Experimental discussion of the Ellsberg paradox
In 1961, Daniel Ellsberg published the results of a hypothetical experiment he had conducted, which, to many, constitutes an even worse violation of the expected utility axioms than the Allais Paradox. Ellsberg's subjects in his thought experiment seemed to run the gamut of noted economists of the time, from Gerard Debreu to Paul Samuelson and Howard Raiffa.
Structure of the Game
Subjects are presented with 2 urns. Urn I contains 100 red and black balls, but in an unknown ratio. Urn II has exactly 50 red and 50 black balls. Subjects must choose an urn to draw from, and bet on the color that will be drawn - they will receive a $100 payoff if that color is drawn, and $0 if the other color is drawn. Subjects must decide which they would rather bet on:
Explaining the Paradox
One would expect subjects to be indifferent in the first two cases, and they are. However, people uniformly prefer a draw from Urn I in cases 3 and 4. It is impossible to infer judgements about probabilities from these choices - do people regard a draw of a particular color from Urn I as more likely? Certainly not, because otherwise they would not choose Urn I in both cases 3 and 4.
An Alternative Formulation
Subjects are presented an urn containing 30 red balls and 60 black and yellow balls, the latter in an unknown proportion. Once again, subjects must bet on the color that will be drawn - they will receive a $100 payoff if that color is drawn, and $0 if either of the other colors is drawn. Let action I be a bet on red; action II be a bet on black.
Playing the game online
Ellsberg, Daniel, Risk, Ambiguity, and the Savage Axioms, The Quarterly Journal of Economics (Nov., 1961)