Answer the questions on the handout labeled: Four Famous Reasoning Problems. Try not to remember what you may have read about these problems!

Transcription

1 Classroom Experiment Answer the questions on the handout labeled: Four Famous Reasoning Problems Try not to remember what you may have read about these problems! Psych 466, Miyamoto, Aut '17 1

2 The Representativeness Heuristic Psychology 466: Judgment & Decision Making Instructor: John Miyamoto 10/17/2017: Lecture 04-1 Note: This Powerpoint presentation may contain macros that I wrote to help me create the slides. The macros aren t needed to view the slides. You can disable or delete the macros without any change to the presentation.

3 Major Steps in Making a Decision Recognizing that you have to make a decision. Understanding what options are available to you. A cognitive psychologist would call this: The Psych 466 lectures Creating a mental representation of the decision. are currently focused on this issue. An "option" refers to something that For each option, you can choose to do. (i) identify the outcomes that could result from taking this option; Options are sometimes called: (ii) judge how likely are the various outcomes. * Alternatives * Choices For each outcome, judge how strongly * Possible you like courses or dislike of action this outcome. What value (good or bad) do you place on each outcome? Psych 466, Miyamoto, Aut '17 Same Slide - No Yellow Boxes 3

4 Major Steps in Making a Decision Recognizing that you have to make a decision. Understanding what options are available to you. A cognitive psychologist would call this: Creating a mental representation of the decision. For each option, (i) identify the outcomes that could result from taking this option; (ii) judge how likely are the various outcomes. For each outcome, judge how strongly you like or dislike this outcome. What value (good or bad) do you place on each outcome? Psych 466, Miyamoto, Aut '17 Lecture Outline 4

5 Outline Kahneman & Tversky proposed three main heuristics: Anchoring & Adjustment, Availability, & Representativeness Lectures this week and next: Representativeness Heuristic - many examples Examples of the representativeness heuristic: The conjunction fallacy a consequence of similarity-based reasoning Insensitivity to sample size Insensitivity to regression effects Base rate neglect Misperceptions of randomness Lecture probably ends here Psych 466, Miyamoto, Aut '17 5

6 Two Implicit Theses in the Representativeness Hypothesis Event A is more representative than Event B Event A is more probable than Event B Representativeness Hypothesis: Events that are more representative are regarded as more probable. I. Irregularity People expect random samples to be Heuristic: irregular (patternless). II. Similarity Heuristic: A potential outcome appears to be representative if it is similar to typical members of a population. Examples of the Irregularity Thesis Psych 466, Miyamoto, Aut '17 6

7 Examples of the Irregularity Heuristic Irregularity Heuristic: People expect random samples to be irregular (patternless) Intuition: Random events are (invariably) patternless. Not true! Inference: Events that display patterns are not random they have underlying causes. EXAMPLES Intuitive coin flips: HTHTTHTHH... Bombing runs on London. Sometimes this is mistaken Intuitive Concept of Randomness Is Too Irregular Psych 466, Miyamoto, Aut '17 7

8 Similarity Heuristic (Part of the Representativeness Heuristic) Similarity Heuristic: People substitute a judgment of similarity for a judgment of probability. E.g., if asked to predict will there be an all-out war between the U.S. and North Korea during the next three years? Similarity heuristic: Base prediction about war on the similarity between the current political situtation in Asia and the situation that preceded other major wars. Schematic Explanation + Example of Similarity Thesis Psych 466, Miyamoto, Aut '17 8

9 Similarity Heuristic: People substitute a judgment of similarity for a judgment of probability. Similarity Heuristic How likely is Event X? Example How likely is it that Bob will be an effective salesman? How similar is X to things that typically occur? How similar is Bob to a typical effective salesman? Judgment of Probability Based On Judgment of Similarity Judged Probability (Effective Salesman) Based On Judged Similarity(Effective Salesman) Examples of Similarity Heuristic Psych 466, Miyamoto, Aut '17 9

10 Psych 466, Miyamoto, Aut '17 10 The Linda Problem These are all consequences of the similarity heuristic Examples of Reasoning Based on the Similarity Heuristic Conjunction errors what are they? why do people make this error? Insensitivity to sample size Insensitivity to regression effects The lecture will probably get this far Bayes Rule: A normative principle for reasoning with base-rates Base-rate neglect people sometimes ignore base rates Why does base-rate neglect occur?

