The Foundations of Decision Under Uncertainty: An Elementary Exposition

Abstract

Abstract Bayesian rules for decision under uncertainty are derived constructively from two principles of consistent behavior and two principles asserting that the decision maker can scale his preferences for consequences and judgments concerning unpredictable events by reference to simple lotteries involving only two consequences and based on an imaginary experiment with subjectively equally likely outcomes. It is shown that the two principles of consistent behavior require the decision maker's scaled judgments to obey the axioms of probability, and by use of one further principle of consistent behavior it is shown that they should also agree with the usual definition of conditional probability and hence with Bayes' rule.