H/T: Machiavellian intelligence
Note: This is a H/T that is most likely false, though it needs to be linked to evidence that falsifies it. See the discussion page.
The theory or the hypothesis
This H/T claims that big, intelligent brains are required to live in structured groups. It says that big brains are required for groups where each individual has a place. It does accept that small-brained beings can live in unstructured groups or herds, without social relationships. The H/T places the human brain as capable of a few hundred social relationships at most, less in smaller-brained animals.
The predictions regarding small brains
The hypothesis predicts that many small-brained animals should live solitary lives. It does not demand that all small-brained species must be solitary, but this H/T predicts that the only social groups present in very small-brained animals should be unstructured, and that such beings should have no social relationships or places in the group.
The predictions on big brains
Since the H/T demands human brains to be adaptive to social groups well over a hundred individuals, it predicts that modern, large human brains should have evolved under conditions capable of feeding such large groups. The H/T predicts that at the time during which modern human brain size evolved, humans should be living in groups significantly larger than a hundred people. It does not demand pre-humanoids with miniature brains at the proto-sapient level to have lived in that size of groups.
Irrelevant predictions of brain structures
The Machiavellian intelligence hypothesis is said to predict that living in groups should influence details in brain structure that are neither related to brain size nor to the nutrient cost of the brain nor the neuron density. However, the hypothesis that any learning have some effect on brain structure also predict that. Such a prediction is therefore completely non-unique.
Homo naledi survival until recently
Homo naledi lived close in time to the origin of Homo sapiens and had been living with their small chimp-sized brains alongside bigger-brained hominids for a long time. They were at least two million years behind in brain size and also in the blood supply of the brain. While it is true that brain size alone does not determine intelligence, Homo naledi's blood flow in the brain was not much greater than that of chimpanzees either and a more compact intelligent brain would require more of some types of nutrients to compensate for the increased cost of neurons firing strong signals capable of efficient communication in a low myelin brain with small neurons and thin axons and dendrites (similar to bird brains having much higher blood flow per surface unit of brain than primate brains do). So the blood flow data on naledi brains does not match the description of a compact and efficient brain. And yet they were not outcompeted by the supposedly more alliance-forming groups of bigger-brained hominins for all that time.
Homo naledi also show signs of very organized social cooperation such as burying their dead deeply into caves with difficult access, which is way beyond the social cooperation that the Machiavellian intelligence hypothesis predict is possible for ape type brains.