A Cardinal Comparison of Experts

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Tác giả: Itay Kavaler, Rann Smorodinsky

Ngôn ngữ: eng

Ký hiệu phân loại: 239.8 Apologetics and polemics

Thông tin xuất bản: 2019

Mô tả vật lý:

Bộ sưu tập: Báo, Tạp chí

ID: 163283

Comment: arXiv admin note: text overlap with arXiv:1710.09461In various situations, decision makers face experts that may provide conflicting advice. This advice may be in the form of probabilistic forecasts over critical future events. We consider a setting where the two forecasters provide their advice repeatedly and ask whether the decision maker can learn to compare and rank the two forecasters based on past performance. We take an axiomatic approach and propose three natural axioms that a comparison test should comply with. We propose a test that complies with our axioms. Perhaps, not surprisingly, this test is closely related to the likelihood ratio of the two forecasts over the realized sequence of events. More surprisingly, this test is essentially unique. Furthermore, using results on the rate of convergence of supermartingales, we show that whenever the two experts\textquoteright{} advice are sufficiently distinct, the proposed test will detect the informed expert in any desired degree of precision in some fixed finite time.
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