is more than 50 percent of the value attached to a gain of $200, which entails
preference for the sure $100 gain and, hence, risk aversion. Expected utility
theory and the assumption of risk aversion play a central role in the standard
economic analysis of choice between risky prospects.
Let us turn now to choice involving losses. Suppose you are forced to choose
between a prospect that offers a 50 percent chance to lose $200 (and a 50 per-
cent chance to lose nothing) and the alternative of losing $100 for sure. In this
problem, most people reject the sure loss of $100 and prefer to take an even
chance at losing $200 or nothing. Notice that, as in the choice above involving
gains, the prospects have the same expected value. This preference for a risky
prospect over a sure outcome that has the same expected value is an instance of
risk seeking. Evidently, risk aversion does not always hold, in contrast to tra-
ditional economic analysis. In fact, except for prospects that involve very small
probabilities, risk aversion is generally observed in choices involving gains,
whereas risk seeking tends to hold in choices involving losses.
The combination of risk aversion for gains and risk seeking for losses can
be explained by assuming that diminishing sensitivity applies to negative as
well as to positive outcomes. Consequently, the subjective value function for
losses is convex, as depicted in figure 26.3. (A function is convex if a line joining
any two points on the curve lies entirely above the curve.) According to such
a function, the worth of a gamble that offers a 50 percent chance to lose $200
is greater (that is, less negative) than that of a sure loss of $100. That is,
.50uð$200Þ>uð$100). This result implies a risk-seeking preference for the
gambleoverthesureloss.
By conjoining figures 26.2 and 26.3, we obtain anS-shaped value function
that is concave for gains and convex for losses, as illustrated in figure 26.4. This
functionformspartofadescriptiveanalysisofchoice,knownasProspect
Theory, which accounts for observed regularities in risky choice (Kahneman
and Tversky 1979; Tversky and Kahneman 1992). The value function of Pros-
pect Theory has three important properties: (1) it is defined on gains and losses
rather than total wealth, (2) it is steeper for losses than for gains, and (3) it is
concave for gains and convex for losses. The first property states that people
Figure 26.2
The subjective value curve can be used to illustrate risk behaviors. Here, the subjective value of a
$100 gain is seen to be more than^12 the value of a $200 gain, entailing preference for the ‘‘sure thing’’
$100 gain described in the text.
Decision Making 603