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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 7 decision analysis

IE 2030 Lecture 7Decision Analysis

Expected Value

Utility

Decision Trees


Topics today ie 2030 lecture 7

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

Decision Tree

Value of information

Sensitivity analysis

Topics Today IE 2030 Lecture 7


Party example r howard

900

Clear

.6

Party Example (R. Howard)

Rain

.4

100

OUT

IN

600

Clear

.6

Rain

.4

500


Decision trees
Decision 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
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
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



Risk aversion
Risk aversion by stupidity

  • Choice of sure thing versus lottery

  • Size

  • Gain or loss

  • Expected value criterion

  • Utility


It is expensive to be poor
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 based on r howard s notes
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
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 simple example
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 party example
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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