Persuasion by Dimension Reduction. (arXiv:2110.08884v2 [stat.ML] UPDATED)

How should an agent (the sender) observing multi-dimensional data (the state
vector) persuade another agent to take the desired action? We show that it is
always optimal for the sender to perform a (non-linear) dimension reduction by
projecting the state vector onto a lower-dimensional object that we call the
"optimal information manifold." We characterize geometric properties of this
manifold and link them to the sender's preferences. Optimal policy splits
information into "good" and "bad" components. When the sender's marginal
utility …

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