Introduction to Prospect Theory
Psychology 466: Judgment & Decision Making
Instructor: John Miyamoto
11/17/2015: Lecture 08-2
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Outline
• Risk attitude & origins of prospect theory
• The reflection effect
• Framing effects that result from reflection effects
• Loss aversion
• Framing effects that result from loss aversion
♦
Endowment effect
♦
Chasing sunk costs
Psych 466, Miyamoto, Aut '15
Reminder: Concept of Risk Attitude
2
Risk Attitude
Risk averse action: A person chooses a sure-thing X over a gamble
G where X is less than the expected value of G.
♦
A risk averse person prefers
a sure win of $500
over
a 50-50 gamble for $1,010 or $0.
(Note: Expected value of gamble = $505)
Risk seeking action: A person chooses a gamble G over a sure
thing X where the expected value of G is less than X.
♦
A risk seeking person prefers
a 50-50 gamble for $1000 or $0
over
a sure win of $505.
(Note: Expected value of gamble = +$500)
Psych 466, Miyamoto, Aut '15
Examples of Risk Aversion & Risk Seeking
3
Kahneman & Tversky’s Insights into Risk Attitude
• Important Idea #1:
People tend to risk averse for gains and risk seeking for losses.
• Even More Important Idea #2:
These concepts, risk aversion and risk seeking,
apply to gains and losses, not to states of wealth.
Psych 466, Miyamoto, Aut '15
Table: The Fourfold Pattern of Risk Attitude
4
The Fourfold Pattern of Risk Attitude
Small Probabilities
Medium to Large Probabilities
Gains
Risk-Seeking
Risk Averse
Losses
Risk-Averse
Risk-Seeking
• To understand this table, we need to remember how
EU theory explains risk attitude.
Psych 466, Miyamoto, Aut '15
Risk Aversion & Utility Curvature
5
• The certainty equivalent (CE) is the surething that is equally desirable as a gamble.
Utility
Assuming EU Theory, risk aversion is related to the curvature of the utility function
Two 90% Truths*:
Expected
Value
• When the utility function is more concave
(bulge in curve on upper side), then
choices become more risk averse.
Utility
• When the utility function is more convex
(bulge in curve on lower side), then
choices become more risk seeking.
$ in Thousands
Expected
Value
* "90% Truth" means "unambiguously true if you are an undergrad" and
"usually true, but there are exceptions" if you are a grad student.
Psych 466, Miyamoto, Aut '15
$ in Thousands
Same Analysis with respect to Risk Seeking Utility Function
6
Reflection Effect (More Accurate Version) – the Fourfold Pattern
Small Probabilities
Medium to Large Probabilities
Gains
Risk-Seeking
Risk Averse
Losses
Risk-Averse
Risk-Seeking
• Definition: The reflection effect is the finding that preferences
switch from risk averse to risk seeking if we change the
outcomes from gains or losses.
♦
The direction of the change, from risk averse to risk seeking or from risk
seeking to risk averse, depends on the size of the probabilities.
Psych 466, Miyamoto, Aut '15
Ask the Class for Examples in Each Cell of this Table
7
Reflection Effect (More Accurate Version) – the Fourfold Pattern
Small Probabilities
Medium to Large Probabilities
Gains
Examples?
Examples?
Losses
Examples?
Examples?
• Definition: The reflection effect is the finding that preferences switch from
risk averse to risk seeking if we change the outcomes from gains or losses.
Psych 466, Miyamoto, Aut '15
Show Class Your Examples in Each Cell of This Table
8
Reflection Effect (More Accurate Version) – the Fourfold Pattern
• Definition: The reflection effect is the finding that preferences
switch from risk averse to risk seeking if we change the
outcomes from gains or losses.
Psych 466, Miyamoto, Aut '15
Same Slide w-o the Emphasis Rectangles
9
Reflection Effect (More Accurate Version) – the Fourfold Pattern
• Definition: The reflection effect is the finding that preferences
switch from risk averse to risk seeking if we change the
outcomes from gains or losses.
