Thinking and Deciding

THE AMBIGUITY EFFECT 281
Table 11.7: Demonstration of the effect of ambiguity. (The relative number of black
and yellow balls is unknown.)
The ambiguity effect
30 balls 60 balls
red black yellow
Option X $100 $0 $0
Option Y $0 $100 $0
Option V $100 $0 $100
Option W $0 $100 $100
Another phenomenon was discovered by Daniel Ellsberg (of “Pentagon Papers”
fame) in 1961. Ellsberg found that subjects violate the axioms of expected-utility
theory by seeking to avoid risks associated with situations in which the probability
appears to be “unknown.” Suppose an urn contains ninety balls. Thirty of them are
red, and sixty of them are either black or yellow — we do not know how many of
each. A ball is to be drawn from the urn, and we can win some money, depending on
which ball is drawn and which option we take.
Ambiguity and “unknown probability”
Consider first a choice between options X and Y, whose payoffs are shown in the
top half of Table 11.7. You get the choice once. It is not repeated. Most subjects
lean strongly toward option X. They “know” that they have a 1/3 chance of winning
$100 in this case (30 out of 90 balls). They do not like option Y because they feel that
they do not even know what the “real probability” of winning is. It appears to them
that it could be as high as 2/3 or as low as 0. Note, however, that if the principle of
insufficient reason (p. 110) is adopted, we can assume that the probability of winning
is 1/3, given either option, and we conclude that we ought to be indifferent between
the two options.
Now consider options V and W, whose outcomes are shown in the bottom half of
Table 11.7. Here, most subjects strongly prefer option W, because they “know” that
their chance of winning is 2/3, whereas their chance of winning with option V could
be as low as 1/3 or as high as 1. (Again, the principle of insufficient reason would
dictate indifference.)
Together, this pattern of choices violates the sure-thing principle. Subjects reversed
their choices merely because the “yellow” column was changed. By the surething
principle, this column should be ignored when choosing between X and Y, or
when choosing between V and W, because it is identical for the two options in each
pair.