As you've stated the view, I think it would violate transitivity. Consider the following three populations, where each position in the vector denotes the wellbeing of a specific person, and a dash represents the case where that person does not exist:
A: (2, 1)
A': (1, 2)
B: (2, -)

A is better than (or perhaps equally as good as?) B, because we match the first person with  themselves, then settle by comparing the second person at 1 (in A) to non-existence in B. You didn't say how exactly to do this, but I assume A is supposed to be at least as good as B, since that's what you wanted to say (and I guess you mean to say that it's better).

However, A and A' are equally good.

Transitivity would entail that A' is therefore at least as good as B, but on the procedure you described, A is worse than B because we compare them first according to wellbeing levels for those who exist in both, and the first person exists in both and is better off in B.

I don't doubt that the view can be modified to solve this problem, but it's common in population ethics that solving one problem creates another.

I probably won't reply further, by the way - just because I don't go on EA forums much. Best of luck.

No problem. It's always good to see people getting into population ethics.

>>maybe there's a different "fix" altogether that avoids both issues.

Unfortunately, there isn't. Specifically, consider the following three conditions:

1) A condition encoding avoidance of what you call the "birth paradox" (usually called the Mere Addition Principle) 

2) Another condition which prevents us from being radically elitist in the sense that we prefer to give LESS wellbeing to people who already have a lot, rather than MORE wellbeing to people who have less. (Notice that this can be stated without appealing to the importance of "total wellbeing" - I just did it earlier as a convenient shorthand.) These conditions are usually called things like "Non Anti-Egalitarianism", "Pigou-Dalton", or "Non-Elitism".

3) Transitivity.

It can be shown that every population satisfying these three conditions implies the Repugnant Conclusion. There's also a big literature on impossibility results for avoiding the Repugnant Conclusion, and to cut a long story short, these conditions (1), (2) and (3) can be weakened or replaced.

If you're interested in this topic, I would recommend trying to slog through some of the extensive literature first, if you haven't already. A good place to start is Hilary Greaves' Philosophy Compass article, "Population Axiology". 

If you find that article interesting, you can follow up some of the references there. There's a precise and easy-to-follow rendition of the original Mere Addition Paradox in Ng (1989), "What should we do about future generations? Impossibility of Parfit's Theory X". And I think Parfit's original discussion of population ethics in Reasons and Persons (part 4) is still well worth reading, even if it's outdated in some regards. 

The most important discussion of impossibility theorems is in an unpublished manuscript by Gustaf Arrhenius, "Population Ethics: The Challenge of Future Generations". The main results in that book are also published in papers from 2003, 2009 and 2011. The 2022 Spears/Budolfson paper, "Repugnant Conclusions", is also well worth a read in my opinion, as is Jacob Nebel's "An Intrapersonal Addition Paradox" (2019 I think). Jake also has a very nice paper, "Totalism Without Repugnance", where he puts forward a lexical view and tries to answer some of the standard objections to them. 

I think this post is too long for what it's trying to do. There's no need to frontload so many technicalities - just compare finite sequences of real numbers. The other details don't matter too much.

If I've understood your view correctly, it's a lexical view that's got the same problem that basically all lexical views have: it prioritises tiny improvements for some over any improvements, no matter how large, for others. The key point is this: the reason your view avoids the Repugnant Conclusion is that it recommends populations where there is much less total wellbeing but some people have great lives (the "A+ world" from the Mere Addition Paradox) over populations where there is more total wellbeing but everyone has a mediocre life (the "Z world" from the Mere Addition Paradox).

Actually, when it comes to comparing same-person populations of people with positive wellbeing, it looks to me like your view always recommends the one with the highest maximum wellbeing. That's because you're using the leximax ordering. Thus, a population (10, 1) is better than a population (9, 9), since the first pair to be compared is 10 vs 9, an the first population wins that comparison. You *can* avoid the Repugnant Conclusion if you're willing to go down this route. But I suspect most people would think that the cure is worse than the disease. I also think it's inaccurate to call this view a version of "prioritarianism" - again, unless I've misunderstood how it works.

She currently holds a research position at the Institute for Futures Studies in Stockholm.

Just a small note here about Frick's case you mentioned in footnote 34. I believe Frick's case is now in print, in "Context-Dependent Betterness and the Mere Addition Paradox", which I think is in Ethics and Existence (2022). You know the book I guess. I've only got a preprint in front of me, but the case there is called "Change of Plans". I'd guess he kept the name.

Thanks for reading! I totally agree with you that there's a lot to talk about when it comes to non-transitive moral theories. I did consider going into it in more depth. I agree with you that there's a good reason to do so: it might not be clear, especially to non-philosophers, how secure principles like transitivity really are. But there are also two good reasons on the other side for not going into it further, and I thought on balance they were a bit stronger. 

The first one is that I was summarising the paper, so I didn't want to spend too much time giving my own views (and it would have to be my own views, given that the original paper doesn't really discuss it). The second reason, which is probably more important, is that I was really trying hard to keep the word count down, and I felt that if I were to say more about non-transitivity than I already did, it would probably take a lot of space/words to do so. 

(Suppose I did something very quick - for example, suppose I just gave Broome's standard line that we should accept transitivity because it's a consequence of the logic of comparatives. Setting aside whether that's actually a good argument, if I just said that without explaining it further I think there are very few people it would help: people who aren't familiar with that argument won't find out what it means from my saying that, while people who do know what it means already know what it means! And if I wanted to explain the argument in detail, I think it would take a couple of paragraphs at least.)

Thanks for reading James! It's a good question, let me get to it.

It's probably easier to see what's going on if we set some concrete numbers down. So let's say n is ten, and the states of nature are decided by rolling a six-sided die. The state with probability p (= 2/6)  is where the die rolls 1 or 2, and the state with probability q (= 1/6) is where the die rolls 3. The last state with probability 1 - p - q (= 1/2) is where the die rolls anything else, so 4-6.

The table's then supposed to mean that on A, you save 10 lives if the die rolls 1 or 2, you also save 10 lives if the die rolls 3, and you save nobody if it rolls 4-6. Or, putting it another way, you save 10 lives if the die rolls between 1 and 3 (with probability 1/6 + 2/6 = 1/2) and save nobody otherwise.

I think something that maybe wasn't clear is that the probabilities in the tables are supposed to be attached to mutually exclusive events. That is, if you rolled a 1, you can't also have rolled a 3. So there's no way of saving 10 + 10 lives, because if you save 10 lives in one way (by rolling a 1), that means you didn't save 10 lives in another way (by rolling a 3).

On "A Paradox":

" According to assumption (1), this act is not worse than A. Standard person-affecting view says that it is not wrong to cause someone to exist whose life is net positive, so A is not worse than B. Under act C, you cause Afiya to be born and prevent her from getting malaria. This beats act A according to (2), and is not better than act B according to (1). Thus, A = B, B ≥ C, and C > A. But this creates a contradiction: B > A and B = A. "

This argument appears to assume completeness, but it's far from clear that those who believe that adding good lives does not make an outcome better should accept completeness. (Broome 2005, "Should We Value Population?", shows that they should not, provided they accept transitivity and the sort of choice-set independence implicitly assumed here).