Information Leakage from Logically Equivalent Frames Summary


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Cognition 101 (2006) 467–494
Information leakage from logically
equivalent frames q
Shlomi Sher
Craig R.M. McKenzie
Department of Psychology, University of California, San Diego, USA
Received 23 May 2005; revised 11 October 2005; accepted 2 November 2005
Framing e?ects are said to occur when equivalent frames lead to di?erent choices. However,
the equivalence in question has been incompletely conceptualized. In a new normative analysis
of framing e?ects, we complete the conceptualization by introducing the notion of information
equivalence. Information equivalence obtains when no choice-relevant inferences can be drawn
from the speakerÕs choice of frame. We show that, to support the normative implications traditionally attributed to framing e?ects, frames must be equivalent in this sense. We also present new evidence for McKenzie and NelsonÕs (2003) reference point hypothesis, which posits a
tendency to cast descriptions in terms of what has increased relative to the reference point.
This leakage of information about relative state violates information equivalence, and gives
rise to a normative account of the most robust ?nding in the attribute framing literature—
the valence-consistency of preference shifts. We argue that, more generally, valenced descriptions leak information about perceived valence. Such ‘‘implicit recommendations’’ may
This research was supported by National Science Foundation Grants SES-0079615 and SES-0242049,
and a National Science Foundation Graduate Research Fellowship. The authors are grateful to Vic
Ferreira and Norbert Schwartz for helpful comments on a previous draft. Some of these results were
presented at the 40th Annual Bayesian Research Conference, Los Angeles, CA (2002); 8th Behavioral
Decision Research in Management Conference, Chicago, IL (2002); 43rd Annual Meeting of the
Psychonomic Society, Kansas City, MO (2002); the 19th Biannual Conference on Subjective Probability,
Utility, and Decision Making, Zurich, Switzerland (2003).
Corresponding author.
E-mail address: (S. Sher).
Present address: Psychology Department, Princeton University, Princeton, NJ 08544, USA.
0010-0277/$ – see front matter Ó 2005 Elsevier B.V. All rights reserved.
S. Sher, C.R.M. McKenzie / Cognition 101 (2006) 467–494
generalize the reference point explanation of the valence-consistent shift. Normative and
psychological implications of the information leakage framework are discussed.
Ó 2005 Elsevier B.V. All rights reserved.
Keywords: Framing e?ects; Pragmatics; Rationality
1. Introduction
A framing e?ect is said to occur when equivalent descriptions of a decision
problem lead to systematically di?erent decisions. Framing e?ects thus purportedly violate a bedrock principle of ‘‘description invariance’’, ‘‘[a]n essential condition
for a theory of choice that claims normative status. . .so basic that it is tacitly
assumed in the characterization of options rather than explicitly stated as a testable axiom’’ (Tversky & Kahneman, 1986, p. S253). It is largely from the robust
existence of framing e?ects that Tversky and Kahneman (1986) conclude that ‘‘no
theory of choice can be both normatively adequate and descriptively accurate’’.
(p. S251).
This paper raises a basic question about the basic principle of description invariance and about the standard de?nition of ‘‘framing e?ect’’. The standard characterization of framing e?ects refers, as above, to ‘‘equivalent descriptions of a
decision problem’’—but what does it mean for a pair of descriptions to be ‘‘equivalent’’? And what must it mean for a pair of descriptions to be equivalent if equivalent descriptions leading to di?erent decisions is to raise normative eyebrows?
That is, just what is the invariance in ‘‘description invariance’’? To our knowledge,
these elementary questions have not been satisfactorily addressed in the literature
on framing e?ects and description invariance. In what follows, we propose an
explicit characterization of the normatively relevant equivalence—‘‘information
equivalence’’—and present experimental results which suggest that an important
segment of the framing literature has been concerned with information non-equivalent descriptions.
Much of the time, the questions posed above are not even implicitly addressed.
Furthermore, when ‘‘equivalence’’ is explicated, the explication typically proceeds
via appendage of a single, unexplicated adjective: for example, equivalence may be
?eshed out as ‘‘objective equivalence’’ (Dunegan, 1996; Levin, Schneider, & Gaeth,
1998) or ‘‘formal equivalence’’ (Frisch, 1993; Ku?hberger, 1998). In our view, such
adjectives add little more than emphasis.
