I don’t think it’s the specifics of the multiplicative accumulation of individual utilities that matters; just imagine that however I calculate the utility of torture and papercuts there is some lottery where I am VNM-indifferent between 10^10 papercuts and torture for 50 years. 10^10 + 1 papercuts would be too much and I would opt for torture; 50 years + 1 second of torture would be too much and I would opt for papercuts. However, given the VNM-indifferent choice, I would still have a preference for papercuts over torture because it maximizes the minimum individual utility while still maximizing overall utility. (-10^12 utility is the minimum individual utility when choosing torture, −100 utility is the minimum individual utility when choosing papercuts, total utility is −10^12 either way, average utility is −10^12 / (10^10 + 1) either way, so I am fairly certain the latter two are indifferent between the choices. If I’ve just made a math error, that would help alleviate my confusion.).
To me, at least, it seems like this preference is not captured by utilitarianism using VNM-utility. I think it’s almost possible to explain it in terms of negative utilitarianism but I don’t actually try to minimize overall harm, just minimize the greatest individual harm while keeping total or average utility maximized (or sufficiently close to maximal).
I don’t think it’s the specifics of the multiplicative accumulation of individual utilities that matters; just imagine that however I calculate the utility of torture and papercuts there is some lottery where I am VNM-indifferent between 10^10 papercuts and torture for 50 years. 10^10 + 1 papercuts would be too much and I would opt for torture; 50 years + 1 second of torture would be too much and I would opt for papercuts. However, given the VNM-indifferent choice, I would still have a preference for papercuts over torture because it maximizes the minimum individual utility while still maximizing overall utility. (-10^12 utility is the minimum individual utility when choosing torture, −100 utility is the minimum individual utility when choosing papercuts, total utility is −10^12 either way, average utility is −10^12 / (10^10 + 1) either way, so I am fairly certain the latter two are indifferent between the choices. If I’ve just made a math error, that would help alleviate my confusion.).
To me, at least, it seems like this preference is not captured by utilitarianism using VNM-utility. I think it’s almost possible to explain it in terms of negative utilitarianism but I don’t actually try to minimize overall harm, just minimize the greatest individual harm while keeping total or average utility maximized (or sufficiently close to maximal).