Judgments and Decisions
Psych 253
• Heuristics and Biases in Probability Judgments
•
•
•
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Availability Heuristic
Anchoring Heuristic
Representativeness Heuristic
Overconfidence
You can play a lottery by selecting A, B, or C. Below are
the payoffs for each option, depending on the throw
of a die. Which one do you want to play?
A
1
$1
2
$2
Die Roll
3
4
$3
$4
B
$6
$2
$5
$2
$2
$2
C
$7
$5
$4
$4
$2
$1
What should you choose?
5
$5
6
$6
A
1
$1
2
$2
Die Roll
3
4
$3 $4
B
$6
$2
$5
$2
$2
$2
$3.17
C
$7
$5
$4
$4
$2
$1
$3.83
5
$5
6
$6
EV
$3.50
Which one would you select if you knew what
number would come up on the die?
A
1
$1
2
$2
Die Roll
3
4
$3 $4
B
$6
$2
$5
$2
$2
$2
C
$7
$5
$4
$4
$2
$1
5
$5
6
$6
What is the expected value of knowing the number
that would come up?
1/6*[ $7 + $5 + $5 + $4 + $5 + $6 ] = $5.33
A
1
$1
2
$2
Die Roll
3
4
$3
$4
B
$6
$2
$5
$2
$2
$2
C
$7
$5
$4
$4
$2
$1
5
$5
6
$6
The value of the information is
$5.33 - $3.83 = $1.50
Value of the
decision
WITH
perfect
information
Value of the
decision
WITHOUT
perfect
information
Which would you prefer?
• $30 for sure
• A gamble in which a fair coin is tossed. If it
comes up heads, you win $100. If tails, you get
$0
• How much should you pay to find out which
side of the coin will come up?
.5*(100) + .5*(30) = $65
Heuristics in Probability Judgments
• When we reason probabilistically, we often use
the wrong information, ignore the right
information, and apply rules that result in logic
errors.
Kahneman and Tversky identified three
judgmental heuristics – all of which involve
associations.
• Availability Heuristic -- People assess the probability of an event
based on the degree to which instances are readily available.
If you can think of it, it must be important.
• Anchoring Heuristic: People start with an anchor then adjust up or
down, but their adjustments are often insufficient.
Initial associations are hard to shake off.
• Representativeness Heuristic: People often think about the
resemblance between an object and a larger reference class.
If two things are similar, the probability of one given the other
must be higher.
Heaven and Hell
• Heaven is where the Police are British, the
Chefs are French, the Mechanics are German,
the Lovers are Italian, and it's all organized by
the Swiss.
• Hell is where the Chefs are British, the
Mechanics are French, the Lovers are Swiss,
the Police are German, and it's all organized
by the Italians
We make associations about everything –
especially each other!
Availability: Vivid Associations
Which events kill more people?
Homicide or Suicide
Floods or Tuberculosis
Tornados or Asthma
We focus on information that is vivid -- recent or well
publicized, even when it is less likely to occur, and our
perceptions of risk are influenced by these
associations.
Vividness of Cases and the Banality of statistics
“A single death is a tragedy; a million deaths is a statistic." Joseph Stalin
“If I look at the masses I will never act, but if I look at one, I will.” Mother Teresa
Save the Children: Donation Request
Food Shortages in Malawi are
affecting 3 Million children
More than 11 Million in
Ethiopia need immediate
assistance
One-third of Angolans have
been forced to flee their homes
$1.14
Any money you donate will go
to Roika, a seven year old girl
from Mali, Africa. Roika is
desperately poor and faces the
threat of starvation. Her life will
be transformed as a result of
your contribution.
$2.38
Availability: Easily-Recalled Associations
• Married couples were asked to estimate the percentage of work
they contributed to various activities, including cooking, cleaning,
and taking out the garbage. Each member of the couple was asked
independently. In 16 of 20 activities, the total percentage exceeded
100%.
