The Ellsberg Paradox

I'm reading Iconoclast, by Gregory Berns, the distinguished chair of neuroeconomics at Emory University. He's a professor of psychiatry and economics, which makes for an interesting combination. The book is about the way successful and creative people think and act, with a special focus on fear and how it affects behavior. Early in the book, Berns describes something called The Ellsberg Paradox. Berns uses it as an example of people's fear of the unknown.

There are two large urns placed in front of you. The urns are completely opaque, so you cannot see their contents. The urn on the left contains ten black marbles and ten white ones. The urn on the right contains twenty marbles, but you do not know the proportion of black to white. Now, the game is to draw a black marble from one of the urns. If you are successful, you win $(removed) You only have one chance, so which urn will you draw from? Keep the answer in mind.

Let's play again. Now, the game is to draw a white marble. Again, you only have one chance, so which urn will it be?

Most people when confronted with these choices choose the urn on the left -- the one with the known proportions of black and white marbles. And therein lies the paradox. If you choose the left-hand urn when trying to pull a black marble, that means you think your chances are better for that urn. But because there are only two colors in both urns, the odds of pulling a white must be complementary to the odds of pulling a black. Logically, if you thought the left-hand urn was the better choice for a black marble, the right-hand urn should be the better choice for a white marble. The fact that most people avoid the right-hand urn altogether suggests that people have an inherent fear of the unknown (also called the ambiguity aversion).

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