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Cognition in Context Understanding Biases in Reasoning, Learning, and Decision Making Craig R. M. McKenzie Rady School of Management and Department of Psychology UC San Diego

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Brief background… Social scientists often compare how people behave with how they ought to behave Social scientists often compare how people behave with how they ought to behave When systematic differences (biases) occur, heuristics often invoked as explanation When systematic differences (biases) occur, heuristics often invoked as explanation Much research has argued that some of these conclusions misleading Much research has argued that some of these conclusions misleading –Rational analyses can be incomplete or incorrect –People make assumptions about task structure My theme: Taking into account real-world conditions, combined with normative principles that make sense under these conditions, can help explain purported biases My theme: Taking into account real-world conditions, combined with normative principles that make sense under these conditions, can help explain purported biases

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Types of framing effects (Levin et al., 1998) Attribute framing Attribute framing –e.g., 25% fat vs. 75% lean; Levin & Gaeth, 1988; Levin, 1987 Risky choice framing Risky choice framing –e.g., Asian Disease problem; Tversky & Kahneman, 1981 Goal framing Goal framing –e.g., breast self-examination; Meyerowitz & Chaiken, 1987

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Traditional view of framing effects Framing effects violate description invariance Framing effects violate description invariance Based largely on (risky choice) framing effects, Tversky and Kahneman (1986) conclude that...[N]o theory of choice can be both normatively adequate and descriptively accurate Based largely on (risky choice) framing effects, Tversky and Kahneman (1986) conclude that...[N]o theory of choice can be both normatively adequate and descriptively accurate

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Equivalence But what have people meant by equivalence? But what have people meant by equivalence? –Objective equivalence –Formal equivalence –Logical equivalence Information equivalence is what is required Information equivalence is what is required –To make irrational claim, different frames must not communicate choice-relevant information (Sher & McKenzie, 2006)

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Information leakage (Sher & McKenzie, 2006; McKenzie & Nelson, 2003; McKenzie, 2004; McKenzie, Liersch, & Finkelstein, 2006) Logical equivalence does not guarantee information equivalence Logical equivalence does not guarantee information equivalence –E.g., passive and active sentence forms A speakers choice of frame can be informative A speakers choice of frame can be informative –E.g., 1/2 full vs. 1/2 empty Assume exactly 2 frames, F1 and F2, and background condition B: Assume exactly 2 frames, F1 and F2, and background condition B: p(F1|B) > p(F1|~B) p(B|F1) > p(B|F2) p(F1|B) > p(F1|~B) p(B|F1) > p(B|F2) If knowledge of B relevant to choice, then responding differently to F1 and F2 is rational If knowledge of B relevant to choice, then responding differently to F1 and F2 is rational Frames information equivalent only if no choice- relevant inferences can be drawn from speakers choice of frame. Else, information leakage is said to occur. Frames information equivalent only if no choice- relevant inferences can be drawn from speakers choice of frame. Else, information leakage is said to occur.

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Why do attribute framing effects occur? Traditional explanation: Positive frame (e.g., lean) evokes positive associations, negative frame (fat) evokes negative associations, which influence judgments (Levin, 1987; Levin et al., 1998) Traditional explanation: Positive frame (e.g., lean) evokes positive associations, negative frame (fat) evokes negative associations, which influence judgments (Levin, 1987; Levin et al., 1998) Our explanation: Speakers more likely to use label (e.g., fat) that has increased relative to reference point, thereby leaking information about relative abundance Our explanation: Speakers more likely to use label (e.g., fat) that has increased relative to reference point, thereby leaking information about relative abundance

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Information leakage (McKenzie & Sher, in preparation) Imagine that all ground beef is about 40% fat, or 60% lean. Recently, you heard that a new ground beef is going to be sold on the market that is 25% fat, or 75% lean. You happen to be talking to a friend about the new beef. Given that most ground beef is 40% fat, or 60% lean, what is the most natural way to describe the new ground beef to your friend? Place a mark next to one description: _____ The new beef is 25% fat _____ The new beef is 75% lean when other beef 40% fat/60% lean, 53% describe new beef as 75% lean when other beef 10% fat/90% lean, 23% describe new beef as 75% lean Speakers choice of frame leaks info about relative fat content

