Global subjective expected utility representations

In recent work, we developed a new model of decision-making under uncertainty, which can simultaneously accommodate multiple sources of uncertainty and multiple outcome menus, related by analogies and/or changes in awareness. This framework can also accommodate state spaces and outcome spaces with additional structure (e.g. a topology), as well as decision problems where states and outcomes are not explicitly specified. The present paper axiomatically characterizes a subjective expected utility representation that is "global" in two senses. First: it posits probabilistic beliefs for all uncertainty sources and utility functions over all outcome menus, which simultaneously rationalize the agent's preferences across all possible decision problems, and which are consistent with the aforementioned analogies, symmetries, and awareness levels. Second: it applies in many mathematical environments (i.e. categories), making it unnecessary to develop a separate theory for each one. We illustrate this by applying our representation in several categories (sets, measurable spaces, topological spaces, bounded distributive lattices, Riesz spaces, and Banach algebras), and showing that it delivers utility functions suitable to each one.