Thinking and Deciding

THE AMBIGUITY EFFECT 283
not the world, the only way in which a probability could be “unknown” is for a
person not to have reflected enough about the situation. To say that a probability is
“unknown” is to assume that probabilities can be known only if relative frequencies
have been observed or if the possibilities can be analyzed logically into exchangeable
alternatives.
Let us reexamine the ambiguity effect described in the Ellsberg experiment.
Looking more carefully, we can see that any argument for Option X (or W) can
be matched by a comparable argument for Option Y (or V). Yes, it could be the case
(in deciding between Option X and Option Y) that the urn has 60 yellow balls, and
this is an argument for Option X, but it could also turn out that the urn contains 60
black balls, and this is an equally strong argument for Option X. We conclude that
there is no good reason to prefer Option X over Y. If we are not indifferent, we seem
to be contradicting a very fundamental principle of decision making: When there
are equally strong reasons in favor of two choices, then there is no overall reason
to prefer one option or the other. (Likewise, if we must pay extra in order to make
Option X, we would be irrational to choose Option X, because there is one reason to
favor Option Y that is not matched by an equivalent reason for Option X — namely,
the need to pay.)
Ultimately, I would argue, the ambiguity effect is another kind of framing effect,
dependent on the way a problem is described. If we were given a great many choices
like X and Y, but with different urns, we could assume that red and black would be
drawn equally often over the whole sequence of choices. (If we do not assume this,
then we must have some reason to think that one color is more likely than the other,
and we would always bet on that color — choosing X and V, or Y and W, consistently
and therefore not violating the sure-thing principle.) Therefore, a choice between X
and Y is just a choice between one member of a sequence in which the red and black
are equally likely. It would not do any injustice to describe the situation that way.
If the situation were described this way, there would be no difference between the
Ellsberg situation and one in which the probabilities were “known” (Raiffa, 1961).
On the other hand, consider an apparently unambiguous case, in which an urn
has fifty red balls and fifty white ones. It would seem that the probability of a red
ball is .5, but think about the top layer of balls, from which the ball will actually be
drawn. We have no idea what the proportion of red balls is in that layer; it could
be anywhere from 100% to 0%, just like the proportion of black to yellow balls in
the original example. By thinking about the situation in this way, we have turned an
unambiguous situation into an ambiguous one.
In sum, ambiguity may be a result of our perception that important information
is missing from the description of the decision. In the balls-and-urn example, we
brought out the missing information by focusing attention on the top layer of balls.
Information is always missing in any situation of uncertainty, though, and so we can
make any situation ambiguous by attending to the missing information. Conversely,
we can make any ambiguous situation into an unambiguous one by imagining it as
one of a sequence of repeated trials.