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Old Exam Decision Tree 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 Probabilities If trial, Probability that judge allows testimony from state troopers = .1

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Old Exam Decision Tree

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Old exam decision tree l.jpg

Old Exam Decision Tree


Decision should bill settle lawsuit with paula l.jpg

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


Probabilities l.jpg

Probabilities

  • If trial, Probability that judge allows testimony from state troopers = .1

  • Conditional probability = P(A|T)=.1


Slide4 l.jpg

  • If testimony, he either wins or loses

  • If he wins, 60 Democrats

  • If he loses, 30 Democrats


Same outcomes if no testimony l.jpg

Same outcomes if no testimony

But different probabilities


Conditional probability that he loses l.jpg

Conditional probability that he loses

  • P(lose|testimony) = .6

  • P(lose|no testimony) = .3


Slide7 l.jpg

40

settle

30

.6

lose

60

win

testimony

trial

30

.1

lose

.3

60

No testimony

win

60


E x or emv if testimony l.jpg

E(x) or EMV if testimony


Note we do e x from right to left l.jpg

Note we do E(x) from right to left

Draw tree from left

Find optimal decision from right


E x if no testimony l.jpg

E(x) if no testimony


Slide11 l.jpg

40

settle

30

lose

42

60

win

testimony

trial

30

lose

51

60

No testimony

win

60


E x if trial l.jpg

E(x) if trial


Slide13 l.jpg

40

settle

30

lose

42

60

win

testimony

trial

30

lose

51

50.1

60

No testimony

win

60


Decision node l.jpg

Decision Node


Slide15 l.jpg

40

settle

30

lose

42

60

50.1

win

testimony

trial

30

lose

51

50.1

60

No testimony

win

60


Exam format l.jpg

Exam Format

  • Max E(x) = 50.1

  • Interpretation: Bill should go to trial


Post exam update l.jpg

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


Unethical decision trees l.jpg

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”


Another old exam problem l.jpg

Another Old Exam Problem

Two-stage decision


Should david sign contract to do x files 2001 02 l.jpg

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


If he does not sign contract l.jpg

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


Probabilities22 l.jpg

Probabilities

  • P(X-Files cancelled) = .4

  • P(X-Files movie does well) = .2

  • P(Comedy movies do well) = .3


Slide23 l.jpg

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


E x if he signs not cancelled and x files movie l.jpg

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


Slide25 l.jpg

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


Decision node26 l.jpg

Decision Node


Slide27 l.jpg

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


E x if he signs l.jpg

E(x) if he signs


Slide29 l.jpg

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


E x if he does not sign l.jpg

E(x) if he does not sign


Slide31 l.jpg

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


Final decision node l.jpg

Final Decision Node


Slide33 l.jpg

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


Exam format34 l.jpg

Exam Format

  • Max E(x) = 5.28

  • Interpretation: He should sign the contract. If not cancelled, he should do the X-files movie.


Post exam update35 l.jpg

Post-exam update

  • Film “evolution” grossed $37 million


Decision tree minimize cost l.jpg

Decision Tree: MINIMIZE Cost

Managed Health Care Example


Decision maker hmo physician l.jpg

Decision Maker: HMO physician

  • MD must decide whether or not to run test to determine if patient has disease


If md runs test l.jpg

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


If md does not run test l.jpg

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


Probabilities40 l.jpg

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.


Slide41 l.jpg

10+1 = 11

positive

.01

1

Run test

negative

1000

die

.05

.95

Do not run test

positive

0

ok

.01

0

negative


E x if run test l.jpg

E(x) if run test


Slide43 l.jpg

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


E x if do not run test but patient would have tested positive l.jpg

E(x) if do not run test, but patient would have tested positive


Slide45 l.jpg

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


E x if do not run test l.jpg

E(x) if do not run test


Slide47 l.jpg

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


Decision node48 l.jpg

Decision Node


Slide49 l.jpg

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


Exam format50 l.jpg

Exam Format

  • Min E(x) = 0.5 from tree

  • Interpretation: MD should not run test, for expected cost of $ 500


Evpi if minimizing cost l.jpg

EVPI if minimizing cost

Simplified version of previous problem


Payoff table l.jpg

Payoff Table


Ol best actual l.jpg

OL = |Best – Actual|

  • Here: Best = MIN in col

  • OL = |MIN – Actual|


Payoff table54 l.jpg

Payoff Table


Interpretation l.jpg

Interpretation

  • If MD knew test would come out positive, best decision is to run test

  • If MD knew test would come out negative, best decision is to NOT run test


Opportunity loss table l.jpg

Opportunity Loss Table


Expected eol if md runs test l.jpg

Expected EOL if MD runs test


Expected ol if md does not run test l.jpg

Expected OL if MD does not run test


Min eol l.jpg

MIN EOL


Interpretation60 l.jpg

Interpretation

  • Do NOT run test

  • EVPI = Expected Value of Perfect Information = MIN EOL = .39

  • MD would pay up to $ 390 for perfect information about test result before running test


Decision making without probability l.jpg

Decision Making Without Probability


Minimax l.jpg

MINIMAX

  • Return to OL Table


Opportunity loss table63 l.jpg

Opportunity Loss Table


Minimax64 l.jpg

MINIMAX

MINImum of MAXimum OL


Minimax65 l.jpg

Minimax


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