11 Linda Problem & the Conjunction Fallacy 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 social justice, and also participated in anti-nuclear demonstrations. BT = Linda is a bank teller. P(BT) = Probability of Statement T F = Linda is active in the feminist movement. P(F) = Probability of Statement F Psych 466, Miyamoto, Aut '17 Add One More Statement to This Slide 11

12 Linda Problem & the Conjunction Fallacy 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 social justice, and also participated in anti-nuclear demonstrations. BT = Linda is a bank teller. P(BT) = Probability of Statement BT F = Linda is active in the feminist movement. P(F) = Probability of Statement F BT&F = Linda is a bank teller and is active in the feminist movement. P(BT&F) = Probability of Statement BT&F Psych 466, Miyamoto, Aut '17 Linda Problem Preliminary Probabilistic Analysis 12

13 Sentence Stimuli Psych 466, Miyamoto, Aut '17 13

14 Conjunction Fallacy in the Famous Linda Problem BT: Judge the probability that Linda is a bank teller. F: Judge the probability that Linda is a feminist. BT & F: Judge the probability that Linda is a feminist and a bank teller. Probability Theory: P(BT) > P(BT&F), P(F) > P(BT&F) Paradoxical finding: JP(F) > JP(BT&F) > JP(BT) "JP" stands for judged probability. P stands for true probability. Review class responses did they exhibit the fallacy? Psych 466, Miyamoto, Aut '17 Implications of Conjunction Errors for Cog Psych 14

15 Implications of Conjunction Errors for Cognitive Psychology Claim 1: Human reasoning with uncertainty is different from probability theory. Claim 2: Human reasoning with uncertainty is based on a similarity heuristic. 2 QUESTIONS: What is strange about the pattern JP(F) > JP(BT & F) > JP(BT)? Why does human judgment follow this pattern? Psych 466, Miyamoto, Aut '17 Probability & Set Inclusion Principle 15

16 Probability and the Set Inclusion Principle If set B is a subset of set A, then the probability of B must be less than the probability of A. Sample Space (set of all possibilities; not set of all features) B A P(B) P(A) When B occurs, A also occurs, so P(B) cannot exceed P(A). A B Conjunction Principle: The probability of a conjunction of events is always equal or less than the probability of either event in the conjunction. Sample Space for Linda Problem (set of all possibilities; not set of all features) BT BT & F F Conjunction Principle Expressed as a Math Formula Psych 466, Miyamoto, Aut '17 16

17 Probability and the Set Inclusion Principle (cont.) Conjunction Principle: P(BT) P(BT & F), Sample Space for Linda Problem (set of all possibilities; not set of all features) P(F) P(BT & F) BT BT & F F The probability of a conjunction of events is always equal or less than the probability of either event in the conjunction. Psych 466, Miyamoto, Aut '17 Set Inclusion Analysis of Conjunction Fallacy 17

18 Why Are Conjunction Errors Logically Strange? "Linda" Problem: BT: Linda is a bank teller. F: Linda is a feminist. BT & F: Linda is a bank teller who is active in the feminist movement. Sample Space for Linda Problem (set of all possibilities; not set of all features) BT BT & F F Probability Theory: P(F) > P(F & BT), P(BT) > P(F & BT) Paradoxical finding: JP(F) > JP(F & BT) > JP(BT) bank teller & feminist is a subset of bank teller. Therefore "bank teller & feminist" MUST be less likely than bank teller. Psych 466, Miyamoto, Aut '17 Why Do People Make Conjunction Errors? 18

