The Mere Addition Paradox suffices to refute the AVG view. From Nick's link:

Scenario A contains a population in which everybody leads lives well worth living. In A+ there is one group of people as large as the group in A and with the same high quality of life. But A+ also contains a like number of people with a somewhat lower quality of life. In Parfit's terminology A+ is generated from A by “mere addition”. Comparing A and A+ it is reasonable to hold that A+ is better than A or, at least, not worse.

For example, A+ could evolve from A by the choice of some parents to have children whose quality of life is good, though not as good as the average in A. We can even suppose that this makes the parents a little happier, while still lowering the overall average.