By T. Goodall
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Additional resources for Adequate Decision Rules for Portfolio Choice Problems
50 Up to the present day, any discussion of Markowitz’s µ–σ2 rule includes this conclusion on its ‘rationality’. It seems worth emphasising that this entire argument is based on declaring the EU principle the only ‘rational’ one. It is true that there has been a time when the von Neumann–Morgenstern deﬁnition of rationality was irrefutable; and most works on the relationship of the EU principle and Markowitz’s µ–σ2 rule stem from this time. 2, the EU principle’s claim to absolute right cannot be maintained.
This choice of wording is rather unfortunate. 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’.
15 The subsequent empirical ‘falsiﬁcation’ caused by the expected gain rule’s lack of subjectivity dates back to the 18th century. Back then, the expected gain rule was the only means to evaluate games of chance. The expected value served both as the preference index of a game and the ‘fair’ entrance fee to a game. A game was called ‘fair’, if its entrance fee was equal to the expected gain of the gamble. It was simply assumed that if the entrance fee is equal to the expected value, a gamble could not favour one or the other player.