A decision maker is to choose an action from a set A. The set of consequencesis Z. For every action a ? A the consequence z* is realized with probability, and any z ? Z - {z*} is realized with probability r(a, z) = (1 - )q(a, z).

a. Assume that after making his choice he is told that z* will not occur andis given a chance to change his decision. Show that if the decision makerobeys the Bayesian updating rule and follows vNM axioms, he will notchange his decision.

b. Give an example where a decision maker who follows a nonexpectedutility preference relation or obeys a non-Bayesian updating rule is nottime consistent.