Abstract
This chapter reviews the developments of the theory of choice under risk since V.NEUMANN and MORGENSTERN [1947] presented the first axiomatic formulation of the expected utility model. The purpose of this review is to set the stage for the investigations of the following chapters and to give the context of the problems treated there.
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Notes
The terms “risk” and “uncertainty” refer to the Knightian distinction between decision situations whith known and unknown probabilities.
It seems to be an interesting question in this context whether a set of behavioral postulates can be acceptable from a normative viewpoint even if these postulates are systematically violated by most decision makers. I believe the answer to this question is no, but there are of course other positions (see e.g. [Savage 1954], [Raiffa 1961] and [Schneeweiß 1967]).
see section 1.3.
For an analysis of decision making under risk without the reduction axiom and in particular a new foundation of expected utility theory without this axiom see [Segal 1990].
For a further discussion of the common consequence effect and similar generalizations of the Allais paradox see [Machina 1987], [Segal 1987a], [Green and Jullien 1988].
The Machina theory [Machina 1982] is not included here since it plays a special role in the theory of choice under risk. The approach taken by Machina can not be viewed as one model of choice under risk relaxing the independence axiom but rather as a general method of analyzing non-linear utility theory under risk. A version of this method will be used in chapter 3.
Apparently, the development of the general RDU model has its origin in [Segal 1984].
Continuity means here that μ as well as the induced marginal measures are atomless, and μ satisfies μ(Aη)-?μ(A) whenever limsupj4η = liminf Aη = A.
The fact that theorem 1.4.4 gives the representation of preferences only on D°(X) does not really pose a problem since by continuity of preferences a representation on D(X) is uniquely determined by its restriction to D°(X).
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© 1991 Springer-Verlag Berlin Heidelberg
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Puppe, C. (1991). Axiomatic Utility Theory under Risk. In: Distorted Probabilities and Choice under Risk. Lecture Notes in Economics and Mathematical Systems, vol 363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58203-5_2
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DOI: https://doi.org/10.1007/978-3-642-58203-5_2
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