2. Demonstration: Decision-Making Under Uncertainty

3. 2 1.03 Decision-Making Under Uncertainty We will demonstrate the principles using a simple (but real) example. This is a personal investment decision. The outcome is uncertain. The potential gains/losses are real. What is the most that you are willing to invest?

4. 3 1.03 Decision-Making Under Uncertainty 1.The selected participant plays the game once. 2.The cost to play is 20. 3.Payment is cash or check; no refunds. Thumbtack Sweepstakes Rules VISA MasterCard 4.I will “flip” a thumbtack. 5.The player calls:“Point up” “Point down” 6.If the call is correct, the player wins and keeps 100. 7.If the call is incorrect, the player wins nothing. 8.I keep the amount paid to play, regardless of the outcome.

5. 4 1.03 Decision-Making Under Uncertainty A decision tree organizes and displays important factors of a decision in chronological sequence. Invest Don’t Invest Decision – 20 Decision Correct Call Incorrect Call Uncertainty Outcome 100 0 0 – 20 Net Profit 80 0 Time

6. 5 1.03 Decision-Making Under Uncertainty We define a decision as an “irrevocable” allocation of resources. We have a certificate acknowledging this first “decision” of the day.

7. 6 1.03 Decision-Making Under Uncertainty Probabilities quantify the player’s judgment about the likelihood of winning. Correct Call Incorrect Call Probability = p Probability = 1 – p This uncertain situation is called a “deal” or a “lottery.”

8. 7 1.03 Decision-Making Under Uncertainty To evaluate the tree, we must establish a value for the deal, assuming that we’ve made the investment. Invest Don’t Invest Decision 0 – 20 Correct Call Incorrect Call UncertaintyOutcome 100 0 p = 1 – p = Correct Call Incorrect Call UncertaintyOutcome 100 0 p = 1 – p = Deal To value the deal going forward, ignore the “sunk” 20; that’s behind us now.

9. 8 1.03 Decision-Making Under Uncertainty The value of the deal is the player’s minimum selling price or “certain equivalent.” The player is indifferent between having the deal or its certain equivalent. Correct Call Incorrect Call UncertaintyOutcome 100 0 p = 1 – p = Deal Certain Equivalent

10. 9 1.03 Decision-Making Under Uncertainty Another way to value the deal is to calculate its “expected value” (probability-weighted average). The expected (or “mean”) value is the average return from each flip if it were repeated many times. Correct Call Incorrect Call UncertaintyOutcome 100 0 p = 1 – p = Deal p x 100 + (1 – p) x 0 Expected Value

11. 10 1.03 Decision-Making Under Uncertainty The difference between “expected value” and “certain equivalent” reflects attitude toward risk. This is a matter of preference; there is no “correct” risk attitude. Monetary Value Risk Averse Risk Neutral Risk Preferring Expected Value Risk Attitude Certain Equivalent

12. 11 1.03 Decision-Making Under Uncertainty Is it worthwhile to gather information to reduce or to eliminate uncertainty? Correct Call Incorrect Call UncertaintyOutcome 100 0 p = 1 – p = No Info Buy Information Decision ? –? What is the most that our player should pay for perfect information?

13. 12 1.03 Decision-Making Under Uncertainty Certain Equivalent Perfect information about the outcome of the flip guarantees winning the 100. Correct Call Incorrect Call UncertaintyOutcome 100 0 p = 1 – p = Decision No Info Buy Perfect Information 100 Correct Call p = 1.0–? Here the value added by perfect information is 100 – the certain equivalent. How many opportunities do you have to buy perfect information in your business? Value Added

14. 13 1.03 Decision-Making Under Uncertainty Perfect information may not be available. Here are imperfect sources. Experiments—5 trial flips of the tack Opinion polls Experts Mathematical models SURVEY

15. 14 1.03 Decision-Making Under Uncertainty What is your call? Point up? Point down?

16. 15 1.03 Decision-Making Under Uncertainty We must distinguish between good decisions and good outcomes. Preferred Results Good Outcomes Balances the probabilities of good and bad outcomes consistent with preferences Good Decisions 40 –6 15 4.6.4.7.3

17. 16 1.03 Decision-Making Under Uncertainty Making good decisions may not lead to good outcomes. Good decisions guarantee good outcomes. Decisions with Certainty CorrectInvest Don’t Invest Good decisions do not guarantee good outcomes. Decisions with Uncertainty Correct Incorrect Invest Don’t Invest The goal of decision analysis is make the best decisions in the face of uncertainty.

18. 17 1.03 Decision-Making Under Uncertainty Several insights emerge from the demonstration. A decision is an irrevocable allocation of resources. Invest Buy Info.... 30%... Probability is the quantitative language for communicating about uncertainty. Probabilities represent judgment, which includes experience and information. The value of an uncertain deal depends on its characteristics and one’s attitude toward risk. The economic value of gathering more information can be calculated before making a decision. We must distinguish between the quality of the decision and its outcome.

19. 18 1.03 Decision-Making Under Uncertainty Change Log VersionDateChanges 0108/06/27First version for DAF - SDG LS (modified by W Noor from DCW TS v1.08) 0209/23/09Updated to IMS Template (MC) 307/19/10Updated with minor revisions 406/05/12Updated to IMSCG Template (LJ)