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What is a utility function in decision theory?

  • A.The probability that a given outcome will occur
  • B.The cost of performing a particular action
  • C.A ranking of the actions available to the agent
  • D.A numerical measure of how desirable each outcome is

Answer: D

Utility converts a preference ordering over outcomes into numbers that may be combined with probabilities to compute an expectation. It is determined only up to a positive linear transformation, which is why only ratios of differences are meaningful. Probabilities, costs and action rankings are different quantities. That a number can be attached to a preference at all follows from axioms about consistent choice rather than being assumed. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

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