Transcript Chapter 11

Cognitive Processes
PSY 334
Chapter 11 – Judgment &
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.
Burglary Probabilities
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” with
description.
 Effect occurs regardless of the content of
the evidence:

Estimate of .5 regardless of mix for “Dick”
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 and spends most of his spare
time on his many hobbies, which include
home carpentry, sailing and
mathematical puzzles.
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.
Gluck & Bower’s Results
Implicit Judgments
Explicit Judgments
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.
Recognition Heuristic
 Gigerenzer says use of availability of info
in memory is not a fallacy but helpful.
 Recognition heuristic – people attach
greater importance to what they
recognize than what they don’t.


They say Heidelberg is bigger because
they recognize the name, not Bamberg.
This works because size and familiarity are
correlated, but may not work in other areas
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
$2.67
$2.50
Deal or No Deal?
 https://www.youtube.com/watch?v=GxzP
CVX-t3o
 Which would you choose?


A -- 1 million dollars with a probability of 1
B -- 2.5 million dollars with a probability of
½
 Utility theory predicts B but people pick A
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 because enough is enough.
Subjective Utility
 Doubling the amount of money does not double
the value to people:
 For $1 million, U = 1
 Then 2.5 million x ½ = 1.25 million
 If people value the chance to win $2.5 instead
of $1 only slightly more than getting $1 million
for sure, U=1.2 not 2.5
 So, $1 million = U, but $2.5 million = .6 (1.2 x
½), so choosing $1 million wins.
Subjective Utility
The value we place on money is not linear to the face
value of money.
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.
Greater Weight on Losses
 Someone has lost $140 at the races but
can now bet $10 with 15:1 odds.


A – refuse the bet and accept $140 loss
B – Make the bet and face losing $150 or breaking
even.
-140 point on subjective curve
 If expressed differently the decision
changes:


A – Refuse the bet and stay the same
B – Make the bet and lose $10 more with a poor
chance of gaining $140. 0 point on subjective curve
Odds of Living vs Dying
Change Decision-making
A – Save 200 people.
B – 1/3 probability 600 saved,
2/3 probability no one saved
C – 400 people will die
D – 1/3 probability nobody will die
2/3 probability 600 people will die
 72% preferred A but only 22% preferred
C (equivalent to A). D is the same as B.
Impersonal vs Personal
Dilemmas
A – A runaway trolley will kill 5 people unless it is
switched to a different track where it will kill 1
person. Do you do it?
B – The trolley will kill 5 people unless you push a
stranger off a bridge into the path of the trolley,
killing him. Do you do it?
 Most people say yes to A but no to B.
 Different brain regions are active in the two
choices (B is emotional).
Evidence from Neuroscience
 Dopamine neurons in the nucleus
acumbens (basal ganglia) respond to
reward size.
 Probability of reward is evaluated in the
ventromedial prefrontal cortex (which
also integrates probabilities & utilities).

People with damage have trouble with
gambling tasks (such as Iowa gambling
task with good/bad decks).