A handful of researchers have been explicit about the sort of equivalence they
have in mind—namely, logical equivalence (see, e.g., Johnson-Laird & Sha?r,
1993; Rubinstein, 1998; Sha?r, 1993). This explication is substantive: logical equivalence is well-de?ned (a pair of statements is logically equivalent if each member of
the pair necessarily entails the other) and, provided some care is taken in translating
between logical connectives and natural language connectives, straightforward to
S. Sher, C.R.M. McKenzie / Cognition 101 (2006) 467–494
diagnose. However, there is no general normative problem with logically equivalent
descriptions of a choice problem leading to di?erent choices.2
To see this, let A and B be a pair of logically equivalent statements about a
choice problem. Suppose in addition that speakersÕ conversational behavior exhibits the following regularity: speakers, choosing between uttering ‘‘A’’ and uttering
‘‘B’’, are more likely to utter ‘‘A’’ when some background condition C (not explicitly speci?ed in the statements A and B) holds than when C fails. In that case, a
listener who hears a speaker say ‘‘A’’ can safely infer a higher probability of C
being true than if the speaker had said ‘‘B’’ (that is, p (C|speaker says
‘‘A’’) > p (C|speaker says ‘‘B’’)). If knowledge about the background condition C
is relevant to the choice at hand, then the speakerÕs (e.g., experimenterÕs) utterance
of the two logically equivalent statements A and B may with impunity lead to different decisions.
When there is no choice-relevant background condition C about whose probability a listener can draw inferences from the speakerÕs choice between frames
A and B, we say that A and B are ‘‘information equivalent’’. Otherwise, we
say that there has been information leakage from the speakerÕs choice of frame,
and that the frames are therefore information non-equivalent. The simple argument from the previous paragraph shows that, for description invariance to carry
any weight as a normative principle, the invariance in question must be information invariance.
It may seem paradoxical that di?erent inferences can be drawn from di?erent but
logically equivalent frames, A and B. Indeed, there is no statement S that can be
inferred from A but not from B (even if S is a statement about the probability
of certain background conditions C obtaining), because, if one knows that B,
one can also know that A, and hence draw whatever inferences one would draw
knowing that A. However, when one encounters a frame A in a framing problem
(or in a natural conversational environment), one is not merely endowed with
knowledge that A. Instead, one is endowed with knowledge that the speaker said
‘‘A’’ (and not ‘‘B’’). Information non-equivalence stems not from those inferences
At least two other substantive explications of equivalence have been put forward in the literature, but
neither is unproblematic. Tversky and KahnemanÕs (1986) paper appeals to both. (1) Omitting problematic
reference to equivalent descriptions, they refer to di?erent descriptions of the same problem leading to
di?erent decisions. However, taken literally, this characterization is inadequate. For example, if you have
to choose whether to let the axe-murdering priest who wants to use your telephone into your house, it
ought to make a di?erence to you whether you are asked whether you would be willing ‘‘to let this priest
into your house to use the phone’’ or, alternatively, ‘‘to let this axe-murderer into your house to use the
phone’’. The focal issue is the information contained in the description of the decision problem, and not
unmentioned facts about the decision problem. Because virtually all choice-task descriptions underdetermine relevant aspects of the state of the described world, we cannot speak of whether two descriptions
describe the same problem, but rather whether the set of problems which the descriptions truly describe is
the same. That is, we are back to logical equivalence. (2) Alternatively, two descriptions of a decision
problem are said to be ‘‘equivalent’’ if, on re?ection, people would endorse their equivalence. However, no
normative theory of decision making has anything to say about the correctness of peopleÕs beliefs about
equivalence—which, as we argue here with reference to most framing researchersÕ beliefs, may after all be
S. Sher, C.R.M. McKenzie / Cognition 101 (2006) 467–494
which can be drawn from A but not from B (there are none), but instead from
those inferences which can be drawn from the fact that the speaker said ‘‘A’’ rather
than ‘‘B’’ (there are many).3
Information non-equivalence of logically equivalent descriptions has been demonstrated in other contexts. For example, Johnson-Laird (1968a, 1968b) argued
