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Stuart_Armstrong comments on Embracing the "sadistic" conclusion - Less Wrong Discussion
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Mixed systems (welfarist+other stuff) still fall prey to the argument. You can see this by holding "other stuff" constant, and considering the choices between populations that differ only in welfare. Or you can allow "other stuff" to vary, which makes it easy to violate more of the six conditions (the Dominance principle, the Addition principle, the Minimal Non-Extreme Priority principle, the Repugnant conclusion, the Sadistic conclusion, and the Anti-Egalitarian conclusion), maybe violating them all.
It doesn't seem clear that it is always possible to keep "other stuff" constant when varying welfare?
I guess I don't see how you're defining mixed systems. My first version makes any axiology at all "mixed", since you can just take the reliance on welfare to be trivial (which is a trivial example of a welfarist system).
If you have broader theorems about violating this set of conditions, they would be very interesting to know about.
Actually I'm not sure the anti-egalitarian conclusion is even well-formed for non-welfarist systems. You can look at welfare levels (if you think those exist) to get what looks like a form of the conclusion, but then we might say that what looks like it's anti-egalitarian is not better because of the less equal arrangement of welfare, but for some other, non-welfare, reasons. Which doesn't seem necessarily pathological (if you are happy with non-welfare reasons entering in).