No matter what x and y are, N^2 y > Nx if N is large enough. 3^^^3 is gigantically huge, and thus certainly large enough. Thus if N is large enough, the disutility of 3^^^3 dust specks is greater than that of torture.
Am I not allowed to set my disutility for knowing that another person gets a dust speck to zero? I admit that before I thought about this problem I had no opinion about other people getting dust specks in their eyes or not, but I had a strong opinion against torture. Additionally, even now I would say that the margin for error on my estimation of the disutility of a dust speck in someone else’s eye is far greater in magnitude than my estimation of the disutility itself, and therefore zero may be a reasonable choice to avoid unintuitive conclusions. Maybe occasional dust specks would help all those folks staring at computer screens and forgetting to blink and this would outweigh any annoyance for the rest of humanity, for instance. There’s also the next level of evaluation: z, the utility of knowing that another person would willingly receive a dust speck in their eye to collectively prevent a single person from being tortured. If that utility outweighs the disutility of knowing that another person received a dust speck in their eye then N^2 z outweighs both of the others. I think I would be happier knowing I was in a society that completely agreed with me about not torturing one person to prevent dust specks from getting in their eyes than I would be if no one received that particular dust speck in their eye. Even if only half of the population thought that way the ratio between (N/2)^2 y and (N/2)^2 z would be a constant factor and would still dominate Nx. This may create a paradox because now the utility of getting a dust speck in the eye is zero or positive in the world of N individuals. It may not be a paradox if the utility only becomes non-negative as a condition of dealing with specific ethical meta-questions, and is already playing with the limits of another sort of insanity; If agents are concerned about every possible dilemma of this nature they may precommit to taking on a lot (potentially unbounded) of disutility without the actual existence of a situation requiring them to experience that disutility to save a real person from torture.
Maybe a better attempt is to argue that one person’s sadness about other people’s dust specks does not increase linearly with the number of dust specks. If there is an upper limit to how sad one person can feel about N dust specks that cannot be exceeded no matter how large N is, then your utility function may recommend dust specks over torture. But I suspect this position has problems. I am going to think about it some.
The marginal utility of goods would suggest that marginal disutility exists too. Once everyone experiences something it becomes much more normal than if only one person suffers it. This is, of course, also the reason that not many people are adamant about preventing death from old age and so it’s not necessarily good reasoning in general. Equalizing disutility may sound fair but it is probably not always right.
You can rationally give dust specks to 3^^^3 paperclip maximizers instead of torturing one human if your disutility for giving one paperclip maximizer a dust speck is less than or equal to zero. This seems quite compatible with standard human morality, especially if these paperclip maximizers inspire zero empathy or if their paperclip-maximizing is dangerous to humans. But if you would feel even the slightest bit of remorse about giving a paperclip maximizer a dust speck, torture one human instead of multiplying that remorse by a stupefyingly huge number like 3^^^3.
I think you are correct, and it becomes more apparent if you just form the question as a limit. As N tends toward infinity, do you apply -x utility to N individuals or apply -y utility to 1 individual? The only way to ever choose -x utility to N individuals is if you weight all but a finite number of the N individuals’ utility at zero. This may mean we have to weight every individual who doesn’t share our exact morality at zero to avoid making our own immoral decisions.
Am I not allowed to set my disutility for knowing that another person gets a dust speck to zero? I admit that before I thought about this problem I had no opinion about other people getting dust specks in their eyes or not, but I had a strong opinion against torture. Additionally, even now I would say that the margin for error on my estimation of the disutility of a dust speck in someone else’s eye is far greater in magnitude than my estimation of the disutility itself, and therefore zero may be a reasonable choice to avoid unintuitive conclusions. Maybe occasional dust specks would help all those folks staring at computer screens and forgetting to blink and this would outweigh any annoyance for the rest of humanity, for instance. There’s also the next level of evaluation: z, the utility of knowing that another person would willingly receive a dust speck in their eye to collectively prevent a single person from being tortured. If that utility outweighs the disutility of knowing that another person received a dust speck in their eye then N^2 z outweighs both of the others. I think I would be happier knowing I was in a society that completely agreed with me about not torturing one person to prevent dust specks from getting in their eyes than I would be if no one received that particular dust speck in their eye. Even if only half of the population thought that way the ratio between (N/2)^2 y and (N/2)^2 z would be a constant factor and would still dominate Nx. This may create a paradox because now the utility of getting a dust speck in the eye is zero or positive in the world of N individuals. It may not be a paradox if the utility only becomes non-negative as a condition of dealing with specific ethical meta-questions, and is already playing with the limits of another sort of insanity; If agents are concerned about every possible dilemma of this nature they may precommit to taking on a lot (potentially unbounded) of disutility without the actual existence of a situation requiring them to experience that disutility to save a real person from torture.
The marginal utility of goods would suggest that marginal disutility exists too. Once everyone experiences something it becomes much more normal than if only one person suffers it. This is, of course, also the reason that not many people are adamant about preventing death from old age and so it’s not necessarily good reasoning in general. Equalizing disutility may sound fair but it is probably not always right.
I think you are correct, and it becomes more apparent if you just form the question as a limit. As N tends toward infinity, do you apply -x utility to N individuals or apply -y utility to 1 individual? The only way to ever choose -x utility to N individuals is if you weight all but a finite number of the N individuals’ utility at zero. This may mean we have to weight every individual who doesn’t share our exact morality at zero to avoid making our own immoral decisions.