• The percentage of effort contributed to a collaborative project such
as professor/student or supervisor/supervisee summed to
approximately 130%.
• The salience of what we personally do (relative to the other person)
can lead to an overestimation of our contribution to a joint effort.
• Think of three wonderful things about your significant
other. Now rate your feelings about your significant
other on a scale from 1 = Not at all Satisfied to 10 =
Perfectly Satisfied
• Now think of 10 wonderful things about your
significant other…
• The experienced difficulty (or ease) of recall can
influence our judgments and evaluations.
Availability: Consistent Associations
• When we have stereotypical impressions of a
group, we often make follow up evaluations
that are consistent with those impressions.
• Is music different when a women plays it?
• Auditions were done in front of a panel of
judges before 1970. Since then, auditions are
done behind drapes. (And now they also done
barefoot!)
Representativeness: Detailed Associations
• What are the chances of a massive flood occurring in the next
30 years somewhere in North America in which 1,000 people
drown?
• What are the chances of an earthquake occurring in the next
30 years somewhere in California which causes a massive
flood in which 1,000 people drown?
Rank in terms of probability four possible crimes committed by Mr. P
who is currently under investigation by the police. 1 = the most
probable crime and 4 = the least probable crime.
Group 1 a. Mr. P is a child molester.
b. Mr. P is involved in espionage and the sale of secret
documents.
c. Mr. P is a drug addict.
d. Mr. P. killed one of his employees.
Group 2 a. Mr. P is a child molester.
b. Mr. P is involved in espionage and the sale of secret
documents.
c. Mr. P is a drug addict.
d. Mr. P. killed one of his employees to prevent him from
talking to the police
Representativeness: Expected Associations
• You're playing roulette, and red has just come
up eight times in a row! Is black more likely
on the next spin?
• No, it is not. Both red and black are equally
likely. If you thought otherwise then the
casinos love you.
• A cab was involved in a hit and run accident at night.
Two cab companies, the Green and the Blue, operate
in the city. 85% of the cabs in the city are Green and
15% are Blue.
• A witness identified the cab as Blue. The court tested
the reliability of the witness under the same
circumstances that existed on the night of the
accident and concluded that the witness correctly
identified each color 80% of the time and failed 20%
of the time.
• What is the probability that the cab involved in the
accident was Blue rather than Green knowing that
this witness identified it as Blue?"
Anchoring: Associations
• Are there more than 2 billion mobile phones
in the world?
• What is your best estimate of the number of
mobile phones in the world?
• We often give disproportionate weight to a
single piece of information that becomes the
anchor for our estimate.
No Limit
per Person
(3.3 cans on
average
73 cans sold)
Percentage of Buyers Purchasing N
Cans of Soup
100
80
60
40
20
0
1
2
3
4
5
6
7
8
9
10 11 12
Percentage of Buyers Purchasing N
Cans of Soup
N Cans of Soup
Limit 4
per Person
(3.5 cans on
average
106 cans sold)
100
80
60
40
20
0
1
2
3
4
5
6
7
8
N Cans of Soup
9
10 11 12
Percentage of Buyers Purchasing N
Cans of Soup
100
Limit 12
per Person
(7 cans on
average
188 cans sold)
80
60
40
20
0
1
2
3
4
5
6
7
8
N Cans of Soup
9
10
11
12
Other Examples of Anchors
Initial offers in negotiations
First impressions at the workplace
Anchors set reference points and can be hard to
ignore, even when they’re irrelevant.
Anchors in Real Estate. All participants in this study visited a piece of
property in Tucson. They were each given a 10 page packet including: 1)
The MLS listing sheet, 2) Sale information from the last 6 months,
3)Current listings in the area and the accompanying MLS listing
information.
A questionnaire asked them to
•Appraise the house’s value
•Set an appropriate selling price
•Estimate an actual, reasonable sale price
•The lowest price the house should go for
The actual listing price and appraised value of the house was $74,900
There were two groups of subjects, and the only difference between
groups was the actual listing price.
