In 1944, John von Neumann (1903–1957) and Oskar Morgenstern (1902–1977) proposed an axiomatic formulation of what is known as "expected utility" theory, which provides a decision rule for making choices under risk: a rational person must always choose the option with the greatest utility—that is, the greatest expected value.
Yet in 1953, Maurice Allais devised an experiment that seemed to undermine this axiomatic system: participants did the opposite of what von Neumann and Morgenstern's calculations predicted.
An experiment that contradicts the theory
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Consider a game in which you must choose between options with different prizes and probabilities. Option A offers a 100% chance of winning €100, while option B offers a 10% chance of winning €500, an 89% chance of winning €100 and a 1% chance of winning €0. Those who chose option A are then offered a new choice: option C gives an 11% chance of winning €100 and an 89% chance of winning nothing, while option D gives a 10% chance of winning €500 and a 90% chance of winning nothing.
