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

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.

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? An "option" refers to something that you can choose to do. Options are sometimes called: * Alternatives * Choices * Possible courses of action The Psych 466 lectures are currently focused on this issue. Psych 466, Miyamoto, Aut '17 Same Slide - No Yellow Boxes

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

Lecture probably ends here 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

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 A potential outcome appears to be Heuristic: representative if it is similar to typical members of a population. Examples of the Irregularity Thesis Psych 466, Miyamoto, Aut '17

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

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

Similarity Heuristic: People substitute a judgment of similarity for a judgment of probability. Example How likely is it that Bob will be an effective salesman? How likely is Event X? How similar is X to things that typically occur? How similar is Bob to a typical effective salesman? Remember conjunction fallacy: Adding a likely property to an unlikely property increases the perceived likelihood of the conjunction of the properties, even though this is mathematically impossible. 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

Examples of Reasoning Based on the Similarity Heuristic These are all consequences of 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? Psych 466, Miyamoto, Aut '17 The Linda Problem

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 See handout with probability problems. Add One More Statement to This Slide Psych 466, Miyamoto, Aut '17

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 See handout with probability problems. Linda Problem – Preliminary Probabilistic Analysis Psych 466, Miyamoto, Aut '17

Sentence Stimuli Psych 466, Miyamoto, Aut '17

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? Implications of Conjunction Errors for Cog Psych Psych 466, Miyamoto, Aut '17

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? Probability & Set Inclusion Principle Psych 466, Miyamoto, Aut '17

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. B  A  P(B)  P(A) When B occurs, A also occurs, so P(B) cannot exceed P(A). 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 (set of all possibilities; not set of all features) A B 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

Probability and the Set Inclusion Principle (cont.) Conjunction Principle: P(BT)  P(BT & F), P(F)  P(BT & F) 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 Set Inclusion Analysis of Conjunction Fallacy Psych 466, Miyamoto, Aut '17

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. 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.” Sample Space for Linda Problem (set of all possibilities; not set of all features) BT BT & F F Why Do People Make Conjunction Errors? Psych 466, Miyamoto, Aut '17

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. Evidence that the Similarity Order is the Same as the Probability Order Psych 466, Miyamoto, Aut '17

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. Criticisms of the Similarity Explanation for Conjunction Fallacies Psych 466, Miyamoto, Aut '17

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. Response to Objection 2 Above Psych 466, Miyamoto, Aut '17

Pragmatically unambiguous version: 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) Response to Claim that People Wouldn’t Make Error , if They Were Reasoning Careful Psych 466, Miyamoto, Aut '17

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. Physicians Also Make Conjunction Errors Psych 466, Miyamoto, Aut '17

Related Reasoning Problems – Medical Example 103 internists (internal medicine) were: 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. Psych 466, Miyamoto, Aut '17 Finish the Description of the Study

Related Reasoning Problems – Medical Example The physicians were given five descriptions of patients who had various diseases as in the preceding example; 103 internists (internal medicine) were asked to rank the probability of various conditions. 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. Psych 466, Miyamoto, Aut '17 Transition to Issue – Why Do People Make Conjunction Errors?

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. Why People Make Conjunction Errors Psych 466, Miyamoto, Aut '17

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

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

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

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

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. Evidence for the Contrast Model – Asymmetric Similarity Psych 466, Miyamoto, Aut '17

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.) Return to the Issue of the Role of Similarity in Probability Judgment Psych 466, Miyamoto, Aut '17

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

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. Diagram Showing that Conjunction Error Involves Attribute Substitution Psych 466, Miyamoto, Aut '17

Similarity Heuristic Is a Form of Attribute Substitution Linda Example How likely is it Linda is a feminist and a bank teller? How likely is Event X? How similar is X to things that typically occur? How similar is Linda to person who is a feminist and a bank teller? Remember conjunction fallacy: Adding a likely property to an unlikely property increases the perceived likelihood of the conjunction of the properties, even though this is mathematically impossible. Judgment of Probability Based On Judgment of Similarity Judged Probability (Fem & Bank T) Based On Judged Similarity(Fem & Bank T) Same Slide with Addition of Definition of Attribute Substitution Psych 466, Miyamoto, Aut '17

