The human brain volume has been shrinking over the past 20 000 years or so, after millions years of increase in volume. Not just the brain size, but the brain size relatively to body size as well. We are lacking a tennis-ball sized piece of our earlier brain (and it might even be God-shaped).
Brain is expensive in many ways: energy consumption, birth complications and locomotion impairment for females, lower survival of head impacts i'd guess. The damn thing along with supporting structures is heavy and awkwardly located, etc.
And the big brain can only be advantageous if it improves reproduction substantially, with larger brained individuals being sufficiently more successful at surviving and reproducing than smaller brained individuals, as to negate the above-mentioned cost.
That must have been the case through the evolution up to a couple tens thousands years ago, to produce the big brains that we have. It is clear to see that in past 20 000 years, the environment in which humans live has undergone very significant change due to emergence of societies; the new environment may not be pushing us as hard [in the direction of intelligence], at least on the individual level. [and may have been pushing us too hard for smaller brains, thanks Nornagest for making that point]
We were evolving ability to think, until it got just about to the point of being barely able - with great difficulty and many falls - to think useful thoughts. If we were species that were evolving flight, we'd be the species that could just barely fly, and recently flew over a river, entering new land. In the new land, everything is different. And our wings were shrinking at very rapid rate.
The important question is - Did we lose any functionality since then? Are we dumber? Are we less sane in some way? (The palaeolithic humans did not seem to do any really insane religious stuff)
The notion that our brains just got more efficient and 'therefore' could shrink in size appears very shaky to me. This 'therefore' comes from fallacy of anthropomorphizing the evolution. Evolution doesn't work to a goal of optimizing some sub-unit in the organism while preserving specifications, in the way that a team on an engineering project would.
The optimization could as well instead make brain even larger, if said improvement made larger brain pay off more. One would have to show that some improvement in brain efficiency has actually decreased advantage of big brains over small brains, to explain the smaller brains with them being more optimized.
The evolution optimizes the whole organism, not the brain, and there's very many of other factors that have changed at that specific time that may as well have decreased selection pressure towards intelligence or increased the costs.
In my opinion the sensible default hypothesis should be that we had a decrease in some functionality, and likely are still declining.
My best guess is that it is the capacity to invent solutions on spot and think by ourselves, that we are losing. Before emergence of societies, the technological progress was severely limited by information loss. Any smart individual could massively improve fitness of the relevant genes by (re)inventing some basic, but extremely effective techniques, which he'd teach mostly to genetically related individuals. The technique would easy become lost, creating again an opportunity for intelligence to succeed - reinventing it.
Even very simple invention requires massive search in the vast space of possibilities. Precisely the kind of task that one would expect to benefit from larger raw computational power.
edit:
Some clarification with regards to the need for innovation. In the long run, it is not enough to just do what you're taught. Teaching is a lossy process. You need to improve upon what was taught to you a little to make the tool as good as your ancestor made - you need minor innovation to merely preserve the tools - a little more innovation and you'll improve over time, a little less and you'll lose it over time. The little children have to figure out everything from a few clues; they don't download some braindump of the wisest elder to be able to speak, they essentially figure out an alien language - a very difficult task.
I'm a little confused. Are you disagreeing that shrinkage took place, or are you disagreeing that brain volume relates to the ability?
From earlier post:
There's a perfectly good explanation for having well agreed data that the brain volume varies between populations, yet not having well agreed data that intelligence or other functionality varies between populations: it is straightforwardly true that the variation in intelligence is both dramatically easier to paper over AND we'd be more inclined to paper it over, than craniometry. Ten percent difference between brain volumes can't be papered over. Ten percent difference in any intelligent function easily can.
Basically, the data we have on intelligence (or tendency towards religious craziness) across ethnic groups is utter and complete garbage. That is not same thing as having evidence for zero variation.
edit: that is to say:
I do not believe that if there was 10% variation of some function across races or genders, such a difference would be reliably agreed upon.
If you take IQ test of same person twice - or take two different tests - there's much, much less agreement than if you do craniometry using MRI or between different MRI machines or between different methods of doing craniometry. That is to say, our intelligence-sensor got dramatically larger error than our brain-volume sensor, and the data from intelligence sensor would be judged inconclusive for same degree of difference for which the MRI data would be judged nearly indisputable.
In light of this, lack of agreement on this topic constitutes very poor evidence in favour of zero variation of intelligence or it's various aspects (such as rejecting crazy nonsense). You only stick with zero variation if zero variation is a simplest hypothesis - but independence of intelligence from volume is not a simple hypothesis, but instead a very very surprising one, with potential to overturn much of our understanding of evolution as the larger heads have significant costs.
However, I entirely agree that if we were better able to measure intelligence, and were better able to agree upon the intelligence and its variation across races, then lack of evidence for variation of intelligence and the like across races in presence of variation of brain volume would constitute significant evidence in favour of independence of intelligence and other related functions from brain volume.