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The Representativeness Heuristic
then:
Risk Attitude and Framing Effects
Psychology 355: Cognitive Psychology
Instructor: John Miyamoto
6/1/2016: Lecture 10-3
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Outline
• Review: The Lawyer/Engineer Problem
(representativeness heuristic and base rate neglect)
• The conjunction fallacy
♦
The conjunction fallacy is predicted by the hypothesis that people
use a representativeness heuristic.
Introduction to Preference Under Risk
• Risk attitude (risk aversion and risk seeking)
Lecture probably
ends here
• Reflection effect
• Framing effects: Gain frames and loss frames
• Mental accounting
Psych 355, Miyamoto, Spr ‘16
Diagram that Depicts Use of a Representativeness Heuristic
2
Representativeness Heuristic
Event A
is more representative
than Event B
Event A
is more probable
than Event B
"more representative"
means
"more similar to a stereotype of a class
or to a typical member of a class."
Representativeness Heuristic:
Judge the probability of an event E by the representativeness
of the event E.
♦
We need some example to make this idea more clear (see next).
Psych 355, Miyamoto, Spr '16
The Lawyer/Engineer Problem
3
Lawyer/Engineer Problem (K&T, 1973)
DESCRIPTION OF JACK: Jack is a 45-year-old man.
He is married and has four children. He is generally conservative,
careful, and ambitious. He shows no interest in political and social
issues. (This description is designed to fit the stereotype of an engineer more than
the stereotype of a lawyer.)
• 30:70 Condition: High Base Rate for Engineer
If Jack's description were drawn at random from a set of
30 lawyers and 70 engineers, what would be the probability
that Jack is one of the engineers?
• 70:30 Condition: Low Base Rate for Engineer
If Jack's description were drawn at random from a set of
70 lawyers and 30 engineers, what would be the probability
that Jack is one of the engineers?
Psych 355, Miyamoto, Spr '16
Findings re Lawyer/Engineer Problem
4
Results re Lawyer/Engineer Problem
• Probability of "engineer" was rated to be about the same
in the low and high base rate conditions.
(Insensitivity to Base Rate, a.k.a. Base Rate Neglect)
High versus low base rate
has no effect, even though it
ought to influence the
probability judgment.
♦
High base rate condition = 30:70 Condition
Low base rate condition = 70:30 Condition
♦
Probability theory implies that Jack is much more likely to be
an engineer in the high base rate condition than in the low base
rate condition. (This is an application of Bayes' Rule - an important rule of reasoning.)
• Why do people ignore base rates? See next slide
Psych 355, Miyamoto, Spr '16
Why Do People Ignore Base Rates? The Representativeness Explanation
5
Why does the Representativeness Heuristic
Cause Base Rate Neglect?
Judgment Process for the Representativeness Heuristic
Event A
is more representative
than Event B
Event A
is more probable
than Event B
• The similarity of the particular case to the stereotype of a category influences
how representative this category appears to be. Therefore similarity
influences the judgment of probability.
♦
Example: Similarity of Jack to the stereotype of an engineer influences
the judged likelihood that Jack is an engineer.
• The base rate of events is unrelated to how representative an event seems
to be. Therefore base rate will not influence the judgment of probability.
• Example: The base rate for engineers (70:30 or 30:70) is unrelated to how
representative Jack would be of the engineer category. Therefore the base rate of
engineers should not influence the judged likelihood that Jack is an engineer.
Psych 355, Miyamoto, Spr '16
#
6
Why Do People Often Ignore Base Rates?
The Representativeness Heuristic: People judge probability based
on the similarity of the current case to a stereotype.
(a) Jack is equally similar to a typical engineer in the
low and high base rate conditions.
(b) People ignore the base rate because the base rate is irrelevant
to the judgment of how similar Jack is to a typical engineer.
♦
Probability theory shows that the base rate is very relevant
to judging the probability that Jack is an engineer.
