Transcript Deductive Reasoning drawing firm conclusions from evidence

Decision Making
choice…
maximizing utility
framing effects
Value
• Round 1: Raise your hand if your middle name
starts with the letter ‘M’
• Congratulations, you just won!
• You are entitled to one of our prizes:
– Prize A: $15
– Prize B: $ 10
• Which one do you choose?
– Duh!
– Prize A value > Price B value
Expected value
• Round 2: choose prize first
• Winners will be decided based on the last digit of
their SSN:
– Prize C: $15
• if your SSN digit matches the number that comes out
• for example, if ‘7’ comes out and your SSN ends in ‘7’
– Prize D: $ 10
• if your SSN digit is in the selected category (larger/smaller
than 5)
• For example, if ‘7’ comes out, and your SSN ends in ‘5’, ‘6’, 7,
8 or 9
• Which one do you choose to play?
Please make your selection...
1. C
2. D
89%
D
C
11%
Expected value
• Obviously, you chose prize D. Why?
• Expected value:
– Prize C = $15 x .1 = $1.5
– Price D = $10 x .5 = $5.0
– EV = Value x Probability
Expected Utility
How desirable a bet is depends on:
- Expected value (size of Payout x Probability )
- How much an individual values that payout (Saving a tree, $, etc.)
- This provides a single scale for the goodness of any particular choice
Utility: how happy or satisfied something makes you (how
desirable something is)
Utility theory: A Normative Theory of Choice
• Describes how people should make decisions
• In making a decision, you should:
-
Assess how worthy each outcome is to you (subjective utility)
Assess how likely each outcome is
Compute the expected utility of each possible option
Compare those expected utilities
Select the choice with largest expected utility
Example: should you buy a lottery ticket?
--Largest powerball jackpot ever = $195,000,000 !!
--Probability of winning the powerball 1 in 10,000,000,000.
--The expected value: .00000000001 x 195,000,000 = 2 lousy
cents.
Should you buy a ticket? Only if it costs 2c or less.
Utility theory: Criticism
• There are several problems with Utility theory:
– Probability outcomes are often unknown
• What is the probability that he will say ‘yes’ if I ask him out?
– It’s tricky to assess the expected utility of future
outcomes
• How happy would I be to have chosen ‘Nova?
– Lots of evidence that people do not reason this way
Please make your selection...
Option A. Winning $40 with
probability .80
Option B. Getting $30 for sure
Certainty Effect: People tend to
prefer sure gains (risk averse for
gains)
80%
20%
Eva: $40 x .8 = $32
EVb: $30 x 1 = $30
Option A. Winning
$40 with probability
.80
Option B. Getting
$30 for sure
Certainty Effect
- People’s tendency to be influenced by the manner in which
choices are presented or framed.
A. Winning $40 with probability .80
B. Winning $30 with probability 1.00
if both probabilities are cut in half:
Choice A. Winning $40 with probability .40
Choice B. Winning $30 with probability .50
people pick this
people pick this
Certainty Effect: People tend to prefer sure gains (risk averse
for gains)
Framing effects: Positive Frame
Students in right side of class will answer:
Imagine that the US is preparing for the outbreak of an
unusual tropical disease, which is expected to kill 600
people. Two alternative programs to combat the disease
have been proposed. The estimates of the program’s effects
are as follows:
Program A:
200 people will be saved.
Program B:
1/3 chance that 600 people will be saved.
2/3 chance that 0 people will be saved.
Right side of the class, please make
your selection...
1. Program A
2. Program B
83%
B
ra
m
Pr
og
Pr
og
ra
m
A
17%
Negative Frame
Students in right side of class will answer
Imagine that the US is preparing for the outbreak of
an unusual tropical disease, which is expected to
kill 600 people. Two alternative programs to
combat the disease have been proposed. The
estimates of the program’s effects are as follows:
Program C:
400 people will die.
Program D:
1/3 chance that 0 people will die
2/3 chance that 600 people will die.
left side of the class, please make
your selection...
1. Program A
2. Program B
63%
B
ra
m
Pr
og
Pr
og
ra
m
A
38%
Positive Frame
Program A:
Negative Frame
Program C:
200 people will be saved.
Program B:
400 people will die.
Program D:
1/3 chance that 600 people will be saved.
2/3 chance that 0 people will be saved.
1/3 chance that 0 people will die
2/3 chance that 600 people will die.
80
80
60
60
40
40
20
20
0
A
B
72% of subjects pick Program A
when the problem is framed in terms
of “lives saved.” With the positive
frame, subjects are “risk averse.”
0
C
D
Only 20% of subjects pick Program
C when the problem is framed in
terms of “deaths.” With the negative
frame, subjects become “risk takers.”
Donating money & saving lives
Value of life saving
• Each life is worth the same
Series1
1
2
3
4
5
number of lives saved
6
• How much money would you give to save
• Rokia
• To save people from the village where
Rokia lives
A Hypothetical Value Function
losses
}
}
Value
gains
- “The pain of a loss is greater than the pleasure of a gain.”
- “ small loses hurt (proportionally more) than big losses”
Cash or Credit??
$1.30/gal
5 cent discount
for cash...
gains
Discount seems
negligible, people
use credit card.
$1.25/gal
5 cent charge
for credit...
Surcharge is
outrageous…
people pay cash.
losses
Framing effects are everywhere…
What’s better?
