```Judgments and Decisions
Psych 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
Hurricane
Misses
Safe Conditions, No Damage
Stay
Hurricane
Hits
Dangerous Conditions, probably Damage
Evacuate
Safe Conditions, probably Damage
Political Decision
Win Election
Run
Lose Election
Don’t Run
Stay at the Law Practice
Organizational Restructuring Decision
Increased Profits
Happier, More Motivated Employees
Restructure
Key People Quitting,
Lost Time
Lost Revenues
Don’t
Restructure
Maintain the Current
Organizational Hierarchy
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.
\$4,000 - Fee
Win
Sue
-Fee
Lose
Don’t Sue
\$0
EV(Don’t Sue) = \$0
EV(Sue) = p(W)*(\$4000 - Fee) + (1 – p(Win))*(-Fee)
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)
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)
Risks with each option
No accident
\$0
Small accident
-\$400
Large accident
-\$20,000
No accident
-\$600
Small accident
-\$1,000
Large accident
-\$1,000
Suppose
p(No Accident)
= .75
p(Small Accident) = .20
p(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 oildrilling 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.
Strike
Drill
Positive
Outcome
Do Seismic
Nothing
Don’t Drill
Drill
Negative
Outcome
Dry
Don’t Drill
Strike
Dry
Nothing
Strike
Dry
Bid
No Seismic
Drill
Don’t Drill
Nothing
Nothing
No Bid
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
Sell
Technology
\$23M
\$25M
Patent
Awarded
Demand High
\$55M means \$43M
Sell Product
-\$10M
Continue
Development
-\$2M
No Patent -\$2Mm
Stop
Development
\$0
Demand Medium
\$33M means \$21M
Demand Low
\$15M means \$3M
R&D Decision
Technology
\$25M
\$23M
Patent
Awarded
.25
.7
Continue
Development
-\$2M
Develop and Sell
.3 Product -\$10M
.55
.20
No Patent -\$2Mm
Stop
Development
\$0
Demand High
\$55M means \$43M
Demand Medium
\$33M means \$21M
Demand Low
\$15M means 3M
R&D Decision
Technology
\$25M
Patent
Awarded
\$23M
.7
Continue
Development
-\$2M
EV = \$22.9M
Develop and Sell
Product -\$10M
.3
No Patent -\$2Mm
Stop
Development
\$0
R&D Decision
Company should continue development.
Continue
Development
-\$2M
Stop
Development
EV = \$15.5M
\$0
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
Operate
Failure
Don’t Operate
Utilities of the Consequences
Successful Operation
Avoid
Mental
Deter.
80
Failed Operation
100
0
0
0
90
100
No Operation
Prolong
Life
100
Avoid
Pain &
Costs
0
Utilities of the Consequences
Success
.6
Avoid
Mental
Deter.
80
.3
Failure
100
0
0
60
No Oper
0
90
100
37
Prolong
Life
100
.1
Avoid
Pain &
Costs
0
78
p
Operate
1-p
Success 78
Failure 60
Don’t Operate 37
Success
Eventual Recovery
Operate
Partial Recovery
Eventual Death
Failure
Don’t Operate
Consequences
Life Exp
Success
long
Event Rec long
Partial Rec medium
E Death
little
Failure
none
No Op
medium
Life Qual
good
ok
poor
none
none
poor
Pain
none
much
much
much
none
none
Cost
some
much
much
much
much
none
Consequences
.6
QA L Exp
Success
100
E Rec
80
Partial R -30
E Death
0
Failure-D 0
No Op
-20
.3
Pain
100
0
0
0
100
100
.1
Cost
50
0
0
0
50
100
Agg
95
48
-18
0
35
28
10
p
Operate
Success
95
r
Complications 10
1-p-r
Failure
35
Don’t Operate
28
Prob of Success p
0.1
Prob of
Complications
r
0.3
0.5
0.7
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
0.9
86.5
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!
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