Allais paradox

The Allais paradox is a pair of lottery-choice problems in which many people make choices inconsistent with expected utility theory’s independence axiom.

Expected utility theory: A theory that represents risky choices by the probability-weighted average of utility outcomes. The paradox identifies a systematic failure of this theory’s independence axiom.
Maurice Allais: A French economist who won the 1988 Nobel Memorial Prize in Economic Sciences. He devised the lottery choices that became the Allais paradox.
Expected utility hypothesis: The claim that rational choices under risk can be represented by maximizing expected utility. The paradox challenges its descriptive adequacy through observed preference patterns.
Decision theory: The formal study of how choices can be made under certainty, risk, or uncertainty. The paradox is a central test case for normative and descriptive decision theories.
Independence axiom: A choice axiom requiring preferences between lotteries to persist when both are mixed with the same third lottery. The Allais choices directly violate this requirement.
1953: A calendar year in the Gregorian calendar. Allais presented his challenge to expected utility theory at a 1953 Paris conference.
Cumulative prospect theory: A theory of risky choice that transforms cumulative probabilities and evaluates outcomes relative to a reference point. Unlike expected utility, it can accommodate violations such as the Allais pattern.
Behavioral economics: The study of how psychological and social factors shape economic decisions. Allais’s findings helped establish systematic departures from standard rational-choice predictions.
Common consequence effect: A preference reversal caused when a shared outcome is added to or removed from competing lotteries. The paradox’s two choices alter a common consequence while often reversing preferences.
Paris Colloquium on Risk: A 1953 conference on risk and decision-making held in Paris. Allais presented the paradox’s choice problems at this gathering.

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