Introduction
It seems that "ex ante" views (like ex ante prioritarianism) haven't been discussed much within the EA community. Basically, the approach is to aggregate the utility in each individual first, over their life and by taking the expectation, and then apply whatever social welfare function you like to the resulting individually aggregated utilities.
Furthermore, you could take these individual aggregations/expectations conditional on existence (past, current or future), and only include the terms for actual (past, current or future) individuals; so the set of individuals to aggregate over would be a random variable. You'd then take another expectation, this time of of the social welfare function applied to these aggregated utilities over the set of existing individuals.
The main benefit here is to avoid objections of overriding individual interests while still being prioritarian or negative-leaning, since we can treat personal and interpersonal tradeoffs differently.
We define ui to be the aggregated utility of individual i over all time (or just the future), in a given determined outcome (no expectations applied yet); in the outcomes in which they haven't existed and won't exist, ui is left undefined. Then we define
vi=E[ui | i has existed or will exist ]
and we apply our social welfare function S to the set
V={vi|i has existed or will exist}
E.g., S(V)=∑i:vi∈Vf(vi) for some function f:R→R which is increasing (or non-decreasing) and concave. Some examples here. Total utilitarianism has f(v)=v for all v∈R, and the ex ante view applied to it actually makes no difference. A fairly strong form of negative utilitarianism could be defined by f(v)=min{v,0} for all v∈R, i.e. f(v)=v if v≤0 and f(v)=0, otherwise; this means that as long as an individual is expected to have a good life (net positive value), what happens to them doesn't matter, or could be lexically dominated by concerns for those expected to have negative lives (i.e. only if we can't improve any negative lives, can we look to improving positive ones).
Finally, we rank decisions based on the expectation of S(V) over V:
EV[S(V)]=E[S({E[ui|i has existed or will exist] ∣∣ i has existed or will exist})]
Consequences
We can be both prioritarian or negative-leaning and avoid overriding individual interests; we don't give greater weight to the bad over the good in any individual's life, but we give greater weight to bad lives over good lives. Personal and interpersonal tradeoffs would be treated differently. You would be permitted, under an ex ante prioritarian or negative-leaning view, to choose great suffering together with great bliss or risk great suffering for great bliss, but you can't impose great suffering on one person to give great bliss to another (depending on the exact form of the social welfare function).
Let's look at an illustrative example where the ex ante view disagrees with the usual one, taken from "Prioritarianism and the Separateness of Persons" by Michael Otsuka (2012):
Two-person case with risk and inversely correlated outcomes: There are two people, each of whom you know will develop either the very severe or the slight impairment and each of whom has an equal chance of developing either impairment. You also know that their risks are inversely correlated: i.e., whenever one of them would suffer the very severe impairment, then the other would suffer the slight impairment. You can either supply both with a treatment that will surely improve a recipient's situation if and only if he turns out to suffer the very severe impairment or supply both with a treatment that will surely improve a recipient's situation if and only if he turns out to suffer the slight impairment. An effective treatment for the slight impairment would provide a somewhat greater increase in utility than would an effective treatment for the very severe impairment.
An ex ante prioritarian would choose to treat the slight impairment, while the usual prioritarian who does not first aggregate or take expectations over the individual would choose to treat the very severe impairment. From the point of view of each individual, treating the slight impairment would be preferable.
For what it's worth, under empty individualism (the view that one physical person over time should really be treated as a sequence of distinct individuals from moment to moment, person-moments), applying this ex ante modification actually doesn't make any difference. It'll look like we're overriding preferences, but under empty individualism, there are only interpersonal tradeoffs, no personal tradeoffs. See also.
References and other reading
"Prioritarianism and the Separateness of Persons" by Michael Otsuka (2012) describes this approach, gives examples and raises some objections to it.
That issue of Utilitas is focused on prioritarianism, with a paper by Parfit which also discusses ex ante views (I have yet to read it).
Toby Ord's objections to prioritarianism and negative utilitarianism which do not apply to the ex ante view:
"Why I'm Not a Negative Utilitarian"
"A New Counterexample to Prioritarianism" (2015)
This is an interesting idea that sands off some of the unfortunate Pareto-suboptimal edges of prioritarianism. But it has some problems.
