Adv Behav Econ pdf

124
S T A R M E R
lower ranking consequence, 
x
1
, will be higher than the weight attached to the
larger consequence. This overweighting of the lower-ranked consequences rela-
tive to higher-ranked consequences can be interpreted as a form of pessimism.
Pessimism also has a close connection to risk-aversion: a pessimistic agent with a
concave 
u
(
?
) will be universally risk averse; and an agent with a convex utility
function can be risk averse if he or she is sufficiently pessimistic (see Chew,
Karni, and Safra 1987; Chateauneuf and Cohen 1994).
Although rank-dependent theory does not imply generalized fanning out, the
early evidence of EU violation can be explained either by assuming a simple convex
• (
?
) or by more complex specifications. One possibility is the function displayed in
figure 4.6, which has “(
p
)
5
p
for a unique value of 
p
5
p
*; it is concave below 
p
*
and convex above it, hence “low” probabilities (below 
p
*) are overweighted.
Quiggin (1982) proposes this form with 
p
*
5
0.5. He is drawn to this partly be-
cause it explains the early violations of EU and partly because it has the appealing
property that 50–50 bets will be undistorted by probability weighting. While there
is little empirical support for the crossover at 
p
5
0.5, research over a period of
fifty years, from Malcolm Preston and Phillip Baratta (1948) to Drazen Prelec
(1998), lends support to the hypothesis of an (inverted) s-shaped decision-weighting
0
1
(p)
p
Figure 
4.6 An (inverted) S-shaped probability weighting function.

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