This isn't the exact thing Vladimir_M was talking about, but: An Impossibility Theorem for Welfarist Axiologies seems rather worrying for utilitarianism in particular, though you could argue that no ethical system fully escapes its conclusions.

In brief, the paper argues that if we choose for an ethical system the following three reasonable-sounding premises:

• The Dominance Principle: If population A contains the same number of people as population B, and every person in A has higher welfare than any person in B, then A is better than B.
• The Addition Principle: If it is bad to add a number of people, all of with welfare lower than the original people, then it is at least as bad to add a greater number of people, all with even lower welfare than the original people.
• The Minimal Non-Extreme Priority Principle: There is a number n such that an addition of n people with very high welfare and a single person with negative welfare is at least as good as an addition of the same number of people but with very low positive welfare.

then we cannot help but to accept one of the following:

• The Repugnant Conclusion: For any perfectly equal population with very high positive welfare, there is a population with very low positive welfare which is better.
• The Sadistic Conclusion: When adding people without affecting the original people's welfare, it can be better to add people with negative welfare rather than positive welfare.
• The Anti-Egalitarian Conclusion: A population with perfect equality can be worse than a population with the same number of people, inequality, and lower average (and thus lower total) positive welfare.

This seems rather bad. I haven't had a chance to work through the proof to make sure it checks out, however.

Unfortunately I couldn't find an ungated version of the paper to link to. However I did find this paper by the same author, where he argues that if we define

• The Egalitarian Dominance Condition: If population A is a perfectly equal population of the same size as population B, and every person in A has higher welfare than every person in B, then A is better than B, other things being equal.
• The General Non-Extreme Priority Condition: There is a number n of lives such that for any population X, and any welfare level A, a population consisting of the X-lives, n lives with very high welfare, and one life with welfare A, is at least as good as a population consisting of the X-lives, n lives with very low positive welfare, and one life with welfare slightly above A, other things being equal.
• The Non-Elitism Condition: For any triplet of welfare levels A, B, and C, A slightly higher than B, and B higher than C, and for any one-life population A with welfare A, there is a population C with welfare C, and a population B of the same size as A U C and with welfare B, such that for any population X consisting of lives with welfare ranging from C to A, B U X is at least as good as A U C U X, other things being equal.
• The Weak Non-Sadism Condition: There is a negative welfare level and a number of lives at this level such that an addition of any number of people with positive welfare is at least as good as an addition of the lives with negative welfare, other things being equal.
• The Weak Quality Addition Condition: For any population X, there is a perfectly equal population with very high positive welfare, and a very negative welfare level, and a number of lives at this level, such that the addition of the high welfare population to X is at least as good as the addition of any population consisting of the lives with negative welfare and any number of lives with very low positive welfare to X, other things being equal.

then no axiology can satisfy all of these criteria. (I have not worked through this logic either.)