19 Why Do People Make Conjunction Errors? Kahneman & Tversky s Answer to this Question: People substitute similarity judgment for probability judgment. Human intuitions of similarity differ from the mathematical structure of probability The conjunction fallacy is an example where judgments of probability based on similarity are logically inconsistent. Next, need to substantiate this analysis. Psych 466, Miyamoto, Aut '17 Evidence that the Similarity Order is the Same as the Probability Order 19

20 Probability Judgment Is Based on Similarity Judgment Similarity Ratings: Subjects were asked to rank the statements in the Linda story by "the degree to which Linda resembles the typical member of that class." Finding: 85% respond with the rank order F > BT & F > BT F > BT & F > BT is the similarity ordering. The similarity order is the same as the judge probability order: JP(F) > JP(BT & F) > JP(BT) is the judged probability ordering Order of judged probability same as order of judged similarity! Representativeness is strongly supported. Psych 466, Miyamoto, Aut '17 Criticisms of the Similarity Explanation for Conjunction Fallacies 20

21 Criticisms of This Interpretation The Linda problem is just one problem. Response: Same pattern is found with many similar problems. Maybe people think bank teller means someone who is a bank teller and not a feminist. Maybe this is just a sloppy error. People wouldn t make the error if they were thinking carefully. Psych 466, Miyamoto, Aut '17 Response to Objection 2 Above 21

22 Maybe people think bank teller means someone who is a bank teller and not a feminist Maybe subjects see: T = "Linda is a bank teller," T&F = "Linda is a bank teller and is active in the feminist movement,... and infer that T implicitly means that T&(~F) = "Linda is a bank teller who is not active in the feminist movement.". Pragmatically unambiguous version: F: Linda is a feminist. T*: Linda is a bank teller whether or not she is active in the feminist movement. F&T: Linda is a feminist and a bank teller. 57% judge JP(F&BT) > JP(T*). 16% judge JP(T*) > JP(F&T). (n = 75) Psych 466, Miyamoto, Aut '17 22 Response to Claim that People Wouldn t Make Error, if They Were Reasoning Careful

23 People wouldn t make the error if they were thinking carefully Competing Arguments for Probabilistic Reasoning and Representativeness Probability Theory Argument: Linda is more likely to be a bank teller than she is to be a feminist bank teller, because every feminist bank teller is a bank teller, but some women bank tellers are not feminists, and Linda could be one of them. Representativeness Argument: Linda is more likely to be a feminist bank teller than she is likely to be a bank teller, because she resembles an active feminist more than she resembles a bank teller. 65% prefer the representativeness argument over the probability theory argument. Psych 466, Miyamoto, Aut '17 Physicians Also Make Conjunction Errors 23

24 Psych 466, Miyamoto, Aut '17 Finish the Description of the Study 24 Related Reasoning Problems Medical Example 103 internists (internal medicine) were: a) given a series descriptions of patients who had various diseases; Example: A 55-year-old woman had pulmonary embolism. Please rank order the following in terms of the probability that they will be among the conditions experienced by the patient. dyspnea and hemiparesis (A&B) syncope and tachycardia hemiparesis (B) calf pain pleuritic chest pain Hemoptysis The internists received this problem and four similar problems.

25 Psych 466, Miyamoto, Aut '17 Transition to Issue Why Do People Make Conjunction Errors? 25 Related Reasoning Problems Medical Example The physicians were given five descriptions of patients who had various diseases as in the preceding example; a) 103 internists (internal medicine) were asked to rank the probability of various conditions. b) A separate group of 32 physicians were asked to rank the symptoms "by the degree to which they are representative of the clinical condition of the patient." Correlation between rankings of representativeness and rankings of probability was over.95 in all five problems. The average proportion of conjunction fallacies over the five problems was.91.

