Decisions under subjective information

This paper addresses two closely related aspects of subjective information. First, no two agents necessarily see the same thing when they observe the same object. Second, no two agents have the same concepts in mind when they use the same term in a shared language. I present a framework to give rigorous meaning to these ideas, in particular by modeling them in appropriate topologies. From there I give conditions under which a shared language enables agents with subjective information to trade. These conditions turn out to be equivalent to a form of continuity of the mappings between agents’ perceptions and their use of the shared language, when both are viewed as topological spaces.