## Figure 172

Performance on the Linda problem in the frequentist and control conditions. Data from Fiedler (1988).

The participants were then asked to determine the probability that Steve was a farmer, pilot, doctor, or librarian. As expected, many people chose librarian as a high-probability job for Steve, because he is a good match to the stereotype for this occupation.

Kahneman and Tversky (1973) carried out a study in which use of the representativeness heuristic produced faulty assessments of probability. The participants were provided with a brief description, which they were told had been selected at random from a total of 100 descriptions. Half of the participants were told that the total consisted of descriptions of 70 engineers and 30 lawyers, whereas the others were told that there were 70 lawyers and 30 engineers. Their task was to decide the probability that the person described was an engineer (or lawyer). A sample description was as follows (Kahneman & Tversky, 1973, p. 241):

Jack is a 45-year-old man. He is married and has four children. He is generally conservative, careful, and ambitious. He shows no interest in political and social issues and spends most of his free time on his many hobbies which include home carpentry, sailing, and mathematical puzzles.

The participants decided that there was a .90 probability that Jack was an engineer, and this was so regardless of whether most of the 100 descriptions were of lawyers or engineers. Thus, the participants did not take base-rate information (i.e., the 70:30 split of descriptions) into account.

The representativeness heuristic is also used in a more striking way to produce what is known as the conjunction fallacy. This is the mistaken belief that a conjunction of two events (A and B) is more likely than one of the two events (A or B). Tversky and Kahneman (1983) informed their participants that Linda was a former student activist, very intelligent, single, and a philosophy graduate. They then estimated the likelihood that Linda was a bank teller, a feminist, or a feminist bank teller. The estimated probability that Linda was a feminist bank teller was higher than the probability that she was a bank teller. This cannot be correct, because all feminist bank tellers belong to the larger category of bank tellers.

Some studies have obtained inconsistent evidence for the conjunction fallacy. Fiedler (1988) used two versions of the Linda problem. Of those participants who had to decide whether it was more likely that Linda was a bank teller or a feminist bank teller, 75% incorrectly chose the latter alternative, and so showed the conjunction fallacy (see Figure 17.2). However, other participants were given a frequentist version of the problem. They were asked to estimate how many out of 100 Lindas would be bank tellers and how many would be feminist bank tellers. In this condition, 75% of the participants decided correctly that more of them would be bank tellers.

### Availability heuristic

Tversky and Kahneman (1974) found that people often make use of the availability heuristic. This involves estimating the frequencies of events on the basis of how easy or difficult it is to retrieve relevant information from long-term memory. Tversky and Kahneman (1974) asked participants the following question:

If a word of three letters or more is sampled at random from an English text, is it more likely that the word starts with "r" or has "r"as its third letter?

Tversky and Kahneman (1974) found that most participants reported that a word starting with "r" was more likely to be picked out at random than a word with "r" in its third position. In reality, the reverse is the case. However, words starting with "r" can be retrieved more readily from memory (i.e., are more available) than words with "r" as their third letter. As a result, participants make the wrong judgement about the relative frequency of the two classes of words.

In this case, availability was based on the effectiveness of retrieval of instances from long-term memory. Availability can also be based on frequency of occurrence. In other words, we tend to recall those things that have been encountered most frequently in the past. This strategy often leads to effective judgements. However, availability can also be affected by the relative salience of instances, i.e., happenings or objects that have been encountered recently or have become salient for some reason can be temporarily more available. If you are a US citizen trying to decide where to go on holiday, and there is a sudden rash of terrorist incidents in Europe against US citizens, it is highly likely that you will be swayed into taking a holiday in the United States (even though the probability of getting killed in, say, Florida may be comparable to Europe or higher). Lichtenstein et al. (1978) have shown how causes of death attracting more publicity (e.g., murder) are judged more likely than those attracting less publicity (e.g., suicide), contrary to the true state of affairs.

An issue that is very relevant to the use of the availability heuristic concerns the strategies that people use to judge the frequency of events. Brown (1995) presented his participants with category-exemplar pairs (e.g., Country-Greece). Each category was presented a number of times, and it was either accompanied by the same exemplar each time (same context) or by a different exemplar (different context). The task was to decide how frequently each category name had been presented, and then to indicate the strategy that had been used. About 60% of the responses produced by different-context participants were based on enumeration (retrieving and counting the relevant items), whereas 69% of the responses produced by same-context participants were uninformative (e.g., "There weren't too many of those"). The implication of these findings is that availability is merely one among several strategies for estimating event frequency.

### Support theory

Tversky and Koehler (1994) put forward a support theory of subjective probability, which was subsequently developed by Rottenstreich and Tversky (1997). The key insight lying behind this theory is that any given event may seem more or less likely depending on the way in which it is described, and so we must distinguish between events and descriptions of events. For example, you would undoubtedly argue that the probability that you will die on your next summer holiday is very low indeed. However, the probability of that event occurring might seem somewhat higher if it were described as follows: "What is the probability that you will die on your next summer holiday from a disease, a sudden heart attack, an earthquake, terrorist activity, a civil war, a car accident, a plane crash, or from any other cause?" According to support theory, "Probability judgements are attached not to events but to descriptions of events, the judged probability of an event depends on the explicitness of its description" (Tversky & Koehler, 1994, p. 548).

The most striking prediction of support theory is that a more explicit description of an event will typically be regarded as having greater subjective probability than precisely the same event described in less explicit terms. Why is this prediction made? There are two main reasons:

1. An explicit description may draw attention to aspects of the event that are less obvious in the non-explicit description.

