## The ‘Conjunction Fallacy’ Revisited: How Intelligent Inferences Look Like Reasoning Errors (1999)

Venue: | Journal of Behavioral Decision Making |

Citations: | 50 - 9 self |

### BibTeX

@ARTICLE{Hertwig99the‘conjunction,

author = {Ralph Hertwig and Gerd Gigerenzer},

title = {The ‘Conjunction Fallacy’ Revisited: How Intelligent Inferences Look Like Reasoning Errors},

journal = {Journal of Behavioral Decision Making},

year = {1999},

volume = {12},

pages = {275--305}

}

### Years of Citing Articles

### OpenURL

### Abstract

Findings in recent research on the `conjunction fallacy ' have been taken as evidence that our minds are not designed to work by the rules of probability. This conclusion springs from the idea that norms should be content-blind Ð in the present case, the assumption that sound reasoning requires following the conjunction rule of probability theory. But content-blind norms overlook some of the intelligent ways in which humans deal with uncertainty, for instance, when drawing semantic and pragmatic inferences. In a series of studies, we ®rst show that people infer nonmathematical meanings of the polysemous term `probability' in the classic Linda conjunction problem. We then demonstrate that one can design contexts in which people infer mathematical meanings of the term and are therefore more likely to conform to the conjunction rule. Finally, we report evidence that the term `frequency ' narrows the spectrum of possible interpretations of `probability ' down to its mathematical meanings, and that this fact Ð rather than the presence or absence of `extensional cues ' Ð accounts for the low proportion of violations of the conjunction rule when people are asked for

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Citation Context ...capacity for semantic and pragmatic inferences. To illustrate this argument, let us consider the classical problem designed to demonstrate that people violate the conjunction rule: the Linda problem (=-=Tversky and Kahneman, 1983-=-). In this problem, participants read: `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 so... |

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Citation Context ... of participants who judged T&F to be more probable than T were in error because they violated the conjunction rule. Applied to the Linda problem, the conjunction rule is a narrow norm in two senses (=-=Gigerenzer, 1996-=-). First, the norm is applied in a content-blind way, that is, it assumes that judgments about what counts as sound reasoning may ignore content and context (Gigerenzer and Murray, 1987, Chapter 5). F... |

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Citation Context ... median of 87%. The median proportion of conjunction violations in the frequency estimation representation of the Linda problem in the studies reviewed here is 17% (22%, 17% in Experiments 1 and 2 of =-=Fiedler, 1988-=-; 85% in Experiment 1 of Jones et al., 1995, and 0% and 13% in our Studies 3 and 4). Thus, the median proportion of violations for the probability ranking representation is 70 percentage points higher... |

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Citation Context ...r y, you should do so independently of the other alternatives in the choice set. Are violations of Property a irrational? Not necessarily: our social values can sometimes con¯ict with this principle (=-=Sen, 1993-=-). Consider Property a in the context of social politics at a dinner party. At dessert, it looks as if there are fewer pastries than there are people. By the time the dessert tray gets to you, there i... |

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Citation Context ..., that is, when participants judge a series of events rather than a single event. Finally, Bayesian reasoning improves in lay people (Cosmides & Tooby, 1996; Gigerenzer & Hoffrage, 1995) and experts (=-=Hoffrage & Gigerenzer, 1998-=-) when Bayesian problems are presented in natural frequencies (i.e., absolute frequencies obtained by natural sampling) rather than in a single-event probability format. Natural frequencies have also ... |

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Citation Context ...conjunction problems. In the Linda problem, application of 1 There is a rich research tradition on how people map linguistic probability terms onto numerical equivalents (for an excellent review, see =-=Budescu and Wallsten, 1995-=-). We, in contrast, focus on how the single term `probability' is mapped onto its mathematical and nonmathematical meanings. Copyright # 1999 John Wiley & Sons, Ltd. Journal of Behavioral Decision Mak... |

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Citation Context ...f several authors that content and pragmatic context are indeed relevant from the perspective of conversational principles in the Linda problem and other conjunction problems (e.g. Adler, 1984, 1991; =-=Dulany and Hilton, 1991-=-; Hilton, 1995; Politzer and Noveck, 1991). In addition, our account contributes to an explanation of the empirical ®nding that representing problems in terms of absolute frequencies rather than proba... |

