Sorry, my recall is imperfect. Arrow's result is an extension of the
Blackwell theorem that the only utility of money function in which the value
of information is independent of the rewards is the logarithmic and
corresponds exactly with the Shannon measure of information. Ken Arrow,
The value of and demand for information, Chapter 6 in C.B. McGuire and R.
Radner, Decision and Organization and reprinted in a volume of Arrow's
collected works, Essays in the theory of risk bearing.
Often, it seems, that people want to use valueless measures of information
to avoid the rather difficult issues in assessing value. I am very
uncomfortable with a medical decision process (as in this case the
originator of this thread) that does not attempt to obtain information about
value from the patient.