Ellsberg Paradox

The Ellsberg Paradox is the demonstration that human agents prefer known probabilities over unknown ones — even when the unknown probabilities are not demonstrably worse. Discovered by Daniel Ellsberg in 1961, the paradox shows that people violate the additivity axiom that underlies Leonard Jimmie Savage's derivation of subjective expected utility. The paradox is simple: agents prefer to bet on an urn with 50 red and 50 black balls over an urn with 100 red-and-black balls in unknown proportion, even though the second urn might contain 100 winning balls. This is not irrationality. It is a preference for ambiguity reduction over expected value maximization. The paradox reveals that subjective probability theory treats all uncertainty as quantifiable — a claim that is itself a metaphysical commitment, not an empirical fact. The Allais Paradox challenges the independence axiom. The Ellsberg paradox challenges the very possibility of assigning precise probabilities to every uncertain event. Together, the two paradoxes suggest that the Savage framework is not a theory of rational choice under uncertainty but a theory of rational choice under a very specific kind of uncertainty — the kind that can be represented as a probability distribution. Most real uncertainty cannot.