Thinking and Deciding

270 DESCRIPTIVE THEORY OF CHOICE UNDER UNCERTAINTY
In the second version the reference point is shifted to the present state, in which
nobody has died; the outcomes are described as losses (deaths). The curve is convex,
and subjects are risk-seeking: .67 v(−600 lives) >v(−400 lives). 12
We have here an excellent example of a framing effect, a violation of the invariance
principle. Subjects give different judgments, depending on whether outcomes
are described as gains or losses. Because the lives are those of others, the total experienced
(or true) utility cannot possibly depend on the way the decision is framed.
This effect is a clear divergence between decision utility and experienced utility.
To summarize this description, prospect theory predicts two kinds of deviation
from expected-utility theory. One type concerns distortion of stated probability. At
the very least, subjects do not deal with stated probabilities as they ought to. The
second type of distortion concerns the Value function. There is nothing necessarily
wrong with the function itself, but once we start thinking of outcomes by comparing
them to some imagined reference point, it becomes relatively easy for our perception
of that point to be manipulated. We end up making different decisions depending
on how the reference point is described to us or how we describe it to ourselves. 13
We could, as an antidote to this sort of error, try hard to use a constant imagined
state for all decisions. As yet, no research has been done to determine whether such
corrective heuristics work.
Prospect theory is a formal, mathematical theory of decision making under uncertainty.
As noted, it began as an attempt to modify expected-utility theory so that
it could serve as a descriptive model. (For other attempts along this line, see Weber
and Camerer, 1987.) But prospect theory can also be seen as giving us hints about the
heuristics that people use to make decisions under uncertainty: People tend to simplify
their thinking about probability into categories of sure thing (certain), possible,
or impossible. The distinction between certain and possible is salient even when
“possible” corresponds to a very high probability. This distinction could cause the
certainty effect. A similar distinction between impossible and possible could cause
the overweighting of low probabilities, or the “possibility effect” (Fox and Tversky,
1998). Another possible heuristic is “Avoid risks, but take risks to avoid losses.” We
shall see other examples of heuristics in decision making. Prospect theory can be a
valuable theory whether or not it can be explained in terms of heuristics.
Exercises on prospect theory 14
Assume that someone’s Value function for receiving or losing an amount of dollars X is X .5
12 One may well wonder whether it makes sense to have anything other than a linear utility function for
lives saved or lost. If the function is curved, the six-hundredth person to die is “worth less” than the first
person. This seems highly unfair to the six-hundredth person. If we accept the view (advanced in Chapter
16) that everyone’s utilities are equally important, we are inconsistent if we do not worry as much about
each individual death, when many people die at once, as we worry about individual deaths, when people
die one at a time.
13 Unlike the part of prospect theory dealing with probabilities, to which several alternatives have been
proposed (as we noted earlier), the part dealing with the role of the reference point has not been seriously
challenged.
14 Answers to selected exercises appear at the end of the chapter.