Low Price Group’s packet had it listed as
$65,900 (-12%)
High Group’s packet had it listed as
$83,900 (+12%)
Results for Undergraduate Business Students:
Listing
Price
Appraisal
Value
Estimated
Value
Estimated
Purchase
Price
$65,900
$63,600
$69,400
$63,600
$62,600
$83,900
$72,200
$78,000
$69,500
$69,800
Lowest Offer
Lowest
Offer
Results For Real Estate Agents:
Listing
Price
Appraisal
Value
Estimated
Listing Value
Estimated
Purchase
Price
$65,900
$67,800
$70,000
$66,800
$65,000
$83,900
$75,200
$76,380
$73,000
$72,600
• Increased success rates for women since blind
auditions
– 1st Round – 50% and Final Round – 300%
– Overall Differences in Representation
– Pre 1970 - 5% of top five orchestras had women
– 1990 – 36% of top five orchestras have women
– Today - 50% of top five orchestras have women
• I am an above-average driver.
• I have an above average ability to judge humor.
• My academic performance places me in the top
half of my class.
• To protect our mindsets, we engage in selfserving biases. We claim credit for success and
blame failure on bad luck.
•
•
•
Strong economy during a presidential era
Increase in company stocks
Pay raises
• Overconfidence in Action
• 80% of entrepreneurs perceived their chances
of success as 70% or higher. 33% perceived
their chances as certain, but the average
success rate for similar businesses was only
59%. The five year survival rate of similar
businesses was 33% (Cooper et al, 1988)
• More than 70% of new plants in North America
close within the first decade. 3/4 of mergers
and acquisitions don’t pay off. 2/3 of all small
businesses fail within the first year.
Overconfidence Quotes
1929 (September 16): "A severe depression like that of 1920-21 is
outside the range of probability.“ - Harvard Economic Society.
1932: “There is not the slightest indication that nuclear energy will
ever be attainable. That would mean that the atom would have to
be shattered at will.” - Albert Einstein
1943: "I think there is a world market for about five computers.“ Thomas J. Watson (Chairman of the Board of IBM)
1964: "Reagan doesn't have the presidential look.“ - United Artists
Executive, dismissing the idea that Ronald Reagan be offered the
starring role in the movie THE BEST MAN.
1977: "There is no reason for any individual to have a computer in
their home.“ - Ken Olson (President of Digital Equipment
Corporation), World Future Society Convention, Boston.
1981: “640Kb is enough for anyone.” - Bill Gates
Avoiding Overconfidence requires
• Good Calibration: You know what you know and
you know what you don’t know. (The average subjective
probability of a set of events is equivalent to the relative
frequency of those events.)
• Good Discrimination: You can tell the
difference between signals and noise. (The assignment of
higher probabilities to things that happen than to things that do
not happen.)
Best-Possible Calibration,
Good Discrimination
Objective Frequency
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Subjective Probability
0.8
1
Physicians’ Diagnoses of Suspected Bacteremia
Objective Frequency
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Subjective Probability
0.8
1
Economists’ Predictions of Recession
in 3–6 Months
Objective Frequency
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Subjective Probability
0.8
1
Lawyers’ Predictions of Winning Their Case
Objective Frequency
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Subjective Probability
0.8
1
Meteorologists’ Predictions of Precipitation
Objective Frequency
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
Subjective Probability
0.8
1
Greenspan: 'I was right 70% of the time'
"When you've been in government for 21 years, as I have
been, the issue of retrospect and what you should have
done is a really futile activity," Greenspan said. "I was
right 70% of the time. But I was wrong 30% of the time,
and there were an awful lot of mistakes in 21 years," he
added.
How Can This Be?
• If people just try hard enough, the errors and
biases in human judgment will usually take
care of themselves. True or False?
• The market takes care of these issues – the
fittest will survive and the biases will vanish.
True or False?