I am starting a project on traditional Chinese medicine (TCM) diagnosis.
Before reaching a decision, a TCM doctor normally needs to ask the patient
a number of questions. There are hundreds of possible questions.
It is impossible and unnecessary to ask all the questions. The
problem is what questions to ask and in what order.
The notion of value of information without utilities seems applicable
here.
I have been thinking about using entropy, i.e. one asks, at
each step, the question that brings about the most reduction
in the expected entropy of the posterior probability over diseases.
But this method seems to be flawed. Suppose the diagnosis is
between D1 and D2 and, at the beginng, the belief is inclined to D1.
Now consider two possible questions Q1 and Q2, whose answers are
likely to be in favor of D1 and D2 respectively. Then the
entropy method would probably choose Q1 over Q2.
Repeating this reasoning, one can conclude that the method would
probably only choose questions whose answers are likely to be in favor
of Q1. This is like a lawyer; ask only the questions that are
in favor of the client.
Any thoughts?
Regards,
--Nevin