STAGES OF INDUCTIVE
REASONING
• list current evidence
– P1: Jane smiles at me in class
– P2: Jane asked if we could study together
• form hypotheses: possible conclusions
that see implied by the evidence
– Ci: ? Jane needs help in the class
– Cj: ? Jane wants to see me socially
• evaluate probability that each
hypothesis is true
– Ci:
.30
Cj:
.80
• search for new evidence
– P3: Bob says that Jane failed the first exam
• revise probabilities in light of new
evidence
– Ci: .30
.75
Cj: .80
.30
OBSTACLES TO “INDUCTIVE
RATIONALITY”
• ignore potential hypotheses
• ignore potential evidence
• misinterpret evidence
• err in estimates of hypotheses’
probabilities
• bias in searching for new evidence
• ignore prior probabilities when new
evidence is considered
HEURISTICS OF INDUCTIVE
REASONING
Kahneman & Tversky, 1972
• AVAILABILITY
– ease of generating instances (sample) from
memory
• death from diabetes or accident?
• words with “k” in first or third position?
– estimates of quantities “anchor” our
judgments about possible error
– ease of imagining outcomes (“simulation”)
can be biased by actual outcomes
(hindsight bias)
• REPRESENTATIVENESS
– “typical” events and outcomes are judged
more likely than others
• HHHHTTTT or THHTHTTH?
• is Linda a bank teller and feminist?
AVAILABILITY AND DECISION
MAKING (Alba, 1992)
task: given several arguments for and
against a current issue (e.g., universal
health care), “vote” on issue
2 strong arguments for program
4 weak arguments against program
vote occurs. .
immediate 2 days
% voting
for program:
68%
42
__%
AVAILABILITY AND ILLUSORY
CORRELATIONS
Eats
spinach
Doesn’t eat
spinach
Can barpress
own weight
15
9
Can’t barpress
own weight
5
3
__
positive instances
may be more
available in memory
than negative
“instances”
ESTIMATING EVERYDAY RISKS
• being killed by lightning
– 1 in 2 million
• being killed by husband
or lover
– 1 in 800,000
• emergency treatment for
injury from sink or toilet
– 1 in 7,500
• dying in childbirth
– 1 in 12,000
Paling, 1994
Considering Sample Size
• Two hospitals in town
– One has mean of 45 births / day
– One has mean of 15 births / day
• Both count days with >60% males.
Which is more likely?
– Large hospital has more
– Small hospital has more
– About equal of such days
• Correct answer: small hospital
Why?
RELIANCE ON
REPRESENTATIVENESS
• ignoring small sample size
– the smaller the sample, the less
representative it will be
– how to make sample size salient
• ignoring the laws of probability
– conjunction of two events can’t be more
likely than either event alone
• p(A&B) = p(A) x p(B), both < 1.00
• ignoring prior probabilities
– Bayes’ Theorem: combines old prior
probabilities and “strength” of new
evidence to obtain new odds
SAMPLE SIZE AND
REPRESENTATIVENESS
Nisbett et al., 1983
on imagined trip to Oceana, you find
samples of:
• natives, all of whom are obese
• a new species, shreeble birds, all of whom
are red
• a new element, Floridium, all rocks of which
are conductive
e s tim a te o f %
task: Given samples of size N, estimate
the percent of the whole population
with that trait:
100
80
60
conductive
40
red
20
obese
0
1
3
sample size
20
The conjunction fallacy
Linda is 31 yrs 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 antinuclear demonstrations.
Linda …
– Is a teacher in elementary school
– Works in a bookstore and takes yoga
classes
– Is active in the feminist movement
– Is a psychiatric social worker
– Is a member of the League of Women Voters
– Is a bank teller
– Is an insurance salesperson
– Is a bank teller and is active in the feminist
movement
IGNORING THE “BASE RATE”
Management job interview scenario:
Pool of applicants includes
70% law background
30% engineering background
“Tom R. is 30 yrs. old, married, no children,
intelligent and motivated, well liked by his
colleagues”
How likely is it that Tom R. is a lawyer,
and not an engineer?
Actual: p = .70 (why?)
Obtained: p = .52
Inductive Reasoning and
“Circumstantial Evidence”
• CIRCUMSTANTIAL EVIDENCE
– Circumstantial evidence is a fact
that can be used to infer another
fact.
