On expected utility, part 4: Dutch books, Cox, and Complete Class

Abstract

Building on previous essays in a four-part series, this essay explores Dutch book theorems, Cox’s theorem, and the complete class theorem as justifications for subjective probability and expected utility maximization (EUM). Dutch book arguments derive guaranteed losses from inconsistencies in fair prices, demonstrating the need for consistency with probability axioms. Cox’s theorem establishes an isomorphism between subjective plausibility and standard probability, suggesting that EUM is a natural consequence of rational reasoning. The complete class theorem shows that Pareto optimality in decision-making is equivalent to EUM, given a non-dogmatic probability distribution over possible worlds. These theorems provide varying levels of support for EUM, offering both pragmatic and formal reasons for its plausibility. – AI-generated abstract.