IE 2030 Lecture 7 Decision 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

Party Example (R. Howard) Clear.6 Rain Clear.6 Rain.4 OUT IN

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 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

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

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

It is expensive to be poor 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) Clear.6 Rain.4 out in out in

Value of Information clairvoyantExpected 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 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 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?