Hey Jeffhe- the position you put forward looks structurally really similar to elements of Scanlon’s, and you discuss a dillema that is often discussed in the context of his work (the lifeboat/the rocks example)- It also seems like given your reply to objection 3 you might really like it’s approach (if you are not familiar with it already). Subsection 7 of this SEP article (https://plato.stanford.edu/entries/contractualism/) gives a good overview of the case that is tied to the one you discuss. The idea of the separateness of persons, and the idea that one persons pain can’t cancel out another person pain, is well represented in Scanlon’s work.
I also wonder whether the right way of representing an ‘equal chance of being helped’ in this model is not to flip a coin for each group, but to roll a N sided dice, where N are the total number of people who could be helped, and then choosing whichever group the person whose number is rolled is in: that way everyone, in some sense, has a chance to be saved, and that chance is, in some sense, equal- without leading to the worrying conclusions that Bob and a million peoples lives ought to be settled through a coin flip (The coin-flipping decision theory could also be abused by dividing up groups differently, i.e. I can always re-describe the world in the way where a person I could help in extreme pain is in one group, and all other people are in a different group, but then I can simply redescribed the world to move that person into the ‘all other people’ category, and select another person, which seems to mean we can arbitrarily increase the odds of any one person being the right person to help, simply by moving them between the categories- which seems wrong).
Thanks for directing me to Scanlon’s work. I am adequately familiar with his view on this topic, at least the one that he puts forward in What We Owe to Each Other. There, he tried to put forward an argument to explain why we should save the greater number in a choice situation like the one involving Bob, Amy and Susie, which respected the separateness of persons, but his argument has been well refuted by people like Michael Otsuka (2000, 2006).
Regarding your second point, what reason can you give for giving each person less than the maximum equal chance possible (e.g. 50%) aside from wanting to sidestep a conclusion that is worrying to you? Suppose I choose to give Bob, Amy and Susie each a 1% of being saved, instead of each a 50% of being saved, and I say to them, “Hey none of you have anything to complain about because I’m technically giving each of you an equal chance, even though most likely, none of you will be saved.” Each of them can reasonably protest that doing so does not treat them with the appropriate level of concern. Say then, I give each of them a 1⁄3 chance of being saved (as you propose we do) and again I say to them, “Hey none of you have anything to complain about because I’m technically giving each of you an equal chance”. Don’t you think they can reasonably protest in the same way until I give them each the maximum equal chance (i.e. 50%)?
Regarding your third point, I don’t see how I can divide up the groups differently. They come to me as given. For example, I can’t somehow switch Bob and Amy’s place such that the choice situation is one of either helping Amy or helping Bob and Susie. How would I do that?