Psych 466, Miyamoto, Aut '15
Graphs: Prospect Theory Value Function & Prob Weighting Function
10
Reflection Effect – The Fourfold Pattern of Risk Attitude
Small Probabilities
Medium to Large Probabilities
Gains
Risk-Seeking
Risk Averse
Losses
Risk-Averse
Risk-Seeking
Value Function in Prospect Theory
0.6
0.4
Probability Weight
Gains
0.0
0.2
Losses
0.8
Value
1.0
Probability Weighting Function
in 1979 Prospect Theory
0.0
Psych 466, Miyamoto, Aut '15
Same Slide w-o Emphasis Rectangles
0.2
0.4
0.6
Stated Probability
0.8
1.0
11
Reflection Effect – The Fourfold Pattern of Risk Attitude
Small Probabilities
Medium to Large Probabilities
Gains
Risk-Seeking
Risk Averse
Losses
Risk-Averse
Risk-Seeking
Value Function in Prospect Theory
0.6
0.4
Probability Weight
Gains
0.0
0.2
Losses
0.8
Value
1.0
Probability Weighting Function
in 1979 Prospect Theory
0.0
Psych 466, Miyamoto, Aut '15
Transition: Next We Will Focus on Column 3
0.2
0.4
0.6
Stated Probability
0.8
1.0
12
Reflection Effect (More Accurate Version) – the Fourfold Pattern
Small Probabilities
Medium to Large Probabilities
Gains
Risk-Seeking
Risk Averse
Losses
Risk-Averse
Risk-Seeking
Next: Focus of examples
will be here.
• Definition: The reflection effect is the finding that preferences
switch from risk averse to risk seeking if we change the
outcomes from gains or losses.
Psych 466, Miyamoto, Aut '15
Asian Disease Problem - Gain Frame
13
Asian Disease Problem (Gain Frame)
• Problem 1: Imagine that the US is preparing for the outbreak of
an unusual Asian disease, which is expected to kill 600 people.
Two alternative programs to combat the disease have been
proposed. Assume that the exact scientific estimates of the
consequences of the programs are as follows:
• If Program A is adopted, 200 people will be saved.
• If Program B is adopted, there is 1/3 probability that 600 people
will be saved, and 2/3 probability that no people will be saved.
• Which of the two programs would you favor?
Psych 466, Miyamoto, Aut '15
Asian Disease Problem – Loss Frame
14
Asian Disease Problem (Loss Frame)
• Problem 2: Imagine that the US is preparing for the outbreak of
an unusual Asian disease, which is expected to kill 600 people.
Two alternative programs to combat the disease have been
proposed. Assume that the exact scientific estimates of the
consequences of the programs are as follows:
• If Program C is adopted 400 people will die.
• If Program D is adopted there is 1/3 probability that nobody will
die, and 2/3 probability that 600 people will die.
• Which of the two programs would you favor?
Psych 466, Miyamoto, Aut '15
Results for Asian Disease Problem
15
Results of Outcome Framing & Reflection Effect
Asian Disease Problem: Imagine that the US is preparing for the outbreak
of an unusual Asian disease, which is expected to kill 600 people. Two
alternative programs to combat the disease have been proposed.
Gain Frame (N = 152)
Loss Frame (N = 155)
If Program A is adopted, 200 people
will be saved. 72%
If Program C is adopted 400 people
will die. 22%
If Program B is adopted, there is 1/3
probability that 600 people will be
saved, and 2/3 probability that no
people will be saved. 28%
If Program D is adopted there is 1/3
probability that nobody will die,
and 2/3 probability that 600 people
will die. 78%
Which of the two programs would you
favor?
Psych 466, Miyamoto, Aut '15
Which of the two programs would you
favor?
