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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)

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