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