# Judgments and Decisions Psych 253 Decision Analysis (usually risky or uncertain decisions) Examples.

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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 Safe Conditions, probably Damage Dangerous Conditions, probably Damage Safe Conditions, No Damage Stay Evacuate Hurricane Misses Hurricane Hits

Political Decision Stay at the Law Practice Lose Election Win Election Run Dont Run

Organizational R estructuring Decision Maintain the Current Organizational Hierarchy Key People Quitting, Lost Time Lost Revenues Increased Profits Happier, More Motivated Employees Restructure Dont 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. Jamess 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.

Dont Sue Sue Win Lose \$0 -Fee \$4,000 - Fee EV(Sue) = p(W)*(\$4000 - Fee) + (1 – p(Win))*(-Fee) EV(Dont Sue) = \$0

Set EV(Sue) = EV(Dont 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 Dont Buy -\$600 -\$1,000 \$0 -\$400 -\$20,000 Risks with each option

Supposep(No Accident) =.75 p(Small Accident) =.20 p(Large Accident) =.05 EV(Dont 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(Dont 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 Strike Nothing Strike Dry Strike No Bid Bid Do Seismic No Seismic Positive Outcome Negative Outcome Drill Dont Drill Drill Dont Drill Drill Dont Drill

Suppose that all outcomes can be converted to monetary amounts that reflect the decision makers 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 Sell Technology \$25M Continue Development -\$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 License Technology \$25M Continue Development -\$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 License Technology \$25M Continue Development -\$2M Stop Development Patent Awarded \$23M Develop and Sell Product -\$10M EV = \$22.9M.7.3 =

R&D Decision \$0 Continue Development -\$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 mans father had the same condition and died a terrible death after 7 years of mental deterioration. The doctor considered surgery, but wasnt sure if the patient could survive.

Success Failure Dont Operate Operate

Utilities of the ConsequencesAvoid MentalProlongPain & Deter.LifeCosts Successful Operation 80100 0 Failed Operation100 0 0 No Operation 0 90100

Utilities of the Consequences.6.3.1Avoid MentalProlongPain & Deter.LifeCosts Success 80100 078 Failure100 0 060 No Oper 0 9010037

Success 78 Failure 60 Dont Operate 37 Operate p 1-p

Success Failure Dont Operate Operate Partial Recovery Eventual Recovery Eventual Death

Consequences Life ExpLife QualPainCost Successlonggoodnonesome Event Reclongokmuchmuch Partial Recmediumpoormuchmuch E Deathlittlenonemuchmuch Failurenonenonenonemuch No Opmediumpoornonenone

Consequences.6.3.1 QA L ExpPainCostAgg Success100100 5095 E Rec 80 0 048 Partial R-30 0 0-18 E Death 0 0 00 Failure-D 0100 5035 No Op-2010010028 10

Success 95 Failure35 Dont Operate 28 OperateComplications10 p r 1 - p - r

Prob of Success p 0.10.30.50.70.9 18.5 0.723.535.5 0.528.540.552.5 0.333.545.557.569.5 0.138.550.562.57186.5 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!

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