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timtyler comments on Value is Fragile - Less Wrong
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From the definition of utility function.
That seems like a ridiculous reply - it says nothing about the issue there.
Tim, that's what the term means. This other thing that you have called a "utility function", is not in fact a utility function, because that's not what the term means. It's already been pointed out that not every list of preferences can be derived from a utility function. If you want to define or use a generalization of the notion of utility function, you should do so explicitly.
I have no argument with the definition of the term "utility function". It is a function that maps outcomes to utilities - usually real numbers. The function I described did just that. If you don't understand that, then you should explain what aspects of the function's map from outcomes to utilities you don't understand - since it seemed to be a pretty simple one to me.
I don't think that all preferences can be expressed as a utility function. For example, some preferences are uncomputable.
Note that Tyrrell_McAllister2's reply makes exactly the same point as I am making.
See, this would have been a lot clearer if you had specified initially that your objection was to the domain.
Sorry if there was any confusion. Here are all the possible outcomes - and their associated (real valued) utilities - laboriously spelled out in a table:
Remembers being presented with (A,B) and chooses A - utility 1.0.
Remembers being presented with (A,B) and chooses B - utility 0.0.
Remembers being presented with (B,C) and chooses B - utility 1.0.
Remembers being presented with (B,C) and chooses C - utility 0.0.
Remembers being presented with (C,A) and chooses C - utility 1.0.
Remembers being presented with (C,A) and chooses A - utility 0.0.
Other action - utility 0.0.