A basketball player who makes 75%
of his free-throws, or one who misses 25%
or his free-throws?
Justification Effects:
Another Departure from Expected Value Theory
Imagine that you are planning a vacation in a warm spot over
spring break. You have two options…The travel brochure
give only a limited amount of information about the two
options. Given the information available, which vacation
spot would you prefer?
Spot A:
average weather
average beaches
medium quality hotel
medium temperature water
Spot B:
lots of sunshine
gorgeous beaches and coral reefs
ultra-modern hotel
very cold water
very strong winds
Imagine that you are planning a vacation in a warm spot over
spring break. You have two options…but you can no longer
retain your reservation for both. The travel brochure give
only a limited amount of information about the two options.
Given the information available, which reservation do you
decide to cancel?
Spot A:
average weather
average beaches
medium quality hotel
medium temperature water
Spot B:
lots of sunshine
gorgeous beaches and coral reefs
ultra-modern hotel
very cold water
very strong winds
option A
option B
prefer
33%
67%
cancel
52%
48%
total
85%
115%
- Option B has features that allow subjects to justify a good or
bad rating.
- Thus, subjects decide by referendum on option B
- How the question is framed,
- emphasizes the (very) positive aspects of option B, or
- emphasizes the (very) negative aspects of option B
Justification Effects: Last presidential election
Kerry:
Moderate on gay marriage
Moderate on taxes
Moderate on health insurance
Unknown on Irak
Moderate on Foreign Affairs
Moderately religious
Mixed message on abortion
(personally opposes but
Won’t legislate against it)
Bush:
Strongly opposed to gay marriage
Strong ideas on taxes
Strong ideas on health insurance
Strong position on Irak
Strong unilateralism
Fervent religious
Strongly oppose to abortion
- Election was a referendum on the president
- Both campaigns target Bush and try to frame him to their advantage
- negative frame: anti-civil liberties, regressive taxes, mesianic, anti-choice
- positive frame: moral values,tax relief, religious, pro-life
Justification: living with your decisions
• People make choices that they can justify to themselves
(thus reducing regret)
• Even if those choices are sometimes irrational
• One last example:
– you passed the exam -> you buy ticket to Hawaii (to celebrate)
– You failed the exam -> you buy ticket to Hawaii (to cheer
yourself up)
– You don’t know whether you passed or you failed
• Logically, you should buy the ticket, but
• People are reluctant in this situation (no justification?)
Summary
• Utility theory fails to describe how people
make decisions:
– Frame effects
– Influence of justifications (minimize regret)
Other issues
• Difficulty predicting future values
– Wilson and Gilbert (on happiness)
• Peak and end assessment of pain
• Happiness (California) (Kahneman 1999)
•
•
•
•
The focusing effect (or focusing illusion) is a cognitive bias that occurs when people
place too much importance on one aspect of an event, causing an error in accurately
predicting the utility of a future outcome.
People focus on notable differences, excluding those that are less conspicuous, when
making predictions about happiness or convenience. For example, when people were
asked how much happier they believe Californians are compared to Midwesterners,
Californians and Midwesterners both said Californians must be considerably happier,
when, in fact, there was no difference between the actual happiness rating of
Californians and Midwesterners. The bias lies in that most people asked focused on and
overweighed the sunny weather and ostensible easy-going lifestyle of California and
devalued and underrated other aspects of life and determinants of happiness, such as low
crime rates and safety from natural disasters like earthquakes (both of which large parts
of California lack).[1]
A rise in income has only a small and transient effect on happiness and wellbeing, but
people consistently overestimate this effect. Kahneman et al. proposed that this is a
result of a focusing illusion, with people focusing on conventional measures of
achievement rather than on everyday routine
• Prospect theory wikipedia
Utility theory: Summary
• Each decision has associated costs and benefits.
• Costs and benefits are, to certain extent, subjective
• Most decisions carry certain amount of uncertainty or
risk (probability that the expected outcome will occur)
• expected utility = subjective utility of a particular
outcome * probability of the outcome
• Ideal decision makers should maximize expected utility
that is, they should choose so to maximize benefits, and
minimize costs
Calculating Expected Value
(Expected Utility)
P = probability of a particular outcome (ranges from 0 to 1)
V = value of a particular outcome (the cost or benefit
associated with the outcome)
Expected Value = P x V
If multiple outcomes are possible given a particular decision, then the
expected value of all possible outcomes is added up.
Calculating Expected Value
Suppose you get to choose between two
different games of chance:
(1) Winning $40 with probability .20
or
(2) Winning $30 with probability .25
Which is the better choice?
Calculating Expected Value
(1) Winning $40 with probability .20
The expected value of choice 1 is
.2 x $40 = $8
(2) Winning $30 with probability .25
The expected value of choice 2 is
.25 x $30 = $7.50
Choice 1 has the higher expected value.
Another way to think about expected value is
as “the average outcome over the long run.”
“Better Than Wall Street”
Door 1
-
Door 2
One doors hides $1,000
The other hides $0.
Alternatively, you can take $500 instead.
What do you want to do?
– Door 1
– Door 2
– Take $500 for sure
“Better Than Wall Street”
If you chose the $500:
- How much would the potential prize have to be to
make you reconsider?
- Risk premium
• Option E: A 1/80 chance of winning $80
• Option F: $ 1 for sure
• EVoptionE = $80 x 1/80 = 1
• EVoptionF = $1 x 1 = 1