Ex-ante prioritarianism looks good in the example cases given where it gives an answer that disagrees with regular prioritarianism but agrees with utilitarianism. However, the cases where ex-ante prioritarianism disagrees with
For instance, consider an extension of your experiment:
Suppose there are two people who are equally well off, and you are considering benefitting exactly one of them by a fixed given amount (the amount of benefit would be the same regardless of who receives it).
Suppose there are two people, A and B, who are equally well off with utility 100. Suppose we have the choice between two options. In Lottery 1, A gets a benefit of 100 with certainty, while B gets nothing. In Lottery 2, either A gets 50 with probability 0.4; B gets 50 with probability 0.4, or no-one gets anything (probability 0.2).
Prioritarianism prefers Lottery 1 to Lottery 2, since one person having a welfare of 100 and the other a welfare of 200 is preferred to an 80% chance of (150, 100) and a 20% chance of (100, 100).
Utilitarianism of course prefers the outcome with expected utility 300 to the outcome with expected utility 240.
But a sufficiently concave ex-ante prioritarianism prefers Lottery 2 because B's lower expected value in Lottery 1 is weighted more highly.
It seems perverse to prefer an outcome which is with certainty worse both on utilitarian and prioritarian grounds just to give B a chance to be the one who is on top.
I won't say I'm convinced by my own responses here, but I'll offer them anyway.
I think B could reasonably claim that Lottery 1 is less fair to them than Lottery 2, while A could not claim that Lottery 2 is less fair to them than Lottery 1 (it benefits them less in expectation, but this is not a matter of fairness). This seems a bit clearer with the understanding that von Neumann-Morgenstern rational agents maximize expected (ex ante) utility, so an individual's ex ante utility could matter to that individual in itself, and an ex ante view respects this. (And I think the claim that ex post prioritarianism is Pareto-suboptimal may only be meaningful in the context of vNM-rational agents; the universe doesn't give us a way to make tradeoffs between happiness and suffering (or other values) except through individual preferences. If we're hedonistic consequentialists, then we can't refer to preferences or the veil of ignorance to justify classical utilitarianism over hedonistic prioritarianism.)
Furthermore, if you would imagine repeating the same lottery with the same individuals and independent probabilities over and over, you'd find in the long run, either in Lottery 1, A would benefit by 100 on average and B would benefit by 0 on average, or with Lottery 2, A would benefit by 20 on average and B would benefit by 20 on average. On these grounds, a prioritarian could reasonably prefer Lottery 2 to Lottery 1. Of course, an ex post prioritarian would come to the same conclusion if they're allowed to consider the whole sequence of independent lotteries and aggregate each individual's own utilities within each individual before aggregating over individuals.
(On the other hand, if you repeat Lottery 1, but swap the positions of A and B each time, then Lottery 1 benefits A by 50 on average and B by 50 on average, and this is better than Lottery 2. The utilitairan, ex ante prioritarian and ex post prioritarian would all agree.)
A similar problem is illustrated in "Decide As You Would With Full Information! An Argument Against Ex Ante Pareto" by Marc Fleurbaey & Alex Voorhoeve (I read parts of this after I wrote the post). You can check Table 1 on p.6 and the surrounding discussion. I'm changing the numbers here. EDIT: I suppose the examples can be used to illustrate the same thing (except the utilitarian preference for Lottery 1): Ex post you prefer Lottery 1 and would realize you'd made a mistake, and if you find out ahead of time exactly which outcome Lottery 2 would have given, you'd also prefer Lottery 1 and want to change your mind.
So, in your ignorance, you would treat MILD, but if you found out who had SEVERE and who had MILD, no matter which way it goes, you'd realize you had made a mistake. You also know that seeking out this information of who has which ahead of time, no matter which way it goes, will cause you to change your mind about which disease to treat. EDIT: I suppose both of these statements are true of your example. Ex post you prefer Lottery 1 and would realize you'd made a mistake, and if you find out ahead of time exactly which outcome Lottery 2 would have given, you'd also prefer Lottery 1.