Hm, good point. We can just use the relative utilities. Or, equivalently, we just have to restrict ourselves to the class of normalizations that are only a function of the relative utilities. These may not be “any” normalization scheme, but they’re pretty easy to use.
E.g. for the utility function (dollar, apple, hamburger) → (1010,1005,1000), instead we could write it as (D-A, A-H) → (5, 5). Then if we wanted to average it with the function (1,2,3), which could also be written (-1, −1), we’d get (2,2). So on average you’d still prefer the dollar.
Hm, good point. We can just use the relative utilities. Or, equivalently, we just have to restrict ourselves to the class of normalizations that are only a function of the relative utilities. These may not be “any” normalization scheme, but they’re pretty easy to use.
E.g. for the utility function (dollar, apple, hamburger) → (1010,1005,1000), instead we could write it as (D-A, A-H) → (5, 5). Then if we wanted to average it with the function (1,2,3), which could also be written (-1, −1), we’d get (2,2). So on average you’d still prefer the dollar.