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# Allais paradox

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A paradox of decision making that usually elicits responses inconsistent with expected utility theory. First, a choice is made betweenA $500,000 with probability 1 (certainty)B$2,500,000, $500,000, or$0 with probabilities 10 per cent, 89 per cent, and 1 per cent respectively.Second, a choice is made betweenC $500,000 or$0 with probabilities 11 per cent and 89 per centD $2,500,000 or$0 with probabilities 10 per cent and 90 per cent respectively.Most people prefer A to B, because they prefer the certainty of winning a large amount to the small probability of winning an even larger amount coupled with a risk of winning nothing at all. But most of the same people prefer D to C, because the chances of winning are nearly the same in both cases but the prize is much larger in D than in C. Writing u(2,500,000), u(500,000), and u(0) for the utilities that a person attaches to the corresponding amounts of money, the first preference implies that.11u(500,000) > .10u(2,500,000) + .01u(0),and the second implies that.11u(500,000) < .10u(2,500,000) + .01u(0),a contradiction, showing that expected utility theory does not accurately describe human choice behaviour. See also revealed preference, risk aversion. Compare common ratio effect, Ellsberg paradox, modified Ellsberg paradox, St Petersburg paradox. [Named after the French economist Maurice (Félix Charles) Allais (1911–2010) who formulated it in 1953]

A $500,000 with probability 1 (certainty) B$2,500,000, $500,000, or$0 with probabilities 10 per cent, 89 per cent, and 1 per cent respectively.

C $500,000 or$0 with probabilities 11 per cent and 89 per cent

D $2,500,000 or$0 with probabilities 10 per cent and 90 per cent respectively.

.11u(500,000) > .10u(2,500,000) + .01u(0),

.11u(500,000) < .10u(2,500,000) + .01u(0),