Prospect theory, reference points, and health decisions

Judgment and Decision Making, Vol. 3, No. 2, February 2008, pp. 174–180
Prospect theory, reference points, and health decisions
Alan Schwartz?
Julie Goldberg
Department of Medical Education
Department of Medical Education
University of Illinois at Chicago
University of Illinois at Chicago
Gordon Hazen
IEMS Department
Northwestern University
Abstract
In preventative health decisions, such as the decision to undergo an invasive screening test or treatment, people may be
deterred from selecting the test because its perceived disutility relative to not testing is greater than the utility associated
with prevention of possible disease. The prospect theory editing operation, by which a decision maker’s reference point
is determined, can have important effects on the disutility of the test. On the basis of the prospect theory value function,
this paper develops two approaches to reducing disutility by directing the decision maker’s attention to either (actual)
past or (expected) future losses that result in shifted reference points. After providing a graphical description of the
approaches and a mathematical proof of the direction of their effect on judgment, we brie?y illustrate the potential value
of these approaches with examples from qualitative research on prostate cancer treatment decisions.
Keywords: prospect theory, medical decision making, reference points
1 Introduction
sage framing has tested prospect theory predictions of
how the description of test outcomes as gains or losses
In preventative health decisions, such as the decision to
(as well as the conceptualization of the purpose of the
undergo an invasive screening test or treatment, people
test as preventative vs. diagnostic and the consequent
may be deterred from selecting the test because its disu-
perception of whether the test is "safe" or "risky") can
tility relative to not testing is greater than the utility as-
affect test rates (Rothman & Salovey, 1997; Rothman,
sociated with prevention of possible disease. For ex-
Bartels, Wlaschin, et al., 2006). Speci?cally, message
ample, people may feel that the anticipated disutility of
framing theories predict that when a procedure is per-
a colonoscopy for colorectal cancer screening is great
ceived as risky (e.g., cancer screening tests may cause
enough relative to the expected utilty of prevention of
a patient to ?nd out that they have cancer), loss-framed
possible colorectal cancer to dissuade them from seeking
messages will promote testing more strongly than gain-
colonoscopy.1
framed messages, because people favor risky prospects
The prospect theory editing operation (Kahneman &
over sure prospects in the domain of losses. On the other
Tversky, 1979; Tversky & Kahneman, 1992), by which a
hand, when a procedure is perceived as safe (e.g., sun-
decision maker’s reference point is determined, can have
screen prevents sunburn and skin cancer), gain-framed
important impacts on the perceived disutility of the test.
messages are predicted to be more effective because peo-
The work of Rothman, Salovey, and colleagues on mes-
ple prefer sure prospects to risky prospects in the domain
of gains. Several public health intervention studies have
?The authors thank two anonymous reviewers for comments which
examined message framing and generally found evidence
contributed to the development of the manuscript.
Address cor-
favoring the predictions (Apanovitch, McCarthy, & Sa-
respondence to: Alan Schwartz, Department of Medical Education
(mc 591), 808 S. Wood St, 986 CME, Chicago, IL 60612. Email:
lovey, 2003; Moxey, O’Connell, McGettigan, et al., 2003;
alansz@uic.edu.
Rivers, Salovey, Pizzaro, et al., 2005; but see Finney &
1Although most of the anticipated (and experienced) disutility of
Iannotti, 2002 for a failure to con?rm the predictions).
colonoscopy speci?cally is actually associated with the preparation for
the procedure rather than the procedure itself, we consider the complete
On the basis of the prospect theory value function,
experience of scheduling and undertaking a screening test, including
necessary preparations, to be the "test" about which people make par-
this paper develops two approaches to reducing perceived
ticipation decisions.
disutility by directing the decision maker’s attention to
174

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Judgment and Decision Making, Vol. 3, No. 2, February 2008
Reference points and health
175
either (actual) past or (expected) future losses that can
procedure, Xc), but whose reference point is somehow
serve as reference points and are not consequences of the
shifted to the left (through an editing operation) relative
test itself. These approaches thus differ from message
to R1, to the point marked R3 on Figure 2. This decision
framing, which focuses on how the test outcomes are de-
maker now interprets her baseline health, with or without
scribed and manipulates gain and loss framing. We in-
an invasive procedure, as a relative gain, as X0 and Xc
stead derive the potential impact of directly refocusing
are in the domain of gains relative to R3. Therefore, the
the decision maker’s reference point.
decision maker expects less marginal disutility from the
After providing a graphical description of the ap-
invasive procedure, because the distance between Xc and
proaches and a mathematical proof of the direction of
X0 now results in a value difference of ?v3, which is per-
their effect on judgment, we illustrate the potential value
ceived to be on the gain curve, which is at all points ?atter
of these approaches with examples from qualitative re-
than the steepest portion of the loss curve, and is therefore
search on prostate cancer treatment decisions.
smaller in magnitude than ?v1. From the standpoint of
a low reference point, the marginal disutility associated
with an invasive procedure is valued as a foregone gain,
2 Graphical Description
and is thus perceived as less bad.
