Ramblings & ephemera

The Ellsberg Paradox: People prefer definites over ambiguity

From Nicholas Lemann’s “Paper Tiger” (The New Yorker: 4 November 2002):

Ellsberg devoted a good portion of his life to decision theory, and made quite a significant contribution for somebody so young. People are still publishing comments on his best-known idea, the so-called “Ellsberg paradox.”

The paradox arises from a series of games involving colored balls in urns. Let’s say there are two urns, each of which contains a hundred balls, which are either red or black. One urn contains fifty red balls and fifty black balls. The proportion of red and black in the other urn is unknown. You can draw one ball from one of the urns, without looking, and if you draw a red ball you win a hundred dollars. Which urn will you choose?

There is no good reason to think that the chance of getting a red ball is any better in one urn than in the other, but Ellsberg found that people overwhelmingly chose the urn known to have fifty balls of each color. The person running the game would then say, “O.K., you think that urn is likelier to have a red ball; now I’m going to offer you a hundred dollars if you draw a black ball.” If you turned to the fifty-fifty urn for the red ball, it would seem you had a hunch that the other urn contained more black balls, and therefore you should try to draw your black ball from it. But, overwhelmingly, people chose the fifty-fifty urn again. The Ellsberg paradox is that people so strongly prefer definite information over ambiguity that they make choices consistent neither with the laws of probability nor with themselves.

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