that passive-form sentences and their logically equivalent active-form counterparts
convey di?erent information about the relative prominence of the logical subject
and the logical object of the sentences (e.g., in ‘‘The man was kissed by the woman’’, the man is intended and interpreted to be more prominent than in ‘‘The woman kissed the man’’). Similarly, transposing the subject and object around a
symmetrical action verb leaves logical content undisturbed, but nonetheless conveys
information about causal agency: the subject of a symmetrical action predicate
(e.g., the man in ‘‘The man danced with the woman’’) is typically the causal initiator of the described action (Semin & De Poot, 1997; for a general analysis of ‘‘the
asymmetrical behavior of symmetrical predicates’’, see Gleitman, Gleitman, Miller,
& Ostrin, 1996). That is, di?erent perceptions (of relative prominence, causal agency, etc.) lead speakers to choose di?erent sentence forms, and listeners are able to
draw corresponding conclusions from the speakerÕs choice of sentence form. In the
above cases, two logically equivalent sentences are information non-equivalent,
because information (about relative prominence, causal agency, etc.) ‘‘leaks out’’
from the speakerÕs choice of sentence form. (For additional examples, see Moxey
& Sanford, 2000; Wason, 1965.)
A skeptic might agree with our conceptualizations of ‘‘equivalence’’ and ‘‘invariance’’, and concede the inadequacy of the standard characterization, but
nonetheless maintain that the logically equivalent frames used in actual framing
studies in the literature are in fact information equivalent—or at least that any
information non-equivalence is too marginal to account for major shifts in preference. In the remainder of this paper, we attempt to satisfy the skeptic by documenting actual instances, of direct relevance to the framing literature, in which
logically equivalent frames are demonstrably information non-equivalent. We
begin by normatively re-examining McKenzie and NelsonÕs (2003) reference point
hypothesis in the context of the information leakage framework. We present new
evidence (Experiments 1–4) for this hypothesis, overcoming methodological shortcomings in the original experiments, and we argue that, when frames are valenced, reference point information is widely choice-relevant. Extending the reference
point hypothesis, Experiment 5 provides evidence that speakers tend to describe
positively evaluated things in positive terms, even in the absence of a salient
Note that the present analysis makes no assumptions about the existence of Gricean norms, or, more
generally, about the communication of informative intent (Sperber & Wilson, 1986). The analysis simply
points out that, when a certain kind of regularity in speaking behavior exists, a particular kind of inference
will typically be warranted, norms and intentions aside. Whether and how listeners, in drawing such
inferences, consider informative intentions or conversational norms is a question for further research to
address. (For Gricean perspectives on research in judgment and decision making, see Hilton, 1995;
Schwarz, 1994.)
S. Sher, C.R.M. McKenzie / Cognition 101 (2006) 467–494
reference point. In this way, a speakerÕs choice among valenced frames may communicate a kind of implicit recommendation to the listener. Because of the broad
relevance of relative quality and perceived valence, the information leakage
documented here suggests a natural explanation for the most robust ?nding in
the attribute framing literature—the valence-consistency of shifts in preference.
In short, in many framing experiments, choice-relevant information does in fact
leak out from the experimenterÕs choice among logically equivalent frames.
Finally, we distinguish between information leakage as a normative analysis of
framing problems and information leakage as a psychological hypothesis about
why some framing e?ects occur, and consider our evidence from both angles.
2. How reference points in?uence frame selection
Reference points—the initial, expected, or standard level of a variable, in contrast
with which other objects are implicitly evaluated—have been shown to in?uence a
wide variety of behaviors, ranging from judgments of physical distance (Hirtle &
Jonides, 1985; Sadalla, Burroughs, & Staplin, 1980) to speakersÕ use of Lako?Õs
(1973) linguistic ‘‘hedges’’ (Rosch, 1975). Examining the e?ect of reference points
on the linguistic behaviors which form the subject of the framing literature, McKenzie and Nelson (2003) showed that speakersÕ frame selection and listenersÕ frame
interpretation are systematically in?uenced by implicit reference point information.