Figure 1 depicts a stylized prospect theory value function,
which de?nes the value associated with gains or losses
3 Mathematical Exposition
from a reference point R1, designated by the origin of the
graph. The function displays the three salient characteris-
Although Figure 2 motivates the result, it is possible to
tics of the PT value function: diminishing marginal value
prove that ?v1 will always represent a larger subjective
for gains (the gain portion of the curve is concave down),
loss than ?v2 or ?v3. We use the following lemma,
diminising marginal value for losses (the loss portion of
whose proof is elementary.
the curve is concave up), and loss aversion (the loss curve
is steeper, at all points, than the corresponding point on
Lemma 1
the gain curve).
Consider a decision maker who faces a decision be-
If f is a concave function over some interval of real num-
tween undergoing or avoiding an invasive screening pro-
bers with f (0) = 0, then
cedure. The decision maker’s status quo is his baseline
health, shown as X
f (x + y) ? f (x) + f (y)
0 in Figure 1; this point is also labeled
R1 to indicate that it is the reference point from which
whenever x, y and x + y are in the domain of f , and
evaluation takes place. The decision maker is evaluating
the difference in value associated with the invasive pro-
f (x ? y) ? f (x) ? f (y)
cedure, shown as Xc. ?v1 then represents the disutility
that the decision maker expects as a result of undergoing
whenever x, y and x + y are in the domain of f .
the procedure.
Consider now a decision maker who faces the same
decision, with the same objective outcomes (i.e., current
health, X0, or current health and an invasive procedure,
We suppose a prospect theory value function of the form
Xc), but whose reference point is somehow shifted to the
right (through an editing operation) relative to R1, to the
v+(x)
(x ? 0)
point marked R
v(x) =
2 on Figure 2. This decision maker, who
?v?(?x) (x ? 0)
now sees even their baseline health as poor (as X0 is in
the domain of losses relative to R2), expects less marginal
where v+,v? are increasing concave functions over the
disutility from the invasive procedure, because the dis-
nonnegative reals with v+(0) = v?(0) = 0. We assume
tance between Xc and X0 now results in a value differ-
v+(x) ? v?(x) for all x, in accord with the loss aversion
ence of ?v2, which is perceived to be on a ?atter portion
principle.
of the loss curve, and is therefore smaller in magnitude
Let x0 be the subject’s status quo health state, and xc =
than ?v1. Compared with a relatively poor health state,
x0 ? C be the subject’s status quo health state together
the incremental loss associated with an invasive proce-
with some additional intervention such as colonoscopy,
dure is perceived as “less (additionally) bad.”
where C > 0. We consider the three reference points
Finally, consider a third decision maker who faces the
mentioned above, namely R1 = x0 (the base case), R2 =
same decision, with the same objective outcomes (i.e.,
x0 + D (right-shifted reference point) and R3 = x0 ? D
current health, X0, or current health and an invasive
(left-shifted reference point). In the left-shifted case, we

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Judgment and Decision Making, Vol. 3, No. 2, February 2008
Reference points and health
176
Figure 1: Graphical depiction of PT value function
assume the left shift D exceeds the decrement C due to
intervention. The corresponding decrements in value are
?v2 = v(xc ? R2) ? v(x0 ? R2)
= v(x0 ? C ? x0 ? D) ? v(x0 ? x0 ? D)
?vi = v(xc ? Ri) ? v(x0 ? Ri) i = 1, 2, 3
= v(?C ? D) ? v(?D)
Because x
= ?v?(C + D) + v?(D)
c < x0, these are all negative quantities.
Therefore, we have
Proposition 1 (Right-shifted reference point)
The decrement in value after a right shift in the reference
?v2 ? ?v1 ?? ?v?(C + D) + v?(D) ? ?v?(C)
point is less negative than the original decrement in value,
But the last inequality is true by the concavity of v?
that is,
and the ?rst inequality in Lemma 1. QED.
