Abstract
The modern conception of rational choice under conditions of risk, as formulated in the expected utility theory of Von Neumann and Morgenstern (1944), Herstein and Milnor (1953), Luce and Raiffa (1957), Arrow (1971), and others, presupposes that evaluations of gambles satisfy two very important requirements. The first is a context-free condition (CF) according to which the comparative evaluation of any two gambles g1 and g2 is to be independent of whatever other gambles are in the feasible set. Following Arrow (1959), Sen (1971, 1973), and others, this condition can be interpreted as a constraint on the choices to which such evaluations give rise. So interpreted, the context free requirement factors into what Sen (1970) designates as conditions Alpha and Beta on choice functions. Let X be any feasible set of alternatives, and let C(X) be the subset of X that consists of chosen elements—here to be understood as elements judged to be acceptable. Alpha requires that if x is in C(X), then x is in C(A) for any subset A of X of which x is a member. Beta requires that if x and y are both in C(A), then for any superset Y of A, either both x and y are in C(Y) or neither is.
The author is indebted to T. Seidenfeld, I. Levi, M. Machina, P. Hammond, F. Schick, and P. Lyon for many helpful conversations.
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© 1988 D. Reidel Publishing Company, Dordrecht, Holland
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McClennen, E.F. (1988). Dynamic Choice and Rationality. In: Munier, B.R. (eds) Risk, Decision and Rationality. Theory and Decision Library, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4019-2_28
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DOI: https://doi.org/10.1007/978-94-009-4019-2_28
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