Utility functions need not relate to dollar values. Here is a problem in which we know little about five abstract outcomes. What is important, however, is that a person who does know what A to E represent should be able to compare the outcomes using the lottery procedures we have studied.
A decision maker faces a risky gamble in which she may obtain one of five outcomes. Label the outcomes A, B, C, D, and E. A is the most preferred, and E is least preferred. She has made the following three assessments.
• She is indifferent between having C for sure or a lottery in which she wins A with probability 0.5 or E with probability 0.5.
• She is indifferent between having B for sure or a lottery in which she wins A with probability 0.4 or C with probability 0.6.
• She is indifferent between these two lotteries:
1. A 50% chance at B and a 50% chance at D
2. A 50% chance at A and a 50% chance at E
What are U(A), U(B), U(C), U(D), and U(E)?