today’s topic do you believe in free will? why or why not?

Today’s Topic

Do you believe in free will?

Why or why not?

The “I Want More Pain” Experiment

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A or B

The “I Want More Pain” Experiment

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69% 31%

Memory or ExperienceWhich 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

E(x) : the expected subjective utility of x

E(x) = p(x) u(x)

p(x) : the probability of x

Lottery: 1/1000 odds, $500 prizeOn average, you win$500 for 1000 games= $0.50 per gameThat’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 toaudition 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?



E(c) = p(o1) u(o1) + p(o2) u(o2)How cool would it be to be on The Real World?


Do I like interviews? equals 1: there will be an interview!



E(c) = p(o1) u(o1) + p(o2) u(o2)How cool would it be to be on The Real World?


Do I like interviews? equals 1: there will be an interview!

Being on “Real World” would be really cool, but youdon’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: E(being in class) = p(passing) * E(passing) E(passing) = p(graduating) * E(graduating) E(graduating) = p(getting good job) * E(getting good job) …..

chaining principle

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


subjective utility

losses gains$100 $500 $1000$-100$-500$-1000

Utility


subjective utility

losses gains$100 $500 $1000$-100$-500$-1000

risk aversion:100% chance to get $100,50% chance to get $200

Utility


subjective utility

losses gains$100 $500 $1000$-100$-500$-1000

Utility


subjective utility

losses gains$100 $500 $1000$-100$-500$-1000

loss aversion

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


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


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

+ $400

+ $500 or $300

+ $400

+ $300 or $500

Utility


subjective utility

losses gains$100 $500 $1000$-100$-500$-1000

Framing Effects

Utility


subjective utility

losses gains$100 $500 $1000$-100$-500$-1000

Framing Effects: Choose a sure gain

Utility


subjective utility

losses gains$100 $500 $1000$-100$-500$-1000

Framing Effects: Choose a sure gain Choose risk for a loss

Utility


subjective utility

losses gains$100 $500 $1000$-100$-500$-1000

loss aversion• leads to trade aversion• maintaining the status quo

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 deeplyconcerned with issues of discrimination and social justice,and also participated in antiuclear demonstrations.

Please rank the following by their probability, with 1for the most probable and 6 for the least probable.

A) Linda is a university professorB) Linda is an insurance salespersonC) Linda is a bank tellerD) Linda is an owner of a book storeE) Linda is a single mom and takes classes at night schoolF) 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 deeplyconcerned with issues of discrimination and social justice,and also participated in antiuclear demonstrations.

Please rank the following by their probability, with 1for the most probable and 6 for the least probable.

A) Linda is a university professorB) Linda is an insurance salespersonC) Linda is a bank tellerD) Linda is an owner of a book storeE) Linda is a single mom and takes classes at night schoolF) Linda is a bank teller and is active in the feminist movement

People rank F as more probable.According to probability,it can’t be: P(A&B) = P(A) * P(B)

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.

RepresentativenessTom 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 ofprojective tests Tom’s senior year in highschool. Tom iscurrently 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

What is the probability that a major earthquake will strikethe U.S. in the next year and kill 1,000 people?0.1

What is the probability that a major earthquake will strikeCalifornia in the next year and kill 1,000 people?0.5

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(T) : the probability of being TallP(N) : the probability of being in the NBAP(T | N) : the probability of Tall given that Nba is trueP(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

If Bob plays in the NBA, he is Probably Tall (>6’4”)

0.98

P(T) : the probability of being TallP(N) : the probability of being in the NBAP(T | N) : the probability of T given that N is trueP(N | T) : the probability of N given that T is true


P(T | N) * P(N)P(N | T) = P(T)

Bayes’ Theorem

The probability that Bob is tallGiven that he is in the NBA is High

What is the probability that BobPlays in the NBA given that heIs Tall (>6’4”)

0.98



P(T | N) * P(N)P(N | T) = P(T)

Bayes’ Theorem

The probability that Bob is tallGiven that he is in the NBA is High

What is the probability that BobPlays in the NBA given that heIs Tall (>6’4”)

0.98 0.00001

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P(T | N) * P(N)P(N | T) = P(T)

= .0000098/.01 = .001

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

today’s topic do you believe in free will? why or why not?

Documents

subjective expected

utility ec

utility of outcomes

probability slide

b slide

real world

i th outcome of choice

chaining principle slide