Relation Btwn Asian Disease Problem & Shape of Value Function
16
Asian Disease Problem - Conclusion
• Changing the description of outcomes
from an emphasis on gains to an
emphasis on losses changes the
preferences from risk averse to risk
seeking.
Value
Value Function in Prospect Theory
Losses
Gains
• Asian disease problem is an example
of a framing effect.
• This kind of framing is called
“outcome framing” because outcomes
are described either as potential gains
or potential losses.
Psych 466, Miyamoto, Aut '15
Definition of Framing Effects
17
Framing Effects
By definition, a framing effect is a change in preference that
occurs when:
a) the description of the problem is changed, and ...
b) the content of the problem is not changed (same
outcomes and same probabilities in the two problems).
By “content” I mean the logical structure of the problem. If two problems are logically
equivalent, they have the same content.
• EU theory assumes that framing effects will not occur.
♦
Problem descriptions should not matter if the content stays the same.
♦
EU theory defines the calculation of expected utility in terms of the
actual gambles and outcomes, not in terms of a particular manner
of presenting the gambles and outcomes.
Psych 466, Miyamoto, Aut '15
Why Gain/Loss Framing Changes Preferences
18
Framing Effects Due To Reflection & Gain/Loss Framing
Prospect theory (PT) predicts that framing effects can occur
when we change the problem description from gains to losses
(without changing the objective problem) because ...
1) … people are risk averse for gains and risk seeking
for losses; and ...
2) … people are sensitive to changes in value with respect
to a reference level (usually the status quo) rather
than the objective outcomes.
• EU theory denies (2). Many EU theorists would also deny (1).
Psych 466, Miyamoto, Aut '15
Adjustment of Status Quo in Prospect Theory
19
Adjustment of Reference Level – Redefinition of Gains & Losses
• Do you start becoming risk averse for
small losses?
Value Function in Prospect Theory
Value
• What happens when you get richer?
E.g., you finish school and get a job?
Losses
• Example: Hopefully, 5 years from now you
will be substantially richer. Will your risk
attitude be determined by a shift to the right
along the X-axis of the graph?
Gains
New
Wealth
• Adaptation Level Theory
• Example – Adaptation to ambient lighting in a room.
• Example – Adaptation to current level of wealth.
Redefinition of gains and losses.
Psych 466, Miyamoto, Aut '15
Gain/Loss Framing & Pref Btwn Gambles
20
Framing Effect in Gambles for Apparent Gains or Losses
Assume yourself richer by $300 than you are today.
Now choose between (a) and (b):
(a) A sure gain of $100.
72% prefer (a)
in K&T experiment
(b) A 50% chance to gain $200 and
a 50% chance to gain nothing.
Assume yourself richer by $500 than you are today.
Now choose between (a') and (b'):
(a') A sure loss of $100.
(b') A 50% chance to lose nothing and
a 50% chance to lose $200.
Psych 466, Miyamoto, Aut '15
36% prefer (b’)
in K&T experiment
EU Analysis of This Problem
21
Expected Utility (EU) Analysis of the Preceding Choice
Assume yourself richer by $300 than you are today. Choose between (a) and (b):
(a) A sure gain of $100.
U(a) = U(current wealth + 300 + 100) = U(current wealth + 400)
(b) A 50% chance to gain $200 and a 50% chance to gain nothing.
U(b) = (1/2)U(current wealth + 300 + 200) + (1/2)U(current wealth + 300 + 0)
= (1/2)U(current wealth + 500) + (1/2)U(current wealth + 300)
Assume yourself richer by $500 than you are today. Choose between (a') and (b'):
(a') A sure loss of $100.
U(a') = U(current wealth + 500 – 100) = U(current wealth + 400)
(b') A 50% chance to lose nothing and a 50% chance to lose $200.
U(b') = (1/2)U(current wealth + 500 – 0) + (1/2)U(current wealth + 500 – 200)
= (1/2)U(current wealth + 500) + (1/2)U(current wealth + 300)
NOTE: (a) is equivalent to (a') and (b) is equivalent to (b').
