Savage for dummies and experts

Abstract

Savage's foundation of expected utility is considered to be the most convincing justification of Bayesian expected utility and the crowning glory of decision theory. It combines exceptionally appealing axioms with deep mathematics. Despite the wide influence and deep respect that Savage received in economics and statistics, virtually no one touched his mathematical tools. We provide an updated analysis that is more general and more accessible. Our derivations are self-contained. This helps to better appreciate the depth and beauty of Savage's work and the foundations of Bayesianism, to teach it more easily, and to develop non-Bayesian generalizations incorporating ambiguity more efficiently.