# Old Exam Decision Tree - PowerPoint PPT Presentation

Old Exam Decision Tree

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Old Exam Decision Tree

## Old Exam Decision Tree

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##### Presentation Transcript

1. Old Exam Decision Tree

2. Decision: Should Bill settle lawsuit with Paula? • Actions: settle or trial? • Objective: Maximize number of Democrats in Senate in 1999 • If he settles, 40 Dems

3. Probabilities • If trial, Probability that judge allows testimony from state troopers = .1 • Conditional probability = P(A|T)=.1

4. If testimony, he either wins or loses • If he wins, 60 Democrats • If he loses, 30 Democrats

5. Same outcomes if no testimony But different probabilities

6. Conditional probability that he loses • P(lose|testimony) = .6 • P(lose|no testimony) = .3

7. 40 settle 30 .6 lose 60 win testimony trial 30 .1 lose .3 60 No testimony win 60

8. E(x) or EMV if testimony

9. Note we do E(x) from right to left Draw tree from left Find optimal decision from right

10. E(x) if no testimony

11. 40 settle 30 lose 42 60 win testimony trial 30 lose 51 60 No testimony win 60

12. E(x) if trial

13. 40 settle 30 lose 42 60 win testimony trial 30 lose 51 50.1 60 No testimony win 60

14. Decision Node

15. 40 settle 30 lose 42 60 50.1 win testimony trial 30 lose 51 50.1 60 No testimony win 60

16. Exam Format • Max E(x) = 50.1 • Interpretation: Bill should go to trial

17. Post-exam Update • New Objective: Maximize number of electoral votes for Al Gore in 2000 • If Bill had settled case, scandal would have been forgotten by Nov 2000 • Gore might have won his home state of Tenn (and Arkansas?) if no impeachment trial

18. Unethical Decision Trees • Ford used decision tree to decide NOT to recall Pinto after gas tanks exploded • Firestone used decision tree to decide NOT to recall tires after SUV rollovers • Pop Culture: Ed Norton’s character describes calculation of E(x) for recall decision in film “Fight Club” • Pop Culture: Miguel Ferrer’s character explains decision to smuggle drugs across border in film “Traffic”

19. Another Old Exam Problem Two-stage decision

20. Should David sign contract to do X-Files 2001-02? • Objective: maximize expected monetary value (all numbers in millions of dollars) • If he signs, he earns \$3 • If cancelled after 2002, no further income • If not cancelled, a second decision in 2002: decide between another year on TV for another \$3, or an X-Files movie • If movie does well, an additional \$15, otherwise an additional \$ 1

21. If he does NOT sign contract, • He does comedy movies • If they do well, he earns \$ 10 • If they do not do well, he earns \$ 2

22. Probabilities • P(X-Files cancelled) = .4 • P(X-Files movie does well) = .2 • P(Comedy movies do well) = .3

23. 3 cancel .4 3+3=6 Another yr Not cancel 3+15=18 sign movie well .2 3+1=4 Not well 10 Don’t sign Comedies do well .3 2 Not well

24. E(x) if he signs, not cancelled, and X-files movie

25. 3 cancel .4 3+3=6 Another yr Not cancel 3+15=18 sign movie well .2 6.8 3+1=4 Not well 10 Don’t sign Comedies do well .3 2 Not well

26. Decision Node

27. 3 cancel .4 3+3=6 Another yr Not cancel 6.8 3+15=18 sign movie well .2 6.8 3+1=4 Not well 10 Don’t sign Comedies do well .3 2 Not well

28. E(x) if he signs

29. 3 cancel .4 5.28 3+3=6 Another yr Not cancel 6.8 3+15=18 sign movie well .2 6.8 3+1=4 Not well 10 Don’t sign Comedies do well .3 2 Not well

30. E(x) if he does not sign

31. 3 cancel .4 5.28 3+3=6 Another yr Not cancel 6.8 3+15=18 sign movie well .2 6.8 3+1=4 Not well 10 Don’t sign Comedies do well 4.4 .3 2 Not well

32. Final Decision Node

33. 3 cancel .4 5.28 3+3=6 Another yr Not cancel 6.8 3+15=18 sign movie well .2 6.8 5.28 3+1=4 Not well 10 Don’t sign Comedies do well 4.4 .3 2 Not well

34. Exam Format • Max E(x) = 5.28 • Interpretation: He should sign the contract. If not cancelled, he should do the X-files movie.

35. Post-exam update • Film “evolution” grossed \$37 million

36. Decision Tree: MINIMIZE Cost Managed Health Care Example

37. Decision Maker: HMO physician • MD must decide whether or not to run test to determine if patient has disease

38. If MD runs test • Cost of test = \$ 1000 • If test is positive, assume patient wants treatment, which costs \$ 10,000 • On tree, write in thousands of dollars • Test = 1 • Treatment = 10

39. If MD does not run test • If patient had disease, was diagnosed too late, and died, survivors win lawsuit, and HMO pays out \$ 1,000,000 • Tree: 1000

40. Probabilities • P(test positive) = .01 • P(patient dies|test positive but no treatment) = .05 • P(patient ok|test positive but no treatment) = .95 • This problem assumes only 2 outcomes: dead or ok. In real life, several branches.

41. 10+1 = 11 positive .01 1 Run test negative 1000 die .05 .95 Do not run test positive 0 ok .01 0 negative

42. E(x) if run test

43. 10+1 = 11 positive .01 1.1 1 Run test negative 1000 die .05 .95 Do not run test positive 0 ok .01 0 negative

44. 10+1 = 11 positive .01 1.1 1 Run test negative 1000 die 50 .05 .95 Do not run test positive 0 ok .01 0 negative

45. E(x) if do not run test

46. 10+1 = 11 positive .01 1.1 1 Run test negative 1000 die 50 .05 .95 Do not run test positive 0 ok .01 .5 0 negative

47. Decision Node

48. 10+1 = 11 positive .01 1.1 1 Run test negative 1000 die 0.5 50 .05 .95 Do not run test positive 0 ok .01 .5 0 negative

49. Exam Format • Min E(x) = 0.5 from tree • Interpretation: MD should not run test, for expected cost of \$ 500