Today’s Topic Do you believe in free will? Why or why not?

The “I Want More Pain” Experiment A or B

The “I Want More Pain” Experiment 69% 31%

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 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 prize On average, you win $500 for 1000 games = $0.50 per game That’s expected utility E(c) : the expected subjective utility of choice c E(c) =  i p(o i ) u(o i ) o i : the i th outcome of choice c

Calculating Expected Utility What is my subjective expected utility of deciding to audition for “The Real World”? E(c) = p(o 1 ) u(o 1 ) 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”? E(c) = p(o 1 ) u(o 1 ) + p(o 2 ) u(o 2 ) How cool would it be to be on The Real World? How likely am I to actually be chosen? Do I like interviews? equals 1: there will be an interview!

Calculating Expected Utility What is my subjective expected utility of deciding to audition for “The Real World”? E(c) = p(o 1 ) u(o 1 ) + p(o 2 ) u(o 2 ) How cool would it be to be on The Real World? How likely am I to actually be chosen? Do I like interviews? equals 1: there will be an interview! Being on “Real World” would be really cool, but you don’t have a chance in heck, and you dislike interviews: E(c) = * * (-8) = 2 Expected utility of staying home (no outcomes): E(c) = 0 Now, suppose you REALLY dislike interviews: E(c) = * * (-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 lossesgains

Utility How do we decide how good something is? subjective utility lossesgains $100$500$1000$-100$-500$-1000

Utility How do we decide how good something is? subjective utility lossesgains $100$500$1000$-100$-500$-1000

Utility How do we decide how good something is? subjective utility lossesgains $100$500$1000$-100$-500$-1000 risk aversion: 100% chance to get $100, 50% chance to get $200

Utility How do we decide how good something is? subjective utility lossesgains $100$500$1000$-100$-500$-1000

Utility How do we decide how good something is? subjective utility lossesgains $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 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: 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 How do we decide how good something is? subjective utility lossesgains $100$500$1000$-100$-500$-1000 Framing Effects

Utility How do we decide how good something is? subjective utility lossesgains $100$500$1000$-100$-500$-1000 Framing Effects

Utility How do we decide how good something is? subjective utility lossesgains $100$500$1000$-100$-500$-1000 Framing Effects: Choose a sure gain

Utility How do we decide how good something is? subjective utility lossesgains $100$500$1000$-100$-500$-1000 Framing Effects: Choose a sure gain

Utility How do we decide how good something is? subjective utility lossesgains $100$500$1000$-100$-500$-1000 Framing Effects: Choose a sure gain Choose risk for a loss

Utility How do we decide how good something is? subjective utility lossesgains $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 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) Linda is a university professor B) Linda is an insurance salesperson C) Linda is a bank teller D) Linda is an owner of a book store E) Linda is a single mom and takes classes at night school F) 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) Linda is a university professor B) Linda is an insurance salesperson C) Linda is a bank teller D) Linda is an owner of a book store E) Linda is a single mom and takes classes at night school F) 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.

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 What is the probability that a major earthquake will strike the U.S. in the next year and kill 1,000 people? 0.1 What is the probability that a major earthquake will strike California 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(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 If Bob plays in the NBA, he is Probably Tall (>6’4”) 0.98 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). P(T | N) * P(N) P(N | T) = P(T)

Bayes’ Theorem 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”) 0.98 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). P(T | N) * P(N) P(N | T) = P(T)

Bayes’ Theorem 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”) 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). P(T | N) * P(N) P(N | T) = P(T) = /.01 =.001

A Picture might help

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