Untilt/Doxa

Two urns

Two urns each hold 100 balls, red and black. One holds exactly 50 red and 50 black. The other holds them in an unknown mix: anywhere from 0 to 100 red. You would win €100 if you drew a red ball. Which urn do you draw from?

The urn with 50 red and 50 black
The urn with an unknown mix
No preference

Preferring the 50/50 urn for red makes sense for someone who believes red is the rarer colour in the unknown urn; preferring it for black, for someone who believes black is. No one can believe both, so no single belief about the unknown mix fits that pair, nor the opposite one; no preference, both times, fits the belief that neither colour is rarer. From a large number of informal responses, gathered under what he called “absolutely nonexperimental” conditions, Ellsberg reported in 1961 that most of those who answered preferred the 50/50 urn for both bets, and a small minority the unknown urn for both (Ellsberg, 1961).

Ellsberg, D. (1961). Risk, Ambiguity, and the Savage Axioms. The Quarterly Journal of Economics, 75(4), 643-669.

Ambiguity Aversion

Preferring a known risk to an unknown one, even at a cost

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