Ellsberg paradox

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A paradox of choice that usually elicits responses inconsistent with expected utility theory. Two urns are filled with red and green balls. Urn A contains 50 red balls and 50 green balls randomly mixed; Urn B contains 100 red and green balls randomly mixed in an unknown ratio. You choose an urn and a colour, and you then draw a ball at random from your chosen urn. If the ball is your chosen colour, you win a prize. Most people strongly prefer to draw a ball of either colour from Urn A, although this violates the axioms of expected utility theory. According to expected utility theory, if a decision maker prefers to draw a red ball from Urn A than to draw a red ball from Urn B, then the (subjective) probability of drawing a red ball from Urn B must be less than 1/2; but that means that the (subjective) probability of drawing a green ball from Urn B must be greater than 1/2, and the decision maker should therefore prefer it to drawing a red ball from Urn A, which carries a 1/2 probability of winning. According to Ellsberg, human decision makers tend to maximize expected utility (or subjective expected utility) in judgements involving risk (2), such as exists in Urn A, to use maximin strategies (to maximize minimum utility) in judgements involving uncertainty (2), as in Urn B, and to use compromise strategies when the degree of confidence in their probability estimates is intermediate between risk (high confidence) and uncertainty (low confidence), confidence being derived from the amount, type, reliability, and unanimity of information. This implies that expected utility theory, subjective expected utility theory, and the concept of revealed preferences apply to situations of risk but not to situations involving uncertainty. Also called the Ellsberg-Fellner paradox, in recognition of an article by the US economist William Fellner (1905–83), drawing attention to the same phenomenon, published in 1961 in the same volume of the Quarterly Journal of Economics in which Ellsberg's article appeared. The phenomenon underlying the paradox is called ambiguity aversion. See also modified Ellsberg paradox. Compare Allais paradox, common ratio effect, St Petersburg paradox. [Named after the US political analyst Daniel Ellsberg (born 1931) who published it in 1961]

Subjects: Psychology.

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