Margolis: WASON'S SELECTION TASK WITH A REDUCED ARRAY
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psycoloquy.00.11.005.reduced-wason-task.1.margolis Sat Jan 22 2000
ISSN 1055-0143 (14 paras, 7 refs, 2 notes, 215 lines)
PSYCOLOQUY is sponsored by the American Psychological Association (APA)
Copyright 2000 Howard Margolis
WASON'S SELECTION TASK WITH A REDUCED ARRAY
Target Article on Reduced-Wason-Task
Howard Margolis
Harris School of Public Policy Studies
University of Chicago
1155 E60th Street Chicago IL
60637 773-702-0867
773-702-0926 (fax)
hmarg(a)uchicago.edu
http://www.harrisschool.uchicago.edu/fac_margolis.html
ABSTRACT: A striking aspect of performance on Wason's (1966)
selection task has been largely ignored. This brief target article
discusses the remarkable remedial effectiveness of Wason's "reduced
array" of alternatives.
KEYWORDS: cognitive illusions, modus tollens, reasoning, selection
task, Wason
1. One very odd feature of the Wason (1966) selection task, noticed long
ago by Wason himself but then almost completely ignored, is the
performance of subjects when the cards which nearly all subjects get
right are removed.
2. Consider this common form of the problem. Cards are labelled "A" or
"D" on one side and "3" or "7" on the other. A rule says
that "if A
then 3". Subjects see an array of four of the cards, two letter-side up
(showing "A" and "D") and two number-side up (showing "3"
and "7"). A
subject must decide which cards need to be turned over to know whether
this sample of cards is consistent with the rule.
3. The common responses are "A & 3", or "A" alone. The correct
response
is "A & 7". So there seem to be two easy cards: "A", which is
rarely
missed, and "D", which is rarely chosen; and two hard cards: "3" and
"7", which supply nearly all the errors. Overall, about 90% of subjects
in fact do make errors. So what will happen if subjects are shown only
what Wason called a "reduced array". Delete the two easy cards, and
have subjects judge only the two hard cards. One might suppose, since
essentially all errors are caused in relation to the hard cards, that
subjects will continue to do badly.
4. But they don't! If this test is run on a group of reasonable size
(say a class), those asked to respond to the 4- card version will
typically return the usual 10% correct responses. But those given the
reduced array will return a clear majority of correct responses! What
can possibly account for this large improvement, related to merely
removing the two cards that are ordinarily judged correctly anyway?
5. This odd, even bizarre, improvement can be explained if subjects are
seeing the cards not as particular cards but as indicating categories
of cards. If explicitly asked, subjects understand the intended meaning
of the question. But their responses make logical sense only with
respect to a drastic misreading of the question. The question is
misread as being about which categories of cards should be examined;
for example, any cards with a "D" on either side; rather than about the
particular card shown with a "D" on its upside.
6. This is not a cognitive illusion (cf. Koehler 1993, 1996; Krueger
1998; Margolis 1998) but simply a consequence of the pragmatics of
ordinary language. In everyday conversation, even logicians rarely use
phrasing like "if and only if" (iff) to distinguish this "if/then"
relation from "if but not only if" (if). Distinguishing between "if"
and "iff" is almost always left to context. But the basic Wason problem
provides so little context that if/then here could be interpreted
either way.
7. The two points (ambiguity with respect to "if" vs. "iff",
interacting with the illusory "category" response to the task) will
account not only for the usual errors on the basic problem but also for
the remarkable improvement from removing the two easy cards.
8. If a person might respond to Wason's task as if it were about
categories rather than about the particular cards shown, then the
salient correct response (to that incorrect reading!) is either "A & 3"
when "if/then" is read as "iff", or "A" alone when
"if/then" is read as
"if": just the pair of responses we do indeed see most often [NOTE 1].
In Margolis 1987 (pp. 151-2) I explained how the illusory "categories"
reading can arise from entrenched expectations, so that we ordinarily
first have to choose what sort of approach to take and only then deal
with details of how to do it. In the absence of sufficient context to
differentiate one situation from the other, we tend to fall into seeing
first what we usually do first. In this impoverished context, that
"usual" tendency turns out to override what the words literally tell
the subject to do.
