Allais Paradox

In identical experiments, an Allais paradox occurs when the addition of an independent event influences choice behavior. Consider the choices in the following table (Kahneman and Tversky 1979).

lottery1 to 333435 to 100preference

In Experiment 1, a choice of A and B was given, and most participants picked B. In Experiment 2, a choice of C and D was given, and most participants picked C.

This observed pattern violates the independence axiom, since in both experiments, the payoff is identical if a >=35 ball is picked, while if the >=35 event is disregarded, the two experiments are identical.

To see it another way, consider the >=35 event to be a black box that is always received if the random ball value is >=35. Knowing or not knowing the contents of the black box should not influence behavior.

See also

Independence Axiom, Monty Hall Problem, Newcomb's Paradox, Saint Petersburg Paradox

This entry contributed by Ed Pegg, Jr. (author's link)

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Allais, M. "Le comportement de l'homme rationnel devant le risque: Critique des postulats et axiomes de l'école américaine." Econometrica 21, 503-546, 1953.Allais, M. "An Outline of My Main Contributions to Economic Science." Amer. Econ. Rev. 87, 3-12, 1997.Fishburn, P. C. Utility Theory for Decision Making. New York: Wiley, 1970.Kahneman, D. and Tversky, A. "Prospect Theory: An Analysis of Decision Under Risk." Econometrica 47, 263-292, 1979.Kreps, D. M. Notes on the Theory of Choice. Boulder, CO: Westview Press, p. 192, 1988.Kulish, M. "The Independence Axiom: A Survey." May 2002., L. J. The Foundations of Statistics, 2nd ed. New York: Dover, 1972.

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Allais Paradox

Cite this as:

Pegg, Ed Jr. "Allais Paradox." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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