?v2 ? ?v1
Proof: Note that we have
Proposition 2 (Left-shifted reference point)
The decrement in value after a left shift in the reference
?v1 = v(xc ? R1) ? v(x0 ? R1)
point is less negative than the original decrement in value,
= v(x0 ? C ? x0) ? v(x0 ? x0)
that is,
= v(?C) ? v(0) = v(?C) = ?v?(C)
?v3 ? ?v1

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Judgment and Decision Making, Vol. 3, No. 2, February 2008
Reference points and health
177
Figure 2: Graphical depiction of PT value functions with left and right shifted reference points
Proof: We have
v+(D ? C) ? v+(D) ? ?v+(C)
?v3 = v(xc ? R3) ? v(x0 ? R3)
Therefore, by transitivity,
= v(x0 ? C ? x0 + D) ? v(x0 ? x0 + D)
= v(D ? C) ? v(D)
v+(D ? C) ? v+(D) ? ?v?(C)
= v+(D ? C) ? v+(D)
so ?v
where we have used the assumption that D exceeds C,
3 ? ?v1. QED.
so that D ?C > 0. Then using ?v1 = ?v?(C), we have
4 Examples
?v3 ? ?v1 ?? v+(D ? C) ? v+(D) ? ?v?(C)
As shown above, shifts of reference point, either to the
To demonstrate the latter inequality, note that, by the
right of baseline health or to the left of baseline health
loss aversion principle,
plus the invasive procedure, will shrink the disutility as-
sociated with the invasive procedure. If the invasive
?v+(C) ? ?v?(C)
procedure is a recommended preventative screening test,
By the concavity of v+ and the second inequality in
such as colonoscopy, decreasing its disutility could be
Lemma 1,
an important public health goal, if decisions to undergo

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Judgment and Decision Making, Vol. 3, No. 2, February 2008
Reference points and health
178
screening are related to the perceived disutility of the pro-
5 Other Outcomes of the Screening
cedure. How might potential screening recipients be in-
Decision: Potential Bene?t
duced to view their decision from either of these shifted
reference points? Preliminary work with prostate cancer
If decision makers assume a shifted reference point in
patients has suggested mechanisms which may motivate
evaluating the relatively certain unpleasant experience of
each of these valuable reference point shifts.
an invasive procedure, it is also reasonable to ask what
When a decision maker re?ects upon his future health
the impact of the new reference point might be on their
as he ages, he may recognize that it is likely to worsen
evaluation of other outcomes that should also motivate
naturally over the course of his life. From his current
the decision to accept or reject the procedure. For sim-
vantage point, then, this future health state can appear
plicity, we assume that the primary bene?t of a screening
to be a relative loss. In this situation, it is as if the deci-
test is that it provides a small probability of resulting in
sion maker is examining the future focal health state (X0)
an early detection of a treatable medical condition, and
from a reference point (current health) that is signi?cantly
thus leads to treatment that provides a bene?t that would
higher, such as R2. When he focuses on his future health
not have been realized without the test. For example, a
as a decrement in functioning, the additional disutility of
colonoscopy or pap smear that detects precancerous tis-
an invasive procedure (?v2) is made smaller. This ex-
sue may result in the patient receiving effective treatment
perience of "diminishing marginal loss" was reported in
that prevents the development of cancer, and thus mean-
focus groups with prostate cancer patients through state-
ingfully improves their quantity and quality of future life;
ments like
this assumption is generally the rationale for recommen-
"Ten years from now. ...if I’m ?fty-?ve,
dations of screening tests (e.g., see U.S. Preventive Ser-
sixty...I’m at the end of, as they so call say, at
vices Task Force, 2003).
the end of your rainbow. Ain’t too many peo-
It is possible that different reference points may be ap-
ple going to be hitting a hundred. If you are, are
plied to the evaluation of the utility of the test itself and
you going to be functional? I’m just being real
to the evaluation of its potential bene?t. If this is the case,
... Most elderly people, they need assistance.
and re?ection on past or future experiences can be used to
Ain’t too many walking on their own, taking
shift the reference point for the evaluation of the test itself
care of themselves. So hey, I would go with
without shifting the reference point for evaluation of the
that longevity (and have treatment)." (Goldberg
bene?t, the propositions above predict that patients with
& Schwartz, 2007)
such a reference point constellation ought to be relatively
more likely to accept testing (because their disutility for
Conversely, when a decision maker re?ects about dif-
the test is reduced while their appreciation of the potential
?cult past experiences, she may recognize that undergo-
bene?t is unchanged).
