Thinking and Deciding

CONCLUSION 287
imperfect correlations” (Table 2.1). Prescriptively, we would do well to learn to
distinguish the different kinds of cases. (In the case of ambiguity, I argued that what
matters is whether it is worthwhile to wait until we can obtain the information we
see as missing.) If we thought more about the heuristics that govern our decisions,
we might be able to learn when these heuristics are helpful shortcuts and when they
are self-made blinders that prevent us from achieving our goals.
The violations of utility theory discussed in this chapter indicate clearly that the
options we choose are often not the ones that best achieve our goals in the long run.
Decision utility — the inference from our choices about what we value — does not
match true (experienced) utility. In view of these findings, we can no longer assume
— as many economists do — that we always know what is best for us and express this
knowledge in our choices. The question of how we should deal with these violations
is not fully solved. I have suggested that actively open-minded thinking and the
judicious use of formal decision analysis (discussed in later chapters) are parts of the
answer to this question, but we may also need to learn new heuristics specifically for
making decisions.
Answers to selected exercises:
2. V (30) = 30 .5 =5.48
v(45,.8) = π(.8) · v(45) = .65 · 45 .5 =4.36
v(30,.25) = π(.25) · v(30) = .2375 · 30 .5 =1.30
v(45,.2) = π(.2) · v(45) = .20 · 45 .5 =1.34
3. u(30) = 30 .5 =5.48
u(45,.8) = .8 · u(45) = .8 · 45 .5 =5.37
u(30,.25) = .25 · u(30) = .25 · 30 .5 =1.37
u(45,.2) = .20 · u(45) = .20 · 45 .5 =1.34
Prospect theory overweighs p =1but otherwise underweighs differences in probabilities, such as the
difference between .25 and .20. Hence the reversal of the ordering of the third and fourth gambles,
according to the two theories. Utility theory must order the second pair of gambles by analogy with the
first pair.
4. All values are negative and twice those in question 2. The ordering of the gambles is reversed, because
the preferred gamble is the one that is less negative. This is the “reflection effect.”
5. v(X) =π(.5) · v($10)
X .5 = .425 · $10 .5
X = .4252 · $10 = $1.81
u(X) =.5 · u($10)
X .5 = .5 · $10 .5
X = .52 · $10 = $2.50
Prospect theory makes people seem more risk averse here because of the π function, which changes the
.5 into .425. If gambles were used to measure the utility of money, the obtained function would be too
concave.