Content uploaded by David R. Mandel
Author content
All content in this area was uploaded by David R. Mandel on Jun 01, 2014
Content may be subject to copyright.
Do Framing Effects Reveal Irrational Choice?
David R. Mandel
DRDC Toronto, Toronto, Ontario, Canada, and York University
Framing effects have long been viewed as compelling evidence of irrationality in human decision
making, yet that view rests on the questionable assumption that numeric quantifiers used to convey the
expected values of choice options are uniformly interpreted as exact values. Two experiments show that
when the exactness of such quantifiers is made explicit by the experimenter, framing effects vanish.
However, when the same quantifiers are given a lower bound (at least) meaning, the typical framing
effect is found. A 3rd experiment confirmed that most people spontaneously interpret the quantifiers in
standard framing tests as lower bounded and that their interpretations strongly moderate the framing
effect. Notably, in each experiment, a significant majority of participants made rational choices, either
choosing the option that maximized expected value (i.e., lives saved) or choosing consistently across
frames when the options were of equal expected value.
Keywords: framing effects, decision making, rationality, numeric quantifiers
Making coherent choices is a basic requirement of rational
decision making captured well by the principle of description
invariance, a fundamental coherence axiom of rational-choice the-
ories (Arrow, 1982; Tversky & Kahneman, 1986). Description
invariance requires that a decision maker’s choice among a set of
options should not vary merely because they have been described
or “framed” differently, provided that the alternative frames actu-
ally describe the identical option set (i.e., they are extensionally
equivalent). Demonstrations of framing effects have been regarded
as compelling evidence that people’s choices are incoherent and,
hence, irrational (Dawes, 1988; Shafir & LeBoeuf, 2002; Stanov-
ich & West, 2000). In recent years, framing effects have even been
used as negative indicators to measure decision competence (Bru-
ine de Bruin, Parker, & Fischhoff, 2007) and critical thinking
(West, Toplak, & Stanovich, 2008; but compare Stanovich &
West, 2008).
Framing literature that purportedly supports the substantive ir-
rationality claim focuses mainly on studies of “risky-choice” fram-
ing (Levin, Schneider, & Gaeth, 1998). In such studies, the deci-
sion maker is presented with two options to choose from: One
option offers a certain outcome with both favorable and unfavor-
able components, whereas the other offers an uncertain outcome in
which one possibility is better than the alternative certain outcome
(indeed, entirely favorable) and the other possibility is worse
(indeed, entirely unfavorable).
1
The two options are assumed to be
equal in terms of their expected utility. However, as the reader
shall see, the present research challenges that assumption.
Although the focus in this article is on risky-choice framing,
given the impact it has had on the characterization of human
rationality, it is worth noting at the outset that the present analysis
has broader implications for framing manipulations that involve
describing outcomes or events as potentials gains of a given
magnitude versus potential losses of a complementary magnitude.
Such framing manipulations include the other main types noted in
Levin et al.’s (1998) taxonomy, including attribute framing (e.g.,
Levin & Gaeth, 1988) and health message framing (for a review,
see Rothman & Salovey, 1997). Indeed, the research and concep-
tual analysis presented in this article are of relevance to the
interpretation of virtually all types of framing effects that involve
a reformulation of quantitative information conveyed to a receiver,
such as re-describing a 90% chance of post-operative survival as a
10% chance of post-operative mortality. While there are examples
of framing effects that do not involve the re-description of quan-
tities in complementary ways, such as re-describing an earmarked
tax as an offset (Hardisty, Johnson, & Weber, 2010), the vast
majority of framing studies has focused on such manipulations and
thus may be informed by the present research. Moreover, the
issues raised here are of relevance to a wide array of everyday life
1
Following Knight (1921/1964), the latter is often referred to as the
risky option. However, Tombu and Mandel (2013) have found that a
nontrivial proportion of participants perceive the certain option as riskier,
especially when the options are framed negatively. Thus, the terms certain
and uncertain are used in this article to refer to the respective options.
This article was published Online First August 26, 2013.
David R. Mandel, Socio-Cognitive Systems Section, DRDC Toronto,
Toronto, Ontario, Canada, and Department of Psychology, York Univer-
sity, Toronto, Ontario, Canada.
Portions of this research were presented at the 12th International Con-
ference on Thinking in London, England, on July 6, 2012. This research
was supported by Natural Sciences and Engineering Research Council of
Canada (NSERC) Discovery Grant 249537-07 and Department of National
Defense Applied Research Program Project 15dm. I thank the following
people: Nada Bishir, Irina Kapler, Philip Omorogbe, Karen Richards, Lee
Unger, and Joseph Williams for their research assistance; Bart Geurts,
Denis Hilton, Daniel Kahneman, Karl Teigen, and Neil Thomason for
useful discussions of the ideas and findings presented in this article; and
Sharon Thompson-Schill for her constructive feedback on drafts of this
article.
Correspondence concerning this article should be addressed to David R.
Mandel, DRDC Toronto, 1133 Sheppard Avenue West, Toronto, Ontario
M3K 2C9, Canada. E-mail: drmandel66@gmail.com
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
Journal of Experimental Psychology: General © 2013 The Crown in Right of Canada
2014, Vol. 143, No. 3, 1185–1198 0096-3445/14/$12.00 DOI: 10.1037/a0034207
1185
contexts in which decisions are made about how best to commu-
nicate information with numeric quantifiers to decision makers.
Re-Examining a Core Assumption
in Framing Research
The most influential example of a risky-choice framing manip-
ulation is Tversky and Kahneman’s (1981) “Asian disease” prob-
lem (ADP). In the ADP, participants first read the following:
Imagine that the U.S. is preparing for the outbreak of an unusual
Asian disease, which is expected to kill 600 people. Two alternative
programs to combat the disease have been proposed. Assume that the
exact scientific estimates of the consequences of the programs are as
follows:
Participants in a positive-framing condition were then asked to
choose between Options A and B:
If Program A is adopted, 200 people will be saved.
If Program B is adopted, there is 1/3 probability that 600 people will
be saved, and 2/3 probability that no people will be saved.
By comparison, participants in a negative-framing condition chose
between Options C and D:
If Program C is adopted, 400 people will die.
If Program D is adopted, there is 1/3 probability that nobody will die,
and 2/3 probability that 600 people will die.
With positive framing, 72% chose the certain option (A); but with
negative framing, 78% chose the uncertain option (D).
The findings are theoretically significant because they (ostensi-
bly) show that decision makers’ choices among the same options
could be systematically affected by trivial variations in descrip-
tion—namely, that decision makers are incoherent because they
violate the description invariance principle. As noted earlier, that
conclusion—and indeed the validity of the framing manipula-
tion—rests on a foundational assumption of extensional equiva-
lence. Quite simply, it states that the certain option in the positive
frame is identical to the certain option in the negative frame—and
likewise for the uncertain options across frames.
With few notable exceptions (e.g., Jou, Shanteau, & Harris,
1996; Kühberger & Tanner, 2010; Macdonald, 1986; Mandel,
2001), the extensional-equivalence assumption has remained vir-
tually unchallenged in the framing literature. Kahneman and Tver-
sky (1984) themselves claimed, “it is easy to verify that options C
and D in Problem 2 are undistinguishable in real terms from
options A and B in Problem 1, respectively” (p. 343), leading them
to conclude that “the failure of invariance is both pervasive and
robust” (p. 343). Likewise, in an influential review, Levin et al.
(1998), declaring their belief in the extensional-equivalence as-
sumption, stated, “Problems such as the Asian disease problem
provide ‘pure’ framing effects because the same outcomes are
alternatively phrased as though they were gains or as though they
were losses” (p. 180, italics in original). Acceptance of the
extensional-equivalence assumption in the ADP has been just as
strong outside of psychology. For instance, in a recent article in
Economics and Philosophy, after describing the ADP, Gold and
List (2004) advised readers as follows: “Note that A and C are
extensionally equivalent. They denote the same vaccination pro-
gram, where precisely 200 people will be saved and 400 will die”
(p. 255).
A critical, but neglected, question is how one might verify that
the reframed options are identical. Tversky and Kahneman (1981;
Kahneman & Tversky, 1984) offered no more than an appeal to
intuition. Regarding the certain options (A and C), whose equiv-
alence seems the more controversial because they are not fully
described in terms of expected outcome (i.e., nothing is said about
the remaining 400 lives in the positive-framing condition or about
the remaining 200 lives in the negative-framing condition), the
implicit argument in support of extensional equivalence is easy
enough to construct: If there are 600 threatened lives and 200 are
saved (A), then that leaves 400 who will die (C). In other words,
the arithmetic fact that 600 ⫺ 200 ⫽ 400 is taken as proof that the
alternative frames describe equivalent expected outcomes. In ef-
fect, framing is construed here as merely “refocusing” attention
from the proportion 200/600 to the complementary proportion
400/600 (Mandel, 2008).
The proof-by-arithmetic argument is widely accepted in the
literature (e.g., Fagley, 1993; Kühberger, Schulte-Mecklenbeck, &
Perner, 1999; Levin et al., 1998), even by skeptics of coherence
theorists’ conclusions, such as Hammond (2000), who neverthe-
less advised readers to “take another look at the options and do the
arithmetic” (p. 61) lest they remain skeptical about the reframed
options’ equivalence. Indeed, even McKenzie and colleagues
(McKenzie, 2004; McKenzie & Nelson, 2003), who proposed that
positive and negative frames convey different information to re-
ceivers because of their varying conversational implicatures, still
concede that in problems like the ADP the frames are extension-
ally (or as they put it, logically) equivalent.
Widespread belief in the proof-by-arithmetic argument is sur-
prising, however, given its reliance on the rather dubious linguistic
assumption that numeric quantifiers in noun phrases must be given
a bilateral “exactly” reading, as one would assign to numbers in
simple arithmetic. Linguists agree that interpretations of numeric
quantifiers are variable, affected by semantic and pragmatic con-
siderations. One (neo-Gricean) set of accounts posits that numeric
quantifiers have a unilateral, lower-bound “at least” semantics,
with bilateral interpretations derived by coupling the lower-bound
semantics with an upper-bound (“at most”) conversational impli-
cature (Horn, 1989; cf. Horn, 1992; Levinson, 2000). An alterna-
tive account by Breheny (2008) proposes that numeric quantifiers
have a bilateral semantics but that they could yield unilateral
interpretations via pragmatic inferences (for reviews of yet other
accounts, see Carston, 1998; Geurts, 2006). In spite of the differ-
ences among these accounts, all agree that numeric quantifiers can
take on unilateral or bilateral meanings under particular conditions.
