Offered the same prizes twice, most people flip their own stated preference
Choice 1: a certain $1 million, or a 10% shot at $5 million (89% at $1 million, 1% at nothing). Most pick the certain million. Choice 2: an 11% shot at $1 million versus a 10% shot at $5 million. Most people now switch and prefer the $5 million gamble — even though both choices trade the identical 1% shift in probability between the same two prizes.
Reveal the answer
This is the Allais paradox, devised by economist Maurice Allais in 1953 to show that real choices violate the 'independence axiom' at the heart of expected utility theory, the dominant model of rational decision-making at the time. People weight a move from certainty to any uncertainty far more heavily than an equivalent shift between two gambles that are already uncertain — a pattern later built directly into Kahneman and Tversky's prospect theory.
— Maurice Allais, Le comportement de l'homme rationnel devant le risque — Econometrica, vol. 21, 1953