Language-based Decisions

In Savage’s classic decision-theoretic framework [12], actions are formally defined as functions from states to outcomes. But where do the state space and outcome space come from? Expanding on recent work by Blume, Easley, and Halpern [3], we consider a language-based framework in which actions are identified with (conditional) descriptions in a simple underlying language, while states and outcomes (along with probabilities and utilities) are constructed as part of a representation theorem. Our work expands the role of language from that in [3] by using it not only for the conditions that determine which actions are taken, but also the effects. More precisely, we take the set of actions to be built from those of the form do(φ), for formulas φ in the underlying language. This presents a problem: how do we interpret the result of do(φ) when φ is underspecified (i.e., compatible with multiple states)? We answer this using tools familiar from the semantics of counterfactuals [13]: roughly speaking, do(φ) maps each state to the “closest” φ-state. This notion of “closest” is also something we construct as part of the representation theorem; in effect, then, we prove that (under appropriate assumptions) the agent is acting as if each underspecified action is first made definite and then evaluated (i.e., by maximizing expected utility). Of course, actions in the real world are often not presented in a fully precise manner, yet agents reason about and form preferences among them all the same. Our work brings the abstract tools of decision theory into closer contact with such real-world scenarios.