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1 Wason selection task
Foreword
My interests in conditionals, cognitive biases, rationality and dual processes – in short, the themes which have dominated my entire research career – all have their origins in my earliest work in the 1970s. It begins with my PhD work (1969–1972) under the inspirational supervision of Peter Wason and is a tale of much serendipity. I tried to introduce some novelty into the study of conditional reasoning and in the process discovered some phenomena that were in no way anticipated and led to all manner of unexpected consequences. These were developed initially using the Wason selection task (Wason, 1966) the famous problem which consumed the interest of my supervisor during the time of my PhD studies. At the time, both Wason and Johnson-Laird were intensively studying the Wason selection task and preparing their influential book on the psychology of reasoning (Wason and Johnson-Laird, 1972).
When I started work the selection task had only been studied in its standard abstract form. In a typical example, participants were told that four cards had been selected from a pack where each has a letter on one side and a number on the other. They are given a conditional statement such as
If the letter on the card is an A, then the number on the card is a 3
They are then shown four cards lying on a table whose exposed sides show the values
A D 3 7
The instruction is to decide whether the conditional statement is true or false of the four cards. Participants are invited to select those cards, and only those cards, which need to be turned over to discover whether it is true or false.
Wason insisted that the correct answer was to select the A and 7 cards because only a card with an A on one side and a number other than a 3 on the other could allow one to falsify the statement (much later this was to be disputed, e.g. by Oaksford and Chater, 1994). But he observed this response in 10% or fewer of his participants, with the common answers being A alone or A and 3. He was convinced that this indicated serious irrationality in his participants and was engaged in various “therapeutic” experiments to try to cure them (see Wason and Johnson-Laird, 1972). However, during my time with him at UCL two discoveries were to change this picture dramatically. The first was that when realistic content was introduced into the problem it could become very much easier to solve (Johnson-Laird, Legrenzi, and Legrenzi, 1972; Wason and Shapiro, 1971). My colleague Diana Shapiro, a research assistant at that time, was the first to find this. The second was my own discovery of “matching bias” in the abstract version of the task.
When I started out, I wanted to work on something close – but not too close – to what Wason was doing and so chose to focus on conditional reasoning, with tasks other than the selection task. One of these was the conditional inference task, which has become more and more popular and is currently quite dominant in the psychology of reasoning, 40 years on! However, the current interest is largely in conditional inference with realistic content. My own studies at this time used strictly abstract materials, with statements linking letters and numbers. There are four such inferences that may be drawn from a conditional statement, illustrated below with abstract materials:
Modus Ponens (MP) | If A then 3; A therefore 3 |
Denial of the Antecedent (DA) | If A then 3; not-A, therefore not-3 |
Affirmation of the Consequent (AC) | If A then 3; 3 therefore A |
Modus Tollens (MT) | If A then 3; not-3 therefore not-A |
Two of these inferences – MP and MT – are classically valid and two – DA and AC – are fallacies. My early studies established some basic findings such as (a) MP is very frequently endorsed but MT much less so, (b) both DA and AC are often endorsed despite being logically invalid (Evans, 1977a; 1982).
The framework for these studies was what is now referred to as the deduction paradigm (Evans, 2002, reproduced in Chapter 6). The assumptions on which this paradigm was based are much easier to see in hindsight than at the time, when it was just the way we all thought about things. Standard binary logic – the logic of truth and falsity – was the undisputed normative theory of reasoning. People ought to be logical, and if they were not, they were irrational. Wason’s main argument in his publications of this time was essentially that people were irrational, based on their failure to solve this famous reasoning problems, not just the selection task but also the “2 4 6” problem (Wason, 1968a) and later the THOG problem (Wason and Brooks, 1979). I became and remained very interested in the study of cognitive biases, although I think I was always less judgemental than Wason on the question of whether these implied irrationality. In fact, my approach in these early years was highly descriptive and closely related to the current vogue for mathematical modelling. In fact, I published the first stochastic model of reasoning (Evans, 1977b) which lay uncited and unnoticed for many years as the fashion for deterministic flow chart models swept it aside. (It was some 30 years before this approach to the selection task was to be taken up and implemented in much greater detail by Klauer, Stahl, and Erdfelder, 2007).