9. But consider what happens when we eliminate the two easy cards ("A"
& "D"). If the "category" illusion is guiding intuition, then the
proper response (to that illusory interpretation) is "7 & 3" for the
"iff" reading of "if/then", or "7" only for the
"if" reading. So we can
expect that subjects will no longer miss the "7". And a norm of
language then favours "7" alone as the response. Other than for
rhetorical purposes, we do not ask questions with obvious answers. This
favours the "if" (rather than "iff") reading, which gives the solver a
bit more to think about - which in turn favours "7" alone over "7 &
3". On this account, subjects still seem to be misinterpreting the
cards as categories. But with the reduced array, the only available
correct response for the "category" reading is also the correct
response for the intended reading! "A" is still salient in the
question, but since it is no longer available, subjects must pick the
"7".
10. Is it plausible that the too-easy character of the question -- when
read to make the checking of all the choices correct -- pushes subjects
toward an "if" (rather than "iff") response? More generally, can
subtle
changes in the salience of one reading against another have notable and
substantial effects? Anyone familiar with the ways of stage magicians
will know that the answer to this must be yes. Griggs (1990) confirmed
a particularly startling salience effect in the present context of
performance on the Wason task. A variation in the task was used which
forced responses especially heavily towards "A & 3". But then a
logically insignificant alteration in wording shifts responses very
heavily to the otherwise almost never seen response of "D & 7"!
11. The "D & 7" response (in logical notation, the not-P, not-Q
response) is in fact another correct response to the illusory reading
of the cards as categories (see NOTE 1). That "D & 7" is almost never
seen shows the effect of the salience of "A" and "3" in the rule. But
the wording of the question has a recency advantage over the wording in
the rule. This turns out to be so strong that the predominant response
is reversed by reversing the order in which the two clauses in the
question are presented [NOTE 2].
12. The "categories" account of Wason reviewed here makes sense of BOTH
of the otherwise exceedingly puzzling effects just presented. And it
has other significant consequences. In particular, if merely reducing
the array greatly improves performance, it is hardly surprising that
more strenuous manipulations (making a permission context or social
norm context, etc.) can also greatly improve performance. But, of
course, the converse is not true.
13. Note that on this account the cognitive illusion comes at the stage
of interpreting the task, not from the inability to handle modus
tollens that is the usual explanation. That claimed inability has
always warranted more suspicion than it has received, since anyone who
listens to their children will hear them quite readily make what are
functional equivalents of modus tollens inferences. And not very
surprisingly, since the world provides us with endless occasions to
make such inferences. (If I picked my keys off the desk, they would now
be in my pocket. My keys are not in my pocket. So they are probably on
my desk.)
14. And if this interpretation of Wason is correct, it has relevance to
many issues in the long-continuing debate over the nature and
significance of cognitive illusions.
NOTES
[1] The salient responses are those prompted by the cards mentioned in
the question ("A" and "3"). But three pairs in addition to "A
& 3"
would also be correct for a "categories" response to the "iff"
reading: "A & D", "7 & 3", "D & 7". Any of
these choices will locate
all violations (A/7 or D/3 cards). And for the "if" reading "7" as
well
as "A" would be correct, finding any A/7 cards.
[2] The exceptionally heavy "A & 3" responses are elicited by making
the task read: "Circle two cards to turn over to check whether the rule
has been violated." But "A & 3" as the dominant response switches to
"D
& 7" when the instruction is turned around to read: "Figure out which
two cards could violate the rule, and circle them."
REFERENCES
Griggs, R. (1990) "Instructional effects on responses in Wason's
selection task". British Journal of Psychology 81:197-204.
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normative, and methodological challenges. Behavioral and Brain Sciences
19(1): 1-53.
http://www.cogsci.soton.ac.uk/bbs/Archive/bbs.koehler.html
Krueger, J. (1998). The bet on bias: A forgone conclusion? PSYCOLOQUY
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http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?9.46
Margolis, H. (1987) Patterns, Thinking and Cognition. University of
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Margolis, H. (1998) Tycho's Illusion: How It Lasted 400 Years, and What
That Implies About Human Cognition PSYCOLOQUY 9 (32)
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Wason, P.C. (1966) Reasoning. In B. M. Foss (Ed.) New Horizons in
Psychology I. Penguin