ing the invasive procedure, though unpleasant, is still bet-
It is perhaps more likely, however, that the new
ter than the past state - if she handled the past state, she
(shifted) reference point is applied to both the evalua-
knows she can handle the procedure. From this vantage
tion of the test and the evaluation of the potential bene?t,
point (R3), even the prospect of the procedure (Xc) is
shown as X
an improvement in comparison to past experiences, and
T in Figure 2. In the case of a right-shifted
reference point (e.g. R
treated like a foregone gain in utility rather than an ad-
2), the bene?t will always be eval-
uated more positively than in the base case, because one
ditional loss. Thus, when she uses her past experience
portion (from X
as her reference point, the disutility of the invasive pro-
0 to R2) will now be evaluated on the
loss curve, which is steeper than the corresponding gain
cedure (?v3) is again made smaller. This experience of
curve, and the remaining portion (from R
"resiliency" was also reported in focus groups with men
2 to XT ) will
be evaluated on a steeper portion of the gain curve. That
at high risk for prostate cancer in interactions like:
is, when the reference point is shifted to the right, the test
"P1: I’d have surgery, I’d get it out."
is subjectively less unpleasant and the potential bene?t is
"F: ... Even though you’re going to live
subjectively greater, which predicts a greater preference
with these side effects."
for the test. This result is independent of the probability
"P1: Yeah, I mean, I was partially para-
of the bene?t, but does assume that the reference point
lyzed in my left hand, three and a half years,
shift is not so extreme that R2 falls to the right of XT ; that
I had nerve damage really bad. So I mean...
is, decision makers must consider the potential bene?t of
I’ve been through some rough times, so I mean
a true positive screen to be greater than their anticipated
="
natural loss of functioning due to age. For screening tests
"P2: You live with it."
intended to prevent diseases associated with high mortal-
"P1: Yeah, I’d have the surgery." (Goldberg
ity and morbidity, like colorectal or cervical cancer, we
& Schwartz, 2007)
believe these are reasonable (and testable) assumptions.

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Judgment and Decision Making, Vol. 3, No. 2, February 2008
Reference points and health
179
In the case of a left-shifted reference point (e.g. R3),
ture disability (the right-shifted reference point), has an
however, the conditions under which a higher expected
impact on prospective decision that remains even when
utility for the test would be perceived require consider-
considering changes in the evaluation of the uncertain
ably stronger assumptions that have no a priori justi?ca-
bene?t of the test or potential uncertain risks of the test.
tion. These conditions are dependent on the probability
Of the two approaches, focus on future disability is
of bene?t and the relative changes in the valuation of the
also perhaps more widely applicable as an intervention
test disutility and potential bene?t.
strategy, as declining health with age is likely to be a uni-
versal and universally understood phenomenon. In addi-
tion, people seem to be quite capable of making in?uen-
6 Other outcomes of the screening tial comparisons to imagined (counterfactual) states, and
decision: Potential harm
this skill ought to extend to imagined future ("antefac-
tual") states (Kahneman & Miller, 1986; Roese & Olson,
For simplicity, we have also assumed that the disutility of
1995). In contrast, people who do not have sign?cantly
the medical procedure is completely characterized by X
distressing past experiences may not be moved by appeals
c;
that is, we treat the procedure’s outcome as certain. In
to resiliency.
practice, of course, invasive tests often have small but sig-
In effect, the reference point shift induces a contrast
ni?cant risks; for example, the risk of a perforated colon
effect in which smaller losses are discounted in the new
during a colonoscopy has been recently reported to be
context which evokes larger losses (Thaler & Johnson,
0.2-0.4% in purely diagnostic procedures, and 0.3-1.0%
1990; Tversky & Grif?n, 1997). Such contrast effects
when polyps are removed during the procedure (Bonheur
have been observed with past experiences of physical
& Korelitz, 2006). As with the evaluation of X
pain (Dar, Ariely, & Frenk, 1995) as well as in the evalu-
c, a right-
shifted reference point will diminish the subjective disu-
ation of health-related quality of life (Ubel, Loewenstein,
tility associated with other potential negative outcomes,
& Jepson, 2003), but have not, to our knowledge, been
and the predicted greater willingness to accept the test
derived for health care decision making from prospect
should persist, independent of the probability of the po-
theory. We would expect this contrast effect to operate
tential negative outcomes.
alongside (and independently of) any message framing
A left-shifted reference point, however, only uncondi-
effects associated with the description of test outcomes.
tionally attenuates the disutility when the new reference
It remains for empirical investigation to discover the
point is shifted to the left of the potential negative out-
extent to which such an approach is effective in chang-
come, and few people are likely to have a salient referent
ing valuations, individual differences that may moderate
that is worse than bowel perforation (which can constitute
that effectiveness, and the impact of using a combined ap-
a surgical emergency). Accordingly, the impact of shift-
peal to both reference points. Because relatively little is
ing the reference point to the left is likely to be dependent
known about the number of reference points people use
on the likelihood of potential negative outcomes and the
simultaneously or in rapid sequence, or how judgments
associated decision weights.
from multiple reference points are combined or negoti-
ated, there is much work to do.
7 Discussion
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