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) 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) Risks with each option Don’t Buy No accident $0 Small accident -$400 Large accident -$20,000 No accident -$600 Small accident -$1,000 Large accident -$1,000 Buy 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 License 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 License 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!