Cognition in Context Understanding “Biases” in Reasoning, Learning, and Decision Making

1. Cognition in ContextUnderstanding “Biases” in Reasoning, Learning, and Decision Making Craig R. M. McKenzie Rady School of Management and Department of Psychology UC San Diego

2. Brief background… • Social scientists often compare how people behave with how they ought to behave • When systematic differences (biases) occur, heuristics often invoked as explanation • 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

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

4. Traditional view of framing effects • 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”

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

6. Information leakage(Sher & McKenzie, 2006; McKenzie & Nelson, 2003; McKenzie, 2004; McKenzie, Liersch, & Finkelstein, 2006) • Logical equivalence does not guarantee information equivalence • E.g., passive and active sentence forms • A speaker’s 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: 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 • Frames information equivalent only if no choice-relevant inferences can be drawn from speaker’s choice of frame. Else, “information leakage” is said to occur.

7. 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) • Our explanation: Speakers more likely to use label (e.g., “fat”) that has increased relative to reference point, thereby leaking information about relative abundance

8. 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” Speaker’s choice of frame leaks info about relative fat content

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

10. Similar results… • …using medical treatment outcomes (% die vs. % survive) (McKenzie & Nelson, 2003) • illustrate normative issue • …looking at spontaneous, real behavior (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)

11. Framing effects conclusions • 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 • Unclear extent to which information leakage can explain all framing effects

12. Covariation assessment Variable Y Present Absent Present Variable X Absent

13. Cell A “bias” • 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 • P = A/(A+B) – C/(C+D) •  = (AD-BC)/[(A+B)(C+D)(A+C)(B+D)]1/2

14. Who cares? • 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)

15. Bayesian account • 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) • 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)

16. 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)

17. Yeah, but… • …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 • 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)

18. Covariation assessment conclusions • 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 • 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

19. Bayesian account of some classic learning phenomena • 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? • 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

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

21. Trial-by-Trial Updating • 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 • 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(A|H2) = p(X)p(Y) • p(A|H1) = p(A|H2)+rho[sqrt(p(X)*1-p(X)*p(Y)*1-p(Y)] • alphaX  alphaX + 1 • alphaY  alphaY + 1 • p(H1|A)  p(H1)

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

23. Density Bias

24. Density Bias and Rarity

25. Rescorla-Wagner Model • ΔVX = 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)

26. R-W and Density Bias

27. Density Bias, R-W, and alpha/beta

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

29. Partial Reinforcement Effect

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

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

32. What did he say? • Some important “biases” can be seen as rational – which provides more satisfying account • 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 • Many “biases” indicate behavior that is not only more rational, but also psychologically richer, than previously thought

33. Thank you!

34. 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: • 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 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.

35. 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 If Program A is adopted, ________ people will . (write #) die (circle one) If Program B is adopted, be saved there is ________ probability that ________ people will , (write #) (write #) die (circle one) be saved and ________ probability that _______ people will . (write #) (write #) die (circle one)

36. Implicit Recommendation Results (unpublished data) • If prefer sure thing (Program A): • 81% (83/103) word sure thing in terms of “saved” • 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”) • Speakers’ preferences affect phrasing of risky choice option(s) -- which listeners might use to infer speaker’s preference

37. Strength of Preference and Choice of Frame (unpublished data)

38. 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%