It is also worth noting that average utilitarianism has also its share of problems: killing off anyone with below-maximum utility is an improvement.
No it isn't. This can be demonstrated fairly simply. Imagine a population consisting of 100 people. 99 of those people have great lives, 1 of those people has a mediocre one.
At the time you are considering doing the killing the person with the mediocre life, he has accumulated 25 utility. If you let him live he will accumulate 5 more utility. The 99 people with great lives will accumulate 100 utility over the course of their lifetimes.
If you kill the guy now average utility will be 99.25. If you let him live and accumulate 5 more utility average utility will be 99.3. A small, but definite improvement.
I think the mistake you're making is that after you kill the person you divide by 99 instead of 100. But that's absurd, why would someone stop counting as part of the average just because they're dead? Once someone is added to the population they count as part of it forever.
It is also worth noting that average utilitarianism has also its share of problems: killing off anyone with below-maximum utility is an improvement.
It's true that some sort of normalization assumption is needed to compare VNM utility between agents. But that doesn't defeat utilitarianism, it just shows that you need to include a meta-moral obligation to make such an assumption (and to make sure that assumption is consistent with common human moral intuitions about how such assumptions should be made).
As it happens, I do interpersonal utility comparisons all the time in my day-to-day life using the mental capacity commonly referred to as "empathy." The normalizing assumption I seem to be making is to assume that others people's minds are similar to mine, and match their utility to mine on a one to one basis, doing tweaks as necessary if I observe that they value different things than I do.
Consider the following facts:
This sounds a lot like the mere addition paradox, illustrated by the following diagram:
This is seems to lead directly to the repugnant conclusion - that there is a huge population of people who's lives are barely worth living, but that this outcome is better because of the large number of them (in practice this conclusion may have a little less bite than feared, at least for non-total utilitarians).
But that conclusion doesn't follow at all! Consider the following aggregation formula, where au is the average utility of the population and n is the total number of people in the population:
au(1-(1/2)n)
This obeys the two properties above, and yet does not lead to a repugnant conclusion. How so? Well, property 2 is immediate - since only the average utility appears, the reallocating utility in a more egalitarian way does not decrease the aggregation. For property 1, define f(n)=1-(1/2)n. This function f is strictly increasing, so if we add more members of the population, the product goes up - this allows us to diminish the average utility slightly (by decreasing the utility of the people we've added, say), and still end up with a higher aggregation.
How do we know that there is no repugnant conclusion? Well, f(n) is bounded above by 1. So let au and n be the average utility and size of a given population, and au' and n' those of a population better than this one. Hence au(f(n)) < au'(f(n')) < au'. So the average utility can never sink below au(f(n)): the average utility is bounded.
So some weaker versions of the mere addition argument do not imply the repugnant conclusion.