So EU says you should choose (a) and (a’) or (b) and (b’).
Psych 466, Miyamoto, Aut '15
Interpretation of This Result
22
Expected Utility (EU) Analysis of the Preceding Choice
Assume yourself richer by $300 than you are today. Choose between (a) and (b):
(a) A sure gain of $100.
U(a) = U(current wealth + 300 + 100) = U(current wealth + 400)
(b) A 50% chance to gain $200 and a 50% chance to gain nothing.
U(b) = (1/2)U(current wealth + 300 + 200) + (1/2)U(current wealth + 300 + 0)
= (1/2)U(current wealth + 500) + (1/2)U(current wealth + 300)
Assume yourself richer by $500 than you are today. Choose between (a') and (b'):
(a') A sure loss of $100.
U(a') = U(current wealth + 500 – 100) = U(current wealth + 400)
(b') A 50% chance to lose nothing and a 50% chance to lose $200.
U(b') = (1/2)U(current wealth + 500 – 0) + (1/2)U(current wealth + 500 – 200)
= (1/2)U(current wealth + 500) + (1/2)U(current wealth + 300)
NOTE: (a) is equivalent to (a') and (b) is equivalent to (b').
So EU says you should choose (a) and (a’) or (b) and (b’).
Psych 466, Miyamoto, Aut '15
Interpretation of This Result
23
What Does the Preceding Example Show?
• Changing the initial wealth level from +$300 to +$500 changes
the gamble outcomes from gains to apparent losses.
• We can rapidly adjust our reference level, so that what used
to be gains are now losses.
• We tend to be risk averse for gambles whose outcomes
look like gains, and risk seeking for gambles whose
outcomes look like losses.
Psych 466, Miyamoto, Aut '15
Graphical Comparison of EU Theory vs Prospect Theory
24
EU Utility Function versus Prospect Th Value Function
Example 1
Value Function in Prospect Theory
Utility
Value
Utility Function
for EU Theory
Typical Risk Averse
Utility Function
Losses
Gains
Money ($)
Example 2
Utility
Utility Function
for EU Theory
Another Somewhat Strange
Utility Function
Money ($)
Psych 466, Miyamoto, Aut'12
• EU theory – utility function does not
identify the current (status quo) position.
• Prospect theory – status quo determines
shift in shape of value function.
Mental Accounting
25
Mental Accounting
• Mental accounting occurs when we allocate expenses to
particular "mental accounts" without looking at the overall
balance sheet of expenses.
• Mental accounting can produce framing effects, i.e., different
descriptions of expenses produce different choices even though
the real options are the remain the same.
• See next slide for an example.
Psych 466, Miyamoto, Aut '15
Jacket & Calculator Purchase
26
Mental Accounting Example
• Tversky & Kahneman 1981:
Imagine that you are about to purchase a jacket for $125, and
a calculator for $15.
Situation 1: The salesman informs you that the calculator is on
sale for $10 at the other branch of the store, located 20 minutes
drive away. Would you make the trip to the other store?
Situation 2: The salesman informs you that the jacket is on sale
for $120 at the other branch of the store, located 20 minutes
drive away. Would you make the trip to the other store?
The real choice in either situation is:
Option A: Spend $140, save 20 minutes of time.
Option B: Spend $135, use 20 minutes to drive to other store.
Psych 466, Miyamoto, Aut '15
Results for this experiment
27
Results for the Mental Accounting Example
The real choice is
Option A: Spend $140, save 20 minutes of time.
Option B: Spend $135, use 20 minutes to drive to other store.
With either option, you end up owning a jacket and a calculator.
--------------------------------------------------------------------------------------------------------
• Situation 1: 68% of subjects choose Option A.
♦
Attracted to the reduction of the $15 expense to $10 for calculator.
• Situation 2: 29% of subjects choose Option A.
♦
Not attracted to the reduction of the $125 expense to $120 for jacket.