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Citation Context ...gmatic context are indeed relevant from the perspective of conversational principles in the Linda problem and other conjunction problems (e.g., Adler, 1984, 1991; Dulany & Hilton, 1991; Hilton, 1995; =-=Politzer & Noveck, 1991-=-). In addition, our account contributes to an explanation of the empirical finding that representing problems in terms of absolute frequencies rather than probabilities largely reduces the conjunction... |

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Citation Context ...ations. Although Tversky and Kahneman (1983) classi®ed problems by content according to whether they included `representative' or `causal' conjunctions ( for research on causal conjunctions, see e.g. =-=Ahn and Bailenson, 1996-=-; Fabre, Caverni and Jungermann, 1995; ThuÈ ring and Jungermann, 1990), the representativeness explanation does not predict di€erent proportions of conjunction violations for the two types of contents... |

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Citation Context ...not even need to read the description of Linda. All that counts are the terms “probability” and “and,” which the conjunction rule interprets as mathematical probability and logical AND, respectively (=-=Gigerenzer & Regier, 1996-=-; Hertwig, 1995). In addition, probability theory is imposed as a norm for a single event (whether Linda is a bank teller). This would be considered misguided by those statisticians who hold that prob... |

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Citation Context ...participants’ probability judgments in conjunction problems. In the Linda problem, application of the representativeness heuristic has been characterized as a “similarity” or “typicality” assessment (=-=Shafir, Smith, & Osherson, 1990-=-; Smith & Osherson, 1989; Tversky & Kahneman, 1983). 1 There is a rich research tradition on how people map linguistic probability terms onto numerical equivalents (for an excellent review, see Budesc... |

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Citation Context ...ing that in between-subjects comparisons, the e€ect of base rate is too small . . . In within-subject comparisons, however, subjects use the base rate, and the evidence for a ``fallacy'' disappears' (=-=Varey, Mellers, and Birnbaum, 1990-=-, p. 623). Birnbaum (1982) gave a range-frequency analysis of why between-subjects comparisons lead to paradoxical conclusions: They confound the stimulus and the context by allowing the stimulus to e... |

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Citation Context ...percentage points (medium effect: ø = 0.3). Hertwig and Chase attributed this finding to the fact that people apply combination rules in estimation but not in ranking (for their detailed account, see =-=Hertwig & Chase, 1998-=-, pp. 324–329). Does this finding extend to the frequency representation, that is, do more people follow the conjunction rule in frequency estimates than in rankings? We know of only one study that as... |

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Citation Context ...9)s278 Journal of Behavioral Decision Making Vol. 12, Iss. No. 4 the representativeness heuristic has been characterized as a `similarity' or `typicality' assessment (Sha®r, Smith and Osherson, 1990; =-=Smith and Osherson, 1989-=-; Tversky and Kahneman, 1983). SEMANTIC INFERENCE BY SOCIAL RATIONALITY The mind has to decide which of the various meanings of the term `probability' to apply in any given context. Which of the vario... |

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Citation Context ...pective of a conversational analysis, the crux of the Linda problem is that the `initial personality sketch would be an uncooperative, because irrelevant, contribution under a purely formal reading' (=-=Adler, 1991-=-, p. 255). Having not been informed that the relevance maxim is suspended, the participant tries to preserve the relevance maxim. In Study 1, we identi®ed one way in which the participant can do this ... |

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Citation Context ... to the arguments of several authors that content and pragmatic context are indeed relevant from the perspective of conversational principles in the Linda problem and other conjunction problems (e.g. =-=Adler, 1984-=-, 1991; Dulany and Hilton, 1991; Hilton, 1995; Politzer and Noveck, 1991). In addition, our account contributes to an explanation of the empirical ®nding that representing problems in terms of absolut... |

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How do we tell an association from a rule
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(Show Context)
Citation Context ...not even need to read the description of Linda. All that counts are the terms `probability' and `and', which the conjunction rule interprets as mathematical probability and logical AND, respectively (=-=Gigerenzer and Regier, 1996-=-; Hertwig, 1995). In addition, probability theory is imposed as a norm for a single event (whether Linda is a bank teller). This would be considered misguided by those statisticians who hold that prob... |

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Citation Context ... than nouns as paraphrases of “probability”; for the purpose of comparison, we transformed adjective paraphrases into appropriate nouns. Conjunction Violations Consistent with previous results (e.g., =-=Teigen, Martinussen, & Lund, 1996-=-), 15 of the 18 participants (83%) violated the conjunction rule in the Linda problem. Did this happen because nonmathematical meanings of “probability” are inferred under the relevance maxim (Predict... |