Maria Konnikova looked at the research done by anthropologists on the sizes of social groupings. The research initially studied why non-human primates spent so much time on grooming one another but then got extended to humans.
[I]n the nineteen-eighties, the Machiavellian Intelligence Hypothesis (now known as the Social Brain Hypothesis) had just been introduced into anthropological and primatology discourse. It held that primates have large brains because they live in socially complex societies: the larger the group, the larger the brain. Thus, from the size of an animal’s neocortex, the frontal lobe in particular, you could theoretically predict the group size for that animal.
Looking at his grooming data, [anthropologist and psychologist Robin] Dunbar made the mental leap to humans. “We also had humans in our data set so it occurred to me to look to see what size group that relationship might predict for humans,” he told me recently. Dunbar did the math, using a ratio of neocortical volume to total brain volume and mean group size, and came up with a number. Judging from the size of an average human brain, the number of people the average person could have in her social group was a hundred and fifty. Anything beyond that would be too complicated to handle at optimal processing levels.