Can One Hear the Shape of a Decision Problem?
We explore the connection between an agent's decision problem and her ranking of information structures. We find that a finite amount of ordinal data on the agent's ranking of experiments is enough to identify her (finite) set of undominated actions (up to relabeling and duplication) and the beliefs rendering each such action optimal. An additional smattering of cardinal data, comparing the relative value to the agent of finitely many pairs of experiments, identifies her utility function up to an action-independent payoff.
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