Stated differently, all accounts reject naïve bilateralism, the as-
sumption that reasonable people ought to, and will, interpret nu-
meric quantifiers as exact values. Nor is the objection to naïve
bilateralism purely theoretical. For instance, even 5-year-olds with
a good understanding of a context can use pragmatic inferences to
arrive at multiple meanings of numbers including exactly, at least,
and at most (Musolino, 2004).
Linguists also agree that when quantities are interpreted unilat-
erally, they tend to be lower- rather than upper-bounded. This
prediction at least partially reflects the scalar property that higher
scale values imply lower ones but not vice versa. Thus, for the
positive scale {some, all}, if it is true that all were present, it is also
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1186
MANDEL
true that some were. Likewise, if at least 200 lives were saved, it
is also true that one or more sets of exactly 200 lives were saved.
The same does not hold for the upper bound: If at most 200 lives
were saved, it is possible, perhaps even probable, that no set of 200
lives was saved. Supporting this view, Halberg and Teigen (2009)
found that, in various tests using Internet searches, lower-bound
scalar modifiers (e.g., more than) are more frequently coupled with
numbers than their upper-bound counterparts (e.g., less than).
Moreover, consistent with lower- but not upper-bounding, partic-
ipants who considered a financial version of the ADP judged
predictions that fell short of the true value to be less accurate than
predictions that surpassed that value by the same amount (Teigen
& Nikolaisen, 2009).
The Present Research
Surprisingly, even those few authors who have questioned the
extensional equivalence assumption (e.g., Jou et al., 1996; Küh-
berger & Tanner, 2010; Macdonald, 1986; Mandel, 2001) have not
directly examined participants’ linguistic interpretations of nu-
meric quantifiers in framing studies of decision making. Thus, the
present research explored this important topic. It is proposed that
when these linguistic effects are taken into account, a quite dif-
ferent view of human decision making emerges—one where,
generally speaking, decision makers’ choices are rational. Specif-
ically, it is proposed that when the meaning of numeric quantifiers
in the certain options of the ADP (or an ADP variant, as examined
in some of the present experiments) is linguistically modified so
that it is clear that a bilateral “exactly” interpretation is appropri-
ate, choices will tend to be consistent across frames, as the de-
scription invariance principle requires. Given that frames also leak
information that go beyond the purely descriptive content of a
statement (Sher & McKenzie, 2006, 2008, 2011), one might still
expect some effect of framing even when a bilateral interpretation
is adopted. However, bilateral interpreters should at least show
significantly attenuated framing effects in their pattern of choice
between options.
The present account also predicts that when those same quan-
tifiers are modified such that they have a lower-bounded “at least”
interpretation, a pattern of choice consistent with the framing
effect will be observed. This is because, under those conditions,
the expected number of lives saved ought to be maximized by
choosing the certain option in the positive frame and the uncertain
option in the negative frame. That is, in the lower-bounded posi-
tive “frame,” the certain option offers an expectation of saving 200
lives minimum, whereas the uncertain option offers an expectation
of saving precisely 200 lives. In contrast, the lower-bounded
negative “frame” offers an expectation of saving 200 lives maxi-
mum compared to an expectation of saving precisely 200 lives in
the uncertain option.
2
Under these conditions, it is rational (viz.,
“utility maximizing”) to switch, and doing so in no way violates
the description-invariance principle because the two certain op-
tions are not the same (hence the earlier use of scare quotes around
the term “frame”).
Experiment 1 tested these predictions using the ADP in a
within-subjects design, whereas Experiment 2 generalized the re-
sults using a variant of the ADP in a between-subjects design.
Experiment 3 examined participants’ interpretations of numeric
quantifiers when they were left linguistically unmodified. Consis-
tent with the aforementioned prediction, it was hypothesized that,
in Experiment 3, a pattern of choice consistent with a standard
framing effect in which the certain option is more preferable in the
positive-framing condition than in the negative-framing condition
would be evident only among participants who interpreted the
numeric quantifiers as lower bounds and, thus, for whom that
pattern of choosing would maximize the expected number of lives
saved (hereafter described as the expected-value-maximizing
[EVM] choice).
To sum up, the present research aims to examine empirically for
the first time using a variety of experimental methods whether the
extensional-equivalence assumption is tenable and whether the
conclusions that have been drawn from framing research about
human (ir)rationality are indeed valid. It is perhaps worth noting,
as well, to avoid possible confusion, at least one aim that the
present research does not seek to achieve. That is, it does not aim
to show that framing effects, in general, are not real. To the
contrary, this work has very much been motivated by respect for
the theoretical and practical significance of the class of phenom-
enon captured by the term framing, and by a corresponding desire
to correct possible misconceptions regarding the causes and diag-
nostic implications of framing effects so that the scientific study of
framing rests on firm analytical ground.
Experiment 1
Using a within-subjects design, akin to that employed by other
researchers seeking to examine coherent choice at the participant
level (e.g., Schneider, 1992; Stanovich & West, 1998), Experiment
1 tested the prediction that most participants would choose con-
sistently across frames when the numeric quantifiers in the certain
option were given a bilateral meaning (consistent with the descrip-
tion invariance principle), and that most participants would show
a standard framing effect when the same quantifiers were explic-
itly lower-bounded (consistent with making EVM choices). These
two patterns of choice exemplify rational choice.
Experiment 1 also estimated the frequencies of what might be
called excusable and inexcusable choices—choices that violate
requirements of rational choice, but which do so with different
levels of justification. In the present research, excusable patterns of
choice may come in two types: (a) excusable consistencies in
which the first choice made is EVM and the second remains
consistent even though it is not EVM and (b) standard framing
effects made when the numeric quantifiers are given a bilateral
meaning. The former are excusable because the second choice
appears to sacrifice EVM for apparent consistency. Doing so does
not justify the choice, but it does make it excusable. Arguably,
standard framing effects are also excusable because even when the
frames are extensionally equivalent, they “leak” information that,
among other things, may imply a recommendation in favor of the
certain option in the positive frame and a recommendation against
2
These statements about maximum and minimum numbers of lives
expected to be saved are predicated on the following semantics of super-
lative quantifiers: “‘At least n A are B’ means that the speaker is certain
that there is a set of As that are B, and considers it possible that there is a
larger set of As that are Bs. ‘At most n A are B’ means that the speaker
considers it possible that there is a set of n As that are B, and is certain that
there is no larger set of As that are B” (Geurts, Katsos, Cummins, Moons,
& Noordman, 2010, p. 132).
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1187
DO FRAMING EFFECTS REVEAL IRRATIONAL CHOICE?
that option in the negative frame (e.g., McKenzie & Nelson, 2003;
Sher & McKenzie, 2006, 2008, 2011; van Buiten & Keren, 2009).
Again, this does not justify such choice inconsistencies, which
would nevertheless violate the description invariance principle, but
it does make them excusable.
Inexcusable patterns of choice also come in two types: (a)
reversed framing effects that either violate coherence requirements
(when quantifiers have a bilateral meaning) or EVM (when quan-
tifiers have a lower-bound meaning) and (b) consistent choices
made when quantifiers are lower-bounded where the initial choice
is not EVM (i.e., consistently choosing the certain option when the
first frame is negative or consistently choosing the uncertain
option when the first frame is positive). These choice patterns
appear inexcusable because they are neither supported by a plau-
sible reason that is noble (such as wanting to be consistent) nor
pragmatic (such as reasonably reading “leaked information”).
A final aim of Experiment 1 was to examine whether partici-
pants’ rationality in decision making was related to individual
differences in need for cognition (NFC; Cacioppo, Petty, & Kao,
1984) and experimental satisficing (Oppenheimer, Meyvis, & Da-
videnko, 2009). NFC measures an individual’s motivation to en-
gage in mentally challenging activities and reflective thought.
LeBoeuf and Shafir (2003) found that high-NFC participants were
less likely to violate description invariance in framing tasks than
low-NFC participants. Likewise, West et al. (2008) reported a
small but significant correlation between consistent choice in the
ADP and a composite of NFC and a related openness measure.
However, others (Levin, Gaeth, Schreiber, & Lauriola, 2002; Pe-
ters & Levin, 2008) have found that NFC was not related to
coherence violations due to framing. Likewise, Mandel (2005)
found no significant correlation between NFC and the magnitude
of additivity violations in probability judgment (i.e., a different
coherence measure).
Regarding the other measure, Oppenheimer et al. (2009) devel-
oped a simple one-item test of whether participants use a satisfic-
ing strategy in experimental tasks. Although the instructional
manipulation-check (IMC) task seems to require participants to
indicate all the sports from a list that the participant plays regu-
larly, the instructions actually ask the participant to simply click
the heading at the top of the screen. Correct responders were more
sensitive to slight wording manipulations that have been shown to
yield predictable effects, such as willingness to pay more for the
same drink when it is purchased from a fancy resort as opposed to
a run-down grocery store (Thaler, 1985). In one experiment by
Oppenheimer et al. (2009), correct responders scored higher in
NFC than incorrect responders, but that effect was not replicated in
a second experiment. Given the linguistic manipulation in Exper-
iment 1, the IMC task was included.
Method
Participants. One hundred twenty undergraduates were re-
cruited from the general student population at University of
Guelph and paid $20 to complete the experiment. Mean age of the
sample was 20.48 years (SD ⫽ 1.68), and 54% were female.
Sample size was determined using a combination of power anal-
ysis and heuristic strategy. For the primary analysis comparing
independent proportions of consistent choosers in the exactly and
at-least conditions, it was estimated that for an effect in which 2/3
of participants are consistent in the exact condition and 1/3 are
consistent in the at-least condition, a minimum sample size of 84
is required for ensuring a Type I and Type II error rates of .05 and
.10, respectively. Given that additional within-condition analyses
of proportions were also of interest, the between-subjects condi-
tions were increased from 42 to 60 participants each in order to
improve stability of those finer comparisons.
