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# 7 slides about utility theory - PowerPoint PPT Presentation

7 slides about utility theory. Any more wouldn’t be worth the effort. Maximum expected utility. Utility = U(o) Probability of o: P(o) Expected utility: P(o)U(o)

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### 7 slides about utility theory

Any more wouldn’t be worth the effort

Maximum expected utility
• Utility = U(o)
• Probability of o: P(o)
• Expected utility: P(o)U(o)
• “If agent maximized utility function that correctly reflects performance, it will achieve the highest possible performance on average” (Duh)
Utility theory notation
• A > B: A prefers B
• A ~ B: A is indifferent to B
• A >~ B: A either is indifferent or prefers B
• A and B are atomic states or “lotteries” : an ordered set of probabilities and values. Might be just one thing (with probability 1).
Reasonable assumptions
• Transitive: A > B, B>C => A>C (avoids a different kind of sucker bet).
• Orderable: (A>B) or (A<B) or (A~B)
• Continuity: A>B>C => p [p,A; 1-p,C] ~B (indifferent between getting B for sure, and getting either A or C).
More assumptions
• Substitutability: If A~B, then you can substitute B for A (and vice versa) in other lotteries.
• Montonicity: A > B implies perfer lotteries that yield A with more probability that B.
• Decomposability: Can reduce lotteries to simpler lotteries using probabilities.
What kinds of measures?
• Money is always good.
• Micromorts (1/106 chance of dying)=\$30.
• QALY (a year of life with no infirmities)
The value of information
• Gathering information takes effort,
• Having information must have a value
• Really, not much different from any other collected resource.