Date of this Version
Published in Transactions of the Nebraska Academy of Sciences, Volume 2 (1973).
A long standing debate among decision and value theorists concerns the consistency of individual as well as collective preferences. Two traditional yet diametrically opposed positions have been staked out. A von Neumann. Morgenstern decision theorist (hereafter reference to the von Neumann. Morgenstern system will be abbreviated NM) maintains that individual preferences are exhibited behavioristically and that from empirical observations alone a consistent set of axioms can be (or have been) constructed which describe and predict individual decision making and, in addition, may be regarded as norms of future behavior (von Neumann and Morgenstern, 1953: 31-33). Others have denied that such a set of axioms fulfilling these descriptive, predictive and normative demands have been (or can be) constructed. Their counter-argument, in part, is based on the Allais paradox, Following Allais they contend that individual values are an intuitively given normative network which does not exhibit a sufficiently strict correlation with preferences so as to fulfill the NM demands. Consequently they claim that empirical behavioristic observations alone will not provide one with the information from which a consistent set of axioms can be constructed such that these axioms will be complete in the NM sense, i.e., at once descriptive, predictive and normative of individual decision making.
In this paper it will be demonstrated that any proposal which attempts a complete (1) descriptive, (2) predictive and (3) normative account of individual decision making within the NM system is futile. The outline of this proposed demonstration is as follows. First, the NM axioms are presented and the theorem of the maximization of expected utility is derived from them, Secondly, an account is given of the Allais paradox. This paradox resulted from Allais' questioning of the reliability of the NM system for the prediction of an individual's future choices. Thirdly, three proposed resolutions offered by Leonard J. Savage, Donald Morrison and Karl Borch, respectively, are presented. An examination of these proposals will reveal specific weaknesses of each one. Fourthly, it will be shown that all three solutions "fail" in a more general sense for they all exceed the boundaries of the NM system in a very fundamental way. Finally, a suggestion for a possible resolution of the Allais paradox will be put forth which will require the development of a new generalized decision theory.
The NM axioms (von Neumann and Morgenstern, 1953: 26,27):
We consider a system U of entities u,v,w, .... In U a relation is given, u > v, and for any number α, (0 < α < 1), an operation: αu + (1 - α)v = w.