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Information absorption and source of frame (McKenzie & Sher, in preparation)

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…using medical treatment outcomes (% die vs. % survive) (McKenzie & Nelson, 2003) …using medical treatment outcomes (% die vs. % survive) (McKenzie & Nelson, 2003) –illustrate normative issue …looking at spontaneous, real behavior (Sher & McKenzie, 2006) …looking at spontaneous, real behavior (Sher & McKenzie, 2006) …describing outcome of flips of coin and rolls of die (Sher & McKenzie, 2006) …describing outcome of flips of coin and rolls of die (Sher & McKenzie, 2006) –Findings not explained in terms of associative account …examining default effects (McKenzie, Liersch, and Finkelstein, 2006) …examining default effects (McKenzie, Liersch, and Finkelstein, 2006) Similar results…

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Framing effects conclusions Traditional normative view incorrect Traditional normative view incorrect – Frames must be information equivalent, not logically equivalent, for framing effects to be irrational Information leakage has psychological, as well as rational, implications Information leakage has psychological, as well as rational, implications Unclear extent to which information leakage can explain all framing effects Unclear extent to which information leakage can explain all framing effects

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Cell A Cell B Cell C Cell D Present Absent Variable X PresentAbsent Variable Y Covariation assessment

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Robust finding: Cell A has largest impact and Cell D smallest impact; Cells B and C fall in between Robust finding: Cell A has largest impact and Cell D smallest impact; Cells B and C fall in between This bias seen as nonnormative because 4 cells equally important in traditional normative models This bias seen as nonnormative because 4 cells equally important in traditional normative models – P = A/(A+B) – C/(C+D) – = (AD-BC)/[(A+B)(C+D)(A+C)(B+D)] 1/2 Cell A bias

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Who cares? Covariation assessment underlies such fundamental behaviors as learning, categorization, and judging causation Covariation assessment underlies such fundamental behaviors as learning, categorization, and judging causation People's ability to accurately assess covariation allows them to explain the past, control the present, and predict the future (Crocker, 1981) People's ability to accurately assess covariation allows them to explain the past, control the present, and predict the future (Crocker, 1981)

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Cell A bias makes normative (Bayesian) sense if presence of variables tends to be rarer than their absence (Anderson, 1990; McKenzie & Mikkelsen, 2000, 2007) Cell A bias makes normative (Bayesian) sense if presence of variables tends to be rarer than their absence (Anderson, 1990; McKenzie & Mikkelsen, 2000, 2007) Bayesian perspective assumes subjects approach covariation task as one of inference rather than statistical summary (see also Griffiths & Tenenbaum, 2005) Bayesian perspective assumes subjects approach covariation task as one of inference rather than statistical summary (see also Griffiths & Tenenbaum, 2005) –Trying to discriminate between 2 hypotheses about population – relationship (H1) vs. no relationship (H2) –Likelihood ratios, e.g., p(Cell A|H1)/p(Cell A|H2) Bayesian account

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Absolute log-likelihood ratio of cells as function of p(X) and p(Y). |LLR| = Abs(log[p(j|H1)/p(j|H2)]), j = A, B, C, D; H1: rho=0.1; H2: rho=0 When presence of X and Y is rare, Cell A most informative and Cell D least informative (B & C fall in between)

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…is it reasonable to assume that the presence of variables is rare? …is it reasonable to assume that the presence of variables is rare? Well, most people do not have a fever, most things are not red, most people are not accountants, and so on Well, most people do not have a fever, most things are not red, most people are not accountants, and so on –Of categories X and not-X (e.g., red things and non-red things), which would be larger? Cell A bias reversed when subjects know that absence of variables rare (McKenzie & Mikkelsen, 2007) Cell A bias reversed when subjects know that absence of variables rare (McKenzie & Mikkelsen, 2007) Yeah, but…