26 Next: Why Similarity Theory Predicts Conjunction Errors Evidence is clear that people make conjunction errors Evidence is clear that judged probability and judged similarity are ordered the same. This suggests that sometimes people substitute a judgment of similarity for a judgment of probability. Next: Explain why similarity theory predicts that feminist bank teller is more similar to the Linda description than bank teller alone. Psych 466, Miyamoto, Aut '17 Why People Make Conjunction Errors 26

27 Feature Model of Perceived Similarity Objects are represented by features. Three Types of Features: 1) Features that are common to both objects. Psych 466, Miyamoto, Aut '17 Features that Are Distinctive of Los Angeles 27

28 How Similar Are Los Angeles & New York? Objects are represented by features. Three Types of Features: 1) Features that are common to both objects. 2) Features that are distinctive of the first object (Los Angeles). Psych 466, Miyamoto, Aut '17 Features that Are Distinctive of New York 28

29 How Similar Are Los Angeles & New York? Objects are represented by features. Three Types of Features: 1) Features that are common to both objects. 2) Features that are distinctive of the first object (Los Angeles). 3) Features that are distinctive of the second object (New York) Psych 466, Miyamoto, Aut '17 Repeat This Slide Without Any Red Rectangles 29

30 How Similar Are Los Angeles & New York? Objects are represented by features. Three Types of Features: 1) Features that are common to both objects. 2) Features that are distinctive of the first object (Los Angeles). 3) Features that are distinctive of the second object (New York) Psych 466, Miyamoto, Aut '17 Math Formula for the Contrast Model 30

31 Contrast Model of Similarity (cont.) Sim(A, B) = f(a B) f(a B) f(b A),, are positive numbers; f maps sets of features into the positive real numbers. Psych 466, Miyamoto, Aut '17 Evidence for the Contrast Model Asymmetric Similarity 31

32 Evidence for the Contrast Model Asymmetric similarity judgments: Sim(Burma, China) > Sim(China, Burma) (Burma is more similar to China than China is to Burma.) Comment: MDS cannot explain this because the distance from A to B is equal to the distance from B to A. (MDS = multidimensional scaling = alternative model of similarity; MDS claims that similarity is measured as a distance in psychological space.) Psych 466, Miyamoto, Aut '17 Return to the Issue of the Role of Similarity in Probability Judgment 32

33 Contrast Model & Conjunction Fallacies The contrast model explains why Space of Category Features Linda is a bank teller and a feminist is more similar to the description of Linda than is. Linda Description Bank Teller Linda is a bank teller Space of Category Features Similarity heuristic claims that we judge probabilities based on similarity even when we should not. Linda Description Summary of Representativeness Analysis of the Conjunction Problem Psych 466, Miyamoto, Aut '17 33

34 Summary: Why Do People Often Commit Conjunction Errors? Step 1: Similarity between feminist bank teller & Linda s description IS GREATER THAN Similarity between bank teller & Linda s description Step 2: People judge the probability of Linda is an X based on the similarity between the description of Linda and the typical features of an X. Similarity Heuristic: People substitute a judgment of similarity for a judgment of probability. Psych 466, Miyamoto, Aut '17 Diagram Showing that Conjunction Error Involves Attribute Substitution 34

35 Similarity Heuristic Is a Form of Attribute Substitution Similarity Heuristic How likely is Event X? Linda Example How likely is it Linda is a feminist and a bank teller? How similar is X to things that typically occur? How similar is Linda to person who is a feminist and a bank teller? Judgment of Probability Based On Judgment of Similarity Judged Probability (Fem & Bank T) Based On Judged Similarity(Fem & Bank T) Psych 466, Miyamoto, Aut '17 Same Slide with Addition of Definition of Attribute Substitution 35

36 Similarity Heuristic Is a Form of Attribute Substitution Similarity Heuristic How likely is Event X? Linda Example How likely is it Linda is a feminist and a bank teller? How similar is X to things that typically occur? How similar is Linda to person who is a feminist and a bank teller? Judgment of Probability Based On Judgment of Similarity Judged Probability (Fem & Bank T) Based On Judged Similarity(Fem & Bank T) Attribute Substitution: Replace judgment of one attribute, e.g., probability, with a judgment of another attribute, e.g., similarity, that is easier to judge. Dilution Effect Psych 466, Miyamoto, Aut '17 36

