The Ellsberg’s paradox was developed by Daniel Ellsberg in his paper “Risk, Ambiguity, and the Savage Axioms”, 1961. It concerns subjective probability theory, which fails to follow the expected utility theory, and confirms Keynes’ 1921 previous formulation. This paradox is usually explained with the next experiment (you may try it yourself):
An individual is told that an urn contains 90 balls from which 30 are known to be red and the remaining 60 are either black or yellow. He is asked to choose between the following gambles:
Gamble A: – $100 if the ball is red
Gamble B: – $100 if the ball is black
And one between the following:
Gamble C: – $100 if the ball is not black
Gamble D: – $100 if the ball is not red
In most cases people will choose A over B and D over C. It is thought that betting for or against the known information (red ball) is safer than betting for or against the unknown (black ball). Nevertheless, these choices of preferences result in a violation of the sure-thing principle, which would require the ordering of A to B to be preserved in C to D.
We can derive a series of conclusions from this paradox. First, the appearances of a breach in the independence axiom, as common elements are considered in both gambles. Second, how individuals are reluctant to play in complex games, which shows their aversion to ambiguity. This statement also concerns the last conclusion which regards the disjunction effect. Decisions are postponed until having information, although this information may not have an influence is our final decision.