|Robin Dunbar's 2010 book How Many Friends Does One Person Need?: Dunbar’s Number and Other Evolutionary Quarks. |
In short, once group size grows beyond 150, a documented legal system is needed to maintain aggregation.
The Dunbar number is concisely defined as the cognitive limit to the number of individuals with whom any one person can maintain stable relationships. The term was proposed in 1992 by British anthropologist Robin Dunbar.  At or below the number 150, according to Dunbar:
“Orders can be implemented and unruly behavior controlled on the basis of personal loyalties and direct main-to-man contacts. With larger groups, this is impossible.”
To arrive at this number, Dunbar supposedly derived a generalized formula for any given species in which the input is the neocortex ratio (or the neocortex-to-brain size ratio), and the output is maximal size at which a group may retain stability. 
It has been discovered, via observation, that when a social group grows beyond the Dunbar number, it will naturally split apart into two smaller factions, where-after each molecular entity begins to grow in size, and each group tends towards a new Dunbar number. The phenomenon seems to have something to do with stability in connection with the surface law for groupings, or systems of human molecules in combination with the Muller stability ratio. The conception of the Dunbar number is one of the prime theoretical supports of Malcolm Gladwell’s 2000 tipping point theory. 
It has been argued that, according to genetic evidence, a Dunbar size band of humans left Africa some 50,000 years ago, and that all modern humans are descended from this small, stable group of African hominids.
|British anthropologist Robin Dunbar talking in 2010 about his Dunbar number, in particular why the typical person tends not to have more than 150 friends. .|
● Social Avogadro number
● Buffett number
1. (a) Thims, Libb. (2007). Human Chemistry (Volume One) (Dunbar number, pgs. 10, 285). Morrisville, NC: LuLu.
(b) Thims, Libb. (2007). Human Chemistry (Volume Two) (Dunbar number, pgs. 408, 515, 708). Morrisville, NC: LuLu.
2. Armano, David. (2009). “Friendship Isn’t Dead: the Strengthening of the Loose Ties”, Mar 19.
3. Dunbar, Robin. (1992). "Neocortex Size as a Constraint on Group Size in Primates", Journal of Human Evolution, 22: 469-93.
4. Dunbar, Robin. (2010). How Many Friends Does One Person Need?: Dunbar’s Number and Other Evolutionary Quarks (abs). Harvard University Press.
5. Gladwell, Malcolm. (2000). The Tipping Point (pgs. 177-81, 185-86). Little, Brown, and Co.
6. Harris, Sam. (2010). The Moral Landscape (pg. 114). Free Press.
● Dunbar’s number – Wikipedia.