Allais Paradox

What is the Allais paradox?

The Allais paradox is a pattern of choices between risky prospects that violates the independence principle of expected utility theory. The issue is consistency between two choices, rather than simply choosing a smaller expected monetary payoff.

The Maurice Allais Foundation’s explanation gives this example.

1. First choose between a certain 100 and a gamble with an 89% chance of 100, a 10% chance of 500 and a 1% chance of zero.
2. Then choose between an 11% chance of 100 and a 10% chance of 500, with zero otherwise.

Choosing the certain 100 first, but the 10% chance of 500 second, produces the paradox. The second pair changes the same 89% consequence in both options from 100 to zero. Expected utility's independence principle requires the preference ordering to remain the same. Certainty can make that common change matter psychologically.