This is "Allais' Paradox".

Which choice is rational depends upon the subjective value of money. Many people are risk averse, and prefer the better chance of $1 million of option A. This choice is firm when the unknown amount is $1 million, but seems to waver as the amount falls to nothing. In the latter case, the risk averse person favors B because there is not much difference between 10% and 11%, but there is a big difference between $1 million and $2.5 million.

Thus the choice between A and B depends upon the unknown amount, even though it is the same unknown amount independent of the choice. This violates the "independence axiom" that rational choice between two alternatives should depend only upon how those two alternatives differ.

However, if the amounts involved in the problem are reduced to tens of dollars instead of millions of dollars, people's behavior tends to fall back in line with the axioms of rational choice. People tend to choose option B regardless of the unknown amount. Perhaps when presented with such huge numbers, people begin to calculate qualitatively. For example, if the unknown amount is $1 million the

options are

A. a fortune, guaranteed B. a fortune, almost guaranteed

a tiny chance of nothing

Then the choice of A is rational. However, if the unknown amount is

nothing, the options are

A. small chance of a fortune ($1 million)

large chance of nothing

B. small chance of a larger fortune ($2.5 million)

large chance of nothing

In this case, the choice of B is rational. The Allais Paradox then results from the limited ability to rationally calculate with such unusual quantities. The brain is not a calculator and rational calculations may rely on things like training, experience, and analogy, none of which would help in this case. This hypothesis could be tested by studying the correlation between paradoxical behavior and "unusualness" of the amounts involved.

If this explanation is correct, then the Paradox amounts to little more than the observation that the brain is an imperfect rational engine.

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