**7**

**Bayesian Decision Theory**

**7.1 Subjective Probability**

This chapter studies the theory of subjective probabilities invented independently by Frank Ramsey (1931) and Bruno de Finetti (1937). The version of the theory developed by Leonard Savage (1951) in his famous *Foundations of Statistics* is now universally called Bayesian decision theory. My own simplification of his theory in section 7.2 differs from the usual textbook accounts, but the end product will be no less orthodox than my simplification of Von Neumann and Morgenstern’s theory of expected utility in section 3.4.

**7.1.1 Small Worlds**

We last visited the theory of revealed preference when developing a version of Von Neumann and Morgenstern’s theory of expected utility (section 3.4). But ...