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Base-Rate Respect: from Ecological Rationality to Dual Processes

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Base-Rate Respect: from Ecological Rationality to Dual Processes BEHAVIORAL AND BRAIN SCIENCES (2007) 30, 241–297 Printed in the United States of America DOI: 10.1017/S0140525X07001653 Base-rate respect: From ecological rationality to dual processes Aron K. Barbey Cognitive Neuroscience Section, National Institute of Neurological Disorders and Stroke, Bethesda, MD 20892-1440 [email protected] Steven A. Sloman Cognitive and Linguistics Science, Brown University, Providence, RI 02912 [email protected] http://www.cog.brown.edu/sloman/ Abstract: The phenomenon of base-rate neglect has elicited much debate. One arena of debate concerns how people make judgments under conditions of uncertainty. Another more controversial arena concerns human rationality. In this target article, we attempt to unpack the perspectives in the literature on both kinds of issues and evaluate their ability to explain existing data and their conceptual coherence. From this evaluation we conclude that the best account of the data should be framed in terms of a dual- process model of judgment, which attributes base-rate neglect to associative judgment strategies that fail to adequately represent the set structure of the problem. Base-rate neglect is reduced when problems are presented in a format that affords accurate representation in terms of nested sets of individuals. Keywords: Base-rate neglect; Bayesian reasoning; dual process theory; nested set hypothesis; probability judgment 1. Introduction (e.g., a positive mammography). Consider the following Bayesian inference problem presented by Gigerenzer and Diagnosing whether a patient has a disease, predicting Hoffrage (1995; adapted from Eddy 1982): whether a defendant is guilty of a crime, and other every- The probability of breast cancer is 1% for a woman at age forty day as well as life-changing decisions reflect, in part, the who participates in routine screening [base-rate]. If a woman decision-maker’s subjective degree of belief in uncertain has breast cancer, the probability is 80% that she will get a events. Intuitions about probability frequently deviate dra- positive mammography [hit-rate]. If a woman does not have matically from the dictates of probability theory (e.g., Gilo- breast cancer, the probability is 9.6% that she will also get a vich et al. 2002). One form of deviation is notorious: positive mammography [false-alarm rate]. A woman in this people’s tendency to neglect base-rates in favor of specific age group had a positive mammography in a routine screening. case data. A number of theorists (e.g., Brase 2002a; Cos- What is the probability that she actually has breast cancer? _%. mides & Tooby 1996; Gigerenzer & Hoffrage 1995) have (Gigerenzer & Hoffrage 1995, p. 685) argued that such neglect reveals little more than exper- imenters’ failure to ask about uncertainty in a form that naı¨ve respondents can understand – specifically, in the form of a question about natural frequencies. The brunt ARON BARBEY is a doctoral student of Lawrence of our argument in this target article is that this perspec- W. Barsalou in the Cognition and Development tive is far too narrow. After surveying the theoretical per- Program at Emory University. His research ad- spectives on the issue, we show that both data and dresses the cognitive and neural bases of human conceptual considerations demand that judgment be learning and inference. Upon graduation, he understood in terms of dual processing systems: one that will join the Cognitive Neuroscience Section of is responsible for systematic error and another that is the National Institute of Neurological Disorders capable of reasoning not just about natural frequencies, and Stroke as a post-doctoral fellow under the but about relations among any kind of set representation. supervision of Jordan Grafman. Base-rate neglect has been extensively studied in the context of Bayes’ theorem, which provides a normative stan- STEVEN SLOMAN is Professor of Cognitive and dard for updating the probability of a hypothesis in light of Linguistic Sciences at Brown University. He is new evidence. Research has evaluated the extent to which the author of Causal Models: How People Think intuitive probability judgment conforms to the theorem About the World and Its Alternatives (Oxford by employing a Bayesian inference task in which the University Press, 2005). He has also authored respondent is presented a word problem and has to infer numerous publications in the areas of reasoning, the probability of a hypothesis (e.g., the presence versus categorization, judgment, and decision making. absence of breast cancer) on the basis of an observation # 2007 Cambridge University Press 0140-525x/07 $40.00 241 Downloaded from https:/www.cambridge.org/core. University