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PROSPECT
THEORY
that is merely probable over a smaller loss that is certain. The same psychological
principle-the overweighting of certainty-favors risk aversion in the domain of
gains and risk seeking in the domain of losses.
Third, the reflection effect eliminates aversion for uncertainty or variability as
an explanation of the certainty effect. Consider, for example, the prevalent
preferences for (3,000) over (4,000,
.80) and for (4,000, .20) over (3,000, .25). To
resolve this apparent inconsistency one could invoke the assumption that people
prefer prospects that have high expected value and small variance (see,
e.g., Allais
[2]; Markowitz [30]; Tobin [41]). Since (3,000) has no variance while (4,000, .80)
has large variance, the former prospect could be chosen despite its lower expected
value. When the prospects are reduced, however, the difference in variance
between (3,000,
.25) and (4,000, .20) may be insufficient to overcome the
difference in expected value. Because (-3,000) has both higher expected value
and lower variance than (-4,000,
.80), this account entails that the sure loss
should be preferred, contrary to the data. Thus, our data are incompatible with the
notion that certainty is generally desirable. Rather, it appears that certainty
increases the aversiveness of losses as well as the desirability of gains.
Probabilistic Insurance
The prevalence of the purchase of insurance against both large and small losses
has been regarded by many as strong evidence for the concavity of the utility
function for money. Why otherwise would people spend so much money to
purchase insurance policies at a price that exceeds the expected actuarial cost?
However, an examination of the relative attractiveness of various forms of
insurance does not support the notion that the utility function for money is
concave everywhere. For example, people often prefer insurance programs that
offer limited coverage with low or zero deductible over comparable policies that
offer higher maximal coverage with higher deductibles-contrary to risk aversion
(see,
e.g., Fuchs
[16]).
Another type of insurance problem in which people's
responses are inconsistent with the concavity hypothesis may be called prob-
abilistic insurance. To illustrate this concept, consider the following problem,
which was presented to 95 Stanford University students.
PROBLEM
9: Suppose
YOU
consider the possibility of insuring some property
against damage, e.g., fire or theft. After examining the risks and the premium you
find that you have no clear preference between the options of purchasing
insurance or leaving the property uninsured.
It is then called to your attention that the insurance company offers a new
program called
probabilistic insurance.
In this program you pay half of the regular
premium. In case of damage, there is a 50 per cent chance that you pay the other
half of the premium and the insurance company covers all the losses; and there is a
50 per cent chance that you get back your insurance payment and suffer all the
losses. For example, if an accident occurs on an odd day of the month, you pay the
other half of the regular premium and your losses are covered; but if the accident