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 '15

2. The Representativeness Heuristic
Psychology 466: Judgment & Decision Making Instructor: John Miyamoto 10/22/2015: Lecture 04-2
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3. 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 '15

4. 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 appear to be more probable.
I. Irregularity Thesis: A sample or event appears to be representative if it reflects the irregularity of the random process by which it is generated.
II. Similarity Thesis: A potential outcome appears to be representative if it is similar to typical members of a population. Conversely, a population appears to be representative if its typical members are similar to a known event or outcome.
Examples of the Irregularity Thesis
Psych 466, Miyamoto, Aut '15

5. Examples of the Irregularity Thesis
Irregularity Thesis: A sample or event appears to be representative if it reflects the irregularity of the random process by which it is thought to be generated.
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.
Intuitive Concept of Randomness Is Too Irregular
Psych 466, Miyamoto, Aut '15

6. Similarity Thesis (Part of the Representativeness Heuristic)
Similarity Thesis: People substitute a judgment of similarity for a judgment of probability.
E.g., if asked to judge how likely is Jeb Bush to win the Republican presidential nomination, people might base the judgment on how similar he is to previous nominees.
Schematic Explanation + Example of Similarity Thesis
Psych 466, Miyamoto, Aut '15

7. 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)
Schematic Explanation of Why People Commit Conjunction Errors
Psych 466, Miyamoto, Aut '15

8. Examples 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?
These are all consequences of the similarity heuristic
Psych 466, Miyamoto, Aut '15
The Linda Problem

9. 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 548, Miyamoto, Spr '11

10. 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 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 548, Miyamoto, Spr '11

11. Slide inserted after lecture 4-2, a15.
Psych 466, Miyamoto, Aut '15

12. 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 548, Miyamoto, Spr '11

13. 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 representativeness 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 '15

14. 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) Rationale: 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 (set of all possibilities; not set of all features) BT
BT & F F
Conjunction Principle Expressed as a Math Formula
Psych 466, Miyamoto, Aut '15

15. 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 (set of all possibilities; not set of all features) BT
BT & F F
Set Inclusion Analysis of Conjunction Fallacy
Psych 466, Miyamoto, Aut '15

16. Why Are Conjunction Errors Logically Strange?
"Linda" Problem: (Description).
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 it MUST have a lower probability than “bank teller.”
Sample Space (set of all possibilities; not set of all features) BT
BT & F F
Why Do People Make Conjunction Errors?
Psych 466, Miyamoto, Aut '15

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.
These differences produce errors in probabilistic reasoning.
Need to substantiate this analysis next.
Evidence that the Similarity Order is the Same as the Probability Order
Psych 466, Miyamoto, Aut '15

18. 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  the similarity ordering.
The similarity order is the same as the judge probability order:
JP(F) > JP(BT & F) > JP(BT)  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 '15

19. 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 '15

20. 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*) % judge JP(T*) > JP(F&T) (n = 75)
Response to Claim that People Wouldn’t Make Error if They Were Reasoning Carefully
Psych 466, Miyamoto, Aut '15

21. 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 '15

22. Related Reasoning Problems – Medical Example
103 internists (internal medicine) were:
given a series descriptions of patients who had various diseases;
asked to rank the probability of various conditions that the patients could experience. The possible conditions included common symptoms, uncommon symptoms, and conjunctions.
Separate group of 32 physicians ranked the representativeness of the symptoms.
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 '15
Transition to Issue – Why Do People Make Conjunction Errors?

23. 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 '15

24. Why Do People Make Conjunction Errors?
Short answer:
People substitute similarity judgment for probability judgment.
Human intuition of similarity differs from the mathematical structure of probability.
These differences produce errors in probabilistic reasoning.
Begin Explanation of Contrast Model of Similarity
Psych 466, Miyamoto, Aut '15

25. Similarity Heuristic: People substitute a judgment of similarity for a judgment of probability.
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)
Begin Explanation of Contrast Model of Similarity
Psych 466, Miyamoto, Aut '15

26. 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 '15

27. 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 '15

28. 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 '15

29. 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 '15

30. 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 '15

31. 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 '15

32. Contrast Model & Conjunction Fallacies
Space of Category Features
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.
Bank Teller
Linda Description
Space of Category Features
Bank Teller
& Feminist
Linda Description
Psych 466, Miyamoto, Aut '15
Summary of Representativeness Analysis of the Conjunction Problem

33. 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 “Ms X is a Y” based on the similarity between the description of Ms X and the typical features of a Y.
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 '15

34. Similarity Heuristic Is a Form of Attribute Substitution
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)
Dilution Effect
Psych 466, Miyamoto, Aut '15

35. 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’.
Tetlock, P. E., & Boettger, R. (1989). Accountability: A social magnifier of the dilution effect. Journal of Personality and Social Psychology, 57(3),
Same Slide Without Emphasis Rectangles
Psych 466, Miyamoto, Aut '15

36. 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’.
Tetlock, P. E., & Boettger, R. (1989). Accountability: A social magnifier of the dilution effect. Journal of Personality and Social Psychology, 57(3),
Results of Tetlock & Boettger Experiment
Psych 466, Miyamoto, Aut '15

37. Results: Tetlock & Boettger’s Study of 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 '15

38. Results: Tetlock & Boettger’s Study of 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 '15

39. 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’.
Tetlock, P. E., & Boettger, R. (1989). Accountability: A social magnifier of the dilution effect. Journal of Personality and Social Psychology, 57(3),
Introduce Ignorance of Sample Size & Regression Effects
Psych 466, Miyamoto, Aut '15

40. Two More Examples of the Similarity Heuristic
Insensitivity to sample size
Overlooking regression effects
Intuitive Sampling Distributions
Psych 466, Miyamoto, Aut '15

41. 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? – 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 '15

42. 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 '15

43. 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?
3 out of 5 people interviewed wore eyeglasses, or ....
300 out of 500 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 '15

44. 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 '15

45. 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 '15

46. Why Do People Fail to Predict Regression Effects?
Example: Which prediction is most similar to the datum? (datum = prior evidence)
DATUM: 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, but not the highest grade on the second exam.
Statement 1 is the most similar to the evidence, but it is less probable than Statement 2.
Examples of Failures to Account for Regression Effects
Psych 466, Miyamoto, Aut '15

47. 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 '15

48. Business Consequences
Rabin, M. (2002). Inference by believers in the law of small numbers. Quarterly Journal of Economics, 117(3),
Investors choose stock analysts 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 '15

49. 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)
Summary re Similarity Thesis - END
Psych 466, Miyamoto, Aut '15

50. Similarity Thesis (Part of the Representativeness Heuristic)
Similarity Thesis: People substitute a judgment of similarity for a judgment of probability.
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 '15