Introduction to Prospect Theory Psychology 466: Judgment & Decision Making Instructor: John Miyamoto...

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 2Reminder: Concept of Risk Attitude

3Psych 466, Miyamoto, Aut '15

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. o A risk averse person prefers

a sure win of $500over

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. o A risk seeking person prefers

a 50-50 gamble for $1000 or $0over

a sure win of $505. (Note: Expected value of gamble = +$500)

Examples of Risk Aversion & Risk Seeking

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 4Table: The Fourfold Pattern of Risk Attitude


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.

Risk Aversion & Utility Curvature


Assuming EU Theory, risk aversion is related to the curvature of the utility function

• The certainty equivalent (CE) is the sure-thing that

is equally desirable as a gamble.

Two 90% Truths*:

• When the utility function is more concave

(bulge in curve on upper side), then

choices become more risk averse.

• When the utility function is more convex

(bulge in curve on lower side), then

choices become more risk seeking.

* "90% Truth" means "unambiguously true if you are an undergrad" and

"usually true, but there are exceptions" if you are a grad student.

Same Analysis with respect to Risk Seeking Utility FunctionU

tili

ty

$ in Thousands

Expected Value

Uti

lity

$ in Thousands

Expected Value


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.o 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.

Ask the Class for Examples in Each Cell of this Table




Gains Examples? Examples?

Losses Examples? Examples?


risk averse to risk seeking if we change the outcomes from gains or losses.

Show Class Your Examples in Each Cell of This Table





Same Slide w-o the Emphasis Rectangles





Graphs: Prospect Theory Value Function & Prob Weighting Function


Reflection Effect – The Fourfold Pattern of Risk Attitude




Value Function in Prospect Theory

GainsLosses

Valu

e

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Stated Probability

Pro

ba

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eig

ht

Probability Weighting Functionin 1979 Prospect Theory

Same Slide w-o Emphasis Rectangles


Reflection Effect – The Fourfold Pattern of Risk Attitude





GainsLosses

Valu

e

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Stated Probability

Pro

ba

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ty W

eig

ht


Transition: Next We Will Focus on Column 3








Asian Disease Problem - Gain Frame

Next: Focus of examples will be here.


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?

Asian Disease Problem – Loss Frame


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?

Results for Asian Disease Problem


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.

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?

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?

72%

28%

22%

78%

Relation Btwn Asian Disease Problem & Shape of Value Function


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.

• 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.


GainsLosses

Valu

e

Definition of Framing Effects


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. o Problem descriptions should not matter if the content stays the same. o EU theory defines the calculation of expected utility in terms of the

actual gambles and outcomes, not in terms of a particular mannerof presenting the gambles and outcomes.

Why Gain/Loss Framing Changes Preferences


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).

Adjustment of Status Quo in Prospect Theory


Adjustment of Reference Level – Redefinition of Gains & Losses


GainsLosses

Valu

e

• What happens when you get richer?E.g., you finish school and get a job?

• Do you start becoming risk averse for small 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?

NewWealth

• Adaptation Level Theory• Example – Adaptation to ambient lighting in a room. • Example – Adaptation to current level of wealth.

Redefinition of gains and losses.

Gain/Loss Framing & Pref Btwn Gambles


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.

(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.

72% prefer (a) in K&T experiment

EU Analysis of This Problem

36% prefer (b’) in K&T experiment


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’).

Interpretation of This Result


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.

Graphical Comparison of EU Theory vs Prospect Theory

EU Utility Function versus Prospect Th Value Function

• EU theory – utility function does not identify the current (status quo) position.

• Prospect theory – status quo determines shift in shape of value function.

Psych 466, Miyamoto, Aut'12 25


GainsLosses

Valu

e

Money ($)

Util

ity

Utility Functionfor EU Theory

Typical Risk AverseUtility Function

Example 1

Money ($)

Util

ity

Utility Functionfor EU Theory

Another Somewhat StrangeUtility Function

Example 2

Mental Accounting


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.

Jacket & Calculator Purchase


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.

Results for this experiment


Results for the Mental Accounting Example

The real choice isOption 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. o Attracted to the reduction of the $15 expense to $10 for calculator.

• Situation 2: 29% of subjects choose Option A. o 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!

Theater Ticket Example


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]

Comparison Btwn EU & PT

How do you analyze this problem?


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]How do you analyze this problem?

Summary of Theater Ticket Example

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 31Conclusions re Mental Accounting


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."o Purchasing exampleo 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.


Conclusion: Framing effects are important!

Prospect theoryo 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.o 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.

Comment: Manipulating Political Frames to Motivate People to Take Action

Example: Motivating People Towards Political Action

Psych 466, Miyamoto, Aut '15 34

• 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.

Summary – How EU & Prospect Theory Differ


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 one big account.

People evaluate gains and losses with respect to mental accounts.

How Prospect Theory (PT) Differs From Expected Utility (EU) Theory


GainsLossesV

alu

e

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Stated Probability

Pro

ba

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eig

ht


Next: Focus on Loss Aversion


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 one big account.

People evaluate gains and losses with respect to mental accounts.

How Prospect Theory (PT) Differs From Expected Utility (EU) Theory


GainsLossesV

alu

e

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Stated Probability

Pro

ba

bili

ty W

eig

ht


Graph Showing Loss Aversion


Loss Aversion

• Loss aversion –

the pain of losing X is greater

than the pleasure

of gaining X.o Example: Compare the pleasure

of unexpectedly finding $100 to the pain of unexpectedly losing $100.

Credit Cards: Cash Discount versus Credit Card Surcharge

Val

ue

GainsLosses

-xx

Loss Aversion: A loss has greater impactthan an objectively equal gain.

+

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.

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?

♦ This is a practical example of how a framing can influence consumer behavior.

Psych 466, Miyamoto, Aut '15 38Wine Owner Example

Diagram

Val

ue

GainsLosses

-xx

Loss Aversion: A loss has greater impactthan an objectively equal gain.


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?

Endowment Effect & Loss Aversion

Introduction to Prospect Theory Psychology 466: Judgment & Decision Making Instructor: John Miyamoto...

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