Cardinal Representations of Information

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In the spirit of von Neumann and Morgenstern (1947), this paper provides an axiomatic representation of information. Under the von Neumann-Morgenstern axioms, along with an additional continuity, indifference to randomization, and a Blackwell informativeness axiom, I show that any ordering over information can be essentially uniquely represented as, equivalently: (a) a strictly increasing cost of information acquisition; (b) for a given prior, the expected utility from a decision problem; (c) for a given prior, an additive posterior-separable measure of uncertainty; and (d) a separable cost of signals. I discuss the implications of the results for the rational inattention literature.
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