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).

lottery	1 to 33	34	35 to 100	preference
		0		18%
				82%
		0	0	83%
			0	17%

In Experiment 1, a choice of  and  was given, and most participants picked . In Experiment 2, a choice of  and  was given, and most participants picked .

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

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

REFERENCES

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. http://www2.bc.edu/~kulish/papers/indepb.pdf.Savage, L. J. The Foundations of Statistics, 2nd ed. New York: Dover, 1972.