Ellsberg Paradox: Critique to N-M Hypothesis

Ellsberg paradox is the paradox to the theory of expected utility. The expected utility theory argues that the consumer who is facing the choices of items or outcomes with various probability of occurrences has an optimal decision that maximizes his or her expected utility of the choice he or she made.

Hence, the theory of expected utility concludes that consumers make decisions based on the expected utility of an event. The conclusion by the expected utility has been criticized by Ellsberg popularly known as Ellsberg Paradox.

Ellsberg paradox puts forth contradictory views against the expected utility theory. According to the paradox, an individual who is making a choice between two events prefers to choose the event with known probability to the event with unknown probability.

Thus, the individual is not trying to maximize the expected utility rather prefers the event with the specific probability that is known to him or her.
Ellsberg's Paradox Source: https://www.roughdiplomacy.com/[/caption]
According to Ellsberg, people always tend to choose the event with a known probability of winning over the unknown probability of winning even though the known probability of winning is low and unknown could be guaranteed of winning.

It implies that people prefer known devils to the unknown god.

In order to explain the Ellsberg paradox, let us take an example where there is an urn which consists of 10 red balls and 20 other balls which are black and yellow. It is not known how many are black and how many are yellow but in total there are 20 black and yellow balls.

There are different games like:

Game A

An individual receives Rs. 1000 if a red ball is drawn.

Game B

An individual wins Rs. 1000 if a black ball is drawn.

Here, the probability of drawing a red ball is 1.3, and t is known; but, the probability of drawing a black ball is unknown. It can be higher than the probability of drawing red balls or less than that.

In this case, the individual prefers Game A to Game B. though, the expected utility from Game B could be higher. Similarly, if there is another game, Game C, and Game D.

Game C

Rs. 1000 for red or black balls drawn,

Game D

Rs. 1000 for black or yellow balls brawn

In this case, the probability of selecting red or black is not known but the probability of selecting black or yellow is known. So, the individual is choosing Game D.

Therefore, the Ellsberg paradox shows that any individual decision-makers consider where the probability is known or not.

In the two events, if the probability of one event is known and the probability is known for another event.

Then, the individual always chooses the event with the known probability.

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