♦
Cognitive theory shows that the base rate is often not psychologically
relevant to judging the probability that Jack is an engineer.
Psych 355, Miyamoto, Spr '16
When Does It Matter Whether People Ignore Base Rates?
7
When Does It Matter Whether People Ignore Base Rates?
• Evidence shows that physicians sometimes overlook base rates
when attempting to diagnose a disease.
• Evidence suggests that investors are overly influenced by
short-term information regarding the value of stocks.
• Business decisions tend to be overly influenced by short-term trends.
Psych 355, Miyamoto, Spr '16
Criticism of Goldstein’s Description of the Lawyer/Engineer Problem
8
Criticism of Goldstein’s Description
of the Lawyer/Engineer Problem
• The Goldstein description of this study is inadequate because it does
not contrast the 30:70 condition with the 70:30 condition. It only
mentions the 70:30 condition.
• The important finding is that subjects in the 30:70 and 70:30 conditions
are equally confident that Jack is an engineer (subjects in the two
conditions overlook the difference in the base rate).
♦
Knowing only the result for the 70:30 condition does not establish that
subjects ignore base rates.
♦
See Goldstein p. 374.
Psych 355, Miyamoto, Spr '16
The Conjunction Fallacy - The Famous "Linda" Problem
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Conjunction Fallacies – The Famous "Linda" Problem
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.
F:
Judge the probability that Linda is a feminist.
T:
Judge the probability that Linda is a bank teller.
F & T:
Judge the probability that Linda is a feminist and a bank teller.
• Probability Theory: P(F) ≥ P(F & T), P(T) ≥ P(F & T)
• Typical Judgment:
Psych 355, Miyamoto, Spr '16
P(F) > P(F & T) > P(T)
Why Are Conjunction Fallacies Psychologically Interesting?
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Why Conjunction Fallacies
Are Psychologically Interesting?
• Conjunction fallacies strongly support the claim:
Human reasoning with uncertainty is different from
probability theory.
♦
Human reasoning with uncertainty is based on a various heuristics –
the conjunction fallacy is caused by the use of a representativeness heuristic.
Two Question Regarding Conjunction Fallacies:
• What is wrong with the judgment pattern:
P(F) > P(F & T) > P(T)?
• Why do people's judgments have this pattern?
Psych 355, Miyamoto, Spr '16
Probability & the Set Inclusion Principle
11
Probability and the Set Inclusion Principle
• If set B is a subset of set A, then
the probability of B must be
equal or less than the probability
of A.
Sample Space (set of all possibilities)
A
B  A  P(B) < P(A)
B
Rationale: When B occurs,
A also occurs, so the probability
of B cannot exceed the
probability of A.
Psych 355, Miyamoto, Spr '16
Interpretation of Linda Problem in terms of Set Inclusion
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Conjunction Fallacy
Linda Problem: 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.
Sample Space
F
F&T
F:
Judge the probability that Linda is a feminist.
T:
Judge the probability that Linda is a bank teller.
F & T:
T
Judge the probability that Linda is a feminist
and a bank teller.
• Probability Theory: P(F) ≥ P(F & T), P(T) ≥ P(F & T)
• Typical Judgment:
Psych 355, Miyamoto, Spr '16
P(F) > P(F & T) > P(T)
Why Do People Make Conjunction Errors?
13
Why Do People Make Conjunction Errors?
• Remember: The representativeness heuristic predicts that people
judge the probability based on how similar the individual case is to a
typical member (stereotype) of a group.
• The description of Linda sounds more similar to someone who is a
feminist and a bank teller, than to someone who is only a bank teller.
Bank Teller
Prototype
Description
of Linda
Feminist
Bank Teller
Prototype
Psych 355, Miyamoto, Spr '16
Criticisms of the Representativeness Explanation of Conjunction Fallacies
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Criticisms of This Interpretation
• Criticism: The Linda problem is just one problem.
Reply: Same pattern is found with many similar problems.
• Criticism: Maybe people think “bank teller” means someone
who is a bank teller and not a feminist.
