ScienceDaily reports on the work of L. Chittka (here) on the relationship between brain size and complexity.
“Research repeatedly shows how insects are capable of some intelligent behaviours scientists previously thought was unique to larger animals. Honeybees, for example, can count, categorise similar objects like dogs or human faces, understand ‘same’ and ‘different’, and differentiate between shapes that are symmetrical and asymmetrical…. We know that body size is the single best way to predict an animal’s brain size….The size increase allows the brain to function in greater detail, finer resolution, higher sensitivity or greater precision: in other words, more of the same….In bigger brains we often don’t find more complexity, just an endless repetition of the same neural circuits over and over. This might add detail to remembered images or sounds, but not add any degree of complexity. …This must mean that much ‘advanced’ thinking can actually be done with very limited neuron numbers. Computer modelling shows that even consciousness can be generated with very small neural circuits, which could in theory easily fit into an insect brain. In fact, the models suggest that counting could be achieved with only a few hundred nerve cells and only a few thousand could be enough to generate consciousness.”
I believe that this may be a slight over simplification. For a particular kind of animal, after correction for body size, brain size predicts intelligence. It is just that intelligence does not relate to brain size across different types of animal. Also the body size correction must be made. Of course intelligence would have something to do with level of detail, resolution, precision etc. and that relationship would follow brain size within a particular brain architecture. But a particular capability (without reference to its resolution) would not be related to brain size. In that case all animals could have some degree of consciousness.
There is a quote mistakenly attributed to Stalin or Lenin but said by David Glantz about the WW2 Soviet army, “Sometimes, quantity has a quality all its own”. This is probably true of brains.