Howard Margolis (2000) Wason's Selection Task With a Reduced Array. Psycoloquy: 11(005) Reduced Wason Task (1)

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Psycoloquy 11(005): 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)


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.


cognitive illusions, modus tollens, reasoning, selection task, Wason
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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: 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.


[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."


Griggs, R. (1990) "Instructional effects on responses in Wason's selection task". British Journal of Psychology 81:197-204.

Koehler, J.J. (1993). The Base Rate Fallacy Myth. PSYCOLOQUY, 4(49) psyc.93.4.49.base-rate.1.koehler

Koehler, J.J. (1996). The base rate fallacy reconsidered: Descriptive, normative, and methodological challenges. Behavioral and Brain Sciences 19(1): 1-53.

Krueger, J. (1998). The bet on bias: A forgone conclusion? PSYCOLOQUY 9(46)

Margolis, H. (1987) Patterns, Thinking and Cognition. University of Chicago Press.

Margolis, H. (1998) Tycho's Illusion: How It Lasted 400 Years, and What That Implies About Human Cognition PSYCOLOQUY 9 (32) psyc.98.9.32.cognitive-illusion.1.margolis

Wason, P.C. (1966) Reasoning. In B. M. Foss (Ed.) New Horizons in Psychology I. Penguin


    Wason (1983) writes that "the elimination of the antecedent values,
    P and not-P, was sensibly motivated because the discrimination
    between them is trivial. This experiment seems theoretically very
    important. It has been almost totally ignored." But what Wason
    specifically referred to and had published (Johnson-Laird and Wason
    1970) was a variant on his selection task, not the now-canonical
    4-card test."

    Johnson-Laird, P.N. and Wason, P.C. (1970) Insight into a logical
    relation. Qarterly Journal of Experimental Psychychology 22:

    Wason, P.C. (1983) Realism and rationality in the selection task.
    In: Evans, J.S.T.B. (Ed.) "Thinking and Reasoning"  Routledge &
    Kegan Paul.

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