Transcript Inductive Reasoning - University of California, Irvine

Heuristics and Biases
Normative Model
Prior probability
Posterior Probability
Evidence
• Bayes rule tells you how you should reason with
probabilities – it is a normative model
• But do people reason like Bayes?
Tversky & Kahneman
• According to Tversky & Kahneman, Bayesian decision
theory does not describe human decision making very
well  Bayes rate neglect, Conservatism
• Instead, much of decision making may be based on
Biases and heuristics (mental short-cuts)
• Heuristics lower cognitive load and often work, but
results in severe errors in some cases
• Examples
– Representativeness heuristic
– Availability heuristic
The Taxi Problem
• A witness sees a crime involving a taxi in Carborough.
The witness says that the taxi is blue. It is known from
previous research that witnesses are correct 80% of the
time when making such statements.
• What is the probability that a blue taxi was involved in the
crime?
The Taxi Problem
• A witness sees a crime involving a taxi in Carborough.
The witness says that the taxi is blue. It is known from
previous research that witnesses are correct 80% of the
time when making such statements.
• The police also know that 15% of the taxis in Carborough
are blue, the other 85% being green.
• What is the probability that a blue taxi was involved in the
crime?
Base Rate Neglect: The Taxi Problem
• Failure to take prior probabilities (i.e., base rates) into
account
• In the taxi story, the addition of:
“The police also know that 15% of the taxis in Carborough
are blue, the other 85% being green.”
has little influence on rated probability
Base Rate Neglect (2)
• Kahneman & Tversky (1973).
• Names of 100 engineers and lawyers are written on cards
and put in a container. What is probability of picking an
engineer in from container A and B?
Container A: 70 engineers and 30 lawyers
Container B: 30 engineers and 70 lawyers
• People can estimate these probabilities …
Providing additional information
• “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
and spends most of his free time on his many hobbies,
which include home carpentry, sailing, and mathematical
puzzles”
• What now is probability Jack is an engineer?
• For both container A and B, the estimate was P = .9
• Where did the base rate go?
Conservatism
Once people form a probability estimate, they are often slow
to change the estimate given new information
URN A: 70 red balls, 30 blue balls
URN B: 30 red balls, 70 blue balls
A number of balls are selected from a randomly picked urn.
What is probability of getting from urn A:
Estimated Probability
One red
Two red
Three red
.60
.65
.70
Actual Probability
.70
.84
.93
Representativeness Heuristic
All the families having exactly six children in a particular city
were surveyed. In 72 of the families, the exact order of the
births of boys and girls was:
G B G B B G
What is your estimate of the number of families surveyed in
which the exact order of births was:
B G B B B B
Answer:
a) < 72
b) 72
c) >72
Representativeness Heuristic
The sequence “G B G B B G” is seen as
A) more representative of all possible birth
sequences.
B) better reflecting the random process of B/G
Representativeness Heuristic & Gambler’s Fallacy
A coin is flipped. What is a more likely sequence?
A) H T H T T H
B) H H H H H H
A) #H = 3 and #T = 3
B) #H = 6
(in some order)
Gambler’s fallacy: wins are perceived to be more likely
after a string of losses
Does the “hot hand” phenomenon exist?
Most basketball coaches/players/fans refer to
players having a “Hot hand” or being in a “Hot
zone” and show “Streaky shooting”
However, there is little statistical evidence that
basketball players switch between a state of “hot
hand” and “cold hand”
People often see structure in sequences that are
statistically purely random (and nonchanging)
(Gilovich, Vallone, & Tversky, 1985)
Availability Heuristic
• Are there more words in the English language that begin
with the letter V or that have V as their third letter?
• What about the letter R, K, L, and N?
(Tversky & Kahneman, 1973)
Availability Heuristic & Conjunction Fallacy
Estimate the number of words that would fit the following
forms:
A)
B)
_____ing
______n_
(Tversky & Kahneman, 1983)
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.
Rate the likelihood that the following statements about
Linda are true:
a) Linda is active in the feminist movement
b) Linda is a bank teller
c) Linda is a bank teller and is active in the feminist
movement
Result: (c) is rated as more likely than (a) or (b). From a
standard probabilistic point of view, this is strange 
conjunction fallacy
Which city has a larger population?
A) San Diego
B) San Antonio
• 66% accuracy with University of Chicago undergraduates.
However, 100% accuracy with German students.
• San Diego was recognized as American cities by 78% of
German students. San Antonio: 4%
 With lack of information, use recognition heuristic
(Goldstein & Gigerenzer, 2002)
Are heuristics wrong?
No, we use mental shortcuts because they are often right.
Availability and representativeness are often ecologically
valid cues.
Are we really that bad in judging probabilities?
According to some researchers (e.g., Gigerenzer), it
matters how the information is presented and processed.
Processing frequencies is more intuitive than probabilities
(even it leads to the same outcome).