Given that utility functions are only defined up to positive linear transforms, what do total utilitarians and average utilitarians actually mean when they're talking about the sum or the average of several utility functions? I mean, taking what they say literally, if Alice's utility function were twice what it actually is, she would behave the exact same way but she would be twice as ‘important’; that cannot possibly be what they mean. What am I missing?
There isn't a right answer (I think), but some ways of comparing are better than others. Stuart Armstrong is working on some of this stuff, as he mentions here.
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