# da4 - Engineering Risk Benefit Analysis 1.155 2.943 3.577...

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DA 4. Introduction to Utility 1 Engineering Risk Benefit Analysis 1.155, 2.943, 3.577, 6.938, 10.816, 13.621, 16.862, 22.82, ESD.72, ESD.721 DA 4. Introduction to Utility George E. Apostolakis Massachusetts Institute of Technology Spring 2007

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DA 4. Introduction to Utility 2 The Concept of utility Utility of a consequence: A quantification of a person's relative preference for that consequence A simple extension of the indifference probability (or "preference value") concept (Axiom 2a) Utility function: Expresses a person's relative preferences among a set of consequences (often defined over a continuous range)
DA 4. Introduction to Utility 3 Axiom 2a: Quantification of preferences For each C i , the DM can specify a number π (C i ), with 0 ≤π (C i ) 1, such that the DM is indifferent between ¾ possessing C i with certainty and ¾ possessing the lottery L (C*, C * ; π (C i ), 1 - π (C i ))

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DA 4. Introduction to Utility 4 Schematic representation C * C * π (C 1 ) 1−π 1 ) C * C * π 2 ) 1−π 2 ) C * C * π m ) 1−π m ) p m p 2 p 1 ~ C 1 C 2 C m p m p 2 p 1
DA 4. Introduction to Utility 5 Preference measures for lotteries Having established the relative preferences, i.e., the π (C i ), i = 1,…,m, we can derive the relative preferences for lotteries.

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da4 - Engineering Risk Benefit Analysis 1.155 2.943 3.577...

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