Konrad Scheffler writes: > That was an excellent post. However, it seems to me that you are > demolishing a strawman argument. You show (very eloquently) that choosing > an inappropriate utility to maximise does not lead to desired results. > Next, you say: > > > I assume that with a higher number of times one can choose between the > > lotteries, it will turn out that in a certain percentage of the cases > > people will go for the sure payoff and in the rest for the higher > > expected value (which, however, is connected to a higher risk), thus > > achieving a certain expected value to variance (or risk) relation. > > And this is what I believe people are actually optimizing > > Would this (or something similar) not then be a better choice of utility > to maximise when maximising an expected utility? > > This ties in with the hypothesis that many (most? all?) instances of risk > aversion could be shown to be entirely rational in the maximisation of > expected utility sense if only we knew which utility the human in question > was maximising.
Dear Konrad, when I wrote the post, I thought briefly about the choice of the utility function and whether it could be used to handle this case, but I rejected the idea. Maybe I should have added my thoughts right away. One problem I see is this: It seems to me that the basic idea of expected utility theory is to divide the information needed for a decision to be made into a probability part and a utility part. The utility part should describe how much I value a specific outcome. The probability part should model the uncertainty about which outcome actually occurs. A major motive for this division seems to be the hope that it separates subjective elements (how much I value something) from objective elements (the probability of possible events). However, if I incorporate the variance (which surely belongs to the probability part) into the utility function, the clean and appealing division of the probability part and the utility part is destroyed. Of course, if we see the utility part as the place for subjective assessments, you are completely right that it is there, where we have to put our attitude towards risk and variance of outcome. However, the variance itself is (not necessarily) subjective. Another, more severe problem is this: The variance refers to several outcomes or payoffs and thus cannot easily be included into an assessment of a single outcome. Consider the normally distributed payoffs example in my reply to Gordon Hazen: if this is to be modelled by a special utility function, how do I have to change the utility of the individual payoffs? The variance is a property of the distribution of the payoffs, not of a single payoff. It seems to me that the variance has to be taken into account on a different level and I do not see how expected utility theory does this. (Of course, the reason could be that I do not know enough about this theory.) Regards, Chris