37 Dilution Effect Dilution Effect: Combining non-diagnostic information with diagnostic information makes an outcome seem less probability. Explanation: Non-diagnostic information makes the current case less similar to typical cases. Dilution effect is an example of the similarity heuristics Psych 466, Miyamoto, Aut '17 Tetlock Experiment on Dilution Effect 37

38 Tetlock & Boettger's Study of Accountability & the Dilution Effect Tetlock, P. E., & Boettger, R. (1989). Accountability: A social magnifier of the dilution effect. Journal of Personality and Social Psychology, 57(3), Same Slide with Definitions of Diluted and Undiluted Conditions Psych 466, Miyamoto, Aut '17 38

39 Accountability & the Dilution Effect Undiluted Condition: Subjects saw only the diagnostic information before making the probability judgment. Diluted Condition: Subjects saw the diagnostic information plus the non-diagnostic information before making the probability judgment. Psych 466, Miyamoto, Aut '17 Same Slide - Focus on Undiluted Condition 39

40 Tetlock & Boettger's Study of Accountability & the Dilution Effect Undiluted Condition: Subjects saw only the diagnostic information before making the probability judgment. Psych 466, Miyamoto, Aut '17 Same Slide - Focus on the Diluted Condition 40

41 Accountability & the Dilution Effect Undiluted Condition: Subjects saw only the diagnostic information before making the probability judgment. Diluted Condition: Subjects saw the diagnostic information plus the non-diagnostic information before making the probability judgment. Psych 466, Miyamoto, Aut '17 Same Slide Without Emphasis Rectangles 41

42 Tetlock & Boettger's Study of Accountability & the Dilution Effect Undiluted Condition: Subjects saw only the diagnostic information before making the probability judgment. Diluted Condition: Subjects saw the diagnostic information plus the non-diagnostic information before making the probability judgment. Psych 466, Miyamoto, Aut '17 Results of the Experiment 42

43 Results: Dilution Effect Dilution Effect: Non-diagnostic information reduces the impact of diagnostic information. Psych 466, Miyamoto, Aut '17 Same Slide Except Results for Accountable Condition Are Added to Slide 43

44 Results: Accountability and Dilution Effect High accountable subjects were told that they would have to explain their ratings to an experimenter. Low accountable subjects did not expect to have to explain their ratings. Psych 466, Miyamoto, Aut '17 Reminder re Dilution Effect & Similarity 44

45 Dilution Effect Dilution Effect: Combining non-diagnostic information with diagnostic information makes an outcome seem less probability. Explanation: Non-diagnostic information makes the current case less similar to typical cases. Psych 466, Miyamoto, Aut '17 Introduce Ignorance of Sample Size & Regression Effects 45

46 Two More Examples of the Similarity Heuristic Insensitivity to sample size Overlooking regression effects Psych 466, Miyamoto, Aut '17 Intuitive Sampling Distributions 46

47 Intuitive Sampling Distribution for Number of Male Births Question: Approximately N = 1000 (or 100 or 10) babies are born each day in a certain region. What percentage of the days will have the number of boys among 1000 babies as follows: 0 to 50? 50 to 150? 150 to 250? ? ? Mean Response of Subjects True Percentages of Male Births for N = 10, 100, 1000 The curves for N = 100 and N = 1000 are shifted slightly to the right to avoid excessive overlap between the curves. Psych 466, Miyamoto, Aut '17 Law of Large Numbers & Improvement of Estimation with Sample Size 47

48 Intuitive Sampling Distributions Intuitive sampling distributions completely ignore effect of sample size on variance. Law of Large Numbers: The larger the sample, the higher the probability that an estimate of the mean will be close to the true mean. Estimates based on small samples are inferior to estimates based on large samples, but this way of asking for the estimate shows no awareness of this. Psych 466, Miyamoto, Aut '17 Ignoring Sample Size & Similarity Heuristic 48

