More from Dunbar on Magic Numbers

Saturday, February 22, 2003

Robin Dunbar is the Science behind Malcolm Gladwell’s law of 150. Here is Dunbar’s core essay on why 150 is the core human social number.

Why do I keep pressing on this issue? Because I think that social communities on the web are falling into these sets and that all our future design concerning web based human communities will likely need a deep understanding of these limits. Dunbar is scientific in his language but not dull. His book Grooming Gossip and the Evolution of Language is a model of a popular science book. It is informative and entertaining but if you read this short article you will have gained access to his thesis. Why should this idea of Magic Numbers, or natural organizational size limits, concern us?

  • If we design organizations around them – we will need less management and have more “Human”, creative and healthy workplaces.
  • As we design better collaborative tools such as Groove and Weblogs, we will find that these numbers drive virtual Communities (see Ross Mayfield’s work)
  • As we design buildings and workspaces, we can use this knowledge to ensure that design healthy places

In this context we can see that it is inevitable that a school with 1,000 kids has bullying and violence!. A hospital with shifts designed around individuals will be a source of stress and ill health for the staff.

Here is the introduction – “Primates are, above all, social animals….These analyses suggest that although the size of the group in which animals live in a given habitat is a function of habitat-specific ecologically-determined costs and benefits …..The group size identified by this relationship appears to refer to the maximum number of individuals with whom an animal can maintain social relationships by personal contact.

It is not necessary that all these individuals live in the same physical group: chimpanzees ….Rather, the neocortical constraint seems to be on the number of relationships that an animal can keep track of in a complex, continuously changing social world: the function subserved by that level of grouping will depend on the individual species’ ecological and social context. ….current neocortex size sets a limit on the number of relationships that it can maintain through time, and hence limits the maximum size of its group. This means that although the evolution of neocortex size is driven by the ecological factors that select for group size, we can use the relationship in reverse to predict group sizes for living species

It is generally accepted that the cohesion of primate groups is maintained through time by social grooming Social grooming is used both to establish and to service those friendships and coalitions that give primate groups their unique structure. As might be anticipated, the amount of time devoted to social grooming correlates well with group size, notably among the catarrhine primates However, the relationship between group size and time devoted to grooming appears to be a consequence of the intensity with which a small number of key “friendships” (the primary network) is serviced rather than to the total number of individuals in the group

These primary networks function as coalitions whose primary purpose is to buffer their members against harassment by the other members of the group. The larger the group, the more harassment and stress an individual faces and the more important those coalitions are. It seems that a coalition’s effectiveness (in the sense of its members’ willingness to come to each other’s aid) is directly related to the amount of time its members spend grooming each other Hence, the larger the group, the more time individuals devote to grooming with the members of their coalitionary clique.

The mean size of the primary network is, however, related to the mean group size for the species. This suggests that groups are built up by welding together sets of smaller primary networks  and that the total size of the group is ultimately limited not by the number of networks that can be welded together but rather by the size of the networks themselves”

For us the key group size is 150

Here are some of his observations – “ it turns out that most organised (i.e. professional) armies have a basic unit of about 150 men (Table 3). This was as true of the Roman Army (both before and after the reforms of 104BC) as of modern armies since the sixteenth century. In the Roman Army of the classical period (350-100 BC), the basic unit was the maniple (or “double-century”) which normally consisted of 120-130 men; following the reforms instituted by Marius in 104BC, the army was re-organised into legions, each of which contained a number of semi-independent centuries of 100 men each (Haverfield 1955, Montross 1975). The smallest independent unit in modern armies (the company) invariably contains 100-200 men (normally three or four rifle platoons of 30-40 men each, plus a headquarters unit, sometimes with an additional heavy weapons unit) (Table 3). Although its origins date back to the German mercenary Landsknechts groups of the sixteenth century, the modern company really derives from the military reforms of the Swedish king Gustavus Adolphus in the 1620s. Despite subsequent increases in size to accommodate new developments in weaponry and tactics, the company in all modern armies has remained within the 95% confident limits of the predicted size for human groups. The mean size of 179.6 for the twentieth century armies listed in Table 3 does not differ significantly from the 147.8 predicted by equation (1) (z=0.913, P=0.361 2-tailed).

This fact has particular significance in the context of the present argument. Military units have to function very efficiently in coordinating men’s behaviour on the battlefield: the price of failing to do so is extremely high and military commanders cannot afford to miscalculate. Given that the fighting power of a unit is a function of its size, we might expect there to be considerable selection pressure in favour of units that are as large as possible. That the smallest independent unit should turn out to have a maximum size of about 200 even in modern armies (where technology presumably facilitates the coordination of planning) suggests that this upper limit is set by the number of individuals who can work effectively together as a coordinated team. Military planners have presumably arrived at this figure as a result of trial and error over the centuries.

In the context of the present analysis, the reason given by the Hutterites for limiting their communities to 150 is particularly illuminating. They explicitly state that when the number of individuals is much larger than this, it becomes difficult to control their behaviour by means of peer pressure alone (Hardin 1988). Rather than create a police force, they prefer to split the community. Forge (1972) came to a rather similar conclusion on the basis of an analysis of settlement size and structure among contemporary New Guinea “neolithic” cultivators. He argued that the figure 150 was a key threshold in community size in these societies. When communities exceed this size, he suggested, basic relationships of kinship and affinity were insufficient to maintain social cohesion; stability could then be maintained only if formal structures developed which defined specific roles within society. In other words, large communities were invariably hierarchically structured in some way, whereas small communities were not.

Similarly, in an analysis of data from 30 societies ranging from hunter-gatherers to large-scale agriculturalists, Naroll (1956) demonstrated that there was a simple power relationship between the maximum settlement size observed in a given society and both the number of occupational specialities and the number of organisational structures recorded for it. His analyses suggest that there is a critical threshold at a maximum settlement size of 500 beyond which social cohesion can only be maintained if there is an appropriate number of authoritarian officials. Bearing in mind that Naroll’s threshold is expressed as the maximum observed settlement size, it seems likely that the equivalent mean settlement size will not be too far from the value of 150 suggested by the above analyses.

Other evidence suggests that 150 may be a functional limit on interacting groups even in contemporary western industrial societies. Much of the sociometric research on industrial and other comparable organisations, for example, has demonstrated that there is a marked negative effect of group size on both group cohesion and job satisfaction (as indicated by absenteeism and turnover in posts) within the size range under consideration (i.e. 50-500 individuals: see, for example, Indik 1965, Porter & Lawler 1965, Silverman 1970). Indeed, an informal rule in business organisation identifies 150 as the critical limit for the effective coordination of tasks and information-flow through direct person-to-person links: companies larger than this cannot function effectively without sub-structuring to define channels of communication and responsibility (J.-M. Delwart, pers. commun.). Terrien & Mills (1955), for example, found that the larger the organisation, the greater the number of control officials that is needed to ensure its smooth functioning.

Other studies have suggested that there is an upper limit on the number of social contacts that can be regularly maintained within a group. Coleman (1964) presented data on friendships among print shop workers which suggest that the likelihood of having friends within the workplace reaches an asymptote at a shop size of 90-150 individuals. (The small size of the sample for large groups makes it difficult to identify the precise point at which “saturation” is reached.) Coleman explicitly argued that this was a consequence of the fact that there is a limit to the number of individuals within a shop that any one person can come into contact with. Moreover, his results also seemed to suggest that the large number of regular interactants that an individual can expect to have within a large work group limits the number of additional friendships that can be made outside the workplace.”


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