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Even without a formal assessment process, it often is possible to learn something about an individual's utility function just through the preferences revealed by choice behavior. Two persons, A and B, make the following bet: A wins $40 if it rains tomorrow and B wins $10 if it does not rain tomorrow.

a If they both agree that the probability of rain tomorrow is 0.10, what can you say about their utility functions?

b If they both agree that the probability of rain tomorrow is 0.30, what can you say about their utility functions?

c Given no information about their probabilities, is it possible that their utility functions could be identical?

d If they both agree that the probability of rain tomorrow is 0.20, could both individuals be risk-averse? Is it possible that their utility functions could be identical? Explain.

Source: R. L. Winkler (1972) Introduction to Bayesian Inference and Decision. New York: Holt.

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