Classroom Experiment Answer the questions on the handout labeled: “Four Famous Reasoning...

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 1

The Representativeness Heuristic

Psychology 466: Judgment & Decision MakingInstructor: John Miyamoto

10/22/2015: Lecture 04-2

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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

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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.

Two Implicit Theses in the Representativeness Hypothesis

Psych 466, Miyamoto, Aut '15

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.

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.

Examples of the Irregularity Thesis

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Examples of the Irregularity Thesis

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.


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.

Intuitive Concept of Randomness Is Too Irregular

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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

Similarity Heuristic: People substitute a judgment of similarity for a judgment of probability.


How likely is Event X?

How similar is X to things that typically occur?

Judgment of ProbabilityBased On

Judgment of Similarity

How likely is it that Bob will be an effective salesman?

How similar is Bob to a typical effective salesman?

Judged Probability (Effective Salesman)Based On

Judged Similarity(Effective Salesman)

Schematic Explanation of Why People Commit Conjunction Errors

Similarity Heuristic Example

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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?

Psych 466, Miyamoto, Aut '15 The Linda Problem

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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 548, Miyamoto, Spr '11 Add One More Statement to This Slide

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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

Psych 548, Miyamoto, Spr '11 Linda Problem – Preliminary Probabilistic Analysis


Slide inserted after lecture 4-2, a15.

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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 548, Miyamoto, Spr '11 Implications of Conjunction Errors for Cog Psych

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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?

Psych 466, Miyamoto, Aut '15 Probability & Set Inclusion Principle

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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.


A B

BT BT & F F

Sample Space (set of all possibilities; not set of all features)

Conjunction Principle Expressed as a Math Formula


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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.

Psych 466, Miyamoto, Aut '15 Set Inclusion Analysis of Conjunction Fallacy

BT BT & F F


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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.”

Psych 466, Miyamoto, Aut '15 Why Do People Make Conjunction Errors?

BT BT & F F


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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.

Psych 466, Miyamoto, Aut '15 Evidence that the Similarity Order is the Same as the Probability Order

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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.

Psych 466, Miyamoto, Aut '15 Criticisms of the Similarity Explanation for Conjunction Fallacies

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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 '15 Response to Objection 2 Above

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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 '15 Response to Claim that People Wouldn’t Make Error if They Were Reasoning Carefully

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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 '15 Physicians Also Make Conjunction Errors

22

Related Reasoning Problems – Medical Example

• 103 internists (internal medicine) were:a) given a series descriptions of patients who had various diseases;

b) asked to rank the probability of various conditions that the patients could experience. The possible conditions included common symptoms, uncommon symptoms, and conjunctions.

c) 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?

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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 '15 Why People Make Conjunction Errors

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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.

Psych 466, Miyamoto, Aut '15 Begin Explanation of Contrast Model of Similarity







How likely is it Linda is a feminist and a bank teller?

How similar is Linda to person who is a feminist and a bank teller?

Judged Probability (Fem & Bank T)Based On

Judged Similarity(Fem & Bank T)

Begin Explanation of Contrast Model of Similarity


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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 '15 Features that Are Distinctive of Los Angeles

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How Similar Are Los Angeles & New York?




2) Features that are distinctive of the first object (Los Angeles).

Psych 466, Miyamoto, Aut '15 Features that Are Distinctive of New York

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3) Features that are distinctive of the second object (New York)

Psych 466, Miyamoto, Aut '15 Repeat This Slide Without Any Red Rectangles

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3) Features that are distinctive of the second object (New York)

Psych 466, Miyamoto, Aut '15 Math Formula for the Contrast Model

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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 '15 Evidence for the Contrast Model – Asymmetric Similarity

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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 '15 Return to the Issue of the Role of Similarity in Probability Judgment

32Psych 466, Miyamoto, Aut '15

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.

Contrast Model & Conjunction Fallacies

Summary of Representativeness Analysis of the Conjunction Problem

LindaDescription

Bank Teller

LindaDescription

Bank Teller & Fem

inist

Space of Category Features

Space of Category Features

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.


Psych 466, Miyamoto, Aut '15 33Diagram Showing that Conjunction Error Involves Attribute Substitution

Similarity Heuristic Is a Form of Attribute Substitution






How likely is it Linda is a feminist and a bank teller?

How similar is Linda to person who is a feminist and a bank teller?

Judged Probability (Fem & Bank T)Based On

Judged Similarity(Fem & Bank T)

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.


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 Without Emphasis Rectangles

Dilution Effect





Results of Tetlock & Boettger Experiment

Results: Tetlock & Boettger’s Study of Dilution Effect

DilutionEffect:

Non-diagnostic information reduces the impact of diagnostic information.

Psych 466, Miyamoto, Aut '15 37Same Slide Except Results for Accountable Condition Are Added to Slide

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.

Results: Tetlock & Boettger’s Study of Dilution Effect

Psych 466, Miyamoto, Aut '15 38Reminder re Dilution Effect & Similarity

Dilution Effect





Introduce Ignorance of Sample Size & Regression Effects

Two More Examples of the Similarity Heuristic

• Insensitivity to sample size• Overlooking regression effects

Psych 466, Miyamoto, Aut '15 40Intuitive Sampling Distributions

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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?

Psych 466, Miyamoto, Aut '15 Law of Large Numbers & Improvement of Estimation with Sample Size

Mean Response of SubjectsTrue 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.

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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 '15 Ignoring Sample Size & Similarity Heuristic

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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.

Psych 466, Miyamoto, Aut '15 Law of Small Numbers

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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 '15 Next: Regression Effects

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.

Psych 466, Miyamoto, Aut '15 Why Do People Fail to Account for Regression Effects?

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.

Psych 466, Miyamoto, Aut '15 46Examples of Failures to Account for Regression Effects

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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 '15 Business Consequences

48

Business ConsequencesRabin, M. (2002). Inference by believers in the law of small numbers. Quarterly Journal of

Economics, 117(3), 775-816. • 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.

Psych 466, Miyamoto, Aut '15 Quote from Seattle Times

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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)

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

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

END

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Classroom Experiment Answer the questions on the handout labeled: “Four Famous Reasoning...

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