While they did not directly address its normative implications, we argue that this
?nding undermines the assumption of description invariance in a sizeable segment
of the framing literature.
Speci?cally, consider, for 0 6 p 6 1, domains D in which the proportion of D which
is X1 is p if and only if the proportion of D which is X2 is 1 p. For example, in
describing people undergoing a medical treatment (D), ‘‘X1’’ may refer to those
who die within ?ve years of undergoing the treatment and ‘‘X2’’ may refer to those
who are still alive 5 years after undergoing the treatment; in descriptions of ground
beef (D), X1 may be ‘‘lean’’ and X2 may be ‘‘fat’’; and, in descriptions of a cup of
water (D), X1 may be ‘‘full’’ and X2 may be ‘‘empty’’. Much of the framing literature
is concerned with just this variety of framing problem. Indeed, in a recent review,
Levin et al. (1998) proposed a taxonomy of the framing literature into attribute
framing, risky choice framing, and goal framing: the ?rst of these categories is concerned with framing e?ects involving logically equivalent descriptions of a single
McKenzie and Nelson (2003) hypothesized the following regularity in linguistic
behavior: (1) In describing a ?xed state of proportionate a?airs, speakers are more
likely to describe the proportion in terms of ‘‘X1’’ when X1 has increased relative
to the reference point proportion (the norm, or what one would have expected) than
when X1 has decreased relative to the reference point. (2) Listeners are sensitive to
this regularity—that is, listeners are capable of correctly inferring the reference point
proportion from the speakerÕs choice of proportion-frame. Reformulating McKenzie
and NelsonÕs (2003) hypothesis in the terms of our normative framework, reference
S. Sher, C.R.M. McKenzie / Cognition 101 (2006) 467–494
point information is leaked from speakersÕ choices among logically equivalent
descriptions of proportion, and listeners absorb this leaked information. In a later
section, we argue that this leaked information is broadly choice-relevant in most
of the attribute framing literature.4
For example, McKenzie and Nelson presented some subjects with the following
scenario in a ‘‘speaker study’’:
Imagine a 4-ounce measuring cup in front of you that is completely ?lled with
water up to the 4-ounce line. You then leave the room brie?y and come back to
?nd that the water is now at the 2-ounce line. What is the most natural way to
describe the cup now?
Other subjects encountered an otherwise identical scenario in which the cup was
originally empty rather than originally full. Con?rming the reference point
hypothesis, subjects were more likely to describe the cup as ‘‘1/2 full’’ when it
was previously empty (fullness having increased relative to the reference point)
than when it was previously full (fullness having decreased relative to the reference point).
In the corresponding ‘‘listener study’’, also reported in McKenzie and Nelson
(2003), some subjects were presented with the following scenario:
Imagine that Mary was sitting at her kitchen table with a glass in front of her.
She left the room brie?y and came back to ?nd that the contents of the glass
had changed. When asked to describe the glass now, Mary said, ‘‘The glass
is 1/2 full’’. Given how Mary chose to describe the glass after its contents
had changed, please choose the statement below in terms of what you think
was most likely true about the glass before its contents changed.
Other subjects encountered the same scenario, except with Mary describing the cup
as ‘‘1/2 empty’’ rather than ‘‘ 1/2 full’’. Again, subjects were more likely to infer that
the cup was previously full when it was described as ‘‘1/2 empty’’ than when it was
described as ‘‘1/2 full’’. In essence, subjects in the listener study correctly absorbed
the information that subjects in the speaker study leaked. McKenzie and Nelson
(2003) obtained similar results both using di?erent proportions and in the domain
of medical treatments, with some subjects describing treatments in terms of mortality
Some discussions of risky choice framing have been couched in terms of ‘‘reference points’’, but it is
important to distinguish these from the present account. In theoretical treatments of risky choice framing
problems (like the Asian Disease Problem), frames are said to in?uence the psychological zero point in the
decision makerÕs prospect-theoretic value function—this zero point is sometimes labeled ‘‘the reference
point’’ (Kahneman & Tversky, 1979). However, the frames themselves are not taken to convey any
information about the state of the world or of the speakerÕs mind. The present development, by contrast, is
novel in two ways: First, it highlights the information content of frames—the speakerÕs choice of frame
leaks information about an aspect of the world (the usual, expected, or initial level of the variable being
described—‘‘the reference point’’, in our terminology) about which the speaker may have knowledge.