Design. Experiment 1 used a 2 (Frame: positive, negative) ⫻
2 (Modifier: at least, exactly) design, with frame manipulated
within-subjects and modifier manipulated between-subjects.
Procedure and materials. Participants were randomly as-
signed to the between-subjects factor. The order in which framing
conditions were presented was counterbalanced across partici-
pants. All participants were first given the ADP in one frame. The
only variation from the original problem was whether the numeric
quantifier (200 or 400) in the certain option was modified by the
term “at least” or “exactly.” After reading the problem, partici-
pants indicated which option of the two options they favored. The
second ADP was given in the other frame and modified in the
same way as the first problem. Between the first and second ADP
tasks, participants completed a set of unrelated tasks involving
the translation of verbal probabilities into numeric probabilities
and they also completed Cacioppo et al.’s (1984) 18-item NFC
scale. The intervening tasks took approximately 40 min to com-
plete. Oppenheimer et al.’s (2009) IMC task was administered
after the second ADP was completed. The experiment was run in
a supervised laboratory on Macbook computers using FluidSur-
veys scripts. Participants had to complete all questions on any
given page before the script would advance to the next page.
Participants could not go back to review or change answers on
previous pages.
Analysis. Selections of the certain and uncertain options were
dummy coded as 1 and ⫺1, respectively. A measure of framing
effects was taken by subtracting the value in the negative-framing
condition from that in the positive-framing condition. Thus, a
positive value of 2 reveals a standard framing-effect pattern, a
value of 0 reveals consistent choosing (i.e., a null framing-effect
pattern), and a value of ⫺2 reveals a reversed framing-effect
pattern.
Results and Discussion
As predicted, the distribution of choice patterns was contingent
on the linguistic modifier that appeared in the certain option of the
ADP (see Table 1),
2
(2, N ⫽ 120) ⫽ 24.68, p ⬍ .001, ⫽.45.
As Table 1 shows, when the numeric quantifiers were lower-
bounded, a statistically significant majority (67.7%) showed a
standard framing effect, consistent with an EVM choice pattern.
However, when the same quantifiers had a bilateral meaning, an
even greater majority (73.3%) showed consistent choice across the
two decision-making problems. In other words, when the two
options had equal expected value, most participants chose consis-
tently across frames in line with the description invariance prin-
ciple.
Table 1 also reveals that 31.7% (19/60) of participants in the
at-least condition made consistent choices. Among this subsample,
it is useful to distinguish those who made an EVM choice on the
first problem and then opted to remain consistent on the second
problem (an excusable pattern of choice) from those who did not
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1188
MANDEL
make an EVM choice initially but chose to remain consistent on
the second problem (an inexcusable pattern). In fact, a significant
majority of those 19 participants made an initial EVM choice
(78.9%, 95% CI [56.7%, 91.5%]). Over all participants in Exper-
iment 1, then, 70.0% made rational choices, 23.3% made excus-
able choices, and the remaining 6.7% made inexcusable choices.
The 95% confidence intervals for these three groupings are as
follows: rational [61.3%, 77.5%], excusable [16.7%, 31.7%], and
inexcusable [3.4%, 12.6%].
NFC did not significantly differ between participants who made
rational choices (M ⫽ 1.01, SD ⫽ 1.12) and those who did not
(M ⫽ 1.09, SD ⫽ 0.87), t(118) ⫽ 0.39. Likewise, IMC responses
were independent of whether or not participants made rational
choices,
2
(1, N ⫽ 120) ⫽ 1.13, p ⫽ .29. Finally, consistent with
Oppenheimer et al. (2009, Experiment 2), there was no significant
difference in NFC between the 19% who responded incorrectly on
the IMC and the 81% who responded correctly, t(118) ⫽⫺0.55.
Thus, decision makers’ rationality in problems like the ADP does
not seem to be well captured by variables measuring one’s moti-
vation to think deeply, in general, or during an experiment, in
particular.
Experiment 2
Experiment 2 was aimed at replicating the linguistic modifier
effect in a between-subjects design using a modified decision
problem. As other have noted (e.g., Geurts, 2013; Kühberger,
1995; Mandel, 2001; Teigen, 2011), an accurate forecast of an
exact number of threatened lives (viz., 600) in the ADP is unre-
alistic. Yet, tests of coherence in that problem assume a set of
exactly 600 threatened lives. To make this assumption more plau-
sible, Mandel (2001) devised a modified scenario in which 600
people’s lives were already threatened in a war-torn region and he
showed that the problem yielded a standard framing effect when
the options were worded as in the ADP. The present account
predicts a standard framing effect when the quantifier in the certain
option was not explicitly modified (as in the original ADP). The
same pattern of choice should also be evident when the quantifiers
are explicitly lower-bounded because that pattern reflects EVM
choices. Indeed, it was predicted that the effect would be even
stronger in the “at least” condition because the rational basis for
the choice reversal is explicit. Finally, a significantly attenuated or
even null framing effect was predicted when that quantifier was
given a bilateral meaning.
Method
Participants. Two hundred twenty-eight undergraduates were
recruited from three North American university campuses. The
mean age of the sample was 20.01 years (SD ⫽ 3.53), and among
those who indicated their gender 59% were female. A power
analysis for the predicted interaction effect using analysis of vari-
ance (ANOVA) estimated that a minimum of 34 participants per
condition were required to ensure Type I and Type II errors rates
of .05 and .10 assuming a medium effect size (f ⫽ .25). The
slightly larger number of participants recruited was due to over-
booking.
Design. Experiment 2 used a 2 (Frame: positive, negative) ⫻
3 (Modifier: none, exactly, at least) between-subjects design.
Procedure and materials. Participants were randomly as-
signed to one of the six conditions. On a sheet of paper, they were
presented with the following cover story:
In a war-torn region, the lives of 600 stranded people are at stake. Two
response plans with the following outcomes have been proposed.
Assume that the estimates provided are accurate.
In the positive-framing conditions, participants were presented
with these options:
If Plan A is adopted, it is certain that (exactly) [at least] 200 people
will be saved.
If Plan B is adopted, there is a one-third probability that all 600 will
be saved and a two-thirds probability that nobody will be saved.
In the negative-framing conditions, participants were presented
with these options:
If Plan A is adopted, it is certain that (exactly) [at least] 400 people
will die.
If Plan B is adopted, there is a two-thirds probability that all 600 will
die and a one-third probability that nobody will die.
Participants in the no-modifier condition were simply presented
with the original options (omitting the modifiers shown in paren-
theses and brackets).
These option sets are similar to those in the ADP but for two
exceptions. First, Option A states “it is certain that...,”which
makes the assumed certainty of stated outcome explicit. Second, in
the negative-framing condition, the uncertain option expresses the
negative possible outcome first. In the ADP, the positive outcome
is stated first, even in the negative frame. The later change was
mainly precautionary, however, as Peters and Levin (2008) re-
ported no effect of ordering on attractiveness ratings of the risky
option in the ADP.
After considering the problem, participants were first asked,
“Which of the two plans would you choose—A or B?” Next, they
were asked, “How much more preferable is the plan that you chose
compared with the plan that you did not choose?” They responded
Table 1
Percent Distribution of Choice Patterns by Modifier in Experiment 1
Choice pattern
Modifier
OverallAt least Exactly
% 95% CI % 95% CI % 95% CI
Standard framing effect 66.7 [54.1, 77.3] 21.7 [13.1, 33.6] 44.2 [35.6, 53.1]
Consistent choice 31.7 [21.3, 44.2] 73.3 [61.0, 82.9] 52.5 [43.6, 61.2]
Reversed framing effect 1.7 [0.3, 8.9] 5.0 [1.7, 13.7] 3.3 [1.3, 8.3]
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1189
DO FRAMING EFFECTS REVEAL IRRATIONAL CHOICE?
on an 11-point scale (0 ⫽ equally preferable,10⫽ much more
preferable). A measure of weighted choice was later computed by
dummy coding the choices favoring the certain and uncertain
options as 1 and ⫺1, respectively. Those values were multiplied by
the preference rating, yielding values between ⫺10 and 10. An
advantage of this measure is that it allows participants to indicate
that, although they made a forced choice, they may in fact have
been indifferent between the two options. This is important be-
cause even when participants are indifferent between two options,
they may choose systematically when forced to make a binary
choice (Mandel, 2003). The weighted measure also facilitated the
analysis of interaction effects, which are of primary concern here
(see Peters & Levin, 2008, for a similar approach).
Results and Discussion
A Frame ⫻ Modifier ANOVA revealed a main effect of frame,
F(1, 222) ⫽ 38.40, p ⬍ .001,
p
2
⫽ .15, and a main effect of
modifier, F(2, 222) ⫽ 3.62, p ⫽ .028,
p
2
⫽ .03. These effects were
qualified by the predicted two-way interaction effect, F(2, 222) ⫽
6.59, p ⫽ .002,
p
2
⫽ .06. Table 2 shows the percentage of
participants who chose the certain option and mean weighted
choice as a function of frame and modifier, as well as statistics for
interpreting the simple effects of framing (viz., mean difference
between framing conditions and 95% CIs). The interaction effect
confirms the expected pattern of simple effects: When the quan-
tifier in the certain option was left unmodified, there was a
medium-sized, standard framing effect, F(1, 74) ⫽ 8.53, p ⫽ .005,
d ⫽ 0.67. In contrast, when the same quantifiers were given a bilateral
meaning, the framing effect was nonsignificant, F(1, 74) ⫽ 1.36, p ⫽
.25, d ⫽ 0.27. Finally, when the quantifier in the certain option was
lower-bounded, there was a large effect consistent with a standard
framing pattern, F(1, 74) ⫽ 55.46, p ⬍ .001, d ⫽ 1.75. Moreover,
a significant majority of participants in the at-least condition (79%,
95% CI [69%, 87%]) made EVM choices (i.e., by choosing the
certain option in the positive frame and uncertain option in the
negative frame). These findings thus offer additional support for
the view that most decision makers choose rationally in problems
like the ADP. Most participants maximized expected value when
possible (i.e., when the quantifiers were lower-bounded) and there
was no evidence of invariance violations when the quantifiers were
given a bilateral meaning.
Experiment 3
Experiments 1 and 2 offer evidence suggesting that claims of
irrationality in decision making based on framing studies may have
been exaggerated in previous literature. Those findings, however,
do not directly address the earlier critique that the proof-by-
arithmetic argument and the extensional-equivalence assumption it
supports rest on an untenable linguistic assumption—namely, na-
ïve bilateralism. The aim of Experiment 3 was to address those
claims directly by examining how people spontaneously interpret
numeric quantifiers that, in turn, shape the valuation of options in
decision-making problems like the ADP. Moreover, Experiment 3
examined how those interpretations vary as a function of linguistic
aspects of such problems that have received relatively little atten-
tion. Specifically, whereas the uncertain options in the ADP ex-
plicate the probabilities of both the favorable (600 saved) and
unfavorable (600 die) possible outcomes, the certain options only
explicate part of the expected outcome. That is, nothing is said
about the remaining 400 lives in Option A or about the remaining
200 lives in Option C. However, when that asymmetry was elim-
inated, the framing effect disappeared (Kühberger, 1995; Küh-
berger & Tanner, 2010; Mandel, 2001).
Building on that explication effect, it was predicted that varia-
tions in the explication of the options would also influence the
interpretation of numeric quantifiers used to describe the expected
outcomes of those options. Specifically, Experiment 3 tested the
hypothesis that the proportion of participants interpreting numeric
quantifiers as lower bounds would be greater when the expected
outcomes were partially explicated (e.g., “If Program A is adopted,
200 lives will be saved”) rather than fully explicated (e.g., “If
Program A is adopted, 200 lives will be saved and 400 lives won’t
be saved”) because only with full explication is it explicit that the
exact number of lives expected to be saved and to die sum to the
total set of 600. Indeed, it is predicted that, whereas most partic-
ipants will interpret the certain option’s quantifiers bilaterally in
the fully explicated version, most will interpret those quantifiers as
lower bounds in the partially explicated version, contrary to naïve
bilateralism. Stated differently, the integrity of a framing manip-
ulation—namely, ensuring that alternative frames are extension-
ally equivalent—should be promoted by fully explicating choice
options to prospective decision makers. Conversely, partial expli-
cations of choice options, both the certain and risky options,
should increase the likelihood that they will be interpreted in a
single-bounded manner, thus undermining the integrity of any
intended framing manipulation.
A related aim of Experiment 3 was to examine how quantifier
interpretations (both of the integers in the certain options and of
the probabilities in the uncertain options) might moderate the
framing effect. In line with the hypothesis of EVM choosing, it
was predicted that the option of saving 200 lives would be per-
Table 2
Percentage Choosing the Certain Option (% A) and Mean Weighted Choice by Frame and
Modifier in Experiment 2
Modifier
Frame
⌬M
a
95% CI
Negative Positive
%A MSD%A MSD
None 26.3 2.79 5.66 57.9 ⫺0.89 5.33 3.68 [1.17, 6.19]
Exactly 43.2 0.09 5.31 59.0 ⫺1.28 4.97 1.37 [⫺0.98, 3.72]
At least 32.5 2.45 4.77 91.7 ⫺4.75 3.48 7.20 [5.30, 9.10]
a
⌬M is the mean difference in weighted choice (mean in the negative frame minus mean in the positive frame).
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1190
MANDEL
ceived as least favorable when it was upper-bounded (i.e., at most
200 saved) and most favorable when it was lower-bounded (i.e., at
least 200 saved), and vice versa for the option of losing 400 lives.
Likewise, it was predicted that a 1/3 probability of saving every-
body would be perceived as least favorable when it was upper-
bounded (i.e., at most a 1/3 probability of saving 600) and most
favorable when it was lower-bounded (i.e., at least a 1/3 probabil-
ity of saving 600), and vice versa for a 2/3 probability of every-
body dying. It follows from these predictions that a standard
framing effect would be seen mainly among lower-bound inter-
preters of the certain options and upper-bound interpreters of the
uncertain options.
Method
Participants. One hundred forty-seven undergraduates at
University of Victoria were recruited from the psychology depart-
ment participant-research pool and received partial course credit
for participating. Age was not recorded, and 66% were female. An
estimate of 144 participants required was based on a sample-size
calculation that assumes Type I and Type II error rates of .05 and
.10, respectively, with f ⫽ .30. The actual sample size reflects
slight oversampling.
Design. Experiment 3 used a 2 (Frame: positive, negative) ⫻
3 (Explication: A-partial/B-full, A/B-full, A-full/B-partial)
between-subjects design.
Procedure and materials. In a paper-and-pencil task, partic-
ipants were asked to read the decision problem used in Experiment
2, and framing was manipulated in the same manner. Participants
were presented with two options whose wording depended on the
experimental condition to which they were assigned. The explica-
tion factor manipulated which of the two options was partially
explicated and which was fully explicated in terms of expected
outcomes. Specifically, in the positive A/B-full condition, partic-
ipants read these options, including the parenthesized material:
If Plan A is adopted, it is certain that 200 people will be saved (and
400 people will not be saved).
If Plan B is adopted, there is a 1/3 probability that all 600 will be
saved (and a 2/3 probability that nobody will be saved).
In the negative A/B-full condition, participants read these options,
again including the parenthesized material:
If Plan A is adopted, it is certain that 400 people will die (and 200
people will not die).
If Plan B is adopted, there is a 2/3 probability that all 600 will die (and
a 1/3 probability that nobody will die).
In the A-partial/B-full condition, as in the ADP, the parenthesized
material in Option A was excluded. In the A-full/B-partial condi-
tion, the parenthesized material in Option B was excluded, revers-
ing the asymmetry in the ADP.
As in Experiment 2, participants first made a binary choice and
then rated their strength of preference for the selected option. Next,
participants were asked about their interpretations of the two
options. First, they were asked: “Did you interpret Plan A to mean
(a) at most, (b) exactly, or (c) at least (200 will be saved) [400 will
die]?” Then, they were asked: “Did you interpret Plan B to mean
there was (a) at most, (b) exactly, or (c) at least a (1/3 probability
that all 600 people will be saved) [2/3 probability that all 600
people will die]?”
Results
The explication effect. As noted earlier, manipulations of
explication have moderated the framing effect in previous research
(Kühberger, 1995; Kühberger & Tanner, 2010; Mandel, 2001).
The initial analysis tested whether this explication effect was
replicable. A Frame ⫻ Explication ANOVA on weighted choice
revealed that only the predicted interaction effect was significant,
F(2, 141) ⫽ 9.41, p ⬍ .001,
p
2
⫽ .12. Table 3 shows the
percentage of participants who chose the certain option and mean
weighted choice by frame and explication, as well as statistics for
interpreting the simple effects of framing (viz., mean difference
between framing conditions and 95% CIs). As one might expect, in
the standard (A-partial/B-full) format, a standard framing effect
was replicated, F(1, 48) ⫽ 21.21, p ⬍ .001, d ⫽ 1.30. Replicating
previous findings, when both options were fully explicated, the
framing effect was eliminated, F(1, 46) ⫽ 0.06, p ⫽ .81, d ⫽ 0.07.
Finally, when the explication asymmetry was reversed (A-full/B-
partial)—a condition not previously investigated—so was the di-
rection of the “framing effect” (the scare quotes are meant to
underscore that, strictly speaking, the alterative descriptions may
not qualify as alternative frames; i.e., they may not be extension-
ally equivalent): With medium effect size, the uncertain option was
marginally less preferable in the negative condition than in the
positive condition, F(1, 49) ⫽ 2.99, p ⫽ .09, d ⫽⫺0.48. To sum
up, the explication effect appears to be robust and even more
consequential than previously thought because reversals of the
explication asymmetry actually reversed the framing effect.
Explication effects on interpretation. Table 4 shows partic-
ipants’ quantifier interpretations as a function of explication and
the option in which the quantifier appeared. As predicted, the
percentage of participants who had a lower-bound interpretation of
the certain option was significantly greater (and a significant
majority) when that option was partially explicated (64%, 95% CI
Table 3
Percentage Choosing the Certain Option (% A) and Mean Weighted Choice by Frame and Explication in Experiment 3
Explication
Frame
⌬M
a
95% CI
Negative Positive
%A MSD%A MSD
A-partial/B-full 20.0 3.92 5.37 68.0 ⫺2.92 5.13 6.84 [3.85, 9.83]
A/B-full 50.0 0.00 6.38 59.1 ⫺0.41 5.41 0.41 [⫺3.10, 3.92]
B-partial/A-full 68.0 ⫺1.48 5.95 42.3 1.38 5.89 ⫺2.86 [⫺6.19, 0.47]
a
⌬M is the mean difference in weighted choice (mean in the negative frame minus mean in the positive frame).
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1191
DO FRAMING EFFECTS REVEAL IRRATIONAL CHOICE?
[50%, 76%]) than when it was fully explicated (24%, 95% CI
[16%, 33%]), p ⬍ .001 by one-sided Fisher’s Exact Test. In
contrast, but also as predicted, when the certain option was fully
explicated, a significant majority of participants interpreted the
same quantifiers bilaterally (62%, 95% CI [52%, 71%]). The effect
of explication on the tendency to lower-bound quantifier interpre-
tations was not dependent on frame. For instance, examining the
effect size of this contingency, ⫽.36 in the positive-framing
condition, and ⫽.43 in the negative-framing condition, the
difference is not significant (z ⫽⫺0.49, p ⫽ .62).
A majority of participants had a bilateral interpretation of prob-
ability quantifiers regardless of whether the uncertain option was
partially or fully explicated. Nevertheless, as predicted, the per-
centage having a lower-bound interpretation of the probability
quantifiers was significantly greater when the uncertain option was
partially explicated (37%, 95% CI [25%, 51%]) rather than fully
explicated (22%, 95% CI [15%, 31%]), p ⫽ .04 by one-sided
Fisher’s Exact Test. Once again, this effect was not frame depen-
dent: ⫽.15 in the positive-framing condition, and ⫽.18 in the
negative-framing condition (z ⫽⫺0.18, p ⫽ .86).
