Algebraic Properties of Blackwell's Order and A Cardinal Measure of Informativeness

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Tác giả: Andrew Kosenko

Ngôn ngữ: eng

Ký hiệu phân loại: 512.74 Algebraic number theory

Thông tin xuất bản: 2021

Mô tả vật lý:

Bộ sưu tập: Metadata

ID: 168054

 I establish a translation invariance property of the Blackwell order over experiments, show that garbling experiments bring them closer together, and use these facts to define a cardinal measure of informativeness. Experiment $A$ is inf-norm more informative (INMI) than experiment $B$ if the infinity norm of the difference between a perfectly informative structure and $A$ is less than the corresponding difference for $B$. The better experiment is "closer" to the fully revealing experiment
  distance from the identity matrix is interpreted as a measure of informativeness. This measure coincides with Blackwell's order whenever possible, is complete, order invariant, and prior-independent, making it an attractive and computationally simple extension of the Blackwell order to economic contexts.
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