THE WASON SELECTION TASK

One of the best-known tasks in the study of deductive reasoning is the Wason selection task or four card problem. Invented by Peter Wason in the 1960s the task became well known after a series of studies was described in the early textbook on reasoning published by Wason and Johnson-Laird (1972). Studies of this task are generally divided between those using abstract problem materials and those using concrete or thematic material.

A typical abstract version of the task is the following.

There are four cards lying on a table. Each has a capital letter on one side and a single figure number on the other side. The visible sides of the cards are as follows:

A D 3 7

The following statement applies to these four cards and may be true or false:

If there is an A on one side of the card, then there is a 3 on the other side of the card.

Your task is to decide which cards, and only which cards, would need to be turned over in order to check whether the rule is true or false.

Most people give the answer A alone, or A and 3. Neither is logically correct according to the analysis given by Peter Wason and accepted by most later authors in the field. Logically, the statement can only be false if there is a card with an A on one side and without a 3 on the other. For example, if the A is turned over and a 5 is on the back, we know the statement is false.

Because turning the A card could discover such a case, it is logically neces-sary to turn it. But by the same argument the 7 card must be turned as well: 7 is a number that it is not a 3, and discovering an A on the back would similarly disprove the statement. Very few people select this card, however.

What they often do instead is to choose the 3 card, which is not logically necessary. The statement says that As must have 3s on the back, but it does not say that 3s must have As on the back. So if you turn over the 3 and find an A or find a B it would be consistent with the statement either way. In fact, you cannot prove the statement true except by eliminating any possibility that would make it false.

The matching bias effect

Why do people make these logical errors on the Wason selection task?

Wason and Johnson-Laird (1972) suggested that people have a confirmation bias. There is a wide range of studies on cognitive and social psychology that suggest people may be biased to confirm their hypotheses (Klayman, 1995).

The idea is that people tend to look for information that will confirm their hypotheses rather than information that could refute or falsify them.

Such a bias could be important in science, since scientists generally agree that they should try to disprove theories in order to test them thoroughly. So how might confirmation bias explain the selection task findings? Wason suggested that people think that the statement would be true if a card were found with an A and a 3 on it. Because they have a confirmation bias, they turn over the A and the 3 cards trying to find this confirming case.

They overlook the 7 card because they are not focused on trying to find the disconfirming card that has an A and not a 3.

While plausible, this account was abandoned by Wason and others shortly after the publication of his 1972 book with Johnson-Laird. The reason was an experiment reported by Evans and Lynch (1973) that provided strong evidence for an alternative account, known as matching bias. Note that the cards people tend to choose, A and 3, are those that are explicitly named in the conditional statement (If there is an A then there is a 3). What if people are simply matching their card choices to these named values? How could we tell if they were doing this, rather than looking for confirmation as Wason suggested? The answer requires a change to the presentation of the task.

Suppose we introduce a negative into the conditional statement as follows:

If there is an A on one side of the card, then there is not a 3 on the other side of the card.

The instructions are the same as before. Now what will people choose? If they have a confirmation bias, they should choose the A and the 7 cards, in order to discover a card that has an A on one side and does not have a 3 on the other. If they have a matching bias, on the other hand, they choose A and 3 in order to match the cards to the named items. Note that this is now the logically correct answer, as an A3 card would disprove the statement. The results of the Evans and Lynch study were decisively in favour of the match-ing bias. In fact once the effects of matchmatch-ing were controlled, there was no evidence of confirmation bias at all in their study. The effect has been repli-cated many times in subsequent studies using a variety of tasks and linguistic formats (Evans, 1998).

Many researchers in the field were quite disconcerted by this finding when it appeared. Matching bias seemed to make participants in these experi-ments look rather foolish. How could they ignore the logical reasoning instructions and make such a superficial response? After many years of research, summarized by Evans (1998), the nature of matching bias became a lot clearer, although there is still some dispute as to its exact cause. There is strong evidence to suggest that people only think about the matching cards.

