Psychological Review Memory and Representativeness Pedro Bordalo, Katherine Coffman, Nicola Gennaioli, Frederik Schwerter, and Andrei Shleifer Online First Publication, August 27, 2020. http://dx.doi.org/10.1037/rev0000251 CITATION Bordalo, P., Coffman, K., Gennaioli, N., Schwerter, F., & Shleifer, A. (2020, August 27). Memory and Representativeness. Psychological Review. Advance online publication. http://dx.doi.org/10.1037/rev0000251 Psychological Review © 2020 American Psychological Association 2020, Vol. 2, No. 999, 000 ISSN: 0033-295X http://dx.doi.org/10.1037/rev0000251 Memory and Representativeness Pedro Bordalo Katherine Coffman University of Oxford Harvard Business School Nicola Gennaioli Frederik Schwerter Bocconi University University of Cologne Andrei Shleifer Harvard University We explore the idea that judgment by representativeness reflects the workings of memory. In our model, the probability of a hypothesis conditional on data increases in the ease with which instances of that hypothesis are retrieved when cued with the data. Retrieval is driven by a measure of similarity which exhibits contextual interference: a data/cue is less likely to retrieve instances of a hypothesis that occurs frequently in other data. As a result, probability assessments are context dependent. In a new laboratory experiment, participants are shown two groups of images with different distributions of colors and other features. In line with the model’s predictions, we find that (a) decreasing the frequency of a given color in one group significantly increases the recalled frequency of that color in the other group; and (b) cueing different features for the same set of images entails different probabilistic assessments, even if the features are normatively irrelevant. A calibration of the model yields a good quantitative fit with the data, highlighting the central role of contextual interference. Keywords: cued recall, interference, similarity, probabilistic judgments, heuristics and biases Supplemental materials: http://dx.doi.org/10.1037/rev0000251.supp A vast literature in psychology shows that individuals’ proba- several different occupations (Tversky and Kahneman, 1974). bilistic judgments are vulnerable to systematic errors (see Benja- Subjects tend to state that the introverted man is more likely to be min, 2019 for a review). An important body of evidence, ranging a librarian than a salesman, even though there are vastly more from base rate neglect to the disjunction fallacy, focuses on the salesmen than librarians. Being an “introvert,” the reasoning goes, representativeness heuristic, the tendency to judge as likely events makes the man more similar to a librarian than to a salesman, that are merely representative. Representativeness captures “the which causes an inflated assessment of likelihood. degree to which [an event] is similar in essential characteristics to But why do subjects use similarity in making probability judg- its parent population” (Kahneman & Tversky, 1972, p. 430). In a ments? Why should similarity sometimes cause them to think well-known example, subjects are given a short description of an about unlikely events, so that judgments are incorrect? Why introverted man and are asked to rank, in order of likelihood, among introverted men do we think about the unlikely librarian instead of the more likely salesman? Why do we exaggerate the likelihood that an Irish person has red hair even though only 10% of them do (Bordalo, Coffman, Gennaioli, & Shleifer, 2016)? This document is copyrighted by the American Psychological Association or one of its allied publishers. We address these questions starting from the idea that proba- This article is intended solely for the personal use of the individual userPedro and is not to be disseminated broadly. Bordalo, Saïd Business School, University of Oxford; Katherine bility judgments are formed by selectively retrieving information Coffman, Harvard Business School; Nicola Gennaioli, Department of from memory, cued by the problem at hand. In our model, a Finance and Innocenzo Gasparini Institute for Economic Research, Boc- coni University; Frederik Schwerter, Department of Economics, University decision maker assesses the likelihood of different hypotheses in of Cologne; Andrei Shleifer, Department of Economics, Harvard Univer- light of data d. In line with memory research (Kahana, 2012), sity. recall of a hypothesis h is driven by its similarity with the data d, Nicola Gennaioli thanks the European Research Council (Grant GA and is subject to interference, so that hypotheses more similar to 647782) for financial support. Frederik Schwerter and Andrei Shleifer the data prevent less similar ones from coming to mind. When told thank the Sloan Foundation for