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AlexMennen comments on An Attempt at Preference Uncertainty Using VNM - Less Wrong
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There is good reason to pay attention to scale but not to zero-points: any normalization scheme that you come up with will be invariant with respect to adding constants to the utility functions unless you intentionally contrive one not to be. Normalization schemes that are invariant with respect to multiplying the utility functions by positive constants are harder.
Making such modifications to the utilities of outcomes will result in distorted expected utilities and different behaviour.
I meant invariant with respect to adding the same constant to the utility of every outcome in some utility function, not invariant with respect to adding some constant to one outcome (that would be silly).
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.