There seems to be some dispute about how compelling the Allais Paradox is. Savage said that he violated it the first time the example was given, but decided he made a mistake and revised his beliefs. Most economists I know have a similar reaction. (Although, as a personal matter, I find it somewhat more compellig.) However, I do not know of any economist who does not find Ellsberg's Paradox compelling. They agree that even after having the problem pointed out, they wouldn't change their beliefs. -- Joe
>From [EMAIL PROTECTED] Mon Aug 4 11:26:14 2003 X-Authentication-Warning: ghost.CS.ORST.EDU: majordomo set sender to [EMAIL PROTECTED] using -f To: [EMAIL PROTECTED] Subject: [UAI] Allais' paradox (was: Maximum Entropy Principle) From: Konrad Scheffler <[EMAIL PROTECTED]> Date: Mon, 04 Aug 2003 06:57:47 -0700 Dear Lotfi, > We can use, of course, the principle of maximization of expected > utility, but it is well known that the principle leads to > counterintuitive conclusions ( Allais' paradox). Thanks for that reference - I'm always interested in paradoxes. Not having heard of Allais' paradox, I looked it up on 2 sites: http://mathworld.wolfram.com/AllaisParadox.html gives an example which it claims "appears to violate" the independance axiom (also defined on this site). I do not see how anyone could think this: it is based on the suggestion that 0.89x is the same as 0.9x because the value of x is the same in both expressions! So no paradox here. Next, I tried: http://www.sfb504.uni-mannheim.de/glossary/allais.htm This gives a more detailed description, which amounts to an explanation of the well known fact that many humans are risk averse in some situations. Again, no paradox - it seems that Allais' paradox is merely a comment on the psychological phenomenon of risk aversion. But the fact that some instances of risk averse behaviour are contrary to the principle of maximising expected utility is not a criticism of the principle any more than the existence of crime is a criticism of law. Am I missing something here? Certainly I cannot dispute that the principle of maximisation of expected utility leads to conclusions that may be counterintuitive to many people - after all, people's intuitions differ. But I was hoping to see examples of conclusions that _I_ find counterintuitive. As an aside, one reason for people having a range of intuitions about this issue is that it is easy to misuse the principle by maximising the wrong utility, which can easily lead to misunderstandings. E.g. one might maximise the expected value of a payoff when one ought to be maximising the probability of having a payoff > k, in cases where the latter may be more important for the situation at hand - this would explain many examples of risk aversion that do not contradict the principle. Konrad
