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Mark Whitmeyer

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Abstract: For an exogenous source of information and a prespecified number of messages k, I characterize the set of maximal--that is to say, undominated--summaries of the information that use at most k messages. When the exogenous information produces a regular distribution over posteriors (if it has a density on its affine hull, for instance), the maximal summaries take a precise geometric form. They are hierarchical power diagrams: convex subdivisions of the space of beliefs constructed by recursively subdividing cells according to weighted proximity criteria.

Date: 2026-09
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