Define the 'person-affecting view' as the claim that particular persons (or sentient beings) are what ultimately matter, the ultimate source from which practical reasons stem, or that for the sake of which the reasons exert their normative force. The view has prima facie appeal, but I think the non-identity problem - where a bad event doesn't harm anyone in particular - shows that we should reject this in favour of the 'world-affecting view' that it is the world as a whole, not [just] its particular constituents, that is of ultimate import.
As an extreme example, compare these two worlds:
(w1) Mass sterilization, extinction: everyone alive is sterilized, without exception. There will be no future generations. Most folks are pretty unhappy about this (as you might expect), but life goes on - for them, at least - and their personal welfare is not catastrophically affected.
(w2) Temporary hardship, future utopia: everyone alive suffers some hardship, equivalent (in terms of personal welfare) to the harms they suffer in w1. So everyone in w1 does just as poorly in w2. But then they spawn future generations, all of whom have blissfully wonderful lives.
Obviously, w2 is better than w1. We have reason to prefer future utopia to mass sterilization. If someone implements the latter, we have reason to lament this fact. But why, or for whose sake? No-one was made worse-off by the choice to realize w1 rather than w2. And it would hardly make sense to lament it for the sake of those who will now never get to exist. (There are no such individuals, remember! No Platonic souls waiting by the river Lethe to be born into our world.) Instead, I propose, we must be lamenting the loss suffered by the world as a whole (which exists well enough).
I assume here a general principle of 'Actual Reasons': reasons that actually exist can only stem from - and exert their force on behalf of - entities that (likewise) actually exist.
This forces us to reject the person-affecting restriction, if we do not think that actually existing people are the only people that matter. Reasons can also invoke the welfare of merely possible people as being of moral significance. But the principle of Actual Reasons implies that this invocation must ultimately be on behalf of some actually existing entity. The entity in question cannot be a person, because the interests of actual people give us no reason to favour w2 over w1. So we must appeal to some larger, supra-personal entity, such as 'the world'.
Is there any way to escape this argument (without denying the truism that we have moral reason to prefer w2 to w1)? One of my professors suggests that the 'Actual Reasons' principle should be amended to also allow entities that "will exist if we choose one of the options available to us". But this strikes me as metaphysically suspect. Firstly, it is unclear whether there is any determinate possible entity that we can really refer to here. Secondly: notice that the reason will exist whichever choice we make, so its source must likewise exist in either case -- otherwise, where has the reason come from? It would seem a kind of magic, for possible future persons to reach out and create reasons in the present, even if they turn out to never exist at all!
To preempt any possible misunderstandings, I should emphasize that it is not at all mysterious why facts about possible people's welfare could suffice to give us reasons. (These facts reveal ways we could make the world a better place, and there's nothing especially mysterious about the desirability of that.) What I consider mysterious is not just that it's desirable to bring happy people into existence, nor even that this outcome is non-instrumentally desirable or 'good in itself', but the further claim that this is desirable for the sake of those possible people. Note that in case of retrospective lamentation (e.g. post-sterilization, above), "they" will even be definitely non-existent. So for "them" to really do anything -- including providing the ultimate metaphysical grounds of a reason to lament how things turned out -- seems strictly nonsensical, no?