Thinking and Deciding

272 DESCRIPTIVE THEORY OF CHOICE UNDER UNCERTAINTY
Table 11.4: Examples of lotteries used by Lopes (1996). Each I represents a ticket.
Peaked Rectangular
$200 I $200 IIII
$186 I $189 IIII
$172 III $178 IIII
$159 IIIII $168 IIII
$146 IIIIIII $158 IIII
$132 IIIIIIIII $147 IIII
$119 IIIIIIIIIII $136 IIII
$106 IIIIIIIIIIIII $126 IIII
$93 IIIIIIIIIIIII $116 IIII
$80 IIIIIIIIIII $105 IIII
$66 IIIIIIIII $94 IIII
$53 IIIIIII $84 IIII
$40 IIIII $74 IIII
$26 III $63 IIII
$13 I $52 IIII
$0 $42 IIII
$32 IIII
$21 IIII
$10 IIII
$0 IIII
For low probabilities, this subadditivity effect works in the same direction as the
π function itself. As explained earlier, the π function leads to a “possibility effect,”
in which people are more sensitive to changes in probability near zero. As a result,
the possibility effect is larger for when probabilities are not stated numerically, even
if the stated probabilities for the risk correspond to those that subjects would assign
to uncertain events, if they were asked.
Rank-dependent utility theories
If we view prospect theory as a way of expressing various heuristics mathematically,
it fails to capture all the heuristics that people seem to use. This is particularly
apparent when decisions involve many possible outcomes. Table 11.4 shows two
lotteries. Each I represents a ticket. Lopes (1996) asked subjects to choose between
these two (and other pairs) and to explain their reasons.
One subject chose Peaked because, “I like to be able to count on getting a moderate
amount rather than choosing to get much higher or much lower.” Another made
the same choice because there were “too many chances of getting a lower prize” in