Allais Paradox

Choose between the following two alternatives:

1. 90% chance of an unknown amount $x$ and a 10% chance of $1 million, or

2. 89% chance of the same unknown amount $x$, 10% chance of $2.5 million, and 1% chance of nothing.

The Paradox is to determine which choice has the larger Expectation Value, $0.9x+\$100,000$ or $0.89x+\$250,000$. However, the best choice depends on the unknown amount, even though it is the same in both cases! This appears to violate the Independence Axiom.

See also Independence Axiom, Monty Hall Problem, Newcomb's Paradox

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.