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Kaj_Sotala comments on Stupid Questions Open Thread - Less Wrong Discussion
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If two possible futures have different numbers of people, those will be subject to different affine transforms, so the utility function as a whole will have been transformed in a non-affine way. See repugnant conclusion for a concrete example.
I think you misunderstood my question. I wasn't asking about what would the difference between summing and averaging be, but how to sum utility functions of different people together in the first place.
Oh, I completely misunderstood that.
The right answer is that utilitarians aren't summing utility functions, they're just summing some expression about each person. The term hedonic function is used for these when they just care about pleasure or when they aren't worried about being misinterpreted as just caring about pleasure and the term utility function is used when they don't know what a utility function is or when they are willing to misuse it for convenience.