Polyvalent decision theory

A single agent may encounter many sources of uncertainty and many menus of outcomes, which can be combined together into many different decision problems. There may be analogies between different uncertainty sources (or different outcome menus). Some uncertainty sources (or outcome menus) may exhibit internal symmetries. The agent may also have different levels of awareness. In some situations, the state spaces and outcome spaces have additional mathematical structure (e.g. a topology or differentiable structure), and feasible acts must respect this structure (i.e. they must be continuous or differentiable functions). In other situations, the agent might only be aware of a set of abstract "acts", and be unable to specify explicit state spaces and outcome spaces. We introduce a new approach to decision theory that addresses these issues. It posits multiple uncertainty sources and outcome menus, linked by the aforementioned analogies, symmetries, and awareness changes. It makes no assumption about the internal structure of these sources and menus, so it is applicable in diverse mathematical environments (i.e. categories). In this framework, we define a suitable notion of subjective expected utility (SEU) representations, and provide conditions under which such SEU representations are unique.