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?
This is actually an open problem in utilitarianism; there were some posts recently looking to bargaining between agents as a solution, but I can’t find them at the moment, and in any case that’s not a mainstream LW conclusion.
what do total utilitarians and average utilitarians actually mean when they’re talking about the sum or the average of several utility functions?
They don’t know. In most cases, they just sort of wave their hands. You can combine utility functions, but “sum” and “average” do not uniquely identify methods for doing so, and no method identified so far has seemed uniquely compelling.
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.
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.
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.
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?
This is actually an open problem in utilitarianism; there were some posts recently looking to bargaining between agents as a solution, but I can’t find them at the moment, and in any case that’s not a mainstream LW conclusion.
See here.
They don’t know. In most cases, they just sort of wave their hands. You can combine utility functions, but “sum” and “average” do not uniquely identify methods for doing so, and no method identified so far has seemed uniquely compelling.
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.
I think you figure out common units to denote utilons in through revealed preference. This only works if both utility functions are coherent.
also last time this came up I linked this to see if anyone knew anything about it: http://www.jstor.org/pss/2630767 and got downvoted. shrug
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.