation, and that is the small number of close links an individual can maintain. This account states that the maximum number of close links we can maintain is on average about five.

There are a few barriers to understanding what is being claimed. First, you have to be a Royal Fellow, or pay to read the whole article. Secondly, they don’t talk about Dunbar’s number, rather about Erdős–Rényi networks. You have to be a mathematician to understand those. Finally, the authors are engineers rather than social scientists, so we can’t make assumptions as to how they define terms.

We have an article at the ABC and another at Phys.org to enlighten us.

I’ve used the term “close link” rather than just “link”, by which I think they mean the equivalent of a close friend, someone you know well. However, the groups are meant to be cohesive, which means that as a group member you need to know how everyone relates to everyone else, the expectations and obligations that bind them, and how you would expect them to act and react in various situations.

The Phys.org piece explains how it’s meant to work:

    Prior research has shown, the researchers note, that humans are only capable of maintaining a certain number of people in their social world, currently, the upper limit appears to be 132 people. But, not all of those people are directly connected to any one individual, it all happens through links. Harré and Prokopenko suggest the upper limit on the number of direct friends for most people is about five. The upper limits appear to be based on biology, they note—as the human brain developed, people were living together in small groups that lived as hunter-gatherers. That led to the development of links, which are direct connections between two people, generally two people that have some type of emotional attachment. To form a larger group, it isn’t necessary for every person in that group to form a connection with everyone else, all it takes is for a network of connections to exist.

    In primitive terms, the researchers explain, that would mean that not all of the people in a small hunting party would necessarily have to be friends, instead, each would have to be friends with just one or two of the people in the group. They have calculated that to have a social circle of 132 people, each person would only have to have a link with just five people. They also have found that the number of links a person has can be related to group size, as the group grows, more links are needed to maintain cohesiveness. As it grows to 15, for example, there will exist on average 3 links per person; in groups of 45, the number of links would grow to 3 or 4.

The ABC summarises the relationship between “links” and group size thus:

    How many links do you need to maintain a network?

    • Group of five = one to two links
    • Group of 15 = two to three links
    • Group of 45 = three to four links
    • Group of 132 = four to five links

If our capacity for close links is limited to about five, then we could not participate in more than a few cohesive groups. Any way that’s how I understand it.

The authors contrast such social networks with hierarchical networks, which have rules and leaders. Hierarchical networks can be much larger and the need to know anyone within the network is reduced. For example, it would be possible to sing in a choir without knowing anyone else.

Many groups in modern society are to a more or less degree hierarchical, I think.

Nearly two years ago we had a look at Dunbar’s number. The post and comments are worth rereading in the light of the new research.

I would agree with John D’s comment that modern societies are very different from traditional societies. We have more general rules, norms an laws. Individualism is I think a phenomenon that perhaps emerged with the Renaissance.

This comment from John pertains:

    It is interesting to compare the Groote Eylandt Aboriginal and European communities. In the case of the Europeans we have general rules for dealing with each other so we don’t really need to know who someone is before we can deal with someone. (Gender, age etc. may count but they are still general rules.)

    By contrast many of the Aboriginal rules are relationship driven. (For example, the rules for dealing with my father’s sisters daughter are quite different to dealing with my father’s brother’s daughter.) A Groote Eylandt Aborigine not only needs to know who someone is before knowing how to deal with them they also need to know how the person is related to a number of people.

Recently I heard a linguist say that the Aborigines of Botany Bay used different languages in different social settings.

Army units spoken of by Graham Bell are classified as hierarchical networks. But how much more effective are they if they become also social networks?

7 thoughts on “Dunbar’s number revisited”

  1. Brian: Talking about hierarchical systems ignores the complexity of the flow of power in human society, particularly the more sophisticated societies. The use of position (hierarchical) power becomes less and less effective as people become more educated, responsible etc. Under these circumstances things like expert and personality power become more important with the power moving during decision making and group activities depending, for example, on what expertise is relevant at a particular point in a discussion or activity.
    I would agree that groups are more more likely to separate into factions or lapse into other unproductive habits as the group gets larger but the the size at which this starts will depend on the individuals involved and the incentives for long term cooperation. People like Hazel and some of her even more scary friends seem to be able to talk groups much larger than 5 into do things together to achieve good outcomes.

  2. John, I think the authors were systems engineers, interested in ‘self-organizing Erdős–Rényi networks’, in this case as applied to human societies. Sociologists would think in terms of power relations and how power flows.

    Leadership is also a concept they were likely to have been a bit naive about.

    Nevertheless the numbers they came up with may have some validity, but there again, you’d want to see the study replicated by others.

  3. At Newman I ran a concentrator that employed 100 people in addition to a number of contractors from time to time. The total mine employed about 2000 people. In the concentrator I had 13 direct reports with almost all of the concentrator people either reporting direct to me or one of my direct reports. In addition to concentrator people outside important links included senior management, quality control, personnel and union reps.
    So how did the close links compare with the ones in the post?
    Firstly, i didn’t really know all of the people who worked for me but would have said i would have more that 5 close links. I would have said these numbers depended on the nature of the job (you need to be linked to some people to do the job) but others were simply people I got on well with and/or gave me insights re what was actually going on.
    Experience as a commissioning engineer in the construction industry was interesting. All of my experience here was away from home with the norm being to live in a construction camp for all the workers. What struck me was the way the way construction workers, engineers and supervisors were able to form teams and create friendships quickly and then walk away from these friendships when they had done their part of the job. (Living, working and eating together makes a difference – did a long job at Whyalla once where we were all accommodated in houses and flats spread over the town – not the same as a construction camp – camp size made a difference too.)
    To put it another way, lots of people have the skill to create close links quickly when needed and let them lapse when the job or location changes.

  4. John, for much of my time in the Department of Education I had 34 work groups, ranging from one to about 26 in size, but only 3 people directly responsible to me.

    From memory the total number was about 160, but we had several reorganisations and when I left it was 243, with 13 directly responsible to me.

    I was on 18 committees/working groups or internal management groups. Some of them were national, one requiring monthly meetings.

    Up the line I had direct access to divisional and regional directors numbering more than 30, plus lines of communication to other departments and externally.

    Basically it was impossible and would have killed me if I’d stayed.

    This sort of environment is very different from traditional societies, and wouldn’t work at all without rules and hierarchies.

    As a reaction after I left, I had no-one working for me and I could sack my bosses.

  5. Brian,
    Not replacing the level between me and my foremen worked for me. It eliminated vertical power struggles. It made it easier to find someone who was interested in trying to make changes and it meant that many decisions were made at the most appropriate level instead of going too far up the chain. It also meant that the workers were more involved in taking responsibility and making decisions because the foremen were taking over responsibilities that used to belong to the general foremen.
    However, flat structures don’t work if you have a boss who is not in favour of the idea or a boss that doesn’t understand that your job has to change in significant ways.

  6. John, yes I think it is horses for courses. I was in charge of a fairly disparate collection of groups, organised into three branches. The film and video library, for example, which also functioned as a state film library serving the community, had little to do with the departmental publishing group, where you had editors and writers.

    I was an assistant director of a division, of which the department had about half a dozen. As such I was a divisional officer without direct management functions down the line.

  7. Yep. Horses for courses. It takes more competent people to make flatter organizations work and people need to understand that what each layer does will change and some jobs that used to be done in a tall organization wont be done any more or done less often.
    If a layer is removed below you you will spend less time on overview stuff and may have to do some of the stuff the departed layer used to do.
    One of the things I noticed about Hazel’s reports on changes to public service management was that the public service tried to do some of the things that work for business without really understanding what the change was all about.

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