Dunbar and Shultz ask why primates have such large brains, compared to their body mass, compared with other animals. Here is their abstract, followed by a central clip from their article:
The evolution of unusually large brains in some groups of animals, notably primates, has long been a puzzle. Although early explanations tended to emphasize the brain's role in sensory or technical competence (foraging skills, innovations, and way-finding), the balance of evidence now clearly favors the suggestion that it was the computational demands of living in large, complex societies that selected for large brains. However, recent analyses suggest that it may have been the particular demands of the more intense forms of pairbonding that was the critical factor that triggered this evolutionary development. This may explain why primate sociality seems to be so different from that found in most other birds and mammals: Primate sociality is based on bonded relationships of a kind that are found only in pairbonds in other taxa.
Figure - In anthropoid primates, mean social group size increases with relative neocortex volume (indexed as the ratio of neocortex volume to the volume of the rest of the brain). Solid circles, monkeys; open circles, apes. Regression lines are reduced major axis fits.
The important issue in the present context is the marked contrast between anthropoid primates and all other mammalian and avian taxa (including, incidentally, prosimian primates): Only anthropoid primates exhibit a correlation between social group size and relative brain (or neocortex) size. This quantitative relationship is extremely robust; no matter how we analyze the data (with or without phylogenetic correction, using raw volumes, or residuals or ratios against any number of alternative body or brain baselines) or which brain data set we use (histological or magnetic resonance imaging derived, for whole brain, neocortex, or just the frontal lobes), the same quantitative relationship always emerges. This suggests that, at some early point in their evolutionary history, anthropoid primates used the kinds of cognitive skills used for pairbonded relationships by vertebrates to create relationships between individuals who are not reproductive partners. In other words, in primates, individuals of the same sex as well as members of the opposite sex could form just as intense and focused a relationship as do reproductive mates in nonprimates. Given that the number of possible relationships is limited only by the number of animals in the group, primates naturally exhibit a positive correlation between group size and brain size. This would explain why, as primatologists have argued for decades, the nature of primate sociality seems to be qualitatively different from that found in most other mammals and birds. The reason is that the everyday relationships of anthropoid primates involve a form of "bondedness" that is only found elsewhere in reproductive pairbonds.