Ellsberg paradox

The Ellsberg paradox is a well-known phenomenon from decision theory of decision under uncertainty. When people have to choose between two options, and only one option, the probability distribution is known, they opt for this majority. This can lead to the independence axiom of decision theory is violated.

The Ellsberg experiment

1961 Daniel Ellsberg, described the following experiment:

In an urn contains 90 balls, 30 of which are red. The rest are yellow or black, in an unknown distribution.

The subjects will first choose between two bets:

• Bet A: drawing a red ball means more money (eg $ 10), yellow or black means rivet.
• Bet B: drawing a yellow ball means profit, red or black means rivet.

Here, the vast majority of subjects choose to wager A.

Subsequently, these bets will be changed so that now also means black profit in both cases:

• Bet C: drawing a red or black ball means profits, yellow means rivet.
• Bet D: Tighten a yellow or black ball means profit, red means rivet.

Here now decide the vast majority of subjects for bet D. This is in apparent contradiction to the earlier decision to bet A, since the black ball in C as well as in bet bet D now means more money, so makes no difference (hence the designation as paradox).

Ellsberg explains this result by the distinction between risk and uncertainty ( ambiguity in the original ): At risk are the probabilities are known ( examples: classical random experiments such as dice, roulette, etc.) where uncertainty is not.

The subjects suspect " cautiously " that the distribution of the yellow and black balls could turn to their disadvantage and decide both times for the known risk ( chance of winning 1/3 in the first round, 2/3 in the second ).