49 Ignoring Sample Size & Similarity Heuristic People tend to ignore sample size Example: Which is more similar to the conclusion, most UW undergrads wear eyeglasses or contact lenses? Version A: 3 out of 5 people interviewed wore eyeglasses, or... Version B: 30 out of 50 people interviewed wore eyeglasses. Conclusion: Most UW undergrads wear eyeglasses. These two statements are equally similar to the conclusion, although they are not equally strong pieces of evidence. Psych 466, Miyamoto, Aut '17 Law of Small Numbers 49

50 Belief in the "Law of Small Numbers" Representativeness: [P]eople view a sample randomly drawn from a population as highly representative, that is, similar to the population in all essential characteristics." Psychologically, the sample size is not relevant to the representativeness of a sample. Consequently, people overlook the importance of sample size. Psych 466, Miyamoto, Aut '17 Next: Regression Effects 50

51 Misconceptions of Regression Sophomore Slump: A baseball player who does exceptionally well during his rookie season often does noticeably worse during his sophomore (second) season. Why does this happen? Regression effect: A predicted value will be closer to the mean of the predicted values than is the variable on which the prediction is based. Z predicted Y = Z X Z predicted Y = predicted z-score for Y Z X = z-score for X = the population correlation between X and Y Implication: If X and Y are not perfectly correlated, then the predicted value of Y is always closer to its mean than the value of X. Psych 466, Miyamoto, Aut '17 Why Do People Fail to Account for Regression Effects? 51

52 Why Do People Fail to Predict Regression Effects? Example: Which prediction is most similar to the data? DATA: Jim got the highest grade on the first exam. PREDICTION 1: Jim will get the highest grade on the second exam. PREDICTION 2: Jim will get a high grade, but not the highest grade on the second exam. Prediction 1 is the most similar to the evidence. Prediction 2 is less similar to the evidence but it is more probable due to regression to the mean. People who use the similarity heuristic tend to forget that regression to mean affects predictions because regression to the mean is irrelevant to the determination of similarity. Examples of Failures to Account for Regression Effects Psych 466, Miyamoto, Aut '17 52

53 Misconceptions of Regression Sophomore Slump: A baseball player who does exceptionally well during his rookie season often does noticeably worse during his sophomore (second) season. Why does this happen? Regression effect: A predicted value will be closer to the mean of the predicted values than is the variable on which the prediction is based. Other Examples: Israeli flight instructors and the effects of praise and punishment. Evaluating medical treatments or psychotherapies that select patients who are already in extreme difficulty. Psych 466, Miyamoto, Aut '17 Business Consequences 53

54 Business Consequences Rabin, M. (2002). Inference by believers in the law of small numbers. Quarterly Journal of Economics, 117(3), Investors choose stock analysts based on their short-term record of success or failure. Overgeneralization from small samples. Rabin argues that investors are overly responsive to short-term business fluctuation. Over-reliance on small samples and ignorance of regression effects combine to produce misperception of market behavior. Psych 466, Miyamoto, Aut '17 Quote from Seattle Times 54

55 Business Consequences Seattle Times, Tuesday Oct. 14, 2008, p. A14 Oil market analysts thought that oil prices were going to keep going up. $147/barrel during summer Many analysts expected $200/barrel in the near future. October 2009: $80/barrel. Stephen Schork of the Schork Report: It s just amazing that the market gets suckered into this. (quoted in the Times) David Fyfe, an analyst with the International Energy Agency: there is always a tendency in parts of the analyst community to look at short-term trends and assume it s something that will continue in perpetuity. (quoted in the Times) Psych 466, Miyamoto, Aut '17 Summary re Similarity Thesis - END 55

56 Similarity Heuristic (Part of the Representativeness Heuristic) Similarity Heuristic: People substitute a judgment of similarity for a judgment of probability. (Attribute Substitution) The conjunction fallacy a consequence of similarity-based reasoning Insensitivity to sample size Insensitivity to regression effects Base rate neglect Discussed Today. Misperceptions of randomness Discuss Next Tuesday. Psych 466, Miyamoto, Aut '17 56 END