Old Exam Decision Tree

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# Old Exam Decision Tree Decision: Should Bill settle lawsuit with Paula - PowerPoint PPT Presentation

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

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
• Conditional probability = P(A|T)=.1
If testimony, he either wins or loses
• If he wins, 60 Democrats
• If he loses, 30 Democrats

### Same outcomes if no testimony

But different probabilities

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

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

Draw tree from left

Find optimal decision from right

40

settle

30

lose

42

60

win

testimony

trial

30

lose

51

60

No testimony

win

60

40

settle

30

lose

42

60

win

testimony

trial

30

lose

51

50.1

60

No testimony

win

60

40

settle

30

lose

42

60

50.1

win

testimony

trial

30

lose

51

50.1

60

No testimony

win

60

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

Two-stage decision

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,
• He does comedy movies
• If they do well, he earns \$ 10
• If they do not do well, he earns \$ 2
Probabilities
• P(X-Files cancelled) = .4
• P(X-Files movie does well) = .2
• P(Comedy movies do well) = .3

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

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

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

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

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

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 Format
• Max E(x) = 5.28
• Interpretation: He should sign the contract. If not cancelled, he should do the X-files movie.
Post-exam update
• Film “evolution” grossed \$37 million

### Decision Tree: MINIMIZE Cost

Managed Health Care Example

Decision Maker: HMO physician
• MD must decide whether or not to run test to determine if patient has disease
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
• If patient had disease, was diagnosed too late, and died, survivors win lawsuit, and HMO pays out \$ 1,000,000
• Tree: 1000
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.

10+1 = 11

positive

.01

1

Run test

negative

1000

die

.05

.95

Do not run test

positive

0

ok

.01

0

negative

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

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

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

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

### EVPI if minimizing cost

Simplified version of previous problem

OL = |Best – Actual|
• Here: Best = MIN in col
• OL = |MIN – Actual|
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
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

MINIMAX