Representativeness Heuristic and Conjunction Fallacy

REPRESENTATIVE CONJUNCTIONS

Research on categorization of objects and events (Mervis & Rosch, 1981; Rosch, 1978; Smith & Medin, 1981) has shown that information is commonly stored and processed in relation to mental models, such as prototypes and schemata. It is therefore natural and economical for the probability of an event to be evaluated by the degree to which that event is representative of an appropriate mental model (Kahneman & Tversky, 1972, 1973; Tversky & Kahneman, 1971, 1982). Because many of the results reported here are attributed to this heuristic, we first briefly analyze the concept of representativeness and illustrate its role in probability judgment.

Representativeness is an assessment of the degree of correspondence between a sample and a population, an instance and a category, an act and an actor or, more generally, between an outcome and a model. The model may refer to a person, a coin, or the world economy, and the respective outcomes could be marital status, a sequence of heads and tails, or the current price of gold. Representativeness can be investigated empirically by asking people, for example, which of two sequences of heads and tails is more representative of a fair coin or which of two professions is more representative of a given personality. This relation differs from other notions of proximity in that it is distinctly directional. It is natural to describe a sample as more or less representative of its parent population or a species (e.g., robin, penguin) as more or less representative of a superordinate category (e.g., bird). It is awkward to describe a population as representative of a sample or a category as representative of an instance.

When the model and the outcomes are described in the same terms, representativeness is reducible to similarity. Because a sample and a population, for example, can be described by the same attributes (e.g., central tendency and variability), the sample appears representative if its salient statistics match the corresponding parameters of the population. In the same manner, a person seems representative of a social group if his or her personality resembles the stereotypical member of that group. Representativeness, however, is not always reducible to similarity; it can also reflect causal and correlational beliefs (see, e.g., Chapman & Chapman, 1967; Jennings, Amabile, & Ross, 1982; Nisbett & Ross, 1980). A particular act (e.g., suicide) is representative of a person because we attribute to the actor a disposition to commit the act, not because the act resembles the person. Thus, an outcome is representative of a model if the salient features match or if the model has a propensity to produce the outcome.

Representativeness tends to covary with frequency: Common instances and frequent events are generally more representative than unusual instances and rare events. The representative summer day is warm and sunny, the representative American family has two children, and the representative height of an adult male is about 5 feet 10 inches. However, there are notable circumstances in which representativeness is at variance with both actual and perceived frequency. First, a highly specific outcome can be representative but infrequent. Consider a numeric variable, such as weight, that has a unimodal frequency distribution in a given population. A narrow interval near the mode of the distribution is generally more representative of the population than a wider interval near the tail. For example, 68% of a group of Stanford University undergraduates (N = 105) stated that it is more representative for a female Stanford student “to weigh between 124 and 125 pounds” than “to weigh more than 135 pounds.” However, 78% of a different group (N = 102) stated that among female Stanford students, there are more “women who weigh more than 135 pounds” than “women who weigh between 124 and 125 pounds.” Thus, the narrow modal interval (124–125 pounds) was judged to be more representative but less frequent than the broad tail interval (above 135 pounds).

Second, an attribute is representative of a class if it is very diagnostic; that is, if the relative frequency of this attribute is much higher in that class than in a relevant reference class. For example, 65% of the subjects (N = 105) stated that it is more representative for a Hollywood actress “to be divorced more than 4 times” than “to vote Democratic.” Multiple divorce is diagnostic of Hollywood actresses because it is part of the stereotype that the incidence of divorce is higher among Hollywood actresses than among other women. However, 83% of a different group (N = 102) stated that, among Hollywood actresses, there are more “women who vote Democratic” than “women who are divorced more than 4 times.” Thus, the more diagnostic attribute was judged to be more representative but less frequent than an attribute (voting Democratic) of lower diagnosticity. Third, an unrepresentative instance of a category can be fairly representative of a superordinate category. For example, chicken is a worse exemplar of a bird than of an animal, and rice is an unrepresentative vegetable, although it is a representative food.

The preceding observations indicate that representativeness is nonextensional: It is not determined by frequency and is not bound by class inclusion. Consequently, the test of the conjunction rule in probability judgments offers the sharpest contrast between the extensional logic of probability theory and the psychological principles of representativeness. Our first set of studies of the conjunction rule were conducted in 1974, using occupation and political affiliation as target attributes to be predicted singly or in conjunction from brief personality sketches (see Tversky & Kahneman, 1982, for a brief summary). The studies described in the present section replicate and extend our earlier work. We used the following personality sketches of two fictitious individuals, Bill and Linda, followed by a set of occupations and avocations associated with each of them.

Bill is 34 years old. He is intelligent but unimaginative, compulsive, and generally lifeless. In school, he was strong in mathematics but weak in social studies and humanities.

Bill is a physician who plays poker for a hobby.

Bill is an architect.

Bill is an accountant. (A)

Bill plays jazz for a hobby. (J)

Bill surfs for a hobby.

Bill is a reporter.

Bill is an accountant who plays jazz for a hobby. (A&J)

Bill climbs mountains for a hobby.

Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

Linda is a teacher in elementary school.

Linda works in a bookstore and takes Yoga classes.

Linda is active in the feminist movement. (F)

Linda is a psychiatric social worker.

Linda is a member of the League of Women Voters.

Linda is a bank teller. (T)

Linda is an insurance salesperson.

Linda is a bank teller and is active in the feminist movement. (T&F)

These descriptions separate resemblance from probability. Bill may seem more like an accountant who plays jazz than a jazz player considered alone; Linda may seem more like a feminist bank teller than a bank teller considered alone. But adding a condition narrows the set of possible cases. Every accountant who plays jazz belongs to the set of jazz players, and every feminist bank teller belongs to the set of bank tellers. A conjunction therefore cannot be more probable than either of its constituents.