The real serendipity came from my adoption of what later became known as the negations paradigm. Rather than just study the affirmative conditional I systematically varied the presence of negations. Hence there were four conditional statements to study of the following form, shown with examples using typical lexical content:
AA If p then q | If the letter is A then the number is 6 |
AN If p then not-q | If the letter is P then the number is not 3 |
NA If not-p then q | If the letter is not J then the number is 4 |
NN If not-p then not-q | If the letter is not H then the number is not 1 |
I have no clear recollection of why I decided to do this but I do know that the idea was entirely novel to me at the time. It was only much later that I discovered that a developmental psychologist called Roberge had published earlier studies using similar methods (e.g. Roberge, 1971). Fortunately for me he did not analyse the data in the same way and failed to discover the phenomena that I identified. I initially applied the method to the conditional inference task (Evans, 1972c; 1977a) but the big break came, when I used the negations paradigm with a different conditional reasoning problem, known as the truth table task. Wason (1966) had suggested that people have a “defective” truth table. (This is now the basis of the modern suppositional or probabilistic theory of conditionals, see Chapter 3). Standard logic assumes the material conditional, in which “if p then q” is equivalent in meaning to “either not-p or q”. This means that the conditional is always true except when the antecedent is true and the consequent false, known as the TF case. Here is an illustrative example
If it is a dog then it has a tail
cases
TT | A dog with a tail |
TF | A dog without a tail |
FT | Anything not a dog with a tail |
FF | Anything not a dog without a tail |
It seems clear enough that TT makes the conditional true and TF makes it false. But what of FT and FF? Would we say that cat with or without a tail would make it true that “If it is a dog then it has a tail”? Wason (1966) suggested that the statement seems irrelevant rather than true in such case (in philosophical logic this now corresponds with a theory of conditionals in which the truth value is void for these cases, see Adams, 1998; Edgington, 1995). His conjecture was supported by an early experiment of Johnson-Laird and Tagart (1969). I decided to follow this up using a slightly different method, but expanding the scope of study to include the negations paradigm. This turned out to be a life-changing decision!
In my experiment, participants were shown a set of cards showing coloured shapes and asked to pick out any which made the statement true (verification), and in a separate task to pick out ones which made it false (falsification). An AA conditional might be
If the shape is a triangle then it is yellow
On the verification task, participants typically picked a yellow triangle (TT) and selected all the non-yellow triangles on the falsification task (TF). However, in line with the defective truth table, non-triangular shapes were often ignored on both tasks, being irrelevant by implication. When negations were introduced, however, another pattern quite unexpectedly emerged on top of this. I noticed that people often picked out the colour and shape named in the statement, regardless of the presence of negations. For example, given an NA conditional:
If the shape is not a circle then the colour is green
People often picked out the green circle on the falsification task. This is logically FT, a case rarely selected for the AA sentence. On an NN statement such as
If the shape is not a square then the colour is not blue
People often selected the blue square, but sometimes on the verification and sometimes on the falsification task. Statistical analysis confirmed these “matching” cases were preferred when logical case was held constant across the four kinds of statement. I had discovered and named my first new cognitive bias – matching bias, as it has been known ever since.
Why was this a life – or at least career – defining event? The discovery of matching bias really led to everything else, in particular my heuristic-analytic theory of cognitive biases (Chapter 4) and the more general forms of dual process theory that I have explored later in my career. In this chapter 1 focus on how it led to some key developments in understanding the Wason selection task and beyond that to the early forms of dual process theory applied to that problem. I realised as soon as I had run the truth table experiment that matching bias might explain the typical choices on the abstract selection task, but decided to defer the experiment until my PhD was completed. It was the first I ran thereafter (Evans and Lynch, 1973). Wason had claimed that typical choices of A or A and 3 to be due to an irrational verification bias. But of course, I saw that matching could provide an alternative account: A and 3 are also the matching cards. I also realised that I could de-confound the matching and verification biases by applying the negations paradigm. For example, if we give the conditional statement for the task with a negation added (AN) as follows
If the letter on the card is an A, then the number on the card is not a 3
then the verification bias should predict that people still focus on the TT case by choosing an A together with a number not a 3, i.e. the 7 card. Matching bias predicts, however, that they should continue to choose A and 3 which are now the logically correct choices. The results of my study (Evans and Lynch, 1973) were decisive. There was massive evidence of matching bias and none for verification bias, once matching was controlled.
Peter Wason, good Popperian as he was, immediately conceded that his account of the selection task was wrong, even though he had by then written a number of papers and book founded upon it. However, when he and I discussed it, the results seemed at odds with another study in which participants descriptions of the reasons for their choices fitted with the Wason and Johnson-Laird view (Goodwin and Wason, 1972). This led to a collaboration which resulted in the earliest explicit dual process theory – and use of that term – in the psychology of reasoning. The paper is reproduced below (Wason and Evans, 1975) and was followed by another which supported the account offered (Evans and Wason, 1976). These are the only collaborative papers that we ever published.
Wason and Evans (1975) appears to be the first dual process paper in the psychology of reasoning, using the terms type 1 and 2 processes which both Stanovich and I prefer in our current writing (Evans and Stanovich, 2012). The theory was rudimentary and consisted mostly of the assertion of dissociation between the actual causes of behaviour the verbal explanations or introspections that participants offered, an idea to be made famous by a paper published a year later in Psychological Review by authors unconnected with our own programme (Nisbett and Wilson, 1977). Our specific proposal was that matching bias was the cause of card choices, but that participants offered logical sounding rationalisations of their choices. Hence, we also laid down an early marker in the literature concerning the unreliability of introspective reports. In view of the historical importance of this paper, it is reproduced in full. It should als...