Second, our account relates this reference point information implicit in frames to the attribute (as distinct
from risky choice) framing literature.
S. Sher, C.R.M. McKenzie / Cognition 101 (2006) 467–494
or survival rate and other subjects making reference point judgments on the basis of
such descriptions.
However, as the authors themselves noted, one potential shortcoming of the
experiments described above is their arti?ciality. Speci?cally, participants in those
studies may have felt compelled to hypothesize a relationship between the prior
state of the cup and its current description. Because the relationship hypothesized
by McKenzie and Nelson (2003) was intuitively generated, it is possible that subjects, acting as folk psychologists rather than spontaneous conversationalists, intuited the same relationship. The reference point hypothesis, however, concerns
peopleÕs actual speaking and listening behavior, not their beliefs about actual speaking and listening behavior. To certify the McKenzie and Nelson (2003) experiments
as re?ecting regularities inherent in actual discourse, Experiments 1–3 recast those
experiments in a more naturalistic setting with opaque manipulations. How can we
determine whether, in ordinary conversational life, a person spontaneously thinks
of ‘‘half-empty’’ cups as previously full? One way is to give her a completely full
cup and a completely empty cup, ask her for a ‘‘half-empty’’ cup, and see what
she does.
3. Experiment 1
3.1. Method
Participants were 99 UC San Diego (UCSD) undergraduates who received partial course credit for their participation. Four subjects did not provide useable
data (three due to misunderstanding of the instructions, one due to experimenter
error) and were excluded from the analysis. Data were analyzed for the remaining
95 subjects. In this and all subsequent experiments, subjects were randomly
assigned to condition.
Subjects, tested individually, were seated at a desk in one of two small rooms. At
the left edge of the desk, two apparently identical transparent plastic cups stood sideby-side. One was full of water, the other empty. (Order of the cups—whether the full
or empty cup was closest to the subject—was varied between the rooms.) Indicating
the right edge of the desk, the experimenter said to about half of the subjects in each
‘‘Just to get things started, could you pour water from one cup to the other and
set a half-full cup at the edge of the desk’’.
The remaining subjects were asked for ‘‘a half-empty cup’’. (Note the use of the
inde?nite article. Use of the de?nite article might have implied that the experimenter
had a speci?c cup in mind.) After issuing this request, the experimenter left the room,
giving the subject enough time to pour the water and set a cup at the edge of the
desk. When the experimenter returned, the subject was given other tasks not involving the cups.
S. Sher, C.R.M. McKenzie / Cognition 101 (2006) 467–494
The bottom surface of each cup was imperceptibly marked by a manufacturerÕs
number. The even-numbered cup was always initially full, the odd-numbered cup
always initially empty. Therefore, once the subject had left the room, the experimenter
could determine, by reading o? the number, whether the initially full or initially empty
cup had been furnished.
3.2. Results and discussion
Note that, after pouring, a subject would possess two cups with water up to the
halfway point, one of which was initially full, the other initially empty. In line with
McKenzie and NelsonÕs (2003) paper-and-pencil task ?ndings, we predicted that subjects would be more likely to provide the initially full cup when ‘‘a half-empty cup’’
was requested than when ‘‘a half-full cup’’ was requested.
The results are shown by the two columns on the left side of Fig. 1. The prediction was borne out: 69% of subjects furnished the initially full cup when ‘‘a
half-empty cup’’ was requested, whereas only 46% of subjects furnished the
initially full cup when ‘‘a half-full’’ cup was requested (p = .023, 2-tailed FisherÕs
exact test).
These results are not susceptible to the demand characteristics objection outlined
above. The dependent variable in this experiment was peopleÕs behavior in a conversational environment, not their beliefs about such behavior. Furthermore, both the
experimental manipulation (‘‘half-full’’ vs. ‘‘half-empty’’ requests) and the purpose
of the experiment (surveying frame interpretation) were hidden in the between-subjects, ‘‘just to get things started’’ design. Indeed, occasional, informal debrie?ngs
exposed a uniform mysti?cation about the purpose of the experiment (with many
Experiments 1-3
Experiment 1
Experiment 2
“3/4 Full”
“1/4 Empty”
“1/4 Full”
“3/4 Empty”
“1/2 Full”
“1/2 Empty”
% Selecting Previously Full Glass
Experiment 3
Fig. 1. Proportion of subjects selecting the initially full cup in all conditions in Experiments 1–3. Standard
error bars are shown.
S. Sher, C.R.M. McKenzie / Cognition 101 (2006) 467–494
subjects speculating that we were interested in measurement or speed). Subjects who
were queried also indicated that they felt free to furnish either cup.
Extending Experiment 1, Experiments 2 and 3 below employ di?erent proportions, thereby advancing the naturalistic re-examination of the McKenzie and
Nelson (2003) paper-and-pencil studies summarized above. They also include
written rather than spoken instructions (thus ruling out the possibility of experimenter bias), and systematic checks on the opaqueness of the experimental
4. Experiments 2 and 3
4.1. Method
There were 112 participants in Experiment 2, and 178 participants in Experiment
3, drawn from the same population as those in Experiment 1. Five subjects were
excluded from Experiment 2 and 14 were excluded from Experiment 3.5
As in Experiment 1, subjects were seated at a desk in one of two small rooms.
Transparent cups, one full and one empty, stood side-by-side at the left edge of
the desk. (Again, order of the cups was varied between rooms.)
A square, slightly larger than the base of a single cup, was marked on the desk.
Subjects were given a one-page instruction sheet, which, for half of the Experiment
2 subjects, read:
In front of you on the table youÕre sitting at, there should be two cups and a
square. To get things started, please pour water from one cup to the other
and set a 3/4-empty cup in the square. Please go tell the experimenter when
youÕve ?nished, and he will tell you what to do next.
The remaining subjects in Experiment 2 were asked for ‘‘a 1/4-full cup’’ instead of ‘‘a
3/4-empty cup’’.
In Experiment 3, the instruction sheet, otherwise identical to that used in Experiment 2, requested either ‘‘a 1/4-empty cup’’ or ‘‘a 3/4-full cup’’.
In both cases, after completing a series of seemingly unrelated tasks (which, for
some subjects, included Experiment 5 below), subjects were given follow-up questionnaires, asking them (in Experiment 2) what they had thought the purpose of
the water-pouring experiment was while participating in it, or (in Experiment 3)
Of the ?ve unusable data points in Experiment 2, three came from subjects in the ‘‘3/4-empty’’
condition who gave a 3/4-full cup. Similarly, 12 of the 14 unusable data points in Experiment 3 came from
subjects in the ‘‘1/4-empty’’ condition who placed a 1/4-full cup in the square. The high error rate
presumably resulted from the fact, documented in McKenzie and Nelson (2003), that, in describing 1/4full and (especially) 3/4-full cups, speakers have a marked preference for ‘‘full’’ over ‘‘empty’’ descriptions.
Consequently, some readers in Experiments 2 and (especially) 3 probably expected to see ‘‘full’’ where
‘‘empty’’ appeared. One Experiment 3 subject was, erroneously, not administered the follow-up
S. Sher, C.R.M. McKenzie / Cognition 101 (2006) 467–494
whether they had realized that there were two ways of pouring the water to comply
with the instructions, and, if so, what they thought about at the time in deciding how
to pour.
4.2. Results and discussion
As in Experiment 1, the reference point hypothesis predicts that subjects will be
more likely to furnish the initially full cup when ‘‘a p-empty cup’’ is requested
than when ‘‘a (1 p)-full cup’’ is requested (p = 3/4 in Experiment 2, 1/4 in
Experiment 3).
The middle and rightmost pairs of columns in Fig. 1 depict the results of Experiments 2 and 3, respectively. In Experiment 2, 29% of subjects selected the initially full
cup when ‘‘a 3/4-empty cup’’ was requested, whereas only 7% of subjects selected the
initially full cup when ‘‘a 1/4-full cup’’ was requested (p = .005, 2-tailed FisherÕs exact
test). In Experiment 3, the results were weaker (and not signi?cant) but once again
pointed in the predicted direction: 70% of subjects furnished the initially full cup when
‘‘a 1/4-empty cup’’ was requested, whereas only 60% of subjects furnished the initially
full cup when ‘‘a 3/4-full cup’’ was requested (v2 [1, N = 164] = 1.9, p = .17).6
A glance at Fig. 1 reveals a striking di?erence between Experiments 2 and 3. In
Experiment 2, a majority of subjects furnished the initially empty cup, while, in
Experiment 3, most subjects furnished the initially full cup. This discrepancy
arises from a subtle but important property of the task structure in Experiments
2 and 3. In these experiments, subjects had to choose among two ways of pouring
(a little bit or a lot out of the initially full cup), while, after pouring, only one cup
was appropriate for selection. (In this respect, they di?er from Experiment 1, in
which subjects could only pour in one way, and had to choose between two
equivalent cups.) Because, in Experiments 2 and 3, most subjects would presumably ?nd it easier to pour a little rather than a lot from the initially full cup, one
would predict (and we found) a marked bias in favor of that pouring method. In
Experiment 2, pouring a little entails selection of the initially empty cup, which,
after pouring, is 1/4-full. In Experiment 3, pouring a little entails selection of
the initially full cup, which, after pouring, is 1/4-empty. It is not surprising that
subjects typically opted for the easier pouring method. What is interesting is how
the magnitude of this preference was modulated by the experimenterÕs choice of
The follow-up question data in Experiments 2 and 3 con?rm the opaqueness of
the design. There was no indication that subjects felt compelled to intuit the reference point regularity. A closer look at the Experiment 3 responses sheds some
light on underlying cognitive processes. After reading that, ‘‘[t]o comply with the
instructions you were given in that experiment, you could have either poured 1/4
It is noteworthy that McKenzie and Nelson (2003) also obtained their weakest results in the 3/4-full/1/
4-empty conditions of both their speaker and listener studies, suggesting that in such descriptions the
speakerÕs choice of frame may be least informative. In both of their studies, their results for this condition
were in the predicted direction, but were either not at all or only marginally signi?cant.
S. Sher, C.R.M. McKenzie / Cognition 101 (2006) 467–494
of the water out of the full cup and placed the initially full cup in the square or
poured 3/4 of the water out of the full cup and placed the initially empty cup in
the square’’, subjects were asked: ‘‘At the time you participated in the experiment
in the small room, did you realize that you could have poured the water in either
of the two ways described above’’? The ‘‘framing e?ect’’ in Experiment 3 stems
from subjects who reported not having considered both pouring methods. Among
subjects who reported having done so, there was no signi?cant di?erence between
the proportions selecting the initially full cup in the ‘‘3/4 full’’ and ‘‘1/4 empty’’
conditions (77 and 74%, respectively). Irrespective of condition, most subjects in
Experiment 3 chose the more e?cient pouring method when both methods were
contemplated. However, among subjects who reported not having considered both
methods, 59% (13 of 22) furnished the initially full cup when a ‘‘1/4-empty’’ cup
was requested, while only 16% (4 of 25) furnished the initially full cup when a
‘‘3/4-full’’ cup was requested (p = .002, 2-tailed FisherÕs exact test). Apparently,
subjects who automatically ‘‘saw’’ a single pouring method exhibited the reference
point regularity, while those who deliberated over two possibilities were guided by
deliberate (e.g., e?ciency) considerations. (This surmise may not generalize to
Experiment 1, since, after pouring, subjects in that experiment possessed two
obviously suitable cups, and it is not clear what, if any, e?ciency motives would
apply.) Since subjects who only considered one pouring method could not have
felt compelled to intuit a relationship between pouring method and the prior state
of the cup, demand characteristics could not have driven the results of Experiment 3.
In summary, in Experiments 1–3, subjects encountered one of two logically
equivalent requests for a cup. Two methods of compliance di?ered with respect
to one background condition—the prior state of the furnished cup—not