Subjective States Without the Completeness Axiom

Existing work has shown how an agent’s desire to defer choice may reveal the contingencies she considers relevant to her decision. We explore if this conclusion remains true when preferences are incomplete, that is, when the agent is unable to express a clear ranking among all alternatives. Remarkably we show that the incompleteness of preference does not preclude the existence of a subjective state space; rather it reflects an agent who cannot aggregate the various states she considers possible. An application to social choice and some general results concerning the representation of incomplete but transitive relations are also provided.