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.

I don't think this reveals any inconsistencies about moral reasoning at all. Upon reflection it seems obvious to me that the vast majority of the human population accepts the Sadistic Conclusion and considers it morally obvious. And I think that they are right to do so.

What makes me say this? Well, let's dissect the Sadistic Conclusion. Basically, it is a specific variant of another, broader conclusion, which can be stated thusly:

If it the addition of a person or persons with positive welfare can sometimes be bad, then it is sometimes preferable to do other bad things than to add that person or persons. Examples of these other bad things include harming existing people to avoid adding that person, failing to increase the welfare of existing people in order to avoid adding that person, or the Sadistic Conclusion.

What would a world where people accepted this conclusion look like? It would be a world where people refrained from doing pleasurable things in order to avoid adding another person to the world (for instance, abstaining from sex out of fear of getting pregnant). It would be a world where people spent money on devices to prevent the addition of more people, instead of on things that made them happy (for example, using money to buy condoms instead of candy). It would be a world where people chose to risk harm upon themselves rather than add more people to the world (by having surgical procedures like vasectomies, which have a nonzero risk of complications). In other words, it's our world.

So why does the Sadistic Conclusion seem unpalatable, even though it's obvious that pretty much everyone accepts the principle it is derived from? I think it's probably same reason that people reject the transplant variant of the trolley problem, even though nearly everyone accepts the normal version of it. The thought of directly doing something awful to other people makes us squeemish and queasy, even if we accept the abstract principle behind it in other situations.

But how could the addition of more people with positive welfare be bad? I think we probably have some sort of moral principle that smaller populations with higher welfare per person are better than larger populations with lower levels of welfare per person, even if the total amount of welfare per person is larger overall in the larger population. (If you don't believe in the concept of "personal identity" just replace the word "person" with the phrase "sets of experiences that are related in certain ways," it doesn't change anything).

A helpful way of looking at it would be to consider this principle on an individual level, rather than a population wide one. Suppose, as in Parfit's classic example someone gets me addicted to a drug that causes me to have a burning desire to take it, and then gives me a lifetime supply of that drug. I have more satisfied desires than I used to have, but my life has not been made any better. This is because I have a set of higher-order preferences about what sort of desires I want to have, if giving me a new desire conflicts with those higher-order preferences then my life has been made worse or the same, not better.

Similarly if adding more people conflicts with higher-order moral principles about how the world should be, adding them makes the world worse, not better. Before I understood this there was a short, dark time where I actually accepted the Repugnant Conclusion, rather than the Sadistic one. Fortunately those dark days are over.

Incidentally, I think the Sadistic Conclusion is poorly named, as it still considers the addition of people with negative welfare to be a bad thing.