• Criticism: Conjunction errors can be eliminated by stating
the question in terms of frequencies instead of probabilities.
Psych 355, Miyamoto, Spr '16
Summary re Representativeness Heuristic
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Summary re Representativeness Heuristic
• There is nothing wrong with using similarity as a factor
in judging a probability.
♦
The problem is that attention to similarity causes people to ignore
other factors, like base rates, regression effects and set inclusion,
that are also relevant to judging probability.
Bayes' Rule says:
The Base Rate
of the Event X
Representativeness
Heuristic
The Probability of
an Event X
The Evidence
for and against
Event X
Psych 355, Miyamoto, Spr '16
Two Major Issues in Psych of Decision Making - Probability & Preference
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Two Major Issues in Psychology of Decision Making
• Judgments of likelihood
♦
What outcomes are likely? Which are unlikely?
♦
How likely? Slightly possible? Almost certain? Etc.
We’ve been
talking briefly
about this topic.
• Judgments of preference & making choices
♦
How strongly do you like or dislike different
possible outcomes?
♦
How risky are difference choices?
♦
What risks are worth taking for potential gains?
Psych 355, Miyamoto, Spr '16
Next topic.
Digression re Risk Attitude
17
Risk Attitude
Risk averse action: A person chooses a sure-thing X
over a gamble G where X is less than the expected value of G.
Example of a Risk Averse Decision
Prefer a sure win of $500
over
a 50-50 gamble for $1,010 or $0.
(Note: Expected value of gamble = $505)
Risk seeking action: A person chooses a gamble G over a
sure thing X where the expected value of G is less than X.
Example of a Risk Seeking Decision
Prefer a 50-50 gamble for $1000 or $0
over
a sure win of $505.
(Note: Expected value of gamble = +$500)
Psych 355, Miyamoto, Spr '16
Examples of Risk Aversion & Risk Seeking
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Examples of Risk Aversion & Risk Seeking
Whenever you buy insurance, you are acting in a risk averse way.
• The cost of car insurance is a sure loss that is a bigger loss than
the expected value of the gamble of driving an uninsured car.
• Whenever you gamble at a professional casino or
in state lottery, you are acting in a risk seeking way.
♦
The cost of the lottery ticket is greater than the expected value
of the lottery ticket.
♦
In a casino, all of the mechanical gambles (roulette or slot machine)
have a negative expected gamble.
Psych 355, Miyamoto, Spr '16
Is It More Rational to be Risk Averse or Risk Seeking?
19
Is It More Rational to be Risk Averse or Risk Seeking?
• There is no rational requirement to be risk averse.
It is equally rational to be generally risk averse or generally risk
seeking.
♦
It is also rational to be risk seeking for some money quantities,
e.g., small amounts of money,
and risk averse for other money quantities,
e.g., large amounts of money.
♦
It is also rational to be risk averse in some domains,
e.g., gambles for the health of your children,
and risk seeking in other domains,
e.g., gambles for business profit and loss.
• Before the work of Kahneman & Tversky, many theorists thought that
people were generally risk averse.
♦
Next slide: Reflection effect shows that people are risk averse for some
kinds of gambles, and risk seeking for other types of gambles.
Psych 355, Miyamoto, Spr '16
Reflection Effect Example
20
Reflection Effect – Example
Choice 1: Which would you prefer?
Option A: .80 chance to win $4,000.
Option B: 1.0 chance to win $3,000.
Choice 2: Which would you prefer?
Option C: .80 chance to lose $4,000.
Option D: 1.0 chance to lose $3,000.


Typical preference
when gambling for gains
Typical preference
when gambling for losses
• People are typically risk averse for gains and risk seeking for losses.
This pattern is called the reflection effect.
Psych 355, Miyamoto, Spr '16
Reflection Effect - Definition
21
Wednesday, June 01, 2016: The Lecture Ended Here
Psych 355,, Miyamoto, Spr '16
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