Ex ante prioritarianism and negative-leaning utilitarianism do not override individual interests

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.

Suppose there are two diseases, SEVERE and MILD. An individual with SEVERE will have utility 10, while an individual with MILD will have utility 100. If SEVERE is treated, it will instead have utility 20, a gain of 10. If MILD is treated, it will instead have utility 120, a gain of 20.

Now, suppose there are two individuals, A and B. One will have SEVERE, and the other will have MILD. You can treat either SEVERE or MILD, but not both. Which should you treat?

1. If you know who will have SEVERE with certainty, then with a sufficiently prioritarian view, you should treat SEVERE. To see why, suppose you know A has SEVERE. Then, by treating SEVERE, the utilities would be (20, 100) for A and B, respectively, but by treating MILD, they would be (10, 120). (20, 100) is better than (10, 120) if you're sufficiently prioritarian. Symmetrically, if you know B has SEVERE, you get (100, 20) for treating SEVERE or (120, 10) for treating MILD, and again it's better to treat SEVERE.

2. If you think each will have SEVERE or MILD with probability 0.5 each (and one will have SEVERE and the other, MILD), then you should treat MILD. This is because the expected utility if you treat MILD is (10+120)*0.5 = 65 for each individual, while the expected utility if you treat SEVERE is (20+100)*0.5 = 60 for each individual. Treating MILD is ex ante better than treating SEVERE for each of A and B. If neither of them knows who has which, they'd both want to you treat MILD.

What's the difference from your point of view between 1 and 2? Extra information in 1. In 1, whether you find out that A will have SEVERE or B will have SEVERE, it's better to treat SEVERE. So, no matter which you learn is the case in reality, it's better to treat SEVERE. But if you don't know, it's better to treat MILD.

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.

One issue is how you decide whether a given person exists in a given history or not. For example, if I had been born with a different hair color, would I be the same person? Maybe. How about a different personality? At what point do "I" stop existing and someone else starts existing? I guess similar issues bedevil the question of whether a person stays the same person over time, though there we can also use spatiotemporal continuity to help maintain personal identity.

Here are some interesting examples I thought of. If I rearranged someone's brain cells (and maybe atoms) to basically make a (possibly) completely different brain structure with (possibly) completely different memories and personality, should we consider these different individuals? Consider the following cases:

1. What if all brain function stops, I rearrange their brain, and then brain function starts again?

2. What if all brain function stops, I rearrange their brain to have the same structure (and memories and personality), but with each atom/cell in a completely different area from where it started, and then brain function starts again?

3. What if all brain function stops, the cells and atoms move or change as they naturally would without my intervention, and then brain function starts again?

To me, 1 clearly brings about a completely different individual, and unless we're willing to say that two physically separate people with the same brain structure, memories and personality are actually one individual, I think 2 should also bring about a completely different individual. 3 only really differs from 1 and 2 only by degree of change, so I think it should also bring about a completely different individual, too.

What this tells me is that if we're going to use some kind of continuity to track identity at all, it should also include continuity of conscious experiences. Then we have to ask:

Are there frequent (e.g. daily) discontinuities or breaks in a person's conscious experiences?

Whether there are or not, should our theory of identity even depend on this fact? If it happened to be the case that sleep involved such discontinuities/breaks and people woke up as completely different individuals, would our theory of identity be satisfactory?

Maybe a way around this is to claim that there are continuous degrees of identification between a person at different moments in their life, e.g. me now and me in a week are only 99% the same individual. I'm not sure how we could do ethical calculus with this, though.

If I understand the view correctly, it would say that a world where everyone has a 49.99% chance of experiencing pain with utility of -10^1000 and a 50.01% chance of experiencing pleasure with utility of 10^1000 is fine, but as soon as anyone's probability of the pain goes above 50%, things start to become very worrisome (assuming the prioritarian weighting function cares a lot more about negative than positive values)?

Yes, although it's possible that a single individual even having a 100% possibility of pain might not outweigh the pleasure of the others, if the number of other individuals is large enough and the social welfare function is sufficiently continuous and "additive", e.g. it takes the form $S\left(V\right)={\sum }_{i:v_i\in V}f\left(v_i\right)$ for $f:R\to R$ strictly increasing everywhere.

What probability distribution are the expectations taken with respect to? If you were God and knew everything that would happen, there would be no uncertainty (except maybe due to quantum randomness depending on one's view about that). If there's no randomness, I think ex ante prioritarianism collapses to regular prioritarianism.

I intended for your own subjective probability distribution to be used, but what you say here leads to some more weird examples (besides collapsing to regular prioritarianism (possibly while aggregating actual utilities over each individual first before aggregating across them)):

I've played a board game where the player who gets to go first is the one who has the pointiest ears. The value of this outcome would be different if you knew ahead of time who this would be compared to if you didn't. In particular, if there's were morally significant tradeoff between utilities, then this rule could be better or worse than a more (subjectively) random choice, depending on whether the worse off players are expected to benefit more or less. Of course, a random selection could be better or worse than one whose actual outcome you know in advance for utilitarians, but there are some differences.

For ex ante prioritarianism, this is also the case before and after you would realize the outcome of the rolls of dice or coin flips; once you realize what the outcome of the random selection is, it's no longer random, and the value of following through with it changes. In particular, if each person had the same wellbeing before the rolls of the dice and stood to gain or lose the same amount if they won (regardless of the selection process), then random selection would be optimal and better than any fixed selection with whose outcome you know in advance, but once you know the outcome of the random selection process, before you apply it, it reduces to using any particular rule whose outcome you know in advance.

One issue is how you decide whether a given person exists in a given history or not. For example, if I had been born with a different hair color, would I be the same person? Maybe. How about a different personality? At what point do "I" stop existing and someone else starts existing? I guess similar issues bedevil the question of whether a person stays the same person over time, though there we can also use spatiotemporal continuity to help maintain personal identity.

Yes, I think it's basically the same issue. If we can use something like spatiotemporal continuity (I am doubtful that this can be made precise and coherent enough in a way that's very plausible), then we could start before a person is even conceived. Right before conception, the sperm cells and ova could be used to determine the identities of the potential future people. Before the sperm cell used in conception even exists, you could imagine two sperm cells with different physical (spatiotemporal) origins in different outcomes that happen to carry the same genetic information, and you might consider the outcomes in which one is used to have a different person than the outcomes in which the the other is. Of course, you might have to divide up these two groups of outcomes further still. For example, you wouldn't want to treat identical twins as a single individual, even if they originated from some common group of cells.