To sum up, the findings indicate that most people do not treat
quantifiers such as 200 and 400 in problems like the ADP as exact
values. Rather, most interpret them as lower bounds. Moreover,
the findings clearly show that quantifier interpretations depend on
other linguistic factors such as the extent to which a description
fully explicates its referents. Finally, it appears that probability
quantifiers are less likely than cardinal quantifiers to be interpreted
unilaterally, perhaps because they evoke more of a statistical
mindset.
Interpretation effects. A key prediction of this experiment
was that participants’ quantifier interpretations would moderate
the framing effect in a manner consistent with EVM choice. As
noted earlier, that would entail two opposing patterns of interaction
effects. First, for interpretations of the certain option, the EVM
hypothesis predicts a standard framing effect for lower-bound
interpreters, no framing effect for bilateral interpreters, and a
reversed framing effect for upper-bound interpreters. Second, for
interpretations of the uncertain option, the EVM hypothesis pre-
dicts a reversed framing effect for lower-bound interpreters, no
framing effect for bilateral interpreters, and a standard framing
effect for upper-bound interpreters. Figure 1 plots the observed
simple effects of framing as a function of participants’ quantifier
interpretations of both options. As can be seen, the crossover
interaction of interactions strongly supports the predicted pattern.
Providing additional detail, Table 5 shows the percentage of par-
ticipants who chose the certain option and mean weighted choice
as a function of the interaction terms.
Inferential tests confirm what is visually evident from Figure 1.
As predicted, for the certain option, a Frame ⫻ Interpretation
ANOVA revealed only a significant interaction effect on weighted
choice, F(2, 141) ⫽ 12.13, p ⬍ .001,
p
2
⫽ .15. Among lower-
bound interpreters of the certain option, there was a standard
framing effect, F(1, 53) ⫽ 26.13, p ⬍ .001, d ⫽ 1.37. Yet, among
bilateral interpreters, the framing effect was eliminated, F(1, 72) ⫽
0.40, p ⫽ .53, d ⫽⫺0.15. And, among upper-bound interpreters,
the framing effect was reversed, F(1, 16) ⫽ 7.38, p ⫽ .02, d ⫽
⫺1.34. For the uncertain option, once again, only the predicted
interaction effect was significant, F(2, 140) ⫽ 9.29, p ⬍ .001,
p
2
⫽ .12. Among lower-bound interpreters, there was a small, but
non-significant, reversed framing effect, F(1, 38) ⫽ 1.25, p ⫽ .27,
d ⫽⫺0.35. Among bilateral interpreters, the framing effect was
Table 4
Percent Distribution of Interpretations by Explication and
Option in Experiment 3
Option Explication N
Interpretation
At least Exactly At most
Certain (A) A-partial/B-full 50 64.0 30.0 6.0
Certain (A) A/B-full 46 23.9 58.7 17.4
Certain (A) B-partial/A-full 51 23.5 62.7 13.7
Uncertain (B) A-partial/B-full 49 26.5 42.9 30.6
Uncertain (B) A/B-full 46 17.4 47.8 34.8
Uncertain (B) B-partial/A-full 51 37.3 45.1 17.6
Table 5
Percentage Choosing the Certain Option (% A) and Mean
Weighted Choice by Frame and Interpretation in Experiment 3
Interpretation
Frame
Negative Positive
%A MSD%A MSD
Certain option
At least 26.9 3.31 5.62 82.8 ⫺3.66 4.47
Exactly 52.6 ⫺0.08 6.36 44.4 0.83 5.97
At most 70.0 ⫺2.20 5.71 12.5 3.75 2.60
Uncertain option
At least 62.5 0.73 6.25 41.7 ⫺0.63 5.71
Exactly 52.8 ⫺0.36 6.04 46.7 0.17 6.22
At most 23.8 3.67 6.00 89.5 ⫺4.32 3.94
Figure 1. Direction and magnitude of framing effect by participants’
interpretations of the certain and uncertain options in Experiment 3. Error
bars show 95% confidence intervals on the difference between mean
weighted choice in the negative and positive framing conditions. Positive
values show standard framing effects where there is a stronger preference
for the certain option in the positive frame than in the negative frame.
Negative values show reversed framing effects. The y-axis shows the
possible range of effects.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1192
MANDEL
eliminated, F(1, 64) ⫽ 0.12, p ⫽ .73, d ⫽⫺0.09. Finally, among
upper-bound interpreters, a large standard framing effect was
found, F(1, 38) ⫽ 24.13, p ⬍ .001, d ⫽ 1.57.
Finally, a separate analysis of cases in which participants had
bilateral interpretations of both options was conducted. That sub-
sample defines those participants for whom the extensional-
equivalence assumption and proof-by-arithmetic argument should
presumably ring true. Do these participants show a framing effect?
Remarkably, they show a reversed framing effect of medium size
and marginal significance: Participants in the negative-framing
condition (M ⫽⫺1.52, SD ⫽ 6.01) preferred the certain outcome,
whereas those in the positive-framing condition preferred the
uncertain outcome (M ⫽ 1.67, SD ⫽ 6.13), F(1, 42) ⫽ 3.03, p ⫽
.09, d ⫽⫺0.53, 95% CI [⫺0.51, 3.70].
Rational-choice analysis. Building on the main analyses of
the preceding subsection, the present analysis directly tests the
EVM hypothesis by examining participants’ choices contingent
on their joint interpretations of the quantifiers in the two op-
tions presented to them. As Table 6 shows, of the 18 conjunc-
tions in a 2 (Frame) ⫻ 3 (Interpretation of Option A) ⫻ 3
(Interpretation of Option B) matrix, six favor the certain option
(A), six favor the uncertain option (B), and six are indetermi-
nate (i.e., where both options are interpreted in the same man-
ner). As predicted, among the determinate cases (n ⫽ 87), a
significant majority of participants (76%, 99% CI [66%, 84%])
made EVM choices. Moreover, the 24% minority of suboptimal
choosers were not systematically affected by frame, with the
certain option being chosen by 44.4% in the positive-framing
condition and 58.3% in the negative-framing condition,
2
(1,
N ⫽ 21) ⫽ 0.40, p ⫽ .53.
General Discussion
Few word problems in psychology have had the theoretical
impact and widespread recognition that the ADP has had. Indeed,
awareness of and fascination over the ADP has not only tran-
scended behavioral decision research, it has transcended psychol-
ogy. For instance, when Daniel Kahneman was awarded the Nobel
Memorial Prize in Economics for his work with Amos Tversky on
the psychology of decision making, The New York Times captured
the essence of their contribution to understanding systematic de-
partures from rationality in decision making with a single exam-
ple—the ADP (Goode, 2002). The journalist made a point of
writing that “the exact same choice [emphasis added] presented or
‘framed’ in different ways could elicit different decisions” (Goode,
2002, para. 12). This is not surprising given that the framing
literature conveys an almost uniform acceptance of the
extensional-equivalence assumption. Although there have been a
few critical analyses of the assumptions underlying framing stud-
ies (e.g., Berkeley & Humphreys, 1982; Geurts, 2013; Macdonald,
1986; Mandel & Vartanian, 2011; Teigen, 2011), they have largely
been absent of empirical tests of the soundness of that assumptive
scaffolding. Such tests are important, however, precisely because
the findings of framing studies have been treated as unquestioned
demonstrations of irrationality in human decision making. Below,
the implications of the findings from the present set of tests are
discussed.
Implications for the Assumptions
Underlying Framing Research
As noted earlier, the verdict of irrationality drawn in the risky-
choice framing literature rests on the extensional-equivalence as-
sumption. That assumption, in turn, is supported by the proof-by-
arithmetic argument, which relies on yet another assumption: naïve
bilateralism. Although this argument structure is not difficult to
map, it has remained largely implicit in the literature, and perhaps
that is why it has not been adequately tested. The findings of
Experiment 3 clearly refute the descriptive claim of naïve bilater-
alism. In the standard version of the decision task (paralleling the
ADP), most participants treated the quantifier values of 200 and
400 in the certain option as lower bounds rather than as exact
values. This finding converges well with both neo-Gricean theories
of quantification (Horn, 1989; Levinson, 2000) and psychological
research showing a tendency to interpret estimates as lower bounds
(Teigen & Nikolaisen, 2009).
The lower bounding of numeric quantifiers in the standard
version of the problem shows unequivocally that the extensional-
equivalence assumption is untenable: Saving at least 200 lives out
of 600 is clearly not the same thing in real terms as letting at least
400 die. The same finding also shows that the assumption that the
two options presented to a given participant are of equal expected
value is false because saving at least 200 lives for sure has greater
expected value than a 1/3 chance of saving 600, whereas losing at
least 400 lives for sure has lesser expected value than a 2/3 chance
of losing 600. In short, the findings indicate that, for most people,
Options A and C in the ADP are descriptions of different events,
and not merely re-descriptions of the same event. Although effects
of the usual ADP positive-negative manipulation are description
effects, strictly speaking, they are not framing effects, and thus
should not be labeled as such.
Some theorists might still want to accept naïve bilateralism as a
prescriptive stance. That is, even if one were to concede that most
people do not treat such values as exact, one might still argue that
people should. For instance, Shafir and LeBoeuf (2002, p. 506)
proposed that “conversational misinterpretations” could account
for some coherence violations. Their choice of the term misinter-
pretation indicates such a prescriptive stance. In the present con-
text, it implies that people who interpret numeric quantifiers as
anything other than exact values are in some sense adhering to an
Table 6
Predicted Choices Based on the EVM Hypothesis
Interpretation of
certain option (A)
Interpretation of uncertain option (B)
At least Exactly At most
Positive frame
At least I A A
Exactly B I A
At most B B I
Negative frame
At least I B B
Exactly A I B
At most A A I
Note. A ⫽ the certain option is the expected-value-maximizing (EVM)
choice; B ⫽ the uncertain option is the EVM choice; I ⫽ an EVM choice
cannot be defined (indeterminate).
