Simple axioms for countably additive subjective probability

Thispaper refines Savage’s theoryof subjectiveprobability for the caseof countably additive beliefs. First, I replace his continuity axiomsP6 andP7with a simplemodification of Arrow’s (1970) Monotone Continuity. Second, I relax Savage’s primitives: in my framework, the class of events need not be a -algebra, and acts need not have finite or bounded range. By varying the domains of acts and events, I obtain a unique extension of preference that parallels Caratheodory’s unique extension of probability measures. Aside from subjective expected utility, I characterize exponential time discounting in a setting with continuous time and an arbitrary consumption set. © 2010 Elsevier B.V. All rights reserved.