of Basel Library, on 30 May 2017 at 21:05:04, subject to the Cambridge Core terms of use, available at https:/www.cambridge.org/core/terms. https://doi.org/10.1017/S0140525X07001756 Barbey & Sloman: Base-rate respect According to Bayes’ theorem,1 the probability that the answer when presented with single-event probabilities. patient has breast cancer given that she has a positive Cosmides and Tooby then transformed the single-event mammography is 7.8%. Evidence that people’s judgments probabilities into natural frequencies, resulting in a on this problem accord with Bayes’ theorem would be con- remarkably high proportion of Bayesian responses: 72% sistent with the claim that the mind embodies a calculus of of respondents generated the Bayesian solution, support- probability, whereas the lack of such a correspondence ing the authors’ conclusion that Bayesian inference would demonstrate that people’s judgments can be at var- depends on the use of natural frequencies. iance with sound probabilistic principles and, as a conse- Gigerenzer (1996) explored whether physicians, who quence, that people can be led to make incoherent frequently assess and diagnose medical illness, would decisions (Ramsey 1964; Savage 1954). Thus, the extent demonstrate the same pattern of judgments as that of clini- to which intuitive probability judgment conforms to the cally untrained college undergraduates. Consistent with normative prescriptions of Bayes’ theorem has impli- the judgments drawn by college students (e.g., Gigerenzer cations for the nature of human judgment (for a review & Hoffrage 1995), Gigerenzer found that the sample of 48 of the theoretical debate on human rationality, see Stano- physicians tested generated the Bayesian solution in only vich 1999). In the case of Eddy’s study, fewer than 5% of 10% of the cases under single-event probability formats, the respondents generated the Bayesian solution. whereas 46% did so with natural frequency formats. Phys- Early studies evaluating Bayesian inference under single- icians spent about 25% more time on the single-event event probabilities also showed systematic deviations from probability problems, which suggests that they found Bayes’ theorem. Hammerton (1973), for example, found these problems more difficult to solve than problems pre- that only 10% of the physicians tested generated the sented in a natural frequency format. Thus, the physician’s Bayesian solution, with the median response approxi- judgments were consistent with those of non-physicians, mating the hit-rate of the test. Similarly, Casscells et al. suggesting that formal training in medical diagnosis does (1978) and Eddy (1982) found that a low proportion of not lead to more accurate Bayesian reasoning and that respondents generated the Bayesian solution: 18% in the natural frequencies facilitate probabilistic inference former and 5% in the latter, with the modal response in across populations. each study corresponding to the hit-rate of the test. All Further studies have demonstrated that the facilitory of this suggests that the mind does not normally reason effect of natural frequencies on Bayesian inference in a way consistent with the laws of probability theory. observed in the laboratory has the potential for improving the predictive accuracy of professionals in important real- world settings. Gigerenzer and his colleagues have shown, 1.1. Base-rate facilitation for example, that natural frequencies facilitate Bayesian However, this conclusion has not been drawn universally. inference in AIDS counseling (Gigerenzer et al. 1998), Eddy’s (1982) problem concerned a single event, the prob- in the assessment of statistical information by judges ability that a particular woman has breast cancer. In some (Lindsey et al. 2003), and in teaching Bayesian reasoning problems, when probabilities that refer to the chances of a to college undergraduates (Kuzenhauser & Hoffrage single event occurring (e.g., 1%) are reformulated and pre- 2002; Sedlmeier & Gigerenzer 2001). In summary, the sented in terms of natural frequency formats (e.g., 10 out reviewed findings demonstrate facilitation in Bayesian of 1,000), people more often draw probability estimates inference when single-event probabilities are translated that conform to Bayes’ theorem. Consider the following into natural frequencies, consistent with the view that mammography problem presented in a natural frequency coherent probability judgment depends on natural fre- format by Gigerenzer and Hoffrage (1995): quency representations. 10 out of every 1,000 women at age forty who participate in routine screening have breast cancer [base-rate]. 8 out of 1.2. Theoretical accounts every 10 women with breast cancer will get a positive mammo- graphy [hit-rate]. 95 out of every 990 women without breast Explanations of facilitation in Bayesian
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