383-Fall11-Lec16

383-Fall11-Lec16 - Making Simple Decisions Utility Theory...

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1 CMPSCI 383 Nov 3, 2011 Making Simple Decisions: Utility Theory

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2 Today ʼ s topics Maximum expected utility principle Utility and preferences: rational preferences Assessing utility Utility of money Risk averse Risk seeking What do humans do? Multiattribute utility functions Pure dominance Preference structure Decision networks
3 Maximum Expected Utility Principle U(s) : utility of state s Expected utility of an action: MEU principle: formalizes the idea of “doing the right thing” EU ( a | e ) = P (Result( a ) = ʹ s | a , e ) U ( ʹ s ) ʹ s action = argmax a EU ( a | e ) Evidence observations

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4 Why Expected Utility? Why not sum of cubes? Or minimize worst-case loss? Why not just deal with preferences? Why should a utility function with the desired properties exist at all?
5 Preferences (prefers A over B or is indifferent between them)

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6 Rational Preferences
7 Rational Preferences contd.

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8 Maximizing Expected Utility Utility function is not unique: aU ( S )+ b, a>0
9 Utility assessment

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10 Utility Scale
Money You ʼ re on a game show. You have won a \$1M prize. You are offered this gamble: Flip a coin: heads nothing; tails \$2.5M What is the expected monetary value (EMV) of the gamble? .5(\$0) + .5(\$2.5M) = \$1.25M What do you do? Utility is not directly proportional to EMV

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This note was uploaded on 11/29/2011 for the course COMPSCI 383 taught by Professor Andrewbarto during the Fall '11 term at UMass (Amherst).

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383-Fall11-Lec16 - Making Simple Decisions Utility Theory...

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