Savage’s Subjectivism and Countable Additivity
This talk is mainly on the issue of additivity in Savage’s theory of subjective expected utility. It is divided into three parts. First, I will comment, by providing a brief historical survey, on Savage’s reasons for adopting finitely additive probability measure in his decision model. It will argue that Savage’s set-theoretic argument for rejecting countable additivity is inconclusive. In the second part, I will discuss some defects of finite additivity in Savage’s system. This will be followed, in the last part, by a detailed reconstruction and revision of Savage’s theory. It will be shown that Savage’s final representation theorem, which extends the derived utility function for simple acts to general acts, is derivable from the first six of his seven postulates provided countable additivity is in sight, a conjecture made by Savage himself.
Yang Liu is a doctorate candidate in philosophy at Columbia University, specializing in logic and the foundations of probability theory, normative decision theory, and game theory.