FYI
I believe Professor Kenneth Arrow, in a course he gave at MIT and Stanford,
demonstrated an impossibility theorem for Shannon's information measure and
other "value less" measures of information. Given the measure, one can find
a value function such that information content, as measures by the
"valueless" measure, gives incorrect decisions from the point of view of
the value function. Sorry I don't have the reference. Perhaps it is in his
book, the Economics of Information.
Bob Welch