• Indirect evidence that implies something
occurred but doesn't directly prove it
• proof of one or more facts from which
one can find another fact
• proof of a chain of facts and
circumstances indicating that the person
is either guilty or not guilty.
– E.g., If a man accused of embezzling
money from his company had made
several big-ticket purchases in cash around
the time of the alleged embezzlement, that
would be circumstantial evidence that he
had stolen the money.
•
E.g., X is suing his wife, Y, for a divorce, claiming
she is having an affair with Z. Z's fingerprints are
found on a book in X and Y's bedroom. A judge or
jury may infer that Z was in the bedroom. The
fingerprints are circumstantial evidence of Z's
presence in the bedroom. Circumstantial evidence
is usually not as good as direct evidence (an
eyewitness saw Z in the bedroom) because it is
easy to make the wrong inference - Y may have
loaned Z the book and then carried it back to the
bedroom herself after getting it back.
• The law makes no distinction between the
weight given to either direct or circumstantial
evidence
•
“Circumstantial evidence is generally admissible in
court unless the connection between the fact and
the inference is too weak to be of help in deciding
the case. Many convictions for various crimes have
rested largely on circumstantial evidence.”
[‘Lectric Law Library]
– “The case against him is purely
circumstantial.”
– “Theories can’t be proven, only disproven;
therefore, one theory is as good as another.”
– “Evolution is just a theory, not a fact.”
•
We end with a comment on the status of evolution-as fact,
"just a theory," or something in between. In the physical
sciences there are many observations or facts that have given
rise to generalizations: two of these are the law of
conservation of matter and the law of definite proportions
(which states that when two or more elements combine to
form a compound they do so in definite proportions by
weight). The statements of facts and their convenient
generalization to laws are expressed in terms of
macroscopically observable and weighable quantities. The
overarching explanation for these laws is achieved in atomic
theory, which is expressed in terms of invisible atoms and
molecules. No one thinks that atomic theory is "just a theory,"
for it possesses extraordinary explanatory power and
provides the context in which many of the conveniences of
our civilization depend. Thus we proceed from many
observations or facts to their generalization in terms of laws,
both levels macroscopic, to a theory expressed in terms of
invisible entities.
•
If we now apply this scheme to biology, we see that the
concept of evolution is at the law level, as it summarizes the
results of a large number of observations or facts about
organisms. The analogous theory is natural selection or other
means by which evolution is achieved. Unknown nearly 150
years ago to Darwin, explanations of macroscopic evolution
in terms of microscopic genes and molecular sequences of
nucleic bases in DNA are known to us. Placing the concept of
evolution at the law level clarifies its status; it is not a theory.
[Bruce & Francis Martin, Skeptical Enquirer, Nov. 2003]
cf. William A. Dembski: "The Design Inference: Eliminating
chance through small probabilities," Cambridge University
Press, (1998)
CHOOSING ALTERNATIVE
ACTIONS UNDER UNCERTAINTY
consider the costs & benefits of various
combinations of actions and outcomes:
Outcome
Action: take umbrella?
Prob.
NO
YES
RAIN
SUNNY
.40
.60
expected outcome:
- 10 [-4.0]
+ 2 [+1.2]
- 2.8
+ 5 [+2]
- 2 [-1.2]
+0.8
what to choose? Utility theory says pick
action that gives best “average” or
expected outcome.
for each action, expected outcome =
sum of [probs x outcomes]
FRAMING CHOICES FOR GAINS
OR LOSSES
task: choose disease control program. If
no intervention, 600 will die.
prob. of . .
Program A Program B
(low risk)
(high risk)
none saved
0.00
0.67
200 saved
1.00
0.00
600 saved
0.00
0.33
“persons saved” frame: 72
__% choose A
“persons killed” frame:
22
__% choose A
(Kahneman & Tversky, 1982)
COGNITIVE PSYCHOLOGY
Course Goals
In EXP 3604, you will learn about...
• THE COGNITIVE APPROACH
– how to think about cognition like a
cognitive psychologist
• THE METHODS OF THAT APPROACH
– understanding the interplay between
theoretical and experimental tools
• THE NATURE AND LIMITS OF
COGNITION
– how we do those things we do
(e.g., perceive, attend, recall, think…)
• TIPS AND TECHNIQUES FOR
ENHANCING COGNITION
– methods of improving your skills in
learning, remembering and thinking
… and revive that childlike sense of awe