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One of the first objections to Savage’s paradigm was raised by Ellsberg (1961). He suggested the following mind experiment, challenging the expected utility hypotheses: subject is asked to preference rank four bets. He/she is shown two urns, each containing 100 balls each one either red or black. Urn A contains 50 black balls and 50 red ones, while there is no additional information about urn B. One ball is drawn at random from each urn. Bet 1 is “the ball drawn from urn A is black,” and will be denoted by AB. Bet 2 is “the ball drawn from urn A is red,” and will be denoted by AR, and similarly we have BB and BR. Winning a bet entitles the subject $100. The following preferences have been observed empirically: AB & AR > BB & BR. It is easy to see that there is no probability measure supporting these preferences through expected utility maximization.
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