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<p>This paper develops a prior-free model of data-driven decision making in which the decision maker observes the entire distribution of signals generated by a known experiment under an unknown distribution of the state variable and evaluates actions according to their worst-case payoff over the set of state distributions consistent with that observation. We propose a ranking of experiments in which <i>E</i> is <i>robustly more informative</i> than <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(E'\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>E</mi> <mo>′</mo> </msup> </math></EquationSource> </InlineEquation> if the value of the decision maker’s problem after observing <i>E</i> is always at least as high as the value of the decision maker’s problem after observing <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(E'.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>E</mi> <mo>′</mo> </msup> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> This comparison, which is strictly weaker than Blackwell’s classical order, holds if and only if the null space of <i>E</i> is contained in the null space of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(E'.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>E</mi> <mo>′</mo> </msup> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation></p>

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Prior-free Blackwell

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月17日

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  • Maxwell Rosenthal

摘要

This paper develops a prior-free model of data-driven decision making in which the decision maker observes the entire distribution of signals generated by a known experiment under an unknown distribution of the state variable and evaluates actions according to their worst-case payoff over the set of state distributions consistent with that observation. We propose a ranking of experiments in which E is robustly more informative than \(E'\) E ′ if the value of the decision maker’s problem after observing E is always at least as high as the value of the decision maker’s problem after observing \(E'.\) E ′ . This comparison, which is strictly weaker than Blackwell’s classical order, holds if and only if the null space of E is contained in the null space of \(E'.\) E ′ .