Decision-Making Under Uncertainty: The Ellsberg Paradox

by | Feb 14, 2018


Daniel Ellsberg, an economic theorist, discovered and presented a paradox in decision making under uncertainty now known as the Ellsberg Paradox. The Paradox is best presented as a game as follows:

Imagine a container with 100 colored balls. You are told 50 are red 50 are black. You are to choose a color. If the color you selected is drawn you win $100. If the other color is drawn you win nothing. What is the maximum you’d bet to play this game (i.e. if you were competing against someone bidding to play what would you pay)? When graduate students are polled, most say the MAXIMUM they’d bet just below $50, which is the expected value of the game’s payoff. Makes sense.

Now, let’s play the game with 100 balls again. This time, however, you are told this about the composition of the balls: there might be 100 red balls, 100 black balls or any proportion of red vs. black. How much would you bet in this game? This time most people’s maximum bet is much lower.  How about you? Would you bet less than in the first game?

Mathematically, the odds are the same. 50/50 in both situations. In the first game, the odds are clear: there are 50 red and 50 black.  In the second game the odds are harder to understand, but its still 50/50. There are 101 possible combinations as follows (red vs. black): 100/0, 99/1, 98/2, 97/3 . . . 3/97, 2/98/, 1/99, 0/100. It works out to 50/50 odds just like the first game.* Knowing the odds are the same would you bet the same amount for both games? If your answer is “no” – you’d still bet less in the second game you are not alone. The vast majority of people who have played this game came to the same conclusion – they bet less on the second game because it feels more uncertain.

So, what’s the point? It means we are not perfectly rational beings. As humans, we prefer certainty and avoid ambiguity and uncertainty. Even when our rational minds KNOW that the odds are the same, the game with unknown proportion of balls feels much riskier. In terms of making decisions in business, investment and life, it means that uncertainty is likely overpriced. If we can set aside our aversion to uncertainty we can make better decisions.

Another point on Daniel Ellsberg. He’s actually best known not for his eponymous paradox but rather as the military analyst who leaked the Pentagon Papers in  1971 to the New York Times.

*Still having trouble visualizing the 50/50 odds? Try this: Instead of 100 marbles, imagine there are only 2. In the first game there is 1 black and 1 white. In the second game, one-third of the time you’d be picking out of an urn with 2 black marbles. Another third of the time, 2 white marbles. And another third of the time, the urn has 1 of each. Both are 50/50.

1 Comment

  1. Can’t we hear about the Monty Hall problem? 😉


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