Nice point, but I think it comes at a serious cost.

To see how, consider a different case. In X, ten billion people live awful lives. In Y, those same ten billion people live wonderful lives. Clearly, Y is much better than X. 

Now consider instead Y* which is exactly the same as Y except that we also add one extra person, also with a wonderful life. As before, Y* is much better than X for the original ten billion people. If we say that the value of adding the extra person is undefined and that this undefined value renders the value of the whole change from X to Y* undefined, we get the implausible result that Y* is not better than X. Given plausible principles linking betterness and moral requirements, we get the result that we're permitted to choose X over Y*. That seems very implausible, and so it counts against the claim that adding people results in undefined comparisons.

Thanks!

Wait, all the LLMs get 90+ on ARC? I thought LLMs were supposed to do badly on ARC.

You should read the post! Section 4.1.1 makes the move that you suggest (rescuing PAVs by de-emphasising axiology). Section 5 then presents arguments against PAVs that don't appeal to axiology. 

I think my objections still work if we 'go anonymous' and remove direct information about personal identity across different options. We just need to add some extra detail. Let the new version of One-Shot Non-Identity be as follows. You have a choice between: (1) combining some pair of gametes A, which will eventually result in the existence of a person with welfare 1, and (2) combining some other pair of gametes B, which will eventually result in the existence of a person with welfare 100. 

The new version of Expanded Non-Identity is then the same as the above, except it also has available option (3): combine the pair of gametes A and the pair of gametes B, which will eventually result in the existence of two people each with welfare 10.

Narrow views claim that each option is permissible in One-Shot Non-Identity. What should they say about Expanded Non-Identity? The same trilemma applies. It seems implausible to say that (1) is permissible, because (3) looks better. It seems implausible to say that (3) is permissible, because (2) looks better. And if only (2) is permissible, then narrow views imply the implausible-seeming Losers Can Dislodge Winners.

Now consider wide views and Two-Shot Non-Identity, again redescribed in terms of combining pairs of gametes A and B. You first choose whether to combine pair A (which would eventually result in the existence of a person with welfare 1), and then later choose whether to combine pair B (which would eventually result in the existence of a person with welfare 100). Suppose that you know your predicament in advance, and suppose that you choose to combine pair A. Then (your view implies) you're required to combine pair B, even if that choice occurs many decades later, and even though you wouldn't be required to combine pair B if you hadn't (many decades earlier) chose to combine pair A. Now consider a slightly different case: you first choose whether to combine pair C (which would eventually result in the existence of a person with welfare 101), then later choose whether to combine pair B. Suppose that you know your predicament in advance, and suppose that you decline to combine pair C. Many decades later, you face the choice of whether to combine pair B. Your view seems to imply that you're not permitted to do so. There are thus cases where (all else being equal) you're not even permitted to create a person who would enjoy a wonderful life.

Here's my understanding of the dialectic here:

Me: Some wide views make the permissibility of pulling both levers depend on whether the levers are lashed together. That seems implausible. It shouldn't matter whether we can pull the levers one after the other.

Interlocutor: But lever-lashing doesn't just affect whether we can pull the levers one after the other. It also affects what options are available. In particular, lever-lashing removes the option to create both Amy and Bobby, and removes the option to create neither Amy nor Bobby. So if a wide view has the permissibility of pulling both levers depend on lever-lashing, it can point to these facts to justify its change in verdicts. These views can say: it's permissible to create just Amy when the levers aren't lashed because the other options are on the table; it's wrong to create just Amy when the levers are lashed because the other options are off the table.

Me: (Side note: this explanation doesn't seem particularly satisfying. Why does the presence or absence of these other options affect the permissibility of creating just Amy?). If that's the explanation, then the resulting wide view will say that creating just Amy is permissible in the four-button case. That's against the spirit of wide PAVs, so wide views won't want to appeal to this explanation to justfiy their change in verdicts given lever-lashing. So absent some other explanation of some wide views' change in verdicts occasioned by lever-lashing, this implausible-seeming change in verdicts remains unexplained, and so counts against these views.

Thanks! I'd like to think more at some point about Dasgupta's approach plus resolute choice. 

In Parfit's case, we have a good explanation for why you're rationally required to bind yourself: doing so is best for you.

Perhaps you're morally required to bind yourself in Two-Shot Non-Identity, but why? Binding yourself isn't better for Amy. And if it's better for Bobby, it seems that can only be because existing is better for Bobby than not-existing, and then there's pressure to conclude that we're required to create Bobby in Just Bobby, contrary to the claims of PAVs.

And suppose that (for whatever reason) you can't bind yourself in Two-Shot Non-Identity, so that the choice to create Bobby (having previously created Amy) remains open. In that case, it seems like our wide view must again make permissibility depend on lever-lashing or past choices. If the view says that you're required to create Bobby (having previously created Amy), permissibility depends on past choices. If the view says that you're permitted to decline to create Bobby (having previously created Amy), permissibility depends on lever-lashing (since, on wide views, you wouldn't be permitted to pull both levers if they were lashed together).

Interesting, thanks! I hadn't come across this argument before.

Yes, nice points. If one is committed to contingent people not counting, then one has to say that C is worse than B. But it still seems to me like an implausible verdict, especially if one of B and C is going to be chosen (and hence those contingent people are going to become actual). 

It seems like the resulting view also runs into problems of sequential choice. If B is best out of {A, B, C}, but C is best out of {B, C}, then perhaps what you're required to do is initially choose B and then (once A is no longer available) later switch to C, even if doing so is costly. And that seems like a bad feature of a view, since you could have costlessly chosen C in your first choice.