Thinking and Deciding

276 DESCRIPTIVE THEORY OF CHOICE UNDER UNCERTAINTY
Table 11.5: Analysis of “inconsistent” choices according to regret theory
Probability Probability
First pair .80 .20 Second pair .05 .20 .15 .60
Option 1 $30 $30 Option 3 $30 $30 $0 $0
Option 2 $45 $0 Option 4 $45 $0 $45 $0
for a poorly made decision if the outcome is poor. Perhaps we anticipate our own
confusion between the quality of our decision making and the quality of its outcome
(Baron and Hershey, 1988).
Regret theory can explain in principle many of the phenomena that are explained
by the π function in prospect theory. Consider the inconsistency observed by Kahneman
and Tversky between the choice of $30 as opposed to $45 with a probability of
.80 and the choice of $30 with a probability of .25 as opposed to $45 with a probability
of .20. Many people choose the first option in the first pair but the second option
in the second pair. According to regret theory, we can represent these two pairs as
in Table 11.5. The table for the first pair of options (1 and 2) represents outcomes of
these options in two states of the world (with probabilities .80 and .20, respectively).
We think about this decision by comparing v($45) to v($30), in the first column,
and by comparing v($30) to v($0) in the second column. The former difference is
smaller, and we tend to neglect it. Specifically, we think about our regret if we chose
option 2 and receive $0 (knowing that we would have received $30 if we had chosen
option 1), or our rejoicing if we chose option 1 and received $30 (knowing that we
would have received $0 from option 2). The difference between v($45) and v($30)
is not great, so the feelings of regret and rejoicing in this state of nature play little
role in our decision.
For the second pair of options (3 and 4), the situation is more complicated. We
can think of each gamble as being played (or “resolved”), whether we choose it or
not. We see that there are four possible states of the world, corresponding, respectively,
to the four columns: win if either gamble is played; win with option 3 but
lose with option 4; win with option 4 but lose with option 3; and lose with either.
The table is constructed on the assumption that the two gambles are independent;
therefore, the probability of winning with option 3 is the same, whether or not option
4wins.
Here, we have two main sources of regret, corresponding to the second and third
columns. If we take option 3 we might experience regret because we could lose that
gamble but would have won if we had taken option 4. Exactly the opposite could
happen if we take option 4. Further, the potential regret, in both cases, is about
equally strong. (The smaller difference, between $30 and $0 in the second column,
is a little more likely, so the two effects are about equal, if we take probability into
account.) The small difference in the first column (between $30 and $45) does not