Daniel Ellsberg on Democracy Now

Today, Democracy Now aired an interview with Daniel Ellsberg to discuss the new movie The Most Dangerous Man in America regarding Dr. Ellseberg's work during the Nixon administration and his leaking of Pentagon papers regarding the Vietnam war.

Dr. Ellsberg is know to graduate microeconomics students for his popularizing of what is known as the Ellsberg paradox:

Suppose you have an urn containing 30 red balls and 60 other balls that are either black or yellow. You don't know how many black or yellow balls there are, but that the total number of black balls plus the total number of yellow equals 60. The balls are well mixed so that each individual ball is as likely to be drawn as any other. You are now given a choice between two gambles:

Gamble A	Gamble B
You receive $100 if you draw a red ball	You receive $100 if you draw a black ball

Also you are given the choice between these two gambles (about a different draw from the same urn):

Gamble C	Gamble D
You receive $100 if you draw a red or yellow ball	You receive $100 if you draw a black or yellow ball

Since the prizes are exactly the same, it follows that you will prefer Gamble A to Gamble B if, and only if, you believe that drawing a red ball is more likely than drawing a black ball (according to expected utility theory). Also, there would be no clear preference between the choices if you thought that a red ball was as likely as a black ball. Similarly it follows that you will prefer Gamble C to Gamble D if, and only if, you believe that drawing a red or yellow ball is more likely than drawing a black or yellow ball. If drawing a red ball is more likely than drawing a black ball, then drawing a red or yellow ball is also more likely than drawing a black or yellow ball. So, supposing you prefer Gamble A to Gamble B, it follows that you will also prefer Gamble C to Gamble D. And, supposing instead that you prefer Gamble D to Gamble C, it follows that you will also prefer Gamble B to Gamble A.

When surveyed, however, most people strictly prefer Gamble A to Gamble B and Gamble D to Gamble C. Therefore, some assumptions of the expected utility theory are violated.