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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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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


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



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



Slide11 l.jpg

40

settle

30

lose

42

60

win

testimony

trial

30

lose

51

60

No testimony

win

60



Slide13 l.jpg

40

settle

30

lose

42

60

win

testimony

trial

30

lose

51

50.1

60

No testimony

win

60



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



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



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



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



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



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



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



Slide45 l.jpg

10+1 = 11 positive

positive

.01

1.1

1

Run test

negative

1000

die

50

.05

.95

Do not run test

positive

0

ok

.01

0

negative



Slide47 l.jpg

10+1 = 11 positive

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 positive


Slide49 l.jpg

10+1 = 11 positive

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 positive

  • 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 positive

Simplified version of previous problem


Payoff table l.jpg
Payoff Table positive


Ol best actual l.jpg
OL = |Best – Actual| positive

  • Here: Best = MIN in col

  • OL = |MIN – Actual|


Payoff table54 l.jpg
Payoff Table positive


Interpretation l.jpg
Interpretation positive

  • 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




Expected ol if md does not run test l.jpg
Expected OL positive if MD does not run test


Min eol l.jpg
MIN EOL positive


Interpretation60 l.jpg
Interpretation positive

  • 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



Minimax l.jpg
MINIMAX positive

  • Return to OL Table



Minimax64 l.jpg

MINIMAX positive

MINImum of MAXimum OL


Minimax65 l.jpg
Minimax positive


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