We axiomatize subjective probabilities on finite domains without requiring richness in the outcome space or restrictions on risk preference through event exchangeability, defined in Chew and Sagi (2006), which was implicit in the prior literature (Savage, 1954; Machina and Schmeidler, 1992; Grant, 1995). We characterize the unique subjective probability representing the underlying exchangeability relation. This subjective probability can serve as foundation to derive expected utility and rank-linear utility by imposing the sure-thing principle and its comonotonic variant. We next characterize more general lottery based choice—two Savage acts inducing the same lottery are indifferent, and adapt the characterization to small domains to further delivers source preference.
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