Constrained preference elicitation

A planner wants to elicit information about an agent's preference relation, but not the entire ordering. Specifically, preferences are grouped into "types", and the planner only wants to elicit the agent's type. We first assume beliefs about randomization are subjective, and show that a space of types is elicitable if and only if each type is defined by what the agent would choose from some list of menus. If beliefs are objective then additional type spaces can be elicited, though a convexity condition must be satisfied. These results remain unchanged when we consider a setting with multiple agents.