Similarity Heuristic Is a Form of Attribute Substitution Linda Example How likely is it Linda is a feminist and a bank teller? How likely is Event X? How similar is X to things that typically occur? How similar is Linda to person who is a feminist and a bank teller? Remember conjunction fallacy: Adding a likely property to an unlikely property increases the perceived likelihood of the conjunction of the properties, even though this is mathematically impossible. 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. Psych 466, Miyamoto, Aut '17 Dilution Effect

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 Graphics for this slide produced in the file, ‘e:\p466\nts\dilution.effect.docm’. Tetlock Experiment on Dilution Effect Psych 466, Miyamoto, Aut '17

Tetlock & Boettger's Study of Accountability & the Dilution Effect Graphics for this slide produced in the file, ‘e:\p466\nts\dilution.effect.docm’. Tetlock, P. E., & Boettger, R. (1989). Accountability: A social magnifier of the dilution effect. Journal of Personality and Social Psychology, 57(3), 388 398. Same Slide with Definitions of Diluted and Undiluted Conditions Psych 466, Miyamoto, Aut '17

Accountability & the Dilution Effect Graphics for this slide produced in the file, ‘e:\p466\nts\dilution.effect.docm’. 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. Same Slide - Focus on Undiluted Condition Psych 466, Miyamoto, Aut '17

Tetlock & Boettger's Study of Accountability & the Dilution Effect Graphics for this slide produced in the file, ‘e:\p466\nts\dilution.effect.docm’. Undiluted Condition: Subjects saw only the diagnostic information before making the probability judgment. Same Slide - Focus on the Diluted Condition Psych 466, Miyamoto, Aut '17

Accountability & the Dilution Effect Graphics for this slide produced in the file, ‘e:\p466\nts\dilution.effect.docm’. 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. Same Slide Without Emphasis Rectangles Psych 466, Miyamoto, Aut '17

Tetlock & Boettger's Study of Accountability & the Dilution Effect Graphics for this slide produced in the file, ‘e:\p466\nts\dilution.effect.docm’. 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. Results of the Experiment Psych 466, Miyamoto, Aut '17

Results: Dilution Effect Dilution Effect: Non-diagnostic information reduces the impact of diagnostic information. Graphics for this slide produced in the file, ‘e:\p466\nts\dilution.effect.docm’. Same Slide Except Results for Accountable Condition Are Added to Slide Psych 466, Miyamoto, Aut '17

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. Graphics for this slide produced in the file, ‘e:\p466\nts\dilution.effect.docm’. Reminder re Dilution Effect & Similarity Psych 466, Miyamoto, Aut '17

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. Graphics for this slide produced in the file, ‘e:\p466\nts\dilution.effect.docm’. Introduce Ignorance of Sample Size & Regression Effects Psych 466, Miyamoto, Aut '17

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

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? .... 850 – 950? 950 – 1000? 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. Mean Response of Subjects R-code for the graphic is at ‘e:\p466\intuitive.sampling.dist.docm’ Law of Large Numbers & Improvement of Estimation with Sample Size Psych 466, Miyamoto, Aut '17

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. Ignoring Sample Size & Similarity Heuristic Psych 466, Miyamoto, Aut '17

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. Law of Small Numbers Psych 466, Miyamoto, Aut '17

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. Next: Regression Effects Psych 466, Miyamoto, Aut '17

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. Zpredicted Y =   ZX Zpredicted Y = predicted z-score for Y ZX = 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. Regression example: If you observe people who are in an exceptionally bad state of mind, regression alone would predict that most of them will get better. Why Do People Fail to Account for Regression Effects? Psych 466, Miyamoto, Aut '17

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

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. Regression example: If you observe people who are in an exceptionally bad state of mind, regression alone would predict that most of them will get better. Business Consequences Psych 466, Miyamoto, Aut '17

Business Consequences Rabin, M. (2002). Inference by believers in the law of small numbers. Quarterly Journal of Economics, 117(3), 775-816. 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. Quote from Seattle Times Psych 466, Miyamoto, Aut '17

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 2008. 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) Summary re Similarity Thesis - END Psych 466, Miyamoto, Aut '17

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 Misperceptions of randomness Discussed Today . Discuss Next Tuesday . END Psych 466, Miyamoto, Aut '17