• People are more interested in saving $5 out of $15 dollar
expense than saving $5 out of $125 dollar expense.
People don't look at the bottom line.
• Framing effect!
Psych 466, Miyamoto, Aut '15
Theater Ticket Example
28
Theater Example (Mental Accounting) – Lose $10
• Problem 8 [N = 183]: Imagine that you have decided to see a
play where admission is $10 per ticket. As you enter the theater
you discover that you have lost a $10 bill.
Would you still pay $10 for a ticket for the play?
• Yes [88 per cent]
• No [12 per cent]
Psych 466, Miyamoto, Aut '15
How do you analyze this
problem?
Comparison Btwn EU & PT
29
Theater Example (Mental Accounting) – Lose Ticket
• Problem 9 [N = 200]: Imagine that you have decided to see a
play and paid the admission price of $10 per ticket. As you enter
the theater you discover that you have lost the ticket. The ticket
was for open seating and it cannot be recovered.
Would you pay $10 for another ticket?
• Yes [46 per cent]
• No [54 per cent]
Psych 466, Miyamoto, Aut '15
How do you analyze this
problem?
Summary of Theater Ticket Example
30
Theater Example - Summary
Regardless of whether you lose $10 cash or you lose the ticke,
your real choices are:
• Bottom Line for Option 1:
Go home without seeing the play. You are $10 poorer.
• Bottom Line for Option 2:
Get a theater ticket. You see the play. Your are $20 poorer.
• People choose Option 1 if they lose the ticket but
they choose Option 2 if they lose the money for the ticket.
• Example of mental accounting. Violation of EU theory.
Psych 466, Miyamoto, Aut '15
Conclusions re Mental Accounting
31
Conclusions re Mental Accounting
• EU theory says that we should make choices based on how
they affect our total personal assets - not how these assets
are described or labeled as gains and losses.
• Psychologists find that people keep track of utility relative to
separate "mental accounts."
♦
Purchasing example
♦
Lost theater ticket versus lost money for a theater ticket
• Framing effects due to mental accounting:
People sometimes switch preferences when: (a) we keep the
bottom line constant, but (b) we change the way that gains
and losses are assigned to particular mental accounts.
Psych 466, Miyamoto, Aut '15
32
Conclusion: Framing effects are important!
Prospect theory
♦
The value function is concave for gains and convex for losses.
This tends to make people risk averse for gains and risk seeking for losses.
♦
People are sensitive to changes in wealth (gains and losses).
• The Asian disease problem and gamble framing effects show
that people’s preferences change depending on the way a problem is
described.
• Mental accounting shows that we calculate gains and losses with respect to
"mental accounts" (not a total accounting of our state of wealth).
• Labeling as gains or losses influences decisions even when the bottom line
stays the same.
Psych 466, Miyamoto, Aut '15
Comment: Manipulating Political Frames to Motivate People to Take Action
33
Example: Motivating People Towards Political Action
• Getting people to take action – emphasize potential losses due to inaction.
• Example: Lobbying for the Equal Rights Amendment (ERA).
• Example: American Christian conservatives emphasize the Christian faith
of founding Americans (circa the American Revolution).
•
Christians have "lost" their rights to practice their faith in modern
secular America.
•
"Take back America!"
• Example: Politics of victimization - if you are a victim, you must take
action to regain what has been taken from you.
Psych 466, Miyamoto, Aut '15
Summary – How EU & Prospect Theory Differ
34
Probability Weighting Function
in 1979 Prospect Theory
0.6
0.4
Probability Weight
How Prospect Theory (PT) Differs
From Expected Utility (EU) Theory
0.2
Gains
0.0
Losses
0.8
Value
1.0
Value Function in Prospect Theory
0.0
0.2
0.4
0.6
0.8
1.0
Stated Probability
Expected Utility Theory
Prospect Theory
The basic objects of preference are states
of wealth (including non-monetary
resources like health).