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1193
DO FRAMING EFFECTS REVEAL IRRATIONAL CHOICE?
inferior interpretation. Theorists who might wish to adopt such a
view do not start out easily since that view challenges not only
linguistic theories of quantification, but also deeper philosophical
arguments holding that the meaning of words are definable only
through their use in language (e.g., Wittgenstein, 1953).AsAustin
(1979) famously put it, “there is no simple and handy appendage
of a word called ‘the meaning of (the word) x’” (p. 62). Decision
theorists who wish to be arbiters of linguistic meaning should
practice restraint.
It is also worth reminding the reader that, although the focus in
this research was on risky-choice framing, given the latter’s rele-
vance to the question of human rationality in decision making, the
linguistic implications of how numeric quantifiers are interpreted
revealed in the present research extend to other types of framing,
including attribute and health message framing (see Levin et al.,
1998), which, like risky-choice framing, often involve numeric
quantification in language. In health message framing (e.g., Roth-
man & Salovey, 1997), alternative therapy options might be
framed, for instance, in terms of the probability of dying from the
treatment (mortality rate) or the probability of living for a given
time after the treatment (survival rate). For example, a surgical
procedure could be described as having a 10% mortality rate or a
90% survival rate post-surgery. If these quantities tend to be
interpreted as lower bounds, then clearly the alternative frames
would not convey the same information to patients because, in the
former case, one would have at least a 10% chance of dying from
the surgery, whereas, in the latter case, one would have at most a
10% chance. Similarly, in attribute framing (e.g., Levin & Gaeth,
1988), a food product that is described as 75% lean versus 25% fat
would convey objectively different meanings if these quantifiers
are interpreted as lower (or for that matter, upper) bounds. Thus,
the present findings have implications for a wide array of
everyday-life decision-relevant situations in which information
pertinent to choice is communicated using numeric quantifiers.
Implications for Assessments of Rationality
in Decision Making
The present findings shed light on the topic of how rational
decision makers are in two important ways. First, because the
findings of Experiment 3 show that a foundational assumption on
which some past claims of decision-maker irrationality were based
is wrong, they call for a reinterpretation of the findings on which
those claims are based. At minimum, they suggest the need for
greater caution in interpreting previous findings. For instance, they
raise questions about the integrity of measures that use framing
tests modeled on the ADP as indicators of cognitive (in)compe-
tence (e.g., Bruine de Bruin et al., 2007; West et al., 2008). Indeed,
the present findings indicate that the construct validity of such
measures could be improved by omitting such problems. Alterna-
tively, researchers could strengthen the framing manipulations
used in such measures by making explicit that the referenced
quantities are exact values rather than lower or upper bounds (e.g.,
Mandel, 2008). As the present findings indicate, this adjustment in
the context of gain-loss framing manipulations will likely reduce
the frequency with which framing effects are observed. However,
competence measures might be well informed by framing effects
that the corrected methods reveal, given that they may actually
improve their diagnostic value.
The present findings, however, also contribute to the rationality
debate in a more positive sense by showing that a significant
majority of participants made rational decisions by classical
rational-choice criteria in traditional risky-choice framing prob-
lems. In Experiment 1, the majority chose consistently across
frames when it was clear that the numeric quantifiers were to be
interpreted as exact values. In other words, when the extensional-
equivalence assumption held, most decision makers were coherent,
adhering to the principle of description invariance. And, when
expected value in terms of lives saved favored one option over
another, most decision makers made EVM choices. The robustness
of those findings was shown in Experiment 2, which varied the
design (i.e., between-subjects), problem (i.e., by using an ADP
isomorph), and dependent measure (i.e., weighted choice), yet
which replicated the modifier by frame interaction effect. And, it
was further tested in Experiment 3 by examining participants’
choices contingent on their quantifier interpretations of the two
options. That analysis once again revealed that most decision
makers made EVM choices. In short, when ambiguity regarding
the meaning of quantifiers used to convey the value of a given
option was resolved (by the researcher in Experiments 1 and 2 and
by participants themselves in Experiment 3), it was evident that
most participants made substantively rational choices.
The findings of Experiment 1 also revealed that, among the
minority of decision makers who did not make fully rational
choices, most (78%) nevertheless made excusable errors. That is,
they either followed an initial EVM choice with an ostensibly
consistent choice, or they chose in a manner consistent with the
recommended course of action conversationally implied by the
choice of frame (Sher & McKenzie, 2008; van Buiten & Keren,
2009). Only a small percentage (about 7%) of the overall sample
made what one might call irrational or inexcusable choices.
Relations to Alternative Theoretical Accounts
of Framing Effects
The multiply moderated description effects shown in the present
research were predicted on the basis of a rational-choice account
informed by linguistic principles. The latter must be considered in
contexts where decision-making problems are communicated to
decision makers by problem formulators using written or spoken
language. Without a clear understanding of how language in its
communicative context shapes meaning (in the present context, the
communicated value of choice options) it is all too easy for
researchers to mistake rational choices for ostensibly irrational
ones. Indeed, clarifying the communicative context can also result
in ostensibly rational choices being redefined as irrational. For
example, in within-subject experiments (e.g., Schneider, 1992;
Stanovich & West, 1998), consistent choices (i.e., A–C or B–D
patterns) are treated as rational, but as Experiment 1 revealed, such
patterns are actually irrational when the quantifiers in the certain
option are lower-bounded as they typically appear to be. More
generally, the present account is conceptually aligned with litera-
ture underscoring the importance of understanding the conversa-
tional and linguistic context within which behavioral data are
elicited (e.g., Fiedler, 2008; Hilton, 1995; Moxey & Sanford,
2000; Noveck & Reboul, 2008; Schwarz, 1996). That context is
particularly important to bear in mind in experiments where alter-
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1194
MANDEL
native conditions are defined by subtle linguistic alterations, as is
the case in most research on framing.
Although the present findings are well explained by a conver-
sationally informed rational-choice account, it is important to
consider how well alternative accounts of framing effects accom-
modate those findings. Tversky and Kahneman (1981) explained
their original findings in terms of prospect theory (Kahneman &
Tversky, 1979). Prospect theory posits an “S-shaped” value func-
tion in which subjective value is a concave function of utility for
prospective gains and a convex function for losses, where the gain
and loss domains are defined relative to a subjective reference
point. According to this account, decision makers adopt a zero-
lives-saved reference point when the options are positively framed
and a zero-lives-lost reference point when they are negatively
framed. Thus, decision makers are expected to behave as if they
were in the gain domain in the former case and as if they were in
the loss domain in latter case. Because of the value-function
model’s hypothesized inflection around the reference point, risk
attitudes are predicted to vary such that decision makers would
prefer the certain option to the uncertain option in the positive-
framing condition and vice versa in the negative-framing condi-
tion. Although the value-function model does well at explaining
the original effect, it cannot account for the multiply moderated
framing effects shown in the present research. Indeed, it distinctly
predicts a framing effect even when the quantifiers are interpreted
bilaterally, and yet no framing effect was found under such con-
ditions in the three experiments. Therefore, although prospect
theory’s value-function model has much evidence to support it
from a wide range of experimental tasks (e.g., simple lotteries), it
cannot accommodate the present findings.
The present account may also be contrasted with McKenzie and
colleagues’ (McKenzie, 2004; McKenzie & Nelson, 2003; Sher &
McKenzie, 2006, 2008, 2011) information leakage (IL) account.
Like the present account, the IL account emphasizes the impor-
tance of the communicative context within which the participant
must act as a decision maker. The IL account proposes that, even
if alternative frames are logically equivalent, they may be non-
equivalent in terms of the information they convey because a
speaker’s choice of frame may communicate information that goes
beyond the literal meaning expressed. The IL account proposes
multiple pathways through which extensionally-equivalent frames
may nevertheless be “information non-equivalent.” Regarding
ADP-style decision tasks, the IL account posits that positive
frames convey a recommendation for the certain option, whereas
negative frames convey a recommendation for the uncertain option
(Sher & McKenzie, 2008; van Buiten & Keren, 2009). In this
regard, the present account is in agreement with the IL account.
Indeed, these IL tenets were used in Experiment 1 to differentiate
excusable and inexcusable patterns of choosing. And, for the same
reasons, it was predicted that, whereas bilateral interpretations of
quantifiers in the sure options of ADP-style tasks would attenuate
framing effects, such interpretations might not fully eliminate such
effects.
However, the two accounts also differ in distinct ways. The IL
account, for example, does not predict the moderation of the
framing effect by explication (Experiment 3), linguistic modifier
(Experiments 1 and 2), or participants’ linguistic interpretations
(Experiment 3), whereas these effects are predicted by the present
account. Moreover, unlike the present account, the IL account
accepts the extensional-equivalence assumption (e.g., Sher &
McKenzie, 2008), which the present findings show is unfounded.
Notwithstanding the differences, there are good prospects for these
two accounts to mutually reinforce the other.
The present findings also bear on other linguistic proposals that
have been made in the framing literature. For example, in an early
critique of Tversky and Kahneman’s (1981) framing-effect dem-
onstration, Macdonald (1986) proposed that people normally add
“or more” to numeric quantifiers. However, Macdonald never
tested his proposal. Unlike Macdonald’s proposal, the present
account predicts that the interpretation of numeric quantifiers is
not invariant. Just as the present account rejects naïve bilateralism,
it also rejects naïve forms of unilateralism of the sort Macdonald
proposed. The findings of Experiment 3 clearly show that, al-
though most people adopt a lower-bound reading in the standard
problem, most people also adopt a bilateral reading when the
options are fully explicated. The moderation of quantifier inter-
pretations based on linguistic context (i.e., whether frames are
explicated partially or fully) also clearly indicates that numeric
quantifiers are not coarsely interpreted as “some” for non-zero
values, as Reyna and Brainerd (1991) had proposed. Contrary to
the present findings, their fuzzy-trace account predicts no interac-
tion effect of modifier and frame because “at least n” and “exactly
n” should both have the same gist (viz., some).