2. Memory limitations may mean that people do not remember all of the relevant information if it is not supplied.

Evidence consistent with support theory was provided by Johnson, Hershey, Meszaros, and Kunreuther (1993). Some participants were offered hypothetical health insurance covering hospitalisation for any reason, whereas others were offered health insurance covering hospitalisation for any disease or accident. These offers are the same, but participants were prepared to pay a higher premium in the latter case. Presumably the explicit references to disease and accident made it seem more likely that hospitalisation would be required, and so increased the value of being insured.

It might seem reasonable to assume that the phenomenon of higher subj ective probability for an event when it is explicitly described would not be found among those possessing relevant expertise. After all, experts provided with a non-explicit description can presumably fill in the details from their own knowledge. In fact, however, the phenomenon has proved to be surprisingly robust. For example, Redelmeier, Koehler, Liberman, and Tversky (1995) presented doctors at Stanford University with a description of a woman suffering from abdominal pain. Half of them were asked to decide the probabilities of two specified diagnoses (gastroenteritis and ectopic pregnancy) and of a residual category of everything else. The other half assigned probabilities to five specified diagnoses (including gastoenteritis and ectopic pregnancy) and the residual category of everything else. The key comparison was between the subjective probability of the residual category for the former group and the combined probabilities of the three additional diagnoses plus the residual category in the latter group. The former probability was .50, and the latter probability was . 69, indicating that subjective probabilities are higher for explicit descriptions even with experts.

In sum, support theory provides an interesting development of earlier ideas about heuristics. More specifically, some of the assumptions within support theory extend the notion of an availability heuristic in various ways.

### Overall evaluation

Tversky, Kahneman and others have shown that several general heuristics or rules of thumb (e.g., representativeness heuristic; availability heuristic) underlie judgements in many different contexts. Considerable research has been carried out on these biases, and they seem to be of great practical importance. Heuristics are also of relevance in understanding aspects of human reasoning (see Chapter 16).

Gigerenzer (1996) claimed that there are five main limitations of the theoretical approach adopted by Kahneman and Tversky (e.g., 1996). First, Gigerenzer (1996) claimed that Kahneman and Tversky had failed to provide process models that specified in detail when and how the various heuristics are used. According to Gigerenzer (1996, p. 594), "The two major surrogates [substitutes] for modeling cognitive processes have been (a) one-word-labels such as representativeness that seem to be traded as explanations, and (b) explanations by redescription." In other words, we have very limited understanding of what is involved in use of these heuristics.

Second, Gigerenzer (1996) argued that Kahneman and Tversky generally focus on the statistical principles relevant to a problem at the expense of any proper consideration of its real-world content. The dangers of doing this can be seen with reference to the taxi-cab problem discussed earlier. Tversky and Kahneman (1980) claimed there was only one correct answer to this problem. In contrast, Birnbaum (1983) focused on the cognitive processes that might be used by an eyewitness. He found that there are several possible answers to the taxi-cab problem, depending on the theory of eyewitness processing that one favours. For example, the eyewitness was 80% correct when asked to identify a series of cabs, 50% of which were Blue and 50% of which were Green. In those circumstances, there was no advantage in systematically saying Blue or Green when the eyewitness was unsure. However, when 85% of the cabs are Green and only 15% are Blue, it would have made sense for the eyewitness to say Green whenever he/she was unsure.

Third, most of the problems used by Kahneman and Tversky involved the presentation of probability information, and led to apparently error-prone judgements. However, as we have seen, people are sometimes more likely to follow logical or statistical principles when the relevant numerical information is represented by frequencies rather than by probabilities (e.g., Cosmides & Tooby, 1996; Fiedler, 1988). Gigerenzer (1996) has obtained evidence that this occurs more often when absolute frequencies (actual numbers of events or individuals falling into different categories) are used rather than relative frequencies or probabilities. Why is there this difference? According to Gigerenzer (1996, p. 594), "cognitive algorithms [computational procedures] designed to do Bayesian reasoning with absolute frequencies. involve fewer steps of mental computation." However, it should be noted that the use of absolute frequencies does not usually lead to full use of base-rate information (see Gigerenzer, 1996).

Gigerenzer and Hoffrage (1999) developed the theoretical position of Gigerenzer (1996). They emphasised the notion of natural sampling, which is "the process of encountering instances in a population sequentially" (Gigerenzer & Hoffrage, 1999, p. 425). Natural sampling is what typically happens in everyday life, and it allows us to work out absolute frequencies of different kinds of events. According to Gigerenzer and Hoffrage (1999, p. 430), "Humans seem to be developmentally and evolutionarily prepared to handle natural frequencies. In contrast, many of us go through a considerable amount of mental agony to learn to think in terms of fractions, percentages, and other forms of normalised counts."

Fourth, Gigerenzer (1996) argued that some of the biases in judgements reported in the literature owe much to misunderstandings of parts of the problem by the participants. For example, consider the Linda problem discussed earlier. Gigerenzer and others have found that between 20% and 50% of people interpret "Linda is a bank teller" as implying that she is not active in the feminist movement (see Gigerenzer, 1996). Thus, the conjunction fallacy can be obtained for reasons other than use of the representativeness heuristic.

Fifth, there has been a controversy about whether it makes sense to assign probabilities to unique events, as is done in many of the problems used by Kahneman and Tversky. They interpret probability as a subjective measure of belief, and so are willing to attach a probability value to a unique event. In contrast, Gigerenzer and other frequentists interpret probability as being determined by the relative frequencies of different events over time, and so argue that it is meaningless to assign probability to unique events. The complex issues here are discussed by Kahneman and Tversky (1996) and by Gigerenzer (1996).

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