I think the reason why you have such a strong intuition of just saving Amy and Susie in a choice situation like the one I described in my previous reply is that you believe Amy’s burning to death plus Susie’s sore throat involves more or greater pain than Bob’s burning to death. Since you think minimizing aggregate pain (i.e. maximizing aggregate utility) is what we should do, your reason for just Amy and Susie is clear.
But importantly, I don’t share your belief that Amy’s burning to death and Susie’s sore throat involves more or greater pain than Bob’s burning to death. On this note, I have completely reworked my response to Objection 1 a few days ago to make clear why I don’t share this belief, so please read that if you want to know why. On the contrary, I think Amy’s burning to death and Susie’s sore throat involves just as much pain as Bob’s burning to death.
So part of the positive case for giving everyone an equal chance is that the suffering on either side would involve the same LEVEL/AMOUNT of pain (even though the suffering on Amy’s and Susie’s side would clearly involve more INSTANCES of pain: i.e. 2 vs 1.)
But even if the suffering on Amy’s and Susie’s side would involve slightly greater pain (as you believe), there is a positive case for giving Bob some chance of being saved, rather than 0. And that is that who suffers matters, for the reason I offered in my response to Objection 2. I think that response provides a very powerful reason for giving Bob at least some chance, and not no chance at all, even if his pain would be less great than Amy’s and Susie’s together.
(My response to Objection 3 makes clear that giving Bob some chance is not in conflict with being impartial, so that response is relevant too if you think doing so is being partial)
At the end of the day, I think one’s intuitions are based on one’s implicit beliefs and what one implicitly takes into consideration. Thus, if we shared the same implicit beliefs and implicitly took the same things into consideration, then we would share the same intuitions. So one way to view my essay is that it tries to achieve its goal by doing two things:
1) Challenging a belief (e.g. that Amy’s burning to death plus Susie’s sore throat involves more pain than Bob’s burning to death) that in part underlies the differences in intuition between me and people like yourself.
2) Reminding people of another important moral fact that should figure in their implicit thought processes (and thus be reflected in their intuitions): that who suffers matters. This moral fact is often forgotten about, which skews people’s intuitions. Once this moral fact is seriously taken into account, I bet people’s intuitions would not be the same. Importantly, I bet the vast majority of people (including yourself) would feel that giving Bob some chance of being saved is more appropriate than none, EVEN IF you still thought that Amy’s pain and Susie’s pain involve slightly more pain than Bob’s.