Today’s Topic
Do you believe in free will?
Why or why not?
The “I Want More Pain”
Experiment
A
or
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The “I Want More Pain”
Experiment
69%
31%
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
0
1
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Memory or Experience
Which is more important?
How is this possible?
Remembered pain(RP)= (MAX+ENDING)/2
A– (RP=(7+1)/2=4)
B- (RP=(7+7)/2=7)
Experienced pain= sum(pain)
Which should doctors minimize?
How do we choose what we choose?
u(x) : the subjective utility of x
Lottery:
E(x) : the expected subjective utility of x 1/1000 odds,
$500 prize
On average, you win
E(x) = p(x) u(x)
$500 for 1000 games
= $0.50 per game
p(x) : the probability of x
That’s expected utility
E(c) : the expected subjective utility of choice c
E(c) =  i p(oi) u(oi)
oi : the ith outcome of choice c
Calculating Expected Utility
What is my subjective expected utility of deciding to
audition for “The Real World”?
E(c) = p(o1) u(o1)
How cool would it be to be on The Real World?
How likely am I to actually be chosen?
Calculating Expected Utility
What is my subjective expected utility of deciding to
audition for “The Real World”?
equals 1: there will be an interview!
E(c) = p(o1) u(o1) + p(o2) u(o2) Do I like interviews?
How cool would it be to be on The Real World?
How likely am I to actually be chosen?
Calculating Expected Utility
What is my subjective expected utility of deciding to
audition for “The Real World”?
equals 1: there will be an interview!
E(c) = p(o1) u(o1) + p(o2) u(o2) Do I like interviews?
How cool would it be to be on The Real World?
How likely am I to actually be chosen?
Being on “Real World” would be really cool, but you
don’t have a chance in heck, and you dislike interviews:
E(c) = 0.0001 * 10000 + 1 * (-8) = 2
Expected utility of staying home (no outcomes):
E(c) = 0
Now, suppose you REALLY dislike interviews:
E(c) = 0.0001 * 10000 + 1 * (-50) = -40
Rational Choice
These ideas are from Rational Choice Theory in Economics.
 “Rational consumers always maximize expected utility.”
But we can extend these ideas to choice behavior in general.
 “People always maximize subjective expected utility.”
But is this how people actually work?
If it is, people are faced with two problems:
 We often don’t know how probably outcomes are
 Utility of outcomes often depends on other outcomes
For Example:
chaining principle
E(being in class) = p(passing) * E(passing)
E(passing) = p(graduating) * E(graduating)
E(graduating) = p(getting good job) * E(getting good job)
…..
Semi-Rational Choice
Lets assume:
People want to maximize subjective expected utility,
but they can’t (too much computation, too many unknowns)
What do people do?
People make educated guesses (i.e. use heuristics)
to estimate utility and probability values.
Psychologically, there are two critical questions:
How do we decide how good something is? (utility)
How do we decide how likely something is? (probability)
Utility
How do we decide how good something is?
subjective utility
losses
gains
Utility
How do we decide how good something is?
subjective utility
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
Utility
How do we decide how good something is?
subjective utility
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
Utility
How do we decide how good something is?
subjective utility
risk aversion:
100% chance to get $100,
50% chance to get $200
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
Utility
How do we decide how good something is?
subjective utility
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
Utility
How do we decide how good something is?
subjective utility
loss aversion
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
In Class Experiment - Framing
Effects
• There is an outbreak of a disease that’s
expected to kill 600 people. Two plans
have been proposed to deal with the
disease
– Plan A: 200 people will be saved
– Plan B: 1/3 chance that 600 will be saved
–
2/3 chance that 0 will be saved
In Class Experiment - Framing
Effects
• There is an outbreak of a disease that’s
expected to kill 600 people. Two plans
have been proposed to deal with the
disease
– Plan A: 400 people will die
– Plan B: 1/3 chance that 0 will die
–
2/3 chance that 600 will die
Utility
How do we decide how good something is?
Framing Effects
Assume you are richer by $300. Choose between:
• a sure gain of $100
• a 50% chance gain of $200, 50% chance no change
Assume you are richer by $500. Choose between:
• a sure loss of $100
• a 50% chance loss of $200, 50% chance no change
Utility
How do we decide how good something is?
Framing Effects
Assume you are richer by $300. Choose between:
+ $400 • a sure gain of $100
• a 50% chance gain of $200, 50% chance no change
+ $500 or $300
Assume you are richer by $500. Choose between:
+ $400 • a sure loss of $100
• a 50% chance loss of $200, 50% chance no change
+ $300 or $500
Utility
How do we decide how good something is?
subjective utility
Framing Effects
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
Utility
How do we decide how good something is?
subjective utility
Framing Effects
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
Utility
How do we decide how good something is?
Framing Effects:
Choose a sure gain
subjective utility
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
Utility
How do we decide how good something is?
Framing Effects:
Choose a sure gain
subjective utility
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
Utility
How do we decide how good something is?
Framing Effects:
Choose a sure gain
Choose risk for a loss
subjective utility
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
Utility
How do we decide how good something is?
subjective utility
loss aversion
• leads to trade aversion
• maintaining the status quo
losses
gains
$-1000
$-500
$-100 $100
$500
$1000
Probability
How do we decide how likely something is?
 Representativeness: Something is likely to the extent
that it is familiar.