The basic objects of preference are
changes from a neutral reference point
(gains and losses).
The utility function is risk averse
everywhere. (Most theorists)
The value function is risk averse for gains,
risk seeking for losses.
Loss aversion cannot be defined (EU
theory does not identify a status quo.)
The value function implies loss aversion.
People evaluate probabilities linearly.
People evaluate probabilities nonlinearly.
Problem description should have no effect
as long as the problem is logically the
same.
Problem description can change the
reference level; hence the definition of
gains & losses can change.
All outcomes are evaluated with respect to People evaluate gains and losses with
one big account.
respect to mental accounts.
Psych 466, Miyamoto, Aut '15
Next: Focus on Loss Aversion
35
1.0
0.8
0.6
0.4
Gains
0.0
0.2
Losses
How Prospect Theory (PT) Differs
From Expected Utility (EU) Theory
Probability Weighting Function
in 1979 Prospect Theory
Probability Weight
Value
Value Function in Prospect Theory
0.0
0.2
0.4
0.6
0.8
1.0
Stated Probability
Expected Utility Theory
Prospect Theory
The basic objects of preference are states
of wealth (including non-monetary
resources like health).
The basic objects of preference are
changes from a neutral reference point
(gains and losses).
The utility function is risk averse
everywhere. (Most theorists)
The value function is risk averse for gains,
risk seeking for losses.
Loss aversion cannot be defined (EU
theory does not identify a status quo.)
The value function implies loss aversion.
People evaluate probabilities linearly.
People evaluate probabilities nonlinearly.
Problem description should have no effect
as long as the problem is logically the
same.
Problem description can change the
reference level; hence the definition of
gains & losses can change.
All outcomes are evaluated with respect to People evaluate gains and losses with
one big account.
respect to mental accounts.
Psych 466, Miyamoto, Aut '15
Graph Showing Loss Aversion
36
Loss Aversion
♦
Example: Compare the
pleasure of unexpectedly
finding $100 to the pain of
unexpectedly losing $100.
Psych 466, Miyamoto, Aut '15
Loss Aversion: A loss has greater impact
than an objectively equal gain.
Value
• Loss aversion –
the pain of losing X is
greater than the pleasure
of gaining X.
-x
Losses
+x
Gains
Credit Cards: Cash Discount versus Credit Card Surcharge
37
Gasoline Price: Cash Discount or Credit Card Surcharge
During 1979 oil crisis, the oil companies wanted to charge a fee for using a
credit card to buy gasoline. E.g., gas would cost 94¢ per gallon with cash
payment or 97¢ per gallon with a credit card payment. The federal government
got involved in the issue of how the pricing should be labeled.
• Labeling Solution 1: The gas price should be labeled
94¢/gallon for cash with a 3¢/gallon credit card surcharge.
• Labeling Solution 2: The gas price should be labeled
97¢/gallon on a credit card with a 3¢/gallon cash discount.
♦
Value
Question: Assuming that the oil companies
wanted to encourage the use of credit cards,
which solution will cause more consumers
to use credit cards? Why?
Loss Aversion: A loss has greater impact
than an objectively equal gain.
-x
Losses
Diagram
x
Gains
This is a practical example of how a framing
can influence consumer behavior.
Psych 466, Miyamoto, Aut '15
Wine Owner Example
38
The Wine Example (for Endowment Effect)
KK&T: Kahneman, D., Knetsch, J. L., & Thaler, R. H. (1991). The endowment effect, loss
aversion, and status quo bias. Journal of Economic Perspectives, 5, 193-206.
• A wine-lover bought wine for $10/bottle, but now it is worth
$200/bottle at auction.
• This wine-lover is not willing to pay $200/bottle
for more bottles of this wine.
• This wine-lover would not sell any of his wine for $200/bottle.
• Is this behavior odd?
Psych 466, Miyamoto, Aut '15
Endowment Effect & Loss Aversion
39