It is likely that the narrative context matters as well. For in-
stance, Bless, Betsch, and Franzen (1998) replicated the framing
effect in the ADP when the top corner of the page was labeled
“medical research,” but found the effect eliminated when the label
was changed to “statistical research.” As Bless et al. acknowl-
edged, their design did not allow them discover the mediating
mechanism for the moderation they observed. A testable hypoth-
esis is that the cue prompting a statistics narrative would make
participants more likely to interpret quantifiers as exact values,
whereas the cue prompting a health narrative would make them
more likely to adopt a lower-bound reading as in the un-cued ADP.
Likewise, Jou et al. (1996) found that the framing effect was
eliminated in the ADP when a rationale for the options was
provided such that there were only enough vaccines for 200
people. This rationale would seem to be most consistent with an
“at most” interpretation in the positive frame and with an “at least”
interpretation in the negative frame—a pattern that would be
predicted to eliminate the framing effect because EVM choices
should not vary by frame.
As an initial test of this prediction, 97 undergraduate student
participants were given either the standard ADP cover story or a
Canadianized version of Jou et al.’s (1996) ADP-with-rationale
cover story. Participants were asked whether they thought the
value stated in the certain option was “exactly” the number that
would be saved or would be left to die, and they responded by
selecting either a “no” or “yes” option. If they selected “no,” then
a follow-up question appeared, which asked participants whether
they thought it was more likely that “at least” or “at most” the
quantity specified in the certain option would either be saved or be
left to die. In the standard ADP version, a majority responded “at
least” in the positive (58%) and negative (54%) framing condi-
tions. As predicted, however, in the with-rationale condition, a
majority (71%) responded “at most” given the positive frame,
whereas a majority (64%) responded “at least” given the negative
frame. This demonstration shows that the interpretation of numeric
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1195
DO FRAMING EFFECTS REVEAL IRRATIONAL CHOICE?
quantifiers is predictably shaped by context in which such terms
appear. Although a specification of how various types of context
(e.g., conversational, semantic, and sentential) affect the interpre-
tation of such terms is beyond the aims of this article, the present
research, including the latter demonstration, suggests the need for
a comprehensive psycholinguistic account of numeric quantifier
use and interpretation. The studies reported here already show that
quantifier interpretations are influenced by the degree to which
descriptions of choice options are explicated (Experiment 3), by
the type of quantifier (e.g., cardinal numbers vs. probabilities, as
shown in Experiment 3), and by knowledge-based features of
decision tasks (as the former demonstration revealed).
Meta-Theoretical Reflections
When Thomas Kuhn sought to understand what Aristotle had
already explained about physics and what he had left to others like
Galileo and Newton to discover, he was surprised to learn that
much of what the great philosopher had said was wrong. That
conclusion, however, did not sit well with him, for Kuhn knew
that Aristotle had made important strides in understanding in other
areas—how could he have been so misguided in physics, he
thought (Kuhn, 2000). This and other puzzles of ostensible folly
among many of history’s great thinkers eventually led Kuhn to
formulate his influential ideas about incommensurability and rev-
olutionary change in science. Kuhn realized that thinkers in dif-
ferent time periods must have attached different meanings to some
proportion of the words they held in common. Thus, to properly
understand Aristotle’s physics, one had to understand what Aris-
totle would have understood by his statements on the topic. Indeed,
when Kuhn realized what certain terms like motion must have
meant to Aristotle, he could appreciate afresh how sweeping
Aristotle’s physics actually was.
The theme of this article follows a parallel line of thinking,
questioning the soundness of assuming that what an experimenter
takes as the literal meaning of a given statement is what his or her
participants would take as its literal meaning. Moreover, it ques-
tions the coherence of an inferential process that would rely on
such an assumption. To explain the apparent ease with which
researchers seem willing to invoke such assumptions, it is worth
reconsidering William James’s notion of the psychologist’s fal-
lacy.AsJames (1890/1950, p. 196, italics in original) wrote, “The
great snare of the psychologist is the confusion of his own stand-
point with that of the mental fact about which he is making his
report. I shall hereafter call this the ‘psychologist’s fallacy’ par
excellence.”
In the present context, the psychologist’s fallacy occurs when
researchers project their understanding of the ADP in terms of the
proof-by-arithmetic argument onto the participant and then goes
on to evaluate the coherence of the participant’s choices as if that
understanding were in fact the participant’s own. This type of
objection (e.g., Berkeley & Humphreys, 1982; Henle, 1962;
Hilton, 1995; Phillips, 1983) has been variously called the struc-
ture argument (Jungermann, 1983) or the alternative-task-construal
argument (Stanovich & West, 2000), and it has often been char-
acterized as a strategy of “optimists” or “apologists” designed to
challenge allegations of irrationality in human judgment and de-
cision making. That characterization is regrettable because atten-
tion to the psychologist’s fallacy (or the problem of making
assumptions regarding inter-subjectivity) is principally aimed at
improving the conceptual rigor of research and theory, which one
can only hope reflects a bipartisan aspiration widely shared across
meta-theoretical camps.
References
Arrow, K. J. (1982). Risk perception in psychology and economics. Eco-
nomic Inquiry, 20, 1–9. doi:10.1111/j.1465-7295.1982.tb01138.x
Austin, J. L. (1979). The meaning of a word. In J. O. Urmson & G. J.
Warnock (Eds.), Philosophical papers (3rd ed., pp. 55–75). Oxford,
England: Oxford University Press. doi:10.1093/019283021X.003.0003
Berkeley, D., & Humphreys, P. (1982). Structuring decision problems and
the “bias heuristic”. Acta Psychologica, 50, 201–252. doi:10.1016/0001-
6918(82)90042-7
Bless, H., Betsch, T., & Franzen, A. (1998). Framing the framing effect:
The impact of context cues on solutions to the ‘Asian disease’ problem.
European Journal of Social Psychology, 28, 287–291. doi:10.1002/
(SICI)1099-0992(199803/04)28:2⬍287::AID-EJSP861⬎3.3.CO;2-U
Breheny, R. (2008). A new look at the semantics and pragmatics of
numerically quantified noun phrases. Journal of Semantics, 25, 93–139.
doi:10.1093/jos/ffm016
Bruine de Bruin, W., Parker, A. M., & Fischhoff, B. (2007). Individual
differences in adult decision-making competence. Journal of Personality
and Social Psychology, 92, 938–956. doi:10.1037/0022-3514.92.5.938
Cacioppo, J. T., Petty, R. E., & Kao, C. F. (1984). The efficient assessment
of need for cognition. Journal of Personality Assessment, 48, 306–307.
doi:10.1207/s15327752jpa4803_13
Carston, R. (1998). Informativeness, relevance and scalar implicature. In
R. Carston & S. Uchida (Eds.), Relevance theory: Applications and
implications (pp. 179–236). Amsterdam, the Netherlands: Benjamins.
Dawes, R. M. (1988). Rational choice in an uncertain world. San Diego,
CA: Harcourt, Brace, Jovanovich.
Fagley, N. S. (1993). A note concerning reflection effects versus framing
effects. Psychological Bulletin, 113, 451–452. doi:10.1037/0033-2909
.113.3.451
Fiedler, K. (2008). Language: A toolbox for sharing and influencing social
reality. Perspectives on Psychological Science, 3, 38–47. doi:10.1111/
j.1745-6916.2008.00060.x
Geurts, B. (2006). Take “five”: The meaning and use of a number word. In
S. Vogeleer & L. Tasmowski (Eds.), Non-definiteness and plurality (pp.
311–329). Philadelphia, PA: Benjamins.
Geurts, B. (2013). Alternatives in framing and decision making. Mind &
Language, 28, 1–19. doi:10.1111/mila.12005
Geurts, B., Katsos, N., Cummins, C., Moons, J., & Noordman, L. (2010).
Scalar quantifiers: Logic, acquisition, and processing. Language and
Cognitive Processes, 25, 130–148. doi:10.1080/01690960902955010
Gold, N., & List, C. (2004). Framing as path dependence. Economics and
Philosophy, 20, 253–277. doi:10.1017/S0266267104000203
Goode, E. (2002, November 5). A conversation with Daniel Kahneman: On
profit, loss, and the mysteries of the mind. The New York Times.
Retrieved from http://www.nytimes.com
Halberg, A.-M., & Teigen, K. H. (2009). Framing of imprecise quantities:
When are lower interval bounds preferred to upper bounds? Journal of
Behavioral Decision Making, 22, 490–509. doi:10.1002/bdm.635
Hammond, K. R. (2000). Coherence and correspondence theories in judg-
ment and decision making. In T. Connolly, H. R. Arkes, & K. R.
Hammond (Eds.), Judgment and decision making: An interdisciplinary
reader (2nd ed., pp. 53–65). Cambridge, England: Cambridge Univer-
sity Press.
Hardisty, D. J., Johnson, E. J., & Weber, E. U. (2010). A dirty word or a
dirty world? Attribute framing, political affiliation, and query theory.
Psychological Science, 21, 86–92. doi:10.1177/0956797609355572
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1196
MANDEL
Henle, M. (1962). On the relation between logic and thinking. Psycholog-
ical Review, 69, 366–378. doi:10.1037/h0042043
Hilton, D. J. (1995). The social context of reasoning: Conversational
inference and rational judgment. Psychological Bulletin, 118, 248–271.
doi:10.1037/0033-2909.118.2.248
Horn, L. R. (1989). A natural history of negation. Chicago, IL: University
of Chicago Press.
Horn, L. R. (1992). The said and the unsaid. In C. Barker & D. Dowty
(Eds.), Salt II: Proceedings from the second conference on semantics
and linguistic theory (pp. 163–192). Columbus: Ohio State University,
Department of Linguistics.
James, W. (1950). The principles of psychology: Volumes 1 and 2. New
York, NY: Dover. (Original work published 1890)
Jou, J., Shantau, J., & Harris, R. J. (1996). An information processing view
of framing effects: The role of causal schemas in decision making.
