On the Empirical Validity of Cumulative Prospect
Theory: Experimental Evidence of Rank-Independent
Probability Weighting
⇤
B. Douglas Bernheim
†
Stanford University and NBER
Charles Sprenger
‡
UC San Diego
First Draft: December 1, 2014
This Version: January 17, 2020
Abstract
Cumulative Prospect Theory (CPT), the leading behavioral account of decisionmaking
under uncertainty, avoids the dominance violations implicit in Prospect Theory (PT) by
assuming that the probability weight applied to a given outcome depends on its ranking.
We devise a simple and direct non-parametric method for measuring the change in relative
probability weights resulting from a change in payo
ff
ranks. We find no evidence that these
weights are even modestly sensitive to ranks. Conventional calibrations of CPT preferences
imply that the percentage change in probability weights should be an order of magnitude
larger than we observe. It follows either that probability weighting is not rank-dependent,
or that the weighting function is nearly linear. Non-parametric measurement of the change
in relative probability weights resulting from changes in probabilities rules out the second
possibility. Additional tests nevertheless indicate that the dominance patterns predicted
by PT do not arise. We reconcile these findings by positing a form of complexity aversion
that generalizes the well-known certainty e
ff
ect.
JEL classification:
D81, D90
Keywords
: Prospect Theory, Cumulative Prospect Theory, Rank Dependence, Certainty Equiv-
alents.
⇤
Previous versions of this paper were titled ‘Direct Tests of Cumulative Prospect Theory.’ We are grateful
to Ted O’Donoghue, Colin Camerer, Nick Barberis, Kota Saito, seminar participants at Cornell, Caltech, MIT,
UCLA, CIDE, Tel Aviv, UC Santa Barbara, the Stanford Institute for Theoretical Economics, and five anony-
mous referees for helpful and thoughtful comments. Fulya Ersoy, Vincent Leah-Martin, Seung-Keun Martinez,
and Alex Kellogg all provided valuable research assistance.
†
Stanford University, Department of Economics, Landau Economics Building, 579 Serra Mall, Stanford, CA
94305; bernheim@stanford.edu.
‡
University of California San Diego, Rady School of Management and Department of Economics, 9500 Gilman
Drive, La Jolla, CA 92093; csprenger@ucsd.edu.
Electronic copy available at: https://ssrn.com/abstract=3350196
1Introduction
Prospect Theory (PT), as formulated by Kahneman and Tversky (
1979
), provides a flexible
account of decision making under uncertainty that accommodates a wide variety of departures
from the Expected Utility (EU) paradigm. As a result, it has been enormously influential
throughout the social sciences. In contrast to the EU formulations of
von Neumann and Mor-
genstern
(
1944
),
Savage
(
1954
), and
Samuelson
(
1952
), a central premise of PT holds that
attitudes toward objective probabilities display non-linearities, with highly unlikely events re-
ceiving greater proportionate weight than nearly certain ones. This feature reconciles PT with
important behavioral puzzles such as the famous
Allais
(
1953
)paradoxes,aswellasthesimulta-
neous purchase of lottery tickets and insurance, as in
Friedman and Savage
(
1948
). Probability
weighting is also well-supported by simple and widely-replicated laboratory experiments.
1
Unfortunately, the formulation of probability weighting embedded in PT leads to conceptual
di
ffi
culties because it implies violations of first-order stochastic dominance even in relatively
simple settings. This is a serious flaw given the broad consensus that this property renders a
model of decisionmaking unappealing on both positive and normative grounds.
2
To understand
the problem, consider a lottery that pays
X
with probability
p
;forourcurrentpurpose,we
will leave other events and payo
ff
s unspecified. Now imagine a second lottery, identical to the
first, except that it splits the aforementioned event, paying
X
and
X