By T. Goodall
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Extra resources for Adequate Decision Rules for Portfolio Choice Problems
Expected utility analysis has established two major lines of research. 7 Its inﬂuence was such that for a long time a decision rule could only be declared ‘rational’ by its proponents, if it complied with the expected utility’s axioms. The other line of research treated the expected utility principle as descriptive, and exposed it to empirical analysis. Serving both normative and descriptive analysis has undoubtedly contributed to its predominant role. On the other hand, its serving two masters has caused the expected utility principle to become a prime example of the continuing blurring of normative and descriptive decision theory.
U(r) assigns a ‘utility’, that is, a preference index, to all possible results. It is thus quite different from ω(r), which combines this ‘utility’ with what has been called here ‘risk attitude’. 24 It is also more than questionable whether these two concepts can be represented by a single function. Much of Allais’s (1953) critique of the EU principle rests on this point. The necessity to distinguish between ‘utility’ and ‘risk attitude’ has led Shoemaker (1982), as well as Sugden (1986), to call u(r) a ‘utility function 23 chapter three A N A LY S I S O F P R O M I N E N T DECISION RULES A D E Q U AT E D E C I S I O N R U L E S F O R PORTFOLIO CHOICE PROBLEMS under certainty’, and ω(r) a ‘utility function under risk’.
Among them are Machina’s (1982) ‘generalised expected utility’ model, ‘distortion’ models, like Yaari’s (1987) ‘dual choice’ model, and a similar model by Allais (1987). There are, furthermore, a number of models employing different mathematical formulations of the function ϕ(u(r)), like Hagen’s (1979) ‘three moments’ model, or like ‘regret theory’, which has simultaneously been proposed by Bell (1982), Loomes and Sudgen (1982) and Fishburn (1982). More recently, a number of explanations for the violation of the independence axiom have been proposed, which have been dubbed ‘similarity’ models.
Adequate Decision Rules for Portfolio Choice Problems by T. Goodall