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common ratio effect


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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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