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).