Hi all, Some comments on Prof Zadeh's post:
> A broad question which remains on the table is: Is it possible to > construct a precise, rigorous, ,axiomatic and prescriptive (normative) > theory, call it PDT (Prescriptive Decision Theory)--a theory in the > spirit of von Neumann, Morgenstern and Wald-- the superior intellects > who laid its foundations in the middle of last century? Opinions may vary, but one could argue that this is exactly what was achieved by the work of E.T. Jaynes. > The problem of risk aversion. It is quite obvious that risk aversion > plays a key role in human decision-making. Consequently, it must be an > integral part of PDT. An interesting argument. Personally, I'd have found the exact opposite argument more convincing: "It is quite obvious that risk aversion plays a key role in human decision-making. Consequently, it must NOT be an integral part of PDT." (Granted, that conclusion doesn't follow from the premise either; it just seems more plausible to me.) My point is that I take it as obvious that most human decision-making is far from optimal, and that any prescriptive theory which reproduces it in every respect can therefore be rejected out of hand. I might cite the fact that most humans are initially taken in by the Allais and Ellsberg "paradoxes" to support my case. > An example is what may be called " The balls-in-box " problem--a problem > which has some links to Ellsberg's paradox. The measurement-based > version of the problem is : A box contains 20 black and while balls. > Over 70% are black. There are three times as many black balls as white > balls. What is the probability that a ball drawn at random is white? The > perception-based version is: A box contains about 20 black and white > balls. Most are black. There are several times as many black balls as > white balls. What is the probability that a ball drawn at random is white? As was pointed out here recently, this problem really deals with the interpretation of language, not with perception. regards, Konrad