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Rarity affects cell impact as predicted by Bayesian account Rarity affects cell impact as predicted by Bayesian account –Cell A vs. D and Cell B vs. C Second robust phenomenon: Subjects prior beliefs about relationship between variables influence judgments – which is hallmark of Bayesian approach Second robust phenomenon: Subjects prior beliefs about relationship between variables influence judgments – which is hallmark of Bayesian approach Normative principles, combined with consideration of environment, provide parsimonious account of the two most robust phenomena in covariation literature Normative principles, combined with consideration of environment, provide parsimonious account of the two most robust phenomena in covariation literature Different from framing effects, though: Not case that traditional normative model wrong, but a different normative model applies Different from framing effects, though: Not case that traditional normative model wrong, but a different normative model applies Covariation assessment conclusions

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Bayesian account of some classic learning phenomena Previous evidence for Bayesian approach comes from summary descriptions of data and presentation of single cells Previous evidence for Bayesian approach comes from summary descriptions of data and presentation of single cells What about trial-by-trial updating – traditionally the domain of Rescorla-Wagner model? What about trial-by-trial updating – traditionally the domain of Rescorla-Wagner model? Will limit ourselves to the 2-variable case: 1 predictor and 1 outcome Will limit ourselves to the 2-variable case: 1 predictor and 1 outcome Goal is to show, via computer simulation, that Bayes can account for previous updating findings Goal is to show, via computer simulation, that Bayes can account for previous updating findings

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The Bayesian Model (adapted from J. R. Anderson, 1990) Parameters: H1, H2 H1, H2 –H1: rho = 0.5, H2: rho = 0 p(H1) = 1-p(H2) p(H1) = 1-p(H2) alphaX, betaX alphaX, betaX –alphaX/(alphaX+betaX) = p(X) –rarity alphaX < betaX alphaY, betaY alphaY, betaY –alphaY/(alphaY+betaY) = p(Y) –rarity alphaY < betaY A B C D Pr Ab Pr Ab Y X alphaX betaX alphaYbetaY

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Trial-by-Trial Updating p(H1|E) = p(H1)p(E|H1)/[p(H1)p(E|H1)+p(H2)p(E|H2)] p(H1|E) = p(H1)p(E|H1)/[p(H1)p(E|H1)+p(H2)p(E|H2)] alpha and/or beta updated by 1 alpha and/or beta updated by 1 FOR EXAMPLE, if Cell A is observed: FOR EXAMPLE, if Cell A is observed: p(H1|A) = p(H1)p(A|H1)/[p(H1)p(A|H1)+p(H2)p(A|H2)] p(H1|A) = p(H1)p(A|H1)/[p(H1)p(A|H1)+p(H2)p(A|H2)] p(A|H2) = p(X)p(Y) p(A|H2) = p(X)p(Y) p(A|H1) = p(A|H2)+rho[sqrt(p(X)*1-p(X)*p(Y)*1-p(Y)] p(A|H1) = p(A|H2)+rho[sqrt(p(X)*1-p(X)*p(Y)*1-p(Y)] alphaX alphaX + 1 alphaX alphaX + 1 alphaY alphaY + 1 alphaY alphaY + 1 p(H1|A) p(H1) p(H1|A) p(H1)

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Density Bias Initial rise in conditioning or judgments of contingency when presented with uncorrelated data (phi = 0), especially when outcome is common Initial rise in conditioning or judgments of contingency when presented with uncorrelated data (phi = 0), especially when outcome is common

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Density Bias

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Density Bias and Rarity

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Rescorla-Wagner Model ΔV X = αβ(λ-ΣV) ΔV X = αβ(λ-ΣV) …perhaps for an increment in associative connections to occur, it is necessary that the US instigate some mental work on the part of the animal. This mental work will occur only if the US is unpredictable – if it in some sense surprises the animal (Kamin, 1969) …perhaps for an increment in associative connections to occur, it is necessary that the US instigate some mental work on the part of the animal. This mental work will occur only if the US is unpredictable – if it in some sense surprises the animal (Kamin, 1969)

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R-W and Density Bias

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Density Bias, R-W, and alpha/beta

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Partial Reinforcement Effect Initial learning of weak correlation takes longer to extinguish than initial learning of strong correlation Initial learning of weak correlation takes longer to extinguish than initial learning of strong correlation

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Partial Reinforcement Effect

