Estimating utilities from incomplete information

Abstract

This paper shows how numerical values of utility can be estimated from incomplete information, by treating the unknown utilities as random variables. Preferences between the possible decision outcomes, together with the decision-maker's response to various simple hypothetical lotteries involving these outcomes, are - used to define a region oifeasibilityJorthe utilityiunction.This is combined.within Bayes' theorem with a prior probability density function for the unknown utilities. The prior probability is specified through an invariance argument using the uniqueness of utility only up to a positive linear transformation. The invariance argument stems from a maximum entropy principle and the invariance that must obtain under allowable transformations.

Keywords:

• utility theory
• decision analysis
• entropy
• uncertainty