I certainly share your intuition that there is no number of pinpricks such that it would ever be worse than 1 billion people in horrific torture. But if pinpricks can be aggregated to begin with, it seems arbitrary to assign an upper limit to the aggregate disvalue of pinpricks. So here's weird solution that I just thought of (and probably has all kinds of obvious problems that I don't have time to consider): Maybe there are some harms that are so small that they can't aggregate to begin with. For me, this is an easier bullet to bite than the proposal that miniscule harms can be added together but only up to a certain point.
I have the intuition that I would choose 10 hours of pain of intensity X over 1 hour of pain of intensity 10X. I'm not sure that I can justify this intuition: I suspect it might be irrational by definition, but I also suspect that many other people share this intuition. And if this in fact the case, it suggests that superlinear scaling might be a fundamental property of pain itself as opposed to an artifact of the way in which we verbalize pain on the 1 to 10 scale.
If I had more time I'd try to tease out my intuition further. At first blush I think it boils down to the idea that there is some threshold of pain to be crossed (perhaps the point at which the pain becomes "unbearable"), that is qualitatively different from any pain below that threshold in such a way that for almost any choice between y hours of the the below-the-threshold-pain and z hours of the above-the-threshold pain, I would choose the former. This probably violates basic axioms of rationality, not to mention my own generally utilitarian beliefs, but I feel the pull of the intuition nevertheless.
I certainly share your intuition that there is no number of pinpricks such that it would ever be worse than 1 billion people in horrific torture. But if pinpricks can be aggregated to begin with, it seems arbitrary to assign an upper limit to the aggregate disvalue of pinpricks. So here's weird solution that I just thought of (and probably has all kinds of obvious problems that I don't have time to consider): Maybe there are some harms that are so small that they can't aggregate to begin with. For me, this is an easier bullet to bite than the proposal that miniscule harms can be added together but only up to a certain point.
I have the intuition that I would choose 10 hours of pain of intensity X over 1 hour of pain of intensity 10X. I'm not sure that I can justify this intuition: I suspect it might be irrational by definition, but I also suspect that many other people share this intuition. And if this in fact the case, it suggests that superlinear scaling might be a fundamental property of pain itself as opposed to an artifact of the way in which we verbalize pain on the 1 to 10 scale.
If I had more time I'd try to tease out my intuition further. At first blush I think it boils down to the idea that there is some threshold of pain to be crossed (perhaps the point at which the pain becomes "unbearable"), that is qualitatively different from any pain below that threshold in such a way that for almost any choice between y hours of the the below-the-threshold-pain and z hours of the above-the-threshold pain, I would choose the former. This probably violates basic axioms of rationality, not to mention my own generally utilitarian beliefs, but I feel the pull of the intuition nevertheless.
It also occurs to me that my intuition is closely related to the intuition underlying the pinprick argument against negative utilitarianism: https://www.utilitarianism.com/pinprick-argument.html.