If people are asked, in a computer presentation of the task, to point with a mouse at cards they are thinking of choosing, for example, most point little if at all at the 7 card. It is as though the matching bias acts as a kind of preconscious filter, drawing people’s attention to the A and 3 cards. (Of course, the actual letters and numbers given vary for different participants.) When people are asked to “think aloud” on the selection task, it becomes apparent that they are engaged in reasoning and that they do think about the hidden sides of the cards. But once again they focus their attention on the matching values that might be on these hidden sides. With the affirmative conditional – If A then 3 – for example, they might well say that they are turning over the A card, because a 3 on the back would prove the statement true. With the negative statement – If A then not 3 – they say they need to turn the A card because a 3 on the back would prove the statement false. In either case they think only about the matching cards and end up finding a justification for choosing them.

In the past few years we have learned that matching bias is strongly linked to problems in understanding implicit negation. It seems that the difficulty in choosing the 7 card is due to the fact that people have to interpret the 7 as

“not a 3”. In experiments where the mismatching cards are described explicitly, for example as “not A” or “not 3”, the matching bias effect has been shown to disappear completely (Evans, 1998). In spite of this strong evidence, there is a rival account of matching bias in terms of expected information gain (Oaksford & Chater, 1998). The argument here is that people are prone to choose information that is generally informative in

everyday life, and negative information is generally less informative than positive. Evidence for a general positivity bias in thinking and hypothesis testing is quite widespread (Evans, 1989) and other theorists have also argued such a bias reflects a process that would normally be adaptive in everyday life (Klayman & Ha, 1987).

Do realistic materials “debias” reasoning?

Psychologists use the rather ugly word “debias” to refer to factors that remove cognitive biases. Experiments described by Wason and Johnson-Laird (1972) led to a popular hypothesis (now seen as greatly oversimpli-fied) that realistic problem materials facilitate reasoning performance. Of course, we could argue as to whether realistic content debiases performance or whether abstract material biases it! Let us start by examining a version of the Wason selection task that is known to be very easy: the “drinking-age problem” first reported by Griggs and Cox (1982).

Imagine you are a police officer observing people drinking in a bar. You need to check that they are obeying the following rule:

If a person is drinking beer, then that person must be over 18 years of age.

There are four cards, each representing an individual drinking in the bar.

One side shows what beverage they are drinking and the other side shows their age. The four exposed sides of the cards are as follows:

Drinking Drinking 22 years 16 years

Beer Coke of age of age

Which cards would you need to turn over in order to find out whether or not the rule is being obeyed?

These cards are laid out in the same logical order as for the abstract selection task discussed earlier. Hence, the first and last cards are again the correct choices. You should check the person drinking beer and the person who is 16 years of age. The great majority of participants do precisely that.

They get this problem right and they show no evidence of matching bias.

What is the difference between this problem and the original selection task? Actually, there are several. The problem is “realistic”. It also has a context – the police officer scenario. Brief though it is, this context is critical to the facilitation. If the task is presented without an introductory context, performance is little better than on the abstract version. The logic of the problem is also subtly changed. The standard task asks you to decide whether the rule is true or false. In the drinking-age problem you have to

decide whether or not the rule is obeyed. This turns out to be necessary but not sufficient for the full facilitation effect. An abstract task that asks about rules being obeyed does not facilitate, but the benefits of realism are reduced if the task asks for a true/false decision.

You might think that the problem facilitates because people have direct real-world knowledge of drinking-age laws and simply know from experi-ence that underage drinkers are the ones to worry about. However, this is not the correct explanation. The conditional statement in the drinking-age problem is a permission rule. You need to fulfil a condition (over 18) in order to have permission to do something (drink beer). Other problems with permission rules work equally well, even where people have no direct experience of these rules. Consider the following problem – adapted from Manktelow and Over (1991):

You are a company manager. Your firm is trying to increase business by offering free gifts to people who spend money in its shops. The firm’s offer is

If you spend more than £100, then you may take a free gift.

You have been brought in because you have been told that in one of the firm’s shops the offer has run into a problem: you suspect that the store has not given some customers what they were entitled to. You have four receipts in front of you showing on one side how much a customer spent and on the other whether they took a gift. The exposed sides show: