Among the birds and mammals in general, the spezies with the biggest brains relative to body size are precisely those that mate monogamously. Those that live in large anonymous flocks or herds and mate promiscuously have much smaller brains.
The birds make it especially clear that the real issue is strong, resilient, long-lasting pairbonds. Birds that mate monogamously come in two quite different kinds. There are those, like many common garden birds such as robins and tits, that chose a new mate each breeding season. But there are many others, such as many birds of prey, the owls and most of the crow and parrot families, that mate for life. It is this second group, which have the biggest brains of all among the birds, far bigger than those that are seasonally monogamous, and this is true even when we control for differences in lifestyle, diet and body size.
Robin Dunbar, How many... Dunbar's Number and other Evolutionary Quirks