- 1110 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about 'Old Exam Decision Tree Decision: Should Bill settle lawsuit with Paula' - albert

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### Same outcomes if no testimony

### Another Old Exam Problem

### Decision Tree: MINIMIZE Cost

### EVPI if minimizing cost positive

### Decision Making Without Probability positive

### MINIMAX positive

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

But different probabilities

Conditional probability that he loses

- P(lose|testimony) = .6
- P(lose|no testimony) = .3

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”

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

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

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

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

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

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

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

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.

positive

.01

1

Run test

negative

1000

die

.05

.95

Do not run test

positive

0

ok

.01

0

negative

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

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 positive

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 Node positive

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 Format positive

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

Simplified version of previous problem

Payoff Table positive

OL = |Best – Actual| positive

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

Payoff Table positive

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

Opportunity Loss Table positive

Expected EOL if MD runs test positive

Expected OL positive if MD does not run test

MIN EOL positive

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 positive

- Return to OL Table

Opportunity Loss Table positive

MINImum of MAXimum OL

Minimax positive

Download Presentation

Connecting to Server..