judgments and decisions psych 253 decision analysis (usually risky or uncertain decisions) examples

Judgments and DecisionsPsych 253

• Decision Analysis (usually “risky” or uncertain decisions)

• Examples

Symbols in Decision Analysis

Decision Node – under control of decision maker

Chance Node – NOT under control of decision maker

Weather Forecasting Decision

Safe Conditions, probably Damage

Dangerous Conditions, probably Damage

Safe Conditions, No Damage

Stay

Evacuate

HurricaneMisses

HurricaneHits

Political Decision

Stay at the Law Practice

Lose Election

Win Election

Run

Don’t Run

Organizational Restructuring Decision

Maintain the Current Organizational Hierarchy

Key People Quitting, Lost TimeLost Revenues

Increased Profits Happier, More Motivated Employees

Restructure

Don’t Restructure

What is similar about these decisions?

How do you decide what to do?

U(Sure thing)

U(Risky option) = p(B)* U(B) + (1 - p(B)) * U(W)

Can set U(B) = 100 and U(W) = 0

Determine U(Sure thing)

Set the utilities of the options equal to each other and solve for p(B)

U(Sure Thing) = U(Risky Option)

U(Sure Thing) = p(B)*U(B) + (1-p(B))*U(W)

U(Sure Thing) = p(B)*100 + (1-p(B))*0

Suppose U(Sure Thing) = 35

35 = p(B)*100 + (1- p(B))*0

Solve for p(B)

P(B) = 35/100 = 35%

Sometimes more than one variable is unknown. Solutions depend on combinations of variables.

James’s car was severely damaged by an uninsured motorist. James had no collision insurance. He was facing the loss of his car (valued at $4000). James considered suing the driver. If he did sue, how much should he be willing to pay a lawyer to help him? He constructed the following decision tree.

Don’t Sue

Sue

Win

Lose

$0

-Fee

$4,000 - Fee

EV(Sue) = p(W)*($4000 - Fee) + (1 – p(Win))*(-Fee)

EV(Don’t Sue) = $0

Set EV(Sue) = EV(Don’t Sue)

When is EV(Sue) > 0?

p(W)*($4000 - Fee) + (1 – p(W))*(-Fee)= 0

Solve for p(W)

Answer:

EV(Sue) > 0 if p(W) > Fee/$4,000

James found a lawyer who charged $400. Then he did some research to find out how likely he would be to win with the lawyer who charged $400. He should sue if the chances of winning were greater than $400/$4,000 or 1/10.

Sometimes each option is associated with risk. The expected value of each option is compared and the larger one is selected.

Should David pay $600 per year for collision insurance when the deductible is $400 and his car is worth $20,000?

David considers the possibility of no accident, a small accident (under the deductible) or a big accident (over the deductible)

No accident

Small accident

Large accident

No accident

Small accident

Large accident

Buy

Don’t Buy

-$600

-$1,000

-$1,000

$0

-$400

-$20,000

Risks with each option

Suppose p(No Accident) = .75p(Small Accident) = .20p(Large Accident) = .05

EV(Don’t Buy) = .75*0 + .20*(-$400) +.05*(-$20,000) = -$1,080

EV(Buy) = .75*(-$600) + .20*(-$1000) + .05*(-$1,000) = -$700

If he decides his car is really only worth $10,000…

EV(Don’t Buy) = .75*0 + .20*(-$400) +.05*(-$10,000) = -$580

EV(Buy) = .75*(-$600) + .20*(-$1001) + .05*(-$1,001) = -$700

Many business decisions involve some chance events and one or more decisions.

A company is involved in the exploration of oil. The company must decide whether to bid on an off-shore oil-drilling lease. The bid may be accepted or rejected by a government agency.

The company can perform a seismic test before they decide to drill, but only after the bid is accepted. No one knows if there is oil; the site might be dry or it might result in a strike of any size.

Nothing

Nothing

Strike

Nothing

Nothing

Strike

Dry

Dry

Dry

Strike

No Bid

Bid

Do Seismic

No Seismic

Positive Outcome

NegativeOutcome

Drill

Don’t Drill

Drill

Don’t Drill

Drill

Don’t Drill

Suppose that all outcomes can be converted to monetary amounts that reflect the decision maker’s fundamental value which in this case is to maximize profit.

Consider a company that is trying to decide whether to spend $2 million to continue R&D on a product. They have is a 70% chance of getting a patent on the product. If the patent is awarded, the company can sell the technology for $25 million or they can develop the product and sell it themselves. If it sells, it faces an uncertain demand.

R&D Decision

$0

No Patent -$2Mm

SellTechnology$25M

ContinueDevelopment-$2M

Stop Development

Patent Awarded

$23M

Sell Product -$10M

Demand High$55M means $43M

Demand Medium$33M means $21M

Demand Low$15M means $3M

R&D Decision

$0

No Patent -$2Mm

LicenseTechnology$25M

ContinueDevelopment-$2M

Stop Development

Patent Awarded

$23M

Develop and Sell Product -$10M

Demand High$55M means $43M

Demand Medium$33M means $21M

Demand Low$15M means 3M

.7

.3

.25

.55

.20

R&D Decision

$0

No Patent -$2Mm

LicenseTechnology$25M

ContinueDevelopment-$2M

Stop Development

Patent Awarded

$23M

Develop and Sell Product -$10M

EV = $22.9M.7

.3=

R&D Decision

$0

ContinueDevelopment-$2M

Stop Development

EV = $15.5M

Company should continue development.

A sedentary academic remained productive until he was 78. Then his doctor discovered an obstruction in a major artery that provides blood to the brain. The man’s father had the same condition and died a terrible death after 7 years of mental deterioration. The doctor considered surgery, but wasn’t sure if the patient could survive.

Success

Failure

Don’t Operate

Operate

Utilities of the Consequences

Avoid Avoid

Mental Prolong Pain &

Deter.Life Costs

Successful Operation 80 100 0

Failed Operation 100 0 0

No Operation 0 90 100

Utilities of the Consequences

.6 .3 .1

Avoid Avoid

Mental Prolong Pain &

Deter.Life Costs

Success 80 100 0 78

Failure 100 0 0 60

No Oper 0 90 100 37

Success 78

Failure 60

Don’t Operate 37

Operate

p

1-p

Success

Failure

Don’t Operate

Operate Partial Recovery

Eventual Recovery

Eventual Death

Consequences

Life Exp Life Qual Pain Cost

Success long good none some

Event Rec long ok much much

Partial Rec medium poor much much

E Deathlittle none much much

Failure none none none much

No Op medium poor none none

Consequences

.6 .3 .1

QA L Exp Pain Cost Agg

Success 100 100 50 95

E Rec 80 0 0 48

Partial R -30 0 0 -18

E Death 0 0 0 0

Failure-D 0 100 50 35

No Op -20 100 100 28

10

Success 95

Failure 35

Don’t Operate 28

Operate Complications 10

p

r

1 - p - r

Prob of Success p0.1 0.3 0.5 0.7 0.9

0.9 18.5 0.7 23.5 35.5 0.5 28.5 40.5 52.5 0.3 33.5 45.5 57.5 69.5 0.1 38.5 50.5 62.5 71 86.5

Prob of Complications

r

Over a wide range of chances that the operation would be successful, the patient made a good decision.

Conclusion: The more complicated structure pointed to the same option--operate.

Good decisions can have bad outcomes!