The Ellsberg Paradox

Even if he had never leaked the ‘Pentagon Papers’, Daniel Ellsberg would still be famous – though admittedly much less so. In the news again this week defending Edward Snowden for leaking information about classified NSA surveillance programs, Ellsberg is also known for a contribution to behavioral economics. He is the inventor of the Ellsberg Paradox.

The Paradox goes like this: Imagine a friend puts a tall flower pot in front of you containing marbles of three different colors. It’s a clay pot, so you can’t see inside, but your friend tells you that there are 90 marbles in total, and that 30 are red. The other 60 are black or yellow, but you don’t know how many there are of each. Your friend then offers you a choice between two gambles. If you choose gamble A, you will win $100 if you draw a red marble from the pot. If you choose gamble B, you will win $100 if you draw a black marble from the pot. Which would you choose?

If you are like most people, you will go for gamble A and hope to draw a red marble. Fine, but note what this implies. Because you are not indifferent between the gambles, it suggests that you think there are likely to be fewer than 30 black marbles in the pot, and thus that there are more than 30 yellow marbles.

Your friend then offers you a second choice. In this case, if you choose gamble C, you will win $100 if you draw a red or yellow marble. Or, if you choose gamble D, you will win $100 if you draw a yellow or black marble. Which would you choose?

Thinking through it logically, you should choose gamble C. You know there are 30 red marbles, and your first choice suggests you think there are more than 30 yellow marbles. In contrast, you know that there are only 60 yellow and black marbles combined – the choice offered by gamble D. But of course this is a paradox, which means that most people don’t select C. Instead, they tend to choose the seemingly irrational gamble D.

Ellsberg’s Paradox is often taken as evidence that people have an aversion to ambiguity. Although gambles A and D are logically inconsistent, both are options in which you can be certain about the probabilities – you know exactly how many there are of the relevant marbles. The precise probabilities associated with Gambles B and C, in contrast, are unknown.

There is something ironic about this. Daniel Ellsberg, the man whose Paradox demonstrates how much people dislike ambiguous outcomes is also Daniel Ellsberg, the most famous whistleblower in American history. One’s fate doesn’t get much more uncertain than when one leaks large amounts of classified national security information. Pitting your puny self against the full and angry apparatus of the state (in a polite moment, Nixon called Ellsberg a “sonofabitch”; in a less polite one, he raided Ellsberg's psychiatrist's office), hoping that the public will respond is a huge gamble that very few people are willing to take.

But whistleblowers are unusual. There is an alternative interpretation of the Ellsberg Paradox, which suggests that when someone doesn’t provide you with full information about your choices, it is sensible to assume that they are trying to pull a fast one. As such, people may choose the certain gambles because they are averse to being deceived.

High tolerance for uncertainty about their own outcomes, coupled with intolerance for what they perceive as deceit is perhaps what characterizes whistleblowers. Put differently, whistle-blowers are willing to accept ambiguity about the future that lies in store for them in order to reduce the ambiguity of other people’s choices. They open a crack in the clay pot, so that the black and yellow marbles – the hidden contingencies - are revealed.

There is no doubt that things once hidden have been revealed this week. Your reaction to Edward Snowden’s decision to leak information about classified NSA programs likely depends on what you think has been uncovered. Has Snowden has reduced ambiguity that was important for protecting against terrorism, in which case he is a traitor? Or has he exposed an unwarranted, even undemocratic deception, in which case he is a hero?

Either way, he has broken the law and is likely go to jail. Perhaps he will spend some of his time there inventing a paradox of his own.