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Our discussion so far has centered on understanding how people act when the outcomes
of gambles have known objective probabilities. In reality, probabilities are rarely
objectively known. To handle these situations, Savage (1964) develops a counterpart to
expected utility known as subjective expected utility, SEU henceforth. Under certain
axioms, preferences can be represented by the expectation of a utility function, this
time weighted by the individual’s subjective probability assessment.
Experimental work in the last few decades has been as unkind to SEU as it was to
EU. The violations this time are of a different nature, but they may be just as relevant
for financial economists.
The classic experiment was described by Ellsberg (1961). Suppose that there are
two urns, 1 and 2. Urn 2 contains a total of 100 balls, 50 red and 50 blue.Urn 1 also
contains 100 balls, again a mix of red and blue, but the subject does not know
the
proportion of each.
Subjects are asked to choose one of the following two gambles, each of which involves
a possible payment of $100, depending on the color of a ball drawn at random
from the relevant urn
a1 : a ball is drawn from Urn 1, $100 if red, $0 if blue,
a2 : a ball is drawn from Urn 2, $100 if red, $0 if blue.
Subjects are then also asked to choose between the following two gambles:
b1 : a ball is drawn from Urn 1, $100 if blue, $0 if red,
b2 : a ball is drawn from Urn 2, $100 if blue, $0 if red.
a2 is typically preferred to a1, while b2 is chosen over b1. These choices are
inconsistent
with SEU: the choice of a2 implies a subjective probability that fewer than 50%
of
the balls in Urn 1 are red, while the choice of b2 implies the opposite.