Representativeness
Linda is a 31 year 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 antiuclear demonstrations.
Please rank the following by their probability, with 1
for the most probable and 6 for the least probable.
A)
B)
C)
D)
E)
F)
Linda is a university professor
Linda is an insurance salesperson
Linda is a bank teller
Linda is an owner of a book store
Linda is a single mom and takes classes at night school
Linda is a bank teller and is active in the feminist movement
Representativeness
Linda is a 31 year 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 antiuclear demonstrations.
Please rank the following by their probability, with 1
for the most probable and 6 for the least probable.
A)
B)
C)
D)
E)
F)
People rank F as
more probable.
According to probability,
it can’t be:
P(A&B) = P(A) * P(B)
Linda is a university professor
Linda is an insurance salesperson
Linda is a bank teller
Linda is an owner of a book store
Linda is a single mom and takes classes at night school
Linda is a bank teller and is active in the feminist movement
Probability
How do we decide how likely something is?
 Representativeness: Something is likely to the extent
that it is familiar.
This leads to the conjunction fallacy.
Representativeness
Tom W. is of high intelligence, although lacking in true creativity.
He has a need for order and clarity, and for neat and tidy systems
in which every detail finds its appropriate place. His writing is
rather dull and mechanical, occasionally enlivened by somewhat
corney punsand flashes of imagination of the sci-fi type. He has a
strong drive for competence. He seems to have little feel and
sympathy for people, and does not enjoy interacting with others.
Self-centered, he nonetheless has a deep moral sense.
This preceding personality sketch was written on the basis of
projective tests Tom’s senior year in highschool. Tom is
currently working
Is Tom more likely to be a salesman or a librarian?
Probability
How do we decide how likely something is?
 Representativeness: Something is likely to the extent
that it is familiar.
This leads to the conjunction fallacy, and to base
rate beglect.
Probability
How do we decide how likely something is?
 Representativeness: Something is likely to the extent
that it is familiar.
This leads to the conjunction fallacy,
and to base rate beglect.
 Availability: Something is likely to the extent
that examples easily come to mind.
Availability
0.1
What is the probability that a major earthquake will strike
the U.S. in the next year and kill 1,000 people?
0.5
What is the probability that a major earthquake will strike
California in the next year and kill 1,000 people?
Probability
How do we decide how likely something is?
 Representativeness: Something is likely to the extent
that it is familiar.
This leads to the conjunction fallacy,
and to base rate beglect.
 Availability: Something is likely to the extent
that examples easily come to mind.
This leads to the conjunction fallacy also,
and people overestimate the probability of
publicized events.
•
Conditional Probability
Examples
P (having a beard given that you are an
american male)? P(B|M)? (1/50)
• P (being american male given that you have
a beard)? P(M|B)? (99%?)
• P(an american taller than 6’4” given that
you are in the NBA?) (98%)
• P(Being in the NBA given that you are an
american taller than 6’4”?) (<1%)
Bayes’ Theorem
P(X) : the probability of X
P(Y) : the probability of Y
P(X | Y) : the probability of X given that Y is true
P(Y | X) : the probability of Y given that X is true
Bayes Theorem converts P(X | Y) to P(Y | X).
P(X | Y) * P(Y)
P(Y | X) =
P(X)
Bayes’ Theorem
P(T) : the probability of being Tall
P(N) : the probability of being in the NBA
P(T | N) : the probability of Tall given that Nba is true
P(N | T) : the probability of Nba given that Tall is true
Bayes Theorem converts P(T | N) to P(N | T).
P(T | N) * P(N)
P(N | T) =
P(T)
If Bob plays in the NBA, he is
Probably Tall (>6’4”)
Bayes’ Theorem
P(T) : the probability of being Tall
P(N) : the probability of being in the NBA
P(T | N) : the probability of T given that N is true
P(N | T) : the probability of N given that T is true
Bayes Theorem converts P(T | N) to P(N | T).
0.98
P(T | N) * P(N)
P(N | T) =
P(T)
If Bob plays in the NBA, he is
Probably Tall (>6’4”)
Bayes’ Theorem
P(T) : the probability of being Tall
P(N) : the probability of being in the NBA
P(T | N) : the probability of T given that N is true
P(N | T) : the probability of N given that T is true
Bayes Theorem converts P(T | N) to P(N | T).
0.98
P(T | N) * P(N)
P(N | T) =
The probability that Bob is tall
Given that he is in the NBA is
High
P(T)
What is the probability that Bob
Plays in the NBA given that he
Is Tall (>6’4”)
Bayes’ Theorem
P(T) : the probability of being Tall
P(N) : the probability of being in the NBA
P(T | N) : the probability of T given that N is true
P(N | T) : the probability of N given that T is true
Bayes Theorem converts P(T | N) to P(N | T).
0.98
0.00001
P(T | N) * P(N)
P(N | T) =
0.01
P(T)
= .0000098/.01 = .001
The probability that Bob is tall
Given that he is in the NBA is
High
What is the probability that Bob
Plays in the NBA given that he
Is Tall (>6’4”)
A Picture might help
P(>6'4")
P(NBA)
Why is Base Rate Important?
• Need base rate to reason about
conditional probabilities
• Base rate neglect: Failing to consider
the base rates
– A VERY COMMON ERROR -- even
among EXPERTS