Transcript Chap10b

Cognitive Processes
PSY 334
Chapter 11 – Judgment and
Decision-Making
Inductive Reasoning
 Processes for coming to conclusions that
are probable rather than certain.
 As with deductive reasoning, people’s
judgments do not agree with prescriptive
norms.
 Baye’s theorem – describes how people
should reason inductively.

Does not describe how they actually
reason.
Baye’s Theorem
 Prior probability – probability a
hypothesis is true before considering the
evidence.
 Conditional probability – probability the
evidence is true if the hypothesis is true.
 Posterior probability – the probability a
hypothesis is true after considering the
evidence.

Baye’s theorem calculates posterior
probability.
Burglar Example
 Numerator – likelihood the evidence
(door ajar) indicates a robbery.
 Denominator – likelihood evidence
indicates a robbery plus likelihood it
does not indicate a robbery.
 Result – likelihood a robbery has
occurred.
Baye’s Theorem
H
~H
E|H
likelihood
likelihood
likelihood
robbery
E|~H likelihood
of being robbed
of no robbery
of door being left ajar
during a
of door ajar without robbery
P( E | H ) P( H )
P( H | E ) 
P( E | H ) P( H )  P( E |~ H ) P(~ H )
Baye’s Theorem
P(H) = .001
P(~H) = .999
P(E|H) = .8
P(E|~H) = .01
from police statistics
this is 1.0 - .001
Base rate
P( E | H ) P( H )
P( H | E ) 
P( E | H ) P( H )  P( E |~ H ) P(~ H )
(.8)(.001)
P( H | E ) 
 .074
(.8)(.001)  (.01)(.999)
Base Rate Neglect
 People tend to ignore prior probabilities.
 Kahneman & Tversky:


70 engineers, 30 lawyers vs 30 engineers,
70 lawyers
No change in .90 estimate for “Jack”.
 Effect occurs regardless of the content of
the evidence:

Estimate of .5 regardless of mix for “Dick”
Cancer Test Example
 A particular cancer will produce a
positive test result 95% of time.

If a person does not have cancer this gives
a 5% false positive rate.
 Is the chance of having cancer 95%?
 People fail to consider the base rate for
having that cancer: 1 in 10,000.
Cancer Example
Base rate
P(H) = .0001
P(~H) = .9999
P(E|H) = .95
P(E|~H) = .05
likelihood of having cancer
likelihood of not having it
testing positive with cancer
testing positive without cancer
P( E | H ) P( H )
P( H | E ) 
P( E | H ) P( H )  P( E |~ H ) P(~ H )
(.95)(.0001)
P( H | E ) 
 .0019
(.95)(.0001)  (.05)(.9999)
Conservatism
 People also underestimate probabilities
when there is accumulating evidence.
 Two bags of chips:



70 blue, 30 red
30 blue, 70 red
Subject must identify the bag based on the
chips drawn.
 People underestimate likelihood of it
being bag 2 with each red chip drawn.
Probability Matching
 People show implicit understanding of
Baye’s theorem in their behavior, if not in
their conscious estimates.
 Gluck & Bower – disease diagnoses:


Actual assignment matched underlying
probabilities.
People overestimated frequency of the
rare disease when making conscious
estimates.
Frequencies vs Probabilities
 People reason better if events are
described in terms of frequencies
instead of probabilities.
 Gigerenzer & Hoffrage – breast cancer
description:

50% gave correct answer when stated as
frequencies, <20% when stated as
probabilities.
 People improve with experience.
Judgments of Probability
 People can be biased in their estimates
when they depend upon memory.
 Tversky & Kahneman – differential
availability of examples.


Proportion of words beginning with k vs
words with k in 3rd position (3 x as many).
Sequences of coin tosses – HTHTTH just
as likely as HHHHHH.
Gambler’s Fallacy
 The idea that over a period of time things
will even out.
 Fallacy -- If something has not occurred
in a while, then it is more likely due to
the “law of averages.”
 People lose more because they expect
their luck to turn after a string of losses.

Dice do not know or care what happened
before.
Chance, Luck & Superstition
 We tend to see more structure than may
exist:



Avoidance of chance as an explanation
Conspiracy theories
Illusory correlation – distinctive pairings are
more accessible to memory.
 Results of studies are expressed as
probabilities.

The “person who” is frequently more
convincing than a statistical result.
Decision Making
 Choices made based on estimates of
probability.
 Described as “gambles.”
 Which would you choose?


$400 with a 100% certainty
$1000 with a 50% certainty
Utility Theory
 Prescriptive norm – people should
choose the gamble with the highest
expected value.
 Expected value = value x probability.
 Which would you choose?


A -- $8 with a 1/3 probability
B -- $3 with a 5/6 probability
 Most subjects choose B
Subjective Utility
 The utility function is not linear but
curved.

It takes more than a doubling of a bet to
double its utility ($8 not $6 is double $3).
 The function is steeper in the loss region
than in gains:



A – Gain or lose $10 with .5 probability
B -- Lose nothing with certainty
People pick B
Framing Effects
 Behavior depends on where you are on
the subjective utility curve.


A $5 discount means more when it is a
higher percentage of the price.
$15 vs $10 is worth more than $125 vs
$120.
 People prefer bets that describe saving
vs losing, even when the probabilities
are the same.