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IE 2030 Lecture 7 Decision AnalysisPowerPoint Presentation

IE 2030 Lecture 7 Decision Analysis

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Decision tree example: party planning

Concepts:

Uncertainty

Minimax Criterion

Expected Value Criterion

Risk Aversion

Risk Neutral, Risk Averse, Risk Seeking

Utility

Outcome and Decision

Decision Tree

Value of information

Sensitivity analysis

Topics Today IE 2030 Lecture 7Decision Trees

- Use different shapes for decisions and uncertain branchings
- Compute from the leaves back to the root
- Use expected values
- When you make a decision, you know the history, the path from the root to the decision point

Minimax or Maximin Criterion

- Choice to make worst possible outcome as good as possible
- Usually gives poor decisions because excessively risk averse
- Fearful people use this criterion
- Are you afraid of being judged badly afterwards?
- Decisions vs. Outcomes

Probability of regret

Maximin and other Payoff Criteria

- Who is your opponent?
- An indifferent Nature…
- use probability, consider expected value

- A hostile or vengeful Fate...
- Use Maximin, consider a psychiatrist

- A self-interested person…
- use game theory and economics

- A hostile person who desires your failure...
- use game theory, maximin, consider an intermediary or arbitrator

- An indifferent Nature…

Never attribute to malice, what can be adequately explained by stupidity

Trust and Credibility

Risk aversion by stupidity

- Choice of sure thing versus lottery
- Size
- Gain or loss
- Expected value criterion
- Utility

It is expensive to be poor by stupidity

- Companies don’t like to risk going out of business
- Wealthier people can afford to gamble
- get higher average returns

- We model this by setting very low utility values on outcomes below “danger” threshholds
- Can cause problems in environmental decisions. Is going bankrupt as bad as destroying the world’s ecology?

Decision Analysis: Value of Information by stupidity(based on R. Howard’s notes)

900

out

Clear

.6

in

600

Rain

.4

100

out

in

500

Value of Information by stupidity

- Expected value of a clairvoyant (perfect information) is an upper bound on the value of any forecast
- Analysis assumes your probabilities are correct
- Must use conditional probability to find probabilities of imperfect forecasts

Forecast probabilities: by stupiditysimple example

- Consistently 90% accurate forecast: whatever the forecast, it is correct w.p..9
- If it rains 50% of the time, forecast rain w.p. .5
- If it rains 90% of time, forecast rain w.p. 1
- If it rains 100% of time, consistent 90% accuracy is impossible

- Many forecasts have inconsistent accuracy

Forecast probabilities: by stupidityparty example

- Consistently 90% accurate forecast: whatever the forecast, it is correct w.p..9
- If it rains 40% of time, forecast rain w.p. q.
- .9q + .1(1-q) = 0.4
- LHS = Prob(rain), calculated over event partition: {predict rain, don’t predict rain}

- You must decide what to do for each possible forecast
- What if the forecast were 0% accurate?

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