financial support. We thank Rahul Bhui, someone is Irish—that is, when cued with the data d ϭ Irish—the Ben Enke, Paul Fontanier, Sam Gershman, Thomas Graeber, Spencer decision maker selectively recalls the hair color h, in this case red, Kwon, Joshua Schwartzstein, seminar participants at Harvard University and MIT Sloan for helpful comments. that is most similar to this data, and overestimates its likelihood. Correspondence concerning this article should be addressed to Andrei Our theoretical contribution is to formalize similarity between Shleifer, Department of Economics, Harvard University, 1805 Cambridge the data-cue and the hypothesis assessed, which constitute differ- Street, Cambridge, MA 02138. E-mail: [email protected] ent yet overlapping sets. Our formulation of similarity is inspired 1 2 BORDALO ET AL. by Tversky’s (1977) similarity metric, and captures the idea that calibrate the model. We then use the calibrated model to predict, two sets are more similar when the statistical correlation among out of sample, the other results in Studies 2 and 3, as well as the their attributes is higher. In probabilistic judgments, this implies results of additional experiments we ran. This exercise confirms that a hypothesis h is more easily recalled when it is more likely to that contextual interference is a quantitatively important determi- occur with the data d, but also when it is less likely to occur with nant of beliefs and that our model offers a good quantitative fit. other data –d. Similarity-based recall is then context dependent, in In our approach, the representativeness heuristic derives from a that recall about data d depends on the comparison data –d, basic cognitive mechanism: context-dependent, similarity-based sometimes causing neglect of likely events. For instance, when recall. As such, it differs from existing models of faulty probability thinking about d ϭ Irish, it is harder to recall the modal hair color judgments. One strand of the literature invokes limited memory, h ϭ dark because it occurs very often in other nationalities –d, including sampling models (Sanborn & Chater, 2016), the Minerva which interferes with its recall in the Irish group. We refer to this MD model (Dougherty, Gettys, & Ogden, 1999) or the exemplar mechanism as contextual interference, since interference with hy- PROBabilities from EXemplars (PROBEX) model (Nilsson, Ol- pothesis h is determined by the context provided by the alternative sson, & Juslin, 2005). The first two models are based on noisy data –d.1 recall, which yields some biases but not the overestimation of Our second contribution is to present a novel experimental unlikely events. In the PROBEX model, the exemplar hypothesis framework and a set of experimental results that provide evidence of data d does not depend on different data –d, which makes this for this mechanism. The model yields testable predictions for how model unsuitable to account for how probability judgments depend biases in probability judgments depend on the statistical associa- on the decoy group.2 tions between the data and hypotheses. To test these predictions, Bhatia (2017) shows that social stereotypes, such as introverted we run three (main) experiments with the following basic struc- male librarians and red-haired Irish, can be spread through the ture. Participants observe a sequence of 25 numbers and 25 decoy media and personal interactions, through selective repetition of the images (either shapes or words), which come in different colors. more representative cases. This semantic association and repetition Among numbers, 15 are blue and 10 are orange. In one treatment, of unlikely traits improves accessibility in memory that may cause decoy images are all gray shapes so there is no color overlap with their overestimation. While this mechanism contributes to biases in numbers. In another treatment, decoys are all blue words, which is social contexts, it does not explain the source of these biases (why also the modal color among numbers. Participants are then asked does media focus on these specific traits), and why biases are to: (a) recall the numbers they saw, and (b) estimate the likelihood widespread even in abstract judgments such as those in our exper- of different colors among numbers. We think of data as d ϭ iments. numbers, and the possible hypotheses, h ʦ H, as the colors. Several papers explicitly engage with the representativeness In Study 1 we test contextual interference: we predict that the heuristic. Tenenbaum and Griffiths (2001) formalize representa- hypothesis h ϭ orange is deemed more likely when the decoy data tiveness based on Tversky and Kahneman (1983), but do not link –d are blue words than when they are gray shapes, because blue words interfere with