Abstract:
A (Blackwell) experiment specifies the joint distribution of truth and the data generated by the experiment. A signal specifies the joint distribution of truth, the data generated by the signal, and the data generated by any other signal. Describing two experiments does not determine their joint informational content; describing two signals does. Blackwell (1953) studied (equivalent) comparisons of experiments; he characterized when one experiment is more valuable than another regardless of the preferences of the agent. We study (various, non-equivalent) comparisons of signals. Among other comparisons, we characterize when one signal is more valuable than another regardless of the preferences of the agent and regardless of what other information the agent may have. We show this comparison is equivalent to a new condition, termed reveal-or-refine, which says that for every piece of data that could be generated by the more valuable signal, either that data reveals the truth, or it refines the data generated by the less valuable signal.

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