One potential problem: if the two utilities have different asymptotic behavior, then one of them can dominate decision-making. For instance, suppose we’re using 0-1 normalization, but one of the two utilities has a big spike or tail somewhere. Then it’s going to have near-zero slope everywhere else.
More concrete example: on the hedonism axis, humans have more capacity for severe pain than extreme pleasure. So that end of the axis has a big downward spike, and the hedonism-utility would be near-flat at the not-severe-pain end (at least for any of the normalizations you suggest, other than max-mean, which has the same problem with the other end of the axis). But if the preferences-utility lacks a big spike like that, then we’re liable to end up with constant low-grade hedonic unhappiness.
That’s still a lot better than plenty of other possible outcomes—preference-utility still looks good, and we’re not in constant severe pain. But it still seems not very good.
One potential problem: if the two utilities have different asymptotic behavior, then one of them can dominate decision-making. For instance, suppose we’re using 0-1 normalization, but one of the two utilities has a big spike or tail somewhere. Then it’s going to have near-zero slope everywhere else.
More concrete example: on the hedonism axis, humans have more capacity for severe pain than extreme pleasure. So that end of the axis has a big downward spike, and the hedonism-utility would be near-flat at the not-severe-pain end (at least for any of the normalizations you suggest, other than max-mean, which has the same problem with the other end of the axis). But if the preferences-utility lacks a big spike like that, then we’re liable to end up with constant low-grade hedonic unhappiness.
That’s still a lot better than plenty of other possible outcomes—preference-utility still looks good, and we’re not in constant severe pain. But it still seems not very good.