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.
I doubt the premise. Where are you getting that from? It wasn’t in the specification of the problem.
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.