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A famous violation of expected utility theory that seems intuitively appealing to many human decision makers, a typical example being as follows. An urn contains 100 chips numbered 1 to 100. First, you are given a choice between the following pair of options:Option *A*: A chip is drawn at random from the urn. If it is numbered 1–20, you receive nothing; if it is numbered 21–100, you receive £16.Option *B*: You receive £10 with certainty.Now you face a choice between a second pair of options:Option *C*: A chip is drawn at random from the urn. If it is numbered 1–80, you receive nothing; if it is numbered 81–100, you receive £16.Option *D*: A chip is drawn at random from the urn. If it is numbered 1–75, you receive nothing; if it is numbered 76–100, you receive £10.Many people prefer *B* to *A*, because it guarantees a substantial payoff without the risk associated with *A*, and many of the same people also prefer *C* to *D*, because it offers the prospect of a higher payoff than *D* with only slightly greater risk. But it is easy to show that this pattern of preferences violates expected utility theory. Writing *u*(16) for the utility of £16 and *u*(10) for the utility of £10, the preference of *B* over *A* implies that .80 *u*(16) < *u*(10), which means that *u*(16) < 1.25 *u*(10). But the preference of *C* over *D* implies that .20 × *u*(16) > .25 × *u*(10), which simplifies to *u*(16) > 1.25 × *u*(10), a contradiction. In general, if *x* > *y* > *z* are sums of money, and *p* and *q* are non-zero probabilities, then the common ratio effect occurs if a decision maker prefers the prospect *py* + (1 − *p*)*y* to *px* + (1 − *p*)*z*, and also prefers *p*(1 − *q*)*x* + (1 − *p*)(1 − *q*)*z* + *qz* to *p*(1 − *q*)*y* + (1 − *p*)(1 − *q*)*y* + *qz*. Compare Allais paradox, Ellsberg paradox, modified Ellsberg paradox, St Petersburg paradox. CRE abbrev.

*Subjects:*
Psychology.

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