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7 slides about utility theory

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

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  1. 7 slides about utility theory Any more wouldn’t be worth the effort

  2. 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)

  3. 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).

  4. 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).

  5. 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.

  6. What kinds of measures? • Money is always good. • Micromorts (1/106 chance of dying)=$30. • QALY (a year of life with no infirmities)

  7. The value of information • Gathering information takes effort, • Having information must have a value • Really, not much different from any other collected resource.

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