Relativity in Decision Theory

Abstract

Proponents and critics of expected utility, cardinalists and ordinalists seem to agree on one point: Decisions under risk are not actually made through maximizing the expected value of a cardinal utility function in the classical sense (not defined through preferences under risk)¹⁾. Critics with few exceptions further think it is proved that nor is there any other function of wealth for which the expected value is maximised.²⁾ Models have been suggested which in addition to expectation of (cardinal) utility take into account other aspects of the distribution (See survey in Machina 1983). The prospect model (Khanemann and Tversky 1979) takes into account what was, their utility function being a function of gain/loss.) Further they weight utilities by a function of probability. I commented on this in (Hagen, 1983). To adjust the impression, I quote from a letter to professor Tversky:

“Due to restrictions on space I may have failed to make explicit what I did not mean. However, I did not say that the use of decision weights is a weakness, even if I think other means of expressing a similar thought might be better. What I did consider as a weakness was that each weight was a funtion of the corresponding probability and nothing else (compare Allais’ model as quoted).

I admit that your reservation, that dominated games are not evaluated, excludes the predicition of choosing a dominated game. But the necesseity of this reservation reveals a weakness. To my example: Replace the certainty of $ 10.000 with the certainty of $ 9.999.99, with the utility 99.99995, against the utility of the game, 100. 96975. The certainty of $ 9.999.99 is then rejected in favour of the game which it is one cent from dominating.”