Thinking and Deciding

PROSPECT THEORY 267
A similar “threshold effect” for money can provide another explanation of people’s
willingness to buy lottery tickets. People may perceive the $1 spent for the
lottery ticket as trivial compared to the prize, and therefore essentially not worth
considering at all. (Such people do not apparently think about the low probability
of winning.) Of course, for those who play the lottery every week over a period of
years, the dollars add up.
Utility: The Value function and framing effects
Let us now look at the part of prospect theory that concerns utility. According to
prospect theory, individuals evaluate outcomes as changes from a reference point,
which is usually their current state. Because we take different conditions as the reference
point, depending on how a decision is described to us, we can make different,
inconsistent decisions for the same situation, depending on how it is described. Note
that this way of evaluation is unlikely to correspond to experienced or true utility.
This theory is about decision utility, not experienced utility.
The Value function. As noted in Chapter 10, Bernoulli viewed the utility of financial
gains or losses to an individual as a function of the person’s total wealth after
the gain or loss occurred. Therefore, if one already has $10,000, the added utility of
winning $30 would simply be u($10, 030) − u($10, 000). Kahneman and Tversky,
by contrast, suppose that we evaluate the utility of the $30 gain by itself, as u($30),
essentially without regard to our total wealth. They propose that we make decisions
as if we had a Value function for gains and losses, with the curve depicted in Figure
11.2. The horizontal axis is not wealth, but rather monetary gain (to the right), or
loss (to the left), compared with one’s reference point (the middle). The vertical axis
is essentially utility, but these authors use the letter v(.), for Value, instead of u(.)
to indicate the difference between their theory and standard utility theory. They acknowledge
that this Value function might change as a person’s total wealth changes,
but they suggest that such effects of total wealth are small. (Do not confuse this v
with the v used to represent monetary value in ch. 10, even though the two vs look
alike. Note also that Value is capitalized to distinguish it from “value” in “expected
value.” Value in prospect theory is a form of utility.)
The Value function shows that we treat losses as more serious than equivalent
gains. We consider the loss in Value from losing $10 is greater than the gain in Value
from gaining $10. That is why most of us will not accept a bet in which we have an
even chance of winning and losing $10, even though the expected value of that bet
is $0. This property is called loss aversion. It plays a large role in explaining several
other phenomena in decision making. 8
A glance at the graph shows that a second property of the Value function is that
it is convex for losses (increasing slope as we move to the right, as shown in the
8 The principle of declining marginal utility also implies that losses from some point on a utility function
will be weighed more heavily than gains from that point. Loss aversion, however, implies a kink
at the reference point. Also, by manipulating the reference point, we can make a subjective gain into a
subjective loss and vice versa.