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# IE 2030 Lecture 7 Decision Analysis - PowerPoint PPT Presentation

IE 2030 Lecture 7 Decision Analysis. Expected Value Utility Decision Trees. Introduction to PERT Decision tree example: party planning Concepts: Uncertainty Minimax Criterion Expected Value Criterion Risk Aversion. Risk Neutral, Risk Averse, Risk Seeking Utility Outcome and Decision

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### IE 2030 Lecture 7Decision Analysis

Expected Value

Utility

Decision Trees

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 7

Clear

.6

Party Example (R. Howard)

Rain

.4

100

OUT

IN

600

Clear

.6

Rain

.4

500

• 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

• 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

• 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

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?