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 Making
Instructor: 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
Psych 466, Miyamoto, Aut '15
Lecture probably
ends here
3
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.
Psych 466, Miyamoto, Aut '15
Examples of the Irregularity Thesis
4
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.
Psych 466, Miyamoto, Aut '15
Intuitive Concept of Randomness Is Too Irregular
5
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.
Psych 466, Miyamoto, Aut '15
Schematic Explanation + Example of Similarity Thesis
6
Similarity Heuristic:
People substitute a judgment of similarity for a judgment of probability.
Similarity Heuristic
Example
How likely is Event X?
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)
Psych 466, Miyamoto, Aut '15
Schematic Explanation of Why People Commit Conjunction Errors
7
Examples of the Similarity Heuristic
• 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
These are all consequences
of the similarity heuristic
• Conjunction errors – what are they?
– why do people make this error?
• Why does base-rate neglect occur?
Psych 466, Miyamoto, Aut '15
The Linda Problem
8
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
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
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
10
Slide inserted after lecture 4-2, a15.
Psych 466, Miyamoto, Aut '15
11
Conjunction Fallacy in the Famous Linda Problem
BT:
F:
BT & F:
Judge the probability that Linda is a bank teller.
Judge the probability that Linda is a feminist.
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
12
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
13
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)
A
B
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.
Psych 466, Miyamoto, Aut '15
Sample Space (set of all possibilities;
not set of all features)
BT
BT & F
F
Conjunction Principle Expressed as a Math Formula
14
Probability and the Set Inclusion Principle (cont.)
Conjunction Principle:
P(BT)
P(BT & F),
P(F)
P(BT & F)
Sample Space (set of all possibilities;
not set of all features)
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 '15
Set Inclusion Analysis of Conjunction Fallacy
15
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.
Sample Space (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 it MUST have a lower probability than “bank teller.”
Psych 466, Miyamoto, Aut '15
Why Do People Make Conjunction Errors?
16
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
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
 the similarity ordering.
F > BT & F > BT
• 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
18
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
19
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).
Psych 466, Miyamoto, Aut '15
(n = 75)
Response to Claim that People Wouldn’t Make Error if They Were Reasoning Carefully
20
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
21
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?
22
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
23
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
24
Similarity Heuristic:
People substitute a judgment of similarity for a judgment of probability.
Similarity Heuristic
Example
How likely is Event X?
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 '15
Begin Explanation of Contrast Model of Similarity
25
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
26
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 '15
Features that Are Distinctive of New York
27
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 '15
Repeat This Slide Without Any Red Rectangles
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).
3) Features that are distinctive of the second object (New York)
Psych 466, Miyamoto, Aut '15
Math Formula for the Contrast Model
29
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
30
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
31
Contrast Model & Conjunction Fallacies
Space of Category Features
The contrast model explains why ….
Linda is a bank teller and a feminist
Linda
Description
Bank
Teller
is more similar to the description of
Linda than is ….
Space of Category Features
Linda is a bank teller
Similarity heuristic claims that we
judge probabilities based on
similarity even when we should not.
Psych 466, Miyamoto, Aut '15
Linda
Description
Summary of Representativeness Analysis of the Conjunction Problem
32
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.
Psych 466, Miyamoto, Aut '15
Diagram Showing that Conjunction Error Involves Attribute Substitution
33
Similarity Heuristic Is a Form of Attribute Substitution
Similarity Heuristic
Example
How likely is Event X?
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 '15
Dilution Effect
34
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.
Psych 466, Miyamoto, Aut '15
Same Slide Without Emphasis Rectangles
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.
Tetlock, P. E., & Boettger, R. (1989). Accountability: A social magnifier of the dilution effect. Journal of
Personality and Social Psychology, 57(3), 388 398.
Psych 466, Miyamoto, Aut '15
Results of Tetlock & Boettger Experiment
36
Results: Tetlock & Boettger’s Study of Dilution Effect
Dilution
Effect:
Non-diagnostic
information
reduces the
impact of
diagnostic
information.
Psych 466, Miyamoto, Aut '15
Same Slide Except Results for Accountable Condition Are Added to Slide
37
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.
Psych 466, Miyamoto, Aut '15
Reminder re Dilution Effect & Similarity
38
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.
Psych 466, Miyamoto, Aut '15
Introduce Ignorance of Sample Size & Regression Effects
39
Two More Examples of the Similarity Heuristic
• Insensitivity to sample size
• Overlooking regression effects
Psych 466, Miyamoto, Aut '15
Intuitive Sampling Distributions
40
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?
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 '15
Law of Large Numbers & Improvement of Estimation with Sample Size
41
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
42
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
43
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
44
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?
45
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
Examples of Failures to Account for Regression Effects
46
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
47
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 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
48
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
49
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
Psych 466, Miyamoto, Aut '15
Discussed Today .
Discuss Next Tuesday .
END
50