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.

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Keywords Behavioral foundation, Foundations of statistics, Mixture spaces, Subjective expected utility
JEL Mathematical Methods (jel C02), Mathematical Methods and Programming: General (jel C60)
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Journal Journal of Economic Theory
Abdellaoui, M, & Wakker, P.P. (2020). Savage for dummies and experts. Journal of Economic Theory, 186. doi:10.1016/j.jet.2020.104991