发表机构
Wang Yanan Institute for Studies in Economics and the School of Economics, Xiamen University（厦门大学王亚南经济研究院及经济学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究决策者面对不同决策问题时信息来源集的比较，提出布莱克韦尔提升定理，以标记混合和定向勒卡姆缺陷刻画价值优劣，并指出莱曼序下需有限束问题才能恢复等价性。
AI 中文摘要
决策者可能拥有多个可用的信息来源，并且只有在了解自己所面临的决策问题之后，才会选择咨询哪一个。什么时候这样的一组来源比另一组在价值上更优？对于无限制的贝叶斯决策问题，我们表明，答案可以完全用布莱克韦尔比较来表述。通过独立于状态抽取一个来源，并同时揭示其身份及其信号，来形成一个标记混合。当且仅当第二组来源的每个标记混合都被第一组来源的某个标记混合布莱克韦尔支配时，一组来源在每个决策问题中才更有价值。该结果适用于紧致的、可能无限的来源集和一般的信号空间。它也有一个精确的定量对应：最大的归一化价值缺口是来源集标记包之间的定向勒卡姆缺陷。对单调决策问题的类似研究揭示了一个边界。我们将从逐问题来源集优越性到与问题无关的成对支配的转变称为提升。布莱克韦尔提升不能直接扩展到莱曼序：混合单独满足单调似然比性质（MLRP）的来源不一定保持MLRP，即使保持，也不一定存在固定的莱曼支配混合。要求一个来源服务于有限束的单调决策问题则恢复了等价性。
英文摘要
A decision maker may have several information sources available and choose which one to consult only after learning the decision problem she faces. When is one such set of sources uniformly more valuable than another? For unrestricted Bayesian decision problems, we show that the answer can be stated entirely in terms of Blackwell comparisons. Form a tagged mixture by drawing a source independently of the state and revealing both its identity and its signal. One source set is more valuable in every decision problem if and only if each tagged mixture of the second source set is Blackwell dominated by some tagged mixture of the first. The result applies to compact, possibly infinite source sets and general signal spaces. It also has an exact quantitative counterpart: the largest normalized value shortfall is the directed Le Cam deficiency between the source sets' tagged hulls. The analogous program for monotone decision problems reveals a boundary. We call the passage from problem-by-problem source-set superiority to a problem-independent pairwise dominance a lifting. The Blackwell lifting does not extend directly to the Lehmann order: mixing sources that individually satisfy the monotone likelihood ratio property (MLRP) need not preserve MLRP, and even when it does, no fixed Lehmann-dominating mixture need exist. Requiring one source to serve a finite bundle of monotone decision problems restores the equivalence.
