At 08:38 PM 8/15/2003 -0700, Christian Borgelt wrote: >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
This is simply false. For example, if payoffs are normally distributed then expected utility depends on both the mean and the variance of the normal distribution in question. Variance definitely can be taken into account by the theory! >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. No one claims that risk aversion is irrational - that is not what the Allais or Ellsberg paradoxes are saying. Risk aversion consists in preferring a payoff of x to a random payoff with mean x. Such preferences are universally agreed to be rational and can be successfully accommodated by expected utility theory using any concave utility function over payoffs. >In other words, expected utility theory works, as its name says, with >the expected utility of an option. However, the expected utility is the >only relevant value only if I am offered to make the decision several, >(or actually quite a lot of) times. Nowhere in the axioms underlying expected utility theory is there any assumption that a decision is to be made repeatedly. The axioms deal explicitly with one-time decisions. It happens that the axioms imply that the utility of a gamble g with payoffs x is numerically equal to the expected value of the utilities u(x) one realizes from the gamble. However, the theory does not appeal to repeated choice to reach this conclusion. To criticize the theory on this ground is to criticize a particular misinterpretation of the theory. This criticism does not apply to the theory when it is properly interpreted. Gordon Hazen Department of Industrial Engineering and Management Sciences McCormick School of Engineering and Applied Science 2145 Sheridan Road Northwestern University Evanston IL 60208-3119 Fax 847-491-8005 Phone 847-491-5673 Web: www.iems.nwu.edu/~hazen/
