Now, with this function, disutility increases monotonically with the number of people with specks in their eyes, satisfying your “slight aggregation” requirement. However, it’s also easy to see that going from 0 to 1 person tortured is worse than going from 0 to any number of people getting dust specks in their eyes, including 3^^^3.
The basic objection to this kind of functional form is that it’s not additive. However, it’s wrong to assume an additive form, because that assumption mandates unbounded utilities, which are a bad idea, because they are not computationally realistic and admit Dutch books. With bounded utility functions, you have to confront the aggregation problem head-on, and depending on how you choose to do it, you can get different answers. Decision theory does not affirmatively tell you how to judge this problem. If you think it does, then you’re wrong.
Tom, your claim is false. Consider the disutility function
D(Torture, Specks) = [10 * (Torture/(Torture + 1))] + (Specks/(Specks + 1))
Now, with this function, disutility increases monotonically with the number of people with specks in their eyes, satisfying your “slight aggregation” requirement. However, it’s also easy to see that going from 0 to 1 person tortured is worse than going from 0 to any number of people getting dust specks in their eyes, including 3^^^3.
The basic objection to this kind of functional form is that it’s not additive. However, it’s wrong to assume an additive form, because that assumption mandates unbounded utilities, which are a bad idea, because they are not computationally realistic and admit Dutch books. With bounded utility functions, you have to confront the aggregation problem head-on, and depending on how you choose to do it, you can get different answers. Decision theory does not affirmatively tell you how to judge this problem. If you think it does, then you’re wrong.