Consider a program which when given the choices (A,B) outputs A. If you reset it >>and give it choices (B,C) it outputs B. If you reset it again and give it choices (C,A) it >>outputs C. The behavior of this program cannot be reproduced by a utility >>function.
That is silly—the associated utility function is the one you have just explicitly given. >To rephrase:
No it isn’t. It is a list of preferences. The corresponding utility function would be a function U(X) from {A,B,C} to the real numbers such that
1) U(A)>U(B) 2) U(B)>U(C) and 3) U(C)>U(A)
But only some lists of preferences can be described by utility functions, and this one can’t, because 1) and 2) imply that U(A)>U(C), which contradicts 3).
One more reason for the list is that doing new stuff (or doing stuff in new ways, but I repeat myself) promotes neurogenesis.