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His reasoning leads to the conclusion that, if your initial wealth is s, you should prefer the prospect which maximizes the moral expectation: 2,J(x) log (x + s). His arguments are ingenious and seem to take our axioms, or their equivalent, as too obviously true to merit discussion in a learned paper. Up to the time of Bernoulli it seems to have been considered as selfevident that any rational person would seek to maximize the mathematical expectation when making decisions under uncertainty. This was quite natural, since probability theory originated in the study of gambling situations, where the Law of Large Numbers could be assumed to hold.
To make the problem concrete, we can ask, Will a middle-class person who has fire insurance on his home cancel the insurance if he inherits some hundred thousand dollars? We shall not discuss this question at present, mainly because it somehow [ 37 J Applications of the goes outside the legitimate boundaries of our model. The model we have worked with represents a tremendous simplification of the real-life problem. We have, for instance, made no attempt to introduce the time element, which obviously must be very important in a realistic model.
Cardinal Utility for Even-chance Mixtures of Pairs of Sure Prospects," Review of Economic Studies, 1959, pp. 174-177.  Berstein, I. N. and J. Milnor: "An Axiomatic Approach to Measurable Utility," Econometrica, 1953, pp. 291-297.  Luce, R. D. and H. Raiffa: Games and Decisions, Wiley, 1957. : "Note on von Neumann-Morgenstern's Strong Independence Axiom," Econometrica, 1952, p. 679.  Manne, A. : "The Strong Independence Assumption," Econometrica, 1952, pp. 665-668. : "Rational Behavior, Uncertain Prospects and Measurable Utility," Econometrica, 1950, pp.