The Supervenience Theorem is quite strong and interesting, but perhaps too strong for many with egalitarian or prioritarian intuitions. Indeed, this is discussed with respect to the conditions for the theorem. In its proof, it’s shown that we should treat any problem like the original position behind the veil of ignorance (the one-person scenario; for n individuals, we treat ourselves as having probability 1/n of being any of those n individuals, and we consider only our own interests in that case), so that every interpersonal tradeoff is the same as a personal tradeoff. This is something that I’m personally quite skeptical of. In fact, if each individual ought to maximize their own expected utility in a way that is transitive and independent of irrelevant alternatives when only their own interests are at stake, then fixed-population Expected Totalism follows (for a fixed population, we should maximize the unweighted total expected utility). The Supervenience Theorem is something like a generalization of Harsanyi’s Utilitarian Theorem this way. EDIT: Ah, it seems like this link is made indirectly through this paper, which is cited.
That being said, the theorem could also be seen as an argument for Expected Totalism, if each of its conditions can be defended or to whoever leans towards accepting them.
If we’ve already given up the independence of irrelevant alternatives (whether A or B is better should not depend on what other outcomes are available), it doesn’t seem like much of an extra step to give up separability (whether A or B is better should only depend on what’s not common to A and B) or Scale Invariance, which is implied by separability. There are different ways to care about the distribution of welfares, and prioritarians and egalitarians might be happy to reject Scale Invariance this way.
Prioritarians and egalitarians can also care about ex ante priority/equality, e.g. everyone deserves a fair chance ahead of time, and this would be at odds with Statewise Supervenience. For example, given H=heads and T=tails, each with probability 0.5, they might prefer the second of these two options, since it looks fairer to Adam ahead of time, as he actually gets a chance at a better life. Statewise Supervenience says these should be equivalent:
If someone cares about ex post equality, e.g. the final outcome should be fair to everyone in it, they might reject Personwise Supervenience, because personwise-equivalent scenarios can be unfair in their final outcomes. The first option here looks unfair to Adam if H happens (ex post), and unfair to Eve if T happens (ex post), but there’s no such unfairness in the second option. Personwise Supervenience says we should be indifferent, because from Adam’s point of view, ignoring Eve, there’s no difference between these two choices, and similarly from Eve’s point of view. Note that maximin, which is a limit of prioritarian views, is ruled out.
There are, of course, objections to giving these up. Giving up Personwise Supervenience seems paternalistic, or to override individual interests if we think individuals ought to maximize their own expected utilities. Giving up Statewise Supervenience also has its problems, as discussed in the paper. See also “Decide As You Would With Full Information! An Argument Against Ex Ante Pareto” by Marc Fleurbaey and Alex Voorhoeve, as well as one of my posts which fleshes out ex ante prioritarianism (ignoring the problem of personal identity) and the discussion there.