A Simpler and More Realistic Subjective Decision Theory
with Haim Gaifman
The paper presents two mathematical results. The first, and the more difficult one, shows that the probability measures derived in Savage's theory of expected utility can be defined without the σ-algebra assumption. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems---without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of "idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent.