The Allais paradox is a pattern of choices under risk that violates expected utility theory. It matters because many people choose one gamble over another when certainty is involved, but reverse their preference when the same options are changed in a logically equivalent probabilistic way.
Why It Is A Problem For Expected Utility
Expected utility theory says people should evaluate lotteries using weighted average utility. One of its key conditions is the independence axiom. If you prefer option A to option B, then adding the same extra probabilistic consequence to both should not reverse the ranking.
The Allais paradox shows that actual choices often do reverse.
The Certainty Effect
In the classic example, many people prefer a sure payoff over a slightly riskier but higher-expected-value lottery. Yet when both options become uncertain in parallel, they often switch to the riskier option.
This suggests people place special value on certainty itself, not just on expected utility.
Why Economists Care
The Allais paradox helped motivate descriptive alternatives such as prospect theory. It also matters for insurance, portfolio choice, and public policy because it shows that real decision-making under risk may differ from the clean benchmark used in standard models.