Memory & Cognition, 24, 1–15. doi:10.3758/BF03197268
Jungermann, H. (1983). The two camps on rationality. In R. W. Scholz
(Ed.), Decision making under uncertainty (pp. 63–86). Amsterdam, the
Netherlands: Elsevier.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of
decision under risk. Econometrica, 47, 263–291. doi:10.2307/1914185
Kahneman, D., & Tversky, A. (1984). Choices, values, and frames. Amer-
ican Psychologist, 39, 341–350. doi:10.1037/0003-066X.39.4.341
Knight, F. H. (1964). Risk, uncertainty, and profit. New York, NY: Sentry
Press. (Original work published 1921)
Kühberger, A. (1995). The framing of decisions: A new look at old
problems. Organizational Behavior and Human Decision Processes, 62,
230–240. doi:10.1006/obhd.1995.1046
Kühberger, A., Schulte-Mecklenbeck, M., & Perner, J. (1999). The effects
of framing, reflection, probability, and payoff on risk preference in
choice tasks. Organizational Behavior and Human Decision Processes,
78, 204–231. doi:10.1006/obhd.1999.2830
Kühberger, A., & Tanner, C. (2010). Risky choice framing: Task versions
and a comparison of prospect theory and fuzzy-trace theory. Journal of
Behavioral Decision Making, 23, 314–329. doi:10.1002/bdm.656
Kuhn, T. S. (2000). The road since structure. Chicago, IL: The University
of Chicago Press.
LeBoeuf, R. A., & Shafir, E. (2003). Deep thoughts and shallow frames:
On the susceptibility to framing effects. Journal of Behavioral Decision
Making, 16, 77–92. doi:10.1002/bdm.433
Levin, I. P., & Gaeth, G. J. (1988). How consumers are affected by the
framing of attribute information before and after consuming the product.
Journal of Consumer Research, 15, 374–378. doi:10.1086/209174
Levin, I. P., Gaeth, G. J., Schreiber, J., & Lauriola, M. (2002). A new look
at framing effects: Distribution of effect sizes, individual differences,
and independence of types of effects. Organization Behavior and Hu-
man Decision Processes, 88, 411–429. doi:10.1006/obhd.2001.2983
Levin, I. P., Schneider, S. L., & Gaeth, G. J. (1998). All frames are not
created equal: A typology and critical analysis of framing effects.
Organizational Behavior and Human Decision Processes, 76, 149–188.
doi:10.1006/obhd.1998.2804
Levinson, S. C. (2000). Presumptive meanings. Cambridge, MA: MIT
Press.
Macdonald, R. R. (1986). Credible conceptions and implausible probabil-
ities. British Journal of Mathematical and Statistical Psychology, 39,
15–27. doi:10.1111/j.2044-8317.1986.tb00842.x
Mandel, D. R. (2001). Gain-loss framing and choice: Separating outcome
formulations from descriptor formulations. Organizational Behavior
and Human Decision Processes, 85,
56–76. doi:10.1006/obhd.2000
.2932
Mandel, D. R. (2003). Judgment dissociation theory: An analysis of dif-
ferences in causal, counterfactual, and covariational reasoning. Journal
of Experimental Psychology: General, 132, 419–434. doi:10.1037/
0096-3445.132.3.419
Mandel, D. R. (2005). Are risk assessments of a terrorist attack coherent?
Journal of Experimental Psychology: Applied, 11, 277–288. doi:
10.1037/1076-898X.11.4.277
Mandel, D. R. (2008). Violations of coherence in subjective probability: A
representational and assessment processes account. Cognition, 106,
130–156. doi:10.1016/j.cognition.2007.01.001
Mandel, D. R., & Vartanian, O. (2011). Frames, brains, and content
domains: Neural and behavioral effects of descriptive content on pref-
erential choice. In O. Vartanian & D. R. Mandel (Eds.), Neuroscience of
decision making (pp. 45–70). New York, NY: Psychology Press.
McKenzie, C. R. M. (2004). Framing effects in inference tasks—And why
they are normatively defensible. Memory & Cognition, 32, 874–885.
doi:10.3758/BF03196866
McKenzie, C. R. M., & Nelson, J. D. (2003). What a speaker’s choice of
frame reveals: Reference points, frame selection, and framing effects.
Psychonomic Bulletin & Review, 10, 596–602. doi:10.3758/
BF03196520
Moxey, L. M., & Sanford, A. J. (2000). Communicating quantities: A
review of psycholinguistic evidence of how expressions determine per-
spectives. Applied Cognitive Psychology, 14, 237–255. doi:10.1002/
(SICI)1099-0720(200005/06)14:3⬍237::AID-ACP641⬎3.0.CO;2-R
Musolino, J. (2004). The semantics and acquisition of number words:
Integrating linguistic and developmental perspectives. Cognition, 93,
1–41. doi:10.1016/j.cognition.2003.10.002
Noveck, I. A., & Reboul, A. (2008). Experimental pragmatics: A Gricean
turn in the study of language. Trends in Cognitive Sciences, 12, 425–
431. doi:10.1016/j.tics.2008.07.009
Oppenheimer, D. M., Meyvis, T., & Davidenko, N. (2009). Instructional
manipulation checks: Detecting satisficing to increase statistical power.
Journal of Experimental Social Psychology, 45, 867–872. doi:10.1016/
j.jesp.2009.03.009
Peters, E., & Levin, I. P. (2008). Dissecting the risky-choice framing effect:
Numeracy as an individual-difference factor in weighting risky and
riskless options. Judgment and Decision Making, 3, 435–448.
Phillips, L. D. (1983). A theoretical perspective on heuristics and biases in
probabilistic thinking. In P. C. Humphries, O. Svenson, & A. Vari
(Eds.), Analyzing and aiding decision processes (pp. 525–543). doi:
10.1016/S0166-4115(08)62256-6
Reyna, V. F., & Brainerd, C. J. (1991). Fuzzy-trace theory and framing
effects in choice: Gist extraction, truncation, and conversion. Journal of
Behavioral Decision Making, 4, 249–262. doi:10.1002/bdm
.3960040403
Rothman, A. J., & Salovey, P. (1997). Shaping perceptions to motivate
healthy behavior: The role of message framing. Psychological Bulletin,
121, 3–19. doi:10.1037/0033-2909.121.1.3
Schneider, S. L. (1992). Framing and conflict: Aspiration level contin-
gency, the status quo, and current theories of risky choice. Journal of
Experimental Psychology: Learning, Memory, and Cognition, 18, 1040–
1057. doi:10.1037/0278-7393.18.5.1040
Schwarz, N. (1996). Cognition and communication: Judgmental biases,
research methods, and the logic of conversation. Mahwah, NJ: Erlbaum.
Shafir, E., & LeBoeuf, R. A. (2002). Rationality. Annual Review of
Psychology, 53, 491–517. doi:10.1146/annurev.psych.53.100901
.135213
Sher, S., & McKenzie, C. R. M. (2006). Information leakage from logically
equivalent frames. Cognition, 101, 467–494. doi:10.1016/j.cognition
.2005.11.001
Sher, S., & McKenzie, C. R. M. (2008). Framing effects and rationality. In
N. Chater & M. Oaksford (Eds.), The probabilistic mind: Prospects for
Bayesian cognitive science (pp. 79–96). doi:10.1093/acprof:oso/
9780199216093.003.0004
Sher, S., & McKenzie, C. R. M. (2011). Levels of information: A framing
hierarchy. In G. Keren (Ed.), Perspectives on framing (pp. 35–63). New
York, NY: Psychology Press.
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1197
DO FRAMING EFFECTS REVEAL IRRATIONAL CHOICE?
Stanovich, K. E., & West, R. F. (1998). Individual differences in framing
and conjunction effects. Thinking & Reasoning, 4, 289–317. doi:
10.1080/135467898394094
Stanovich, K. E., & West, R. F. (2000). Individual differences in reasoning:
Implications for the rationality debate? Behavioral and Brain Sciences,
23, 645–665. doi:10.1017/S0140525X00003435
Stanovich, K. E., & West, R. F. (2008). On the relative independence of
thinking biases and cognitive ability. Journal of Personality and Social
Psychology, 94, 672–695. doi:10.1037/0022-3514.94.4.672
Teigen, K. H. (2011). When frames meet realities: On the perceived
correctness of inaccurate estimates. In G. Keren (Ed.), Perspectives on
framing (pp. 197–217). London, England: Psychology Press.
Teigen, K. H., & Nikolaisen, M. I. (2009). Incorrect estimates and false
reports: How framing modifies truth. Thinking & Reasoning, 15, 268–
293. doi:10.1080/13546780903020999
Thaler, R. H. (1985). Mental accounting and consumer choice. Marketing
Science, 4, 199–214. doi:10.1287/mksc.4.3.199
Tombu, M., & Mandel, D. R. (2013). When does framing influence
preferences, risk perceptions, and risk attitudes? The role of valence.
Manuscript submitted for publication.
Tversky, A., & Kahneman, D. (1981, January 30). The framing of deci-
sions and the psychology of choice. Science, 211, 453–458. doi:
10.1126/science.7455683
Tversky, A., & Kahneman, D. (1986). Rational choice and the framing of
decisions. Journal of Business, 59, S251–S278. doi:10.1086/296365
van Buiten, M., & Keren, G. (2009). Speaker-listener incompatability:
Joint and separate processing in risky choice framing. Organizational
Behavior and Human Decision Processes, 108, 106–115. doi:10.1016/
j.obhdp.2008.03.002
West, R. F., Toplak, M. E., & Stanovich, K. E. (2008). Heuristics and
biases as measures of critical thinking: Associations with cognitive
ability and thinking dispositions. Journal of Educational Psychology,
100, 930–941. doi:10.1037/a0012842
Wittgenstein, L. (1953). Philosophical investigations. Oxford, England:
Blackwell.
Received September 6, 2012
Revision received July 25, 2013
Accepted July 26, 2013 䡲
This document is copyrighted by the American Psychological Association or one of its allied publishers.
This article is intended solely for the personal use of the individual user and is not to be disseminated broadly.
1198
MANDEL
A preview of this full-text is provided by American Psychological Association.
Content available from Journal of Experimental Psychology General
This content is subject to copyright. Terms and conditions apply.
