Simple axioms for countably additive subjective probability
This paper refines Savage's theory of subjective probability for the case of countably additive beliefs. First, I replace his continuity axioms P6 and P7 with a simple modification of Arrow's (1970) Monotone Continuity. Second, I relax Savage's primitives: in my framework, the class of events need not be a [sigma]-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.
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- Peter Wakker, 1993. "Savage's Axioms Usually Imply Violation of Strict Stochastic Dominance," Review of Economic Studies, Oxford University Press, vol. 60(2), pages 487-493.