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Also… Learned irrelevance/helplessness Learned irrelevance/helplessness –Initial learning of independence between variables retards subsequent learning of real relationship Latent inhibition Latent inhibition –Initial presentations of X (CS) alone retard subsequent learning of CS-UCS relationship UCS pre-exposure effect UCS pre-exposure effect –Initial presentations of Y (UCS) alone retard subsequent learning of CS-UCS relationship

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Some advantages of Bayes in this context Can explain both trial-by-trial updating and responses to summaries of data Can explain both trial-by-trial updating and responses to summaries of data Parsimony Parsimony –Local: Bayes reduces to counting –Global: Bayes used to explain behavior ranging from vision to reasoning Speculation: R-W mimics Bayesian response Speculation: R-W mimics Bayesian response –Marrs levels of analysis?

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What did he say? Some important biases can be seen as rational – which provides more satisfying account Some important biases can be seen as rational – which provides more satisfying account Important interplay between normative models and behavior Important interplay between normative models and behavior Normative principles – combined with considerations of the structure of the environment – can help explain why people behave as they do Normative principles – combined with considerations of the structure of the environment – can help explain why people behave as they do Many biases indicate behavior that is not only more rational, but also psychologically richer, than previously thought Many biases indicate behavior that is not only more rational, but also psychologically richer, than previously thought

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Thank you!

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Risky Choice: Asian Disease Problem (Tversky & Kahneman, 1981) Imagine that U.S. is preparing for outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimate of the consequences of the programs are as follows: Imagine that U.S. is preparing for outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimate of the consequences of the programs are as follows: If Program A adopted, 200 people will be saved. If Program A adopted, 200 people will be saved. If Program B adopted, 1/3 probability that 600 people will be saved, and 2/3 probability that no people will be saved. If Program B adopted, 1/3 probability that 600 people will be saved, and 2/3 probability that no people will be saved. If Program C adopted, 400 people will die. If Program C adopted, 400 people will die. If Program D adopted, 1/3 probability that nobody will die, and 2/3 probability that 600 people will die. If Program D adopted, 1/3 probability that nobody will die, and 2/3 probability that 600 people will die.

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Risky Choice Frame Selection Subjects first chose preferred program from completely described programs. Imagine that your job is to describe the situation, and the programs which have been proposed, to a committee who will then decide which program, A or B, to use. Please complete the sentences below as if you were describing the programs to the committee. be saved be saved If Program A is adopted, ________ people will. (write #) die (write #) die (circle one) (circle one) If Program B is adopted, be saved be saved there is ________ probability that ________ people will, (write #) (write #) die (write #) (write #) die (circle one) (circle one) be saved be saved and ________ probability that _______ people will. (write #) (write #) die (write #) (write #) die (circle one) (circle one)

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Implicit Recommendation Results (unpublished data) If prefer sure thing (Program A): If prefer sure thing (Program A): –81% (83/103) word sure thing in terms of saved If prefer gamble (Program B): If prefer gamble (Program B): –48% (45/93) word sure thing in terms of saved Word gamble same regardless of preference (1/3 prob that 600 saved and 2/3 prob that 600 die) Word gamble same regardless of preference (1/3 prob that 600 saved and 2/3 prob that 600 die) Speakers preferences affect phrasing of risky choice option(s) -- which listeners might use to infer speakers preference Speakers preferences affect phrasing of risky choice option(s) -- which listeners might use to infer speakers preference

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Strength of Preference and Choice of Frame (unpublished data)

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Cell A bias Cell D bias Condition 3 (Concrete) Sample 1 Sample 2 (Cell) Emotionally disturbed: Yes / Drop out: Yes 6 1 (A) Emotionally disturbed: Yes / Drop out: No 1 1 (B) Emotionally disturbed: No / Drop out: Yes 1 1 (C) Emotionally disturbed: No / Drop out: No 1 6 (D) Which sample stronger evidence of relation? 73% 27% Condition 4 (Concrete) Sample 1 Sample 2 (Cell) Emotionally healthy: No / Graduate: No 6 1 (D) Emotionally healthy: No / Graduate: Yes 1 1 (C) Emotionally healthy: Yes / Graduate: No 1 1 (B) Emotionally healthy: Yes / Graduate: Yes 1 6 (A) Which sample stronger evidence of relation? 67% 33%

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