Aggregate then evaluate

We distinguish two frameworks for decisions under ambiguity: evaluate-then-aggregate (ETA) and aggregate-then-evaluate (ATE). Given a statistic that represents the decision maker's pure-risk preferences (such as expected utility) and an ambiguous act, an ETA model first evaluates the act under each plausible probabilistic model using this statistic and then aggregates the resulting evaluations according to ambiguity attitudes. In contrast, an ATE model first aggregates ambiguity by assigning the act a single representative distribution and then evaluates that distribution using the statistic. These frameworks differ in the order in which risk and ambiguity are processed, and they coincide when there is no ambiguity. While most existing ambiguity models fall within the ETA framework, our study focuses on the ATE framework, which is conceptually just as compelling and has been relatively neglected in the literature. We develop a Choquet ATE model, which generalizes the Choquet expected utility model by allowing arbitrary pure-risk preferences. We provide an axiomatization of this model in a Savage setting with an exogenous source of unambiguous events. The Choquet ATE framework allows us to analyze a wide range of ambiguity attitudes and their interplay with risk attitudes.