Peter -- "Rational" has always meant to me that a decision maker has preferences over the set of possible choices or outcomes and acts according to his preferences. Whether those preferences are representable by a utility or expected utility is another matter.
Rational could also be defined in terms of revealed preference: Can one use observations of a decision maker's actions and deduce that his actions are consistent with acting in accordance with a preference relation. I see little evidence or need to identify "rational" with the reparability of preferences into beliefs and utility of outcomes. But operationally, we need some restrictions on "preference relation" to have a meaningful testable theory. Thus we may posit some consistency (transitivity) and some other meaningful axioms. Otherwise Aristotle's definition is no more meaningful than Lange's. If there were no paradoxes in the development of the axioms of these utility theories, the resulting theories would be just as vacuous. Arrow's social choice theory is a much stronger refutation of a theory than a couple of curious paradoxes that lack universal appeal. He shows the inconsistency of a set of reasonable axioms. So far, at least, such a refutation of individual decision theory has not been forthcoming. Bob Welch -----Original Message----- From: Peter McBurney [mailto:[EMAIL PROTECTED] Sent: Monday, August 18, 2003 9:01 PM To: [EMAIL PROTECTED] Subject: Re: [UAI] Allais' paradox Hello all -- Just to add to Christian's insightful post: > It seems to me that the problem with expected utility as a theory of > rational decision making is that it does not properly take into account > the variances of the outcomes for the different options, especially if > the decision is to be made in only few instances, maybe even only once. > I have not followed the discussion really closely, but it seems to me > that the only reference to this is the notion of "risk aversion" that > turned up a few times. My personal problem is that I cannot see risk > aversion as irrational, even if this means choosing the option with > the lower expected value. Part of the problem is that the supporters of the maximum-expected-utility theory of decision-making (MEU) stole the word "rational" for its use. This word had (and still has) a perfectly good meaning in philosophy dating back at least to Aristotle: it refers to the giving of reasons for beliefs or actions. I don't know which statistician or decision-theorist first used the word in the sense of the proponents of MEU. The earliest reference I have been able to find is by Lange: "A unit of economic decision is said to act rationally when its objective is the maximization of a magnitude." O. Lange [1945-1946]: "The scope and method of economics", <The Review of Economic Studies>, 13 (1): 19--32. Arrow took up this definition in his book of 1951, <Social Choice and Individual Values>, and I suppose it then influenced Savage, et al. (In passing, it must be noted that Lange's definition is completely vacuous as an operational definition.) The theft of the word by economists and early decision-theorists is unfortunate. In particular it permits the labeling of non-MEU decision-making as "irrational", as Christian has noted. If economists were better scientists they would be labeling their models (e.